Daily Papers

Sparsely Mixture of Experts (MoE) has received great interest due to its promising scaling capability with affordable computational overhead. MoE converts dense layers into sparse experts, and utilizes a gated routing network to make experts conditionally activated. However, as the number of experts grows, MoE with outrageous parameters suffers from overfitting and sparse data allocation. Such problems are especially severe on tasks with limited data, thus hindering the progress for MoE models to improve performance by scaling up. In this work, we propose Mixture of Expert Clusters - a general approach to enable expert layers to learn more diverse and appropriate knowledge by imposing variance-based constraints on the routing stage. We further propose a cluster-level expert dropout strategy specifically designed for the expert cluster structure. Our experiments reveal that MoEC could improve performance on machine translation and natural language understanding tasks, and raise the performance upper bound for scaling up experts under limited data. We also verify that MoEC plays a positive role in mitigating overfitting and sparse data allocation.

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.

Sparse Mixture-of-Experts (SMoE) models represent a significant advancement in large language model (LLM) development through their efficient parameter utilization. These models achieve substantial performance improvements at reduced inference costs. However, the deployment of SMoE models faces constraints from extensive memory requirements of expert components in resource-limited environments. To address these limitations, this paper introduces Hierarchical Clustering for Sparsely activated Mixture of Experts (HC-SMoE), a task-agnostic expert merging framework for parameter reduction without retraining. HC-SMoE introduces a novel hierarchical clustering approach based on expert outputs to ensure merging robustness independent of routing decisions. The proposed output-based clustering method enables effective capture of functional relationships between experts for large-scale architectures. We provide theoretical analysis and comprehensive evaluations across multiple zero-shot language tasks to demonstrate HC-SMoE's effectiveness in state-of-the-art models including Qwen and Mixtral. The experimental results validate HC-SMoE's superior performance and practical applicability for real-world deployments.

Visual instruction datasets from various distributors are released at different times and often contain a significant number of semantically redundant text-image pairs, depending on their task compositions (i.e., skills) or reference sources. This redundancy greatly limits the efficient deployment of lifelong adaptable multimodal large language models, hindering their ability to refine existing skills and acquire new competencies over time. To address this, we reframe the problem of Lifelong Instruction Tuning (LiIT) via data selection, where the model automatically selects beneficial samples to learn from earlier and new datasets based on the current state of acquired knowledge in the model. Based on empirical analyses that show that selecting the best data subset using a static importance measure is often ineffective for multi-task datasets with evolving distributions, we propose Adapt-infty, a new multi-way and adaptive data selection approach that dynamically balances sample efficiency and effectiveness during LiIT. We construct pseudo-skill clusters by grouping gradient-based sample vectors. Next, we select the best-performing data selector for each skill cluster from a pool of selector experts, including our newly proposed scoring function, Image Grounding score. This data selector samples a subset of the most important samples from each skill cluster for training. To prevent the continuous increase in the size of the dataset pool during LiIT, which would result in excessive computation, we further introduce a cluster-wise permanent data pruning strategy to remove the most semantically redundant samples from each cluster, keeping computational requirements manageable. Training with samples selected by Adapt-infty alleviates catastrophic forgetting, especially for rare tasks, and promotes forward transfer across the continuum using only a fraction of the original datasets.

Mixture of Experts (MoE), an ensemble of specialized models equipped with a router that dynamically distributes each input to appropriate experts, has achieved successful results in the field of machine learning. However, theoretical understanding of this architecture is falling behind due to its inherent complexity. In this paper, we theoretically study the sample and runtime complexity of MoE following the stochastic gradient descent (SGD) when learning a regression task with an underlying cluster structure of single index models. On the one hand, we prove that a vanilla neural network fails in detecting such a latent organization as it can only process the problem as a whole. This is intrinsically related to the concept of information exponent which is low for each cluster, but increases when we consider the entire task. On the other hand, we show that a MoE succeeds in dividing this problem into easier subproblems by leveraging the ability of each expert to weakly recover the simpler function corresponding to an individual cluster. To the best of our knowledge, this work is among the first to explore the benefits of the MoE framework by examining its SGD dynamics in the context of nonlinear regression.

Multimodal Large Language Models (MLLMs) achieve strong performance through instruction tuning, but real-world deployment requires them to continually expand their capabilities, making Multimodal Continual Instruction Tuning (MCIT) essential. Recent methods leverage sparse expert routing to promote task specialization, but we find that the expert routing process suffers from drift as the data distribution evolves. For example, a grounding query that previously activated localization experts may instead be routed to irrelevant experts after learning OCR tasks. Meanwhile, the grounding-related experts can be overwritten by new tasks and lose their original functionality. Such failure reflects two problems: router drift, where expert selection becomes inconsistent over time, and expert drift, where shared experts are overwritten across tasks. Therefore, we propose StAbilized Mixture-of-Experts (SAME) for MCIT. To address router drift, SAME stabilizes expert selection by decomposing routing dynamics into orthogonal subspaces and updating only task-relevant directions. To mitigate expert drift, we regulate expert updates via curvature-aware scaling using historical input covariance in a rehearsal-free manner. SAME also introduces adaptive expert activation to freeze selected experts during training, reducing redundant computation and cross-task interference. Extensive experiments demonstrate its SOTA performance.

Parameter Efficient Tuning has been an prominent approach to adapt the Large Language Model to downstream tasks. Most previous works considers adding the dense trainable parameters, where all parameters are used to adapt certain task. We found this less effective empirically using the example of LoRA that introducing more trainable parameters does not help. Motivated by this we investigate the importance of leveraging "sparse" computation and propose SiRA: sparse mixture of low rank adaption. SiRA leverages the Sparse Mixture of Expert(SMoE) to boost the performance of LoRA. Specifically it enforces the top k experts routing with a capacity limit restricting the maximum number of tokens each expert can process. We propose a novel and simple expert dropout on top of gating network to reduce the over-fitting issue. Through extensive experiments, we verify SiRA performs better than LoRA and other mixture of expert approaches across different single tasks and multitask settings.

The Mixture-of-Experts (MoE) layer, a sparsely-activated model controlled by a router, has achieved great success in deep learning. However, the understanding of such architecture remains elusive. In this paper, we formally study how the MoE layer improves the performance of neural network learning and why the mixture model will not collapse into a single model. Our empirical results suggest that the cluster structure of the underlying problem and the non-linearity of the expert are pivotal to the success of MoE. To further understand this, we consider a challenging classification problem with intrinsic cluster structures, which is hard to learn using a single expert. Yet with the MoE layer, by choosing the experts as two-layer nonlinear convolutional neural networks (CNNs), we show that the problem can be learned successfully. Furthermore, our theory shows that the router can learn the cluster-center features, which helps divide the input complex problem into simpler linear classification sub-problems that individual experts can conquer. To our knowledge, this is the first result towards formally understanding the mechanism of the MoE layer for deep learning.

Deep subspace clustering (DSC) algorithms face several challenges that hinder their widespread adoption across variois application domains. First, clustering quality is typically assessed using only the encoder's output layer, disregarding valuable information present in the intermediate layers. Second, most DSC approaches treat representation learning and subspace clustering as independent tasks, limiting their effectiveness. Third, they assume the availability of a held-out dataset for hyperparameter tuning, which is often impractical in real-world scenarios. Fourth, learning termination is commonly based on clustering error monitoring, requiring external labels. Finally, their performance often depends on post-processing techniques that rely on labeled data. To address this limitations, we introduce a novel single-view DSC approach that: (i) minimizes a layer-wise self expression loss using a joint representation matrix; (ii) optimizes a subspace-structured norm to enhance clustering quality; (iii) employs a multi-stage sequential learning framework, consisting of pre-training and fine-tuning, enabling the use of multiple regularization terms without hyperparameter tuning; (iv) incorporates a relative error-based self-stopping mechanism to terminate training without labels; and (v) retains a fixed number of leading coefficients in the learned representation matrix based on prior knowledge. We evaluate the proposed method on six datasets representing faces, digits, and objects. The results show that our method outperforms most linear SC algorithms with careffulyl tuned hyperparameters while maintaining competitive performance with the best performing linear appoaches.

We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In contrast, our approach is to perform clustering and decision tree training holistically where the decision tree's performance and size also influence the clustering results. We assume the attributes for clustering and explaining are distinct, although this is not necessary. We observe that our problem is a monotonic optimization where the objective function is a difference of monotonic functions. We then propose an efficient branch-and-bound algorithm for finding the best parameters that lead to a balance of cluster distortion and decision tree explainability. Our experiments show that our method can improve the explainability of any clustering that fits in our framework.

We present the Mixture-of-Tunable-Experts (MoTE), a method that extends the Mixture-of-Experts architecture of Large Language Models (LLMs). Without additional training, MoTE enables meaningful and focused behavior changes in LLMs on-the-fly during inference time. By analyzing the digital LLM brain of DeepSeek-R1 using a technique we dub 'functional Token Resonance Imaging' (fTRI) -- inspired by fMRI and using prompts designed to elicit specific behavior (e.g., 'What happened {time}{place}?') -- we empirically identify distinctive experts associated with behaviors like refusal responses. Using MoTE we are able to intervene and control such specific behavior. We switched off the top 10 most refusal-relevant experts (0.07% of R1's 14,848 routed experts), achieving a 52% refusal reduction on sensitive reference prompts without performance degradation on MT-Bench. Random expert deactivation resulted in smaller behavioral shifts with increased noise, whereas forced expert activation led to significantly higher refusal rates. Our approach shares similarities with sparse autoencoders (SAEs) in terms of explainability and steerability. Unlike SAEs, MoTE does not require large training efforts, as within MoEs with a vast number of experts, specialization already emerged naturally during pretraining. Our findings suggest that significant functional mechanisms in Mixture-of-Experts architectures can at least partially be localized in a small number of specific experts, rather than being distributed throughout the model's weights. Expert subgroups can be tuned to trigger significant behavior variations, providing insights into the inner workings of LLMs.

Mixture-of-Experts (MoE) models mostly use a router to assign tokens to specific expert modules, activating only partial parameters and often outperforming dense models. We argue that the separation between the router's decision-making and the experts' execution is a critical yet overlooked issue, leading to suboptimal expert selection and ineffective learning. To address this, we propose Autonomy-of-Experts (AoE), a novel MoE paradigm in which experts autonomously select themselves to process inputs. AoE is based on the insight that an expert is aware of its own capacity to effectively process a token, an awareness reflected in the scale of its internal activations. In AoE, routers are removed; instead, experts pre-compute internal activations for inputs and are ranked based on their activation norms. Only the top-ranking experts proceed with the forward pass, while the others abort. The overhead of pre-computing activations is reduced through a low-rank weight factorization. This self-evaluating-then-partner-comparing approach ensures improved expert selection and effective learning. We pre-train language models having 700M up to 4B parameters, demonstrating that AoE outperforms traditional MoE models with comparable efficiency.

Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies can be achieved by reducing the input space if a minimal loss of information can be achieved. Clustering algorithms, in general, face two common problems: 1) these converge to different settings with different initial conditions and; 2) the number of clusters has to be arbitrarily decided beforehand. This problem has become critical in the realm of big data. Recently, clustering algorithms have emerged which can speedup computations using parallel processing over the grid but face the aforementioned problems. Goals: Our goals are to find methods to cluster data which: 1) guarantee convergence to the same settings irrespective of the initial conditions; 2) eliminate the need to establish the number of clusters beforehand, and 3) can be applied to cluster large datasets. Methods: We introduce a method that combines probabilistic and combinatorial clustering methods to produce repeatable and compact clusters that are not sensitive to initial conditions. This method harnesses the power of k-means (a combinatorial clustering method) to cluster/partition very large dimensional datasets and uses the Gaussian Mixture Model (a probabilistic clustering method) to validate the k-means partitions. Results: We show that this method produces very compact clusters that are not sensitive to initial conditions. This method can be used to identify the most 'separable' set in a dataset which increases the 'clusterability' of a dataset. This method also eliminates the need to specify the number of clusters in advance.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

We study the problem of online clustering where a clustering algorithm has to assign a new point that arrives to one of k clusters. The specific formulation we use is the k-means objective: At each time step the algorithm has to maintain a set of k candidate centers and the loss incurred is the squared distance between the new point and the closest center. The goal is to minimize regret with respect to the best solution to the k-means objective (C) in hindsight. We show that provided the data lies in a bounded region, an implementation of the Multiplicative Weights Update Algorithm (MWUA) using a discretized grid achieves a regret bound of O(T) in expectation. We also present an online-to-offline reduction that shows that an efficient no-regret online algorithm (despite being allowed to choose a different set of candidate centres at each round) implies an offline efficient algorithm for the k-means problem. In light of this hardness, we consider the slightly weaker requirement of comparing regret with respect to (1 + ε) C and present a no-regret algorithm with runtime Oleft(T(poly(log(T),k,d,1/ε)^{k(d+O(1))}right). Our algorithm is based on maintaining an incremental coreset and an adaptive variant of the MWUA. We show that naïve online algorithms, such as Follow The Leader, fail to produce sublinear regret in the worst case. We also report preliminary experiments with synthetic and real-world data.

The Mixtures-of-Experts (MoE) model is a widespread distributed and integrated learning method for large language models (LLM), which is favored due to its ability to sparsify and expand models efficiently. However, the performance of MoE is limited by load imbalance and high latency of All-To-All communication, along with relatively redundant computation owing to large expert capacity. Load imbalance may result from existing routing policies that consistently tend to select certain experts. The frequent inter-node communication in the All-To-All procedure also significantly prolongs the training time. To alleviate the above performance problems, we propose a novel routing strategy that combines load balance and locality by converting partial inter-node communication to that of intra-node. Notably, we elucidate that there is a minimum threshold for expert capacity, calculated through the maximal angular deviation between the gating weights of the experts and the assigned tokens. We port these modifications on the PanGu-Sigma model based on the MindSpore framework with multi-level routing and conduct experiments on Ascend clusters. The experiment results demonstrate that the proposed LocMoE reduces training time per epoch by 12.68% to 22.24% compared to classical routers, such as hash router and switch router, without impacting the model accuracy.

Multi-Task Learning (MTL) aims to boost predictive performance by sharing information across related tasks, yet conventional methods often suffer from negative transfer when unrelated or noisy tasks are forced to share representations. We propose Robust Multi-Task Boosting using Clustering and Local Ensembling (RMB-CLE), a principled MTL framework that integrates error-based task clustering with local ensembling. Unlike prior work that assumes fixed clusters or hand-crafted similarity metrics, RMB-CLE derives inter-task similarity directly from cross-task errors, which admit a risk decomposition into functional mismatch and irreducible noise, providing a theoretically grounded mechanism to prevent negative transfer. Tasks are grouped adaptively via agglomerative clustering, and within each cluster, a local ensemble enables robust knowledge sharing while preserving task-specific patterns. Experiments show that RMB-CLE recovers ground-truth clusters in synthetic data and consistently outperforms multi-task, single-task, and pooling-based ensemble methods across diverse real-world and synthetic benchmarks. These results demonstrate that RMB-CLE is not merely a combination of clustering and boosting but a general and scalable framework that establishes a new basis for robust multi-task learning.

Clustering is a class of unsupervised learning methods that has been extensively applied and studied in computer vision. Little work has been done to adapt it to the end-to-end training of visual features on large scale datasets. In this work, we present DeepCluster, a clustering method that jointly learns the parameters of a neural network and the cluster assignments of the resulting features. DeepCluster iteratively groups the features with a standard clustering algorithm, k-means, and uses the subsequent assignments as supervision to update the weights of the network. We apply DeepCluster to the unsupervised training of convolutional neural networks on large datasets like ImageNet and YFCC100M. The resulting model outperforms the current state of the art by a significant margin on all the standard benchmarks.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

Sparse mixture of experts provides larger model capacity while requiring a constant computational overhead. It employs the routing mechanism to distribute input tokens to the best-matched experts according to their hidden representations. However, learning such a routing mechanism encourages token clustering around expert centroids, implying a trend toward representation collapse. In this work, we propose to estimate the routing scores between tokens and experts on a low-dimensional hypersphere. We conduct extensive experiments on cross-lingual language model pre-training and fine-tuning on downstream tasks. Experimental results across seven multilingual benchmarks show that our method achieves consistent gains. We also present a comprehensive analysis on the representation and routing behaviors of our models. Our method alleviates the representation collapse issue and achieves more consistent routing than the baseline mixture-of-experts methods.

Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to 20times sim 5000times. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.

Class-incremental learning is becoming more popular as it helps models widen their applicability while not forgetting what they already know. A trend in this area is to use a mixture-of-expert technique, where different models work together to solve the task. However, the experts are usually trained all at once using whole task data, which makes them all prone to forgetting and increasing computational burden. To address this limitation, we introduce a novel approach named SEED. SEED selects only one, the most optimal expert for a considered task, and uses data from this task to fine-tune only this expert. For this purpose, each expert represents each class with a Gaussian distribution, and the optimal expert is selected based on the similarity of those distributions. Consequently, SEED increases diversity and heterogeneity within the experts while maintaining the high stability of this ensemble method. The extensive experiments demonstrate that SEED achieves state-of-the-art performance in exemplar-free settings across various scenarios, showing the potential of expert diversification through data in continual learning.

Sparsely-activated Mixture-of-experts (MoE) models allow the number of parameters to greatly increase while keeping the amount of computation for a given token or a given sample unchanged. However, a poor expert routing strategy (e.g. one resulting in load imbalance) can cause certain experts to be under-trained, leading to an expert being under or over-specialized. Prior work allocates a fixed number of experts to each token using a top-k function regardless of the relative importance of different tokens. To address this, we propose a heterogeneous mixture-of-experts employing an expert choice method. Instead of letting tokens select the top-k experts, we have experts selecting the top-k tokens. As a result, each token can be routed to a variable number of experts and each expert can have a fixed bucket size. We systematically study pre-training speedups using the same computational resources of the Switch Transformer top-1 and GShard top-2 gating of prior work and find that our method improves training convergence time by more than 2x. For the same computational cost, our method demonstrates higher performance in fine-tuning 11 selected tasks in the GLUE and SuperGLUE benchmarks. For a smaller activation cost, our method outperforms the T5 dense model in 7 out of the 11 tasks.

Pairwise clustering, in general, partitions a set of items via a known similarity function. In our treatment, clustering is modeled as a transductive prediction problem. Thus rather than beginning with a known similarity function, the function instead is hidden and the learner only receives a random sample consisting of a subset of the pairwise similarities. An additional set of pairwise side-information may be given to the learner, which then determines the inductive bias of our algorithms. We measure performance not based on the recovery of the hidden similarity function, but instead on how well we classify each item. We give tight bounds on the number of misclassifications. We provide two algorithms. The first algorithm SACA is a simple agglomerative clustering algorithm which runs in near linear time, and which serves as a baseline for our analyses. Whereas the second algorithm, RGCA, enables the incorporation of side-information which may lead to improved bounds at the cost of a longer running time.

Mixture-of-Experts (MoE) models are typically pre-trained with explicit load-balancing constraints to ensure statistically balanced expert routing. Despite this, we observe that even well-trained MoE models exhibit significantly imbalanced routing. This behavior is arguably natural-and even desirable - as imbalanced routing allows models to concentrate domain-specific knowledge within a subset of experts. Expert parallelism (EP) is designed to scale MoE models by distributing experts across multiple devices, but with a less-discussed assumption of balanced routing. Under extreme imbalance, EP can funnel a disproportionate number of tokens to a small number of experts, leading to compute- and memory-bound failures on overloaded devices during post-training or inference, where explicit load balancing is often inapplicable. We propose Least-Loaded Expert Parallelism (LLEP), a novel EP algorithm that dynamically reroutes excess tokens and associated expert parameters from overloaded devices to underutilized ones. This ensures that all devices complete their workloads within the minimum collective latency while respecting memory constraints. Across different model scales, LLEP achieves up to 5x speedup and 4x reduction in peak memory usage compared to standard EP. This enables faster and higher-throughput post-training and inference, with ~1.9x faster for gpt-oss-120b. We support our method with extensive theoretical analysis and comprehensive empirical evaluations, including ablation studies. These results illuminate key trade-offs and enable a principled framework for hardware-specific hyper-parameter tuning to achieve optimal performance.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Training and deploying multiple vision transformer (ViT) models for different resource constraints is costly and inefficient. To address this, we propose transforming a pre-trained ViT into a stratified knowledge-density super-network, where knowledge is hierarchically organized across weights. This enables flexible extraction of sub-networks that retain maximal knowledge for varying model sizes. We introduce Weighted PCA for Attention Contraction (WPAC), which concentrates knowledge into a compact set of critical weights. WPAC applies token-wise weighted principal component analysis to intermediate features and injects the resulting transformation and inverse matrices into adjacent layers, preserving the original network function while enhancing knowledge compactness. To further promote stratified knowledge organization, we propose Progressive Importance-Aware Dropout (PIAD). PIAD progressively evaluates the importance of weight groups, updates an importance-aware dropout list, and trains the super-network under this dropout regime to promote knowledge stratification. Experiments demonstrate that WPAC outperforms existing pruning criteria in knowledge concentration, and the combination with PIAD offers a strong alternative to state-of-the-art model compression and model expansion methods.

The Mixture of Experts (MoE) architecture reduces the training and inference cost significantly compared to a dense model of equivalent capacity. Upcycling is an approach that initializes and trains an MoE model using a pre-trained dense model. While upcycling leads to initial performance gains, the training progresses slower than when trained from scratch, leading to suboptimal performance in the long term. We propose Drop-Upcycling - a method that effectively addresses this problem. Drop-Upcycling combines two seemingly contradictory approaches: utilizing the knowledge of pre-trained dense models while statistically re-initializing some parts of the weights. This approach strategically promotes expert specialization, significantly enhancing the MoE model's efficiency in knowledge acquisition. Extensive large-scale experiments demonstrate that Drop-Upcycling significantly outperforms previous MoE construction methods in the long term, specifically when training on hundreds of billions of tokens or more. As a result, our MoE model with 5.9B active parameters achieves comparable performance to a 13B dense model in the same model family, while requiring approximately 1/4 of the training FLOPs. All experimental resources, including source code, training data, model checkpoints and logs, are publicly available to promote reproducibility and future research on MoE.

In this paper, we present the practical problems and the lessons learned at short-video services from Kuaishou. In industry, a widely-used multi-task framework is the Mixture-of-Experts (MoE) paradigm, which always introduces some shared and specific experts for each task and then uses gate networks to measure related experts' contributions. Although the MoE achieves remarkable improvements, we still observe three anomalies that seriously affect model performances in our iteration: (1) Expert Collapse: We found that experts' output distributions are significantly different, and some experts have over 90% zero activations with ReLU, making it hard for gate networks to assign fair weights to balance experts. (2) Expert Degradation: Ideally, the shared-expert aims to provide predictive information for all tasks simultaneously. Nevertheless, we find that some shared-experts are occupied by only one task, which indicates that shared-experts lost their ability but degenerated into some specific-experts. (3) Expert Underfitting: In our services, we have dozens of behavior tasks that need to be predicted, but we find that some data-sparse prediction tasks tend to ignore their specific-experts and assign large weights to shared-experts. The reason might be that the shared-experts can perceive more gradient updates and knowledge from dense tasks, while specific-experts easily fall into underfitting due to their sparse behaviors. Motivated by those observations, we propose HoME to achieve a simple, efficient and balanced MoE system for multi-task learning.

Fine-grained image labels are desirable for many computer vision applications, such as visual search or mobile AI assistant. These applications rely on image classification models that can produce hundreds of thousands (e.g. 100K) of diversified fine-grained image labels on input images. However, training a network at this vocabulary scale is challenging, and suffers from intolerable large model size and slow training speed, which leads to unsatisfying classification performance. A straightforward solution would be training separate expert networks (specialists), with each specialist focusing on learning one specific vertical (e.g. cars, birds...). However, deploying dozens of expert networks in a practical system would significantly increase system complexity and inference latency, and consumes large amounts of computational resources. To address these challenges, we propose a Knowledge Concentration method, which effectively transfers the knowledge from dozens of specialists (multiple teacher networks) into one single model (one student network) to classify 100K object categories. There are three salient aspects in our method: (1) a multi-teacher single-student knowledge distillation framework; (2) a self-paced learning mechanism to allow the student to learn from different teachers at various paces; (3) structurally connected layers to expand the student network capacity with limited extra parameters. We validate our method on OpenImage and a newly collected dataset, Entity-Foto-Tree (EFT), with 100K categories, and show that the proposed model performs significantly better than the baseline generalist model.

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically fix their task predictor to a single linear or Boolean expression, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of experts and the functional form of each expert, exposing an underexplored region of the design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data under user-specified operator vocabularies. Empirical evaluation demonstrates that varying the mixture size and functional form provides a robust framework for navigating the accuracy-interpretability trade-off, adapting to different user and task needs.

Federated Learning (FL) is a widespread and well-adopted paradigm of decentralised learning that allows training one model from multiple sources without the need to transfer data between participating clients directly. Since its inception in 2015, it has been divided into numerous subfields that deal with application-specific issues, such as data heterogeneity or resource allocation. One such sub-field, Clustered Federated Learning (CFL), deals with the problem of clustering the population of clients into separate cohorts to deliver personalised models. Although a few remarkable works have been published in this domain, the problem remains largely unexplored, as its basic assumptions and settings differ slightly from those of standard FL. In this work, we present One-Shot Clustered Federated Learning (OCFL), a clustering-agnostic algorithm that can automatically detect the earliest suitable moment for clustering. Our algorithm is based on computing the cosine distance between the gradients of the clients and a temperature measure that detects when the federated model starts to converge. We empirically evaluate our methodology by testing various one-shot clustering algorithms for over forty different tasks on five benchmark datasets. Our experiments showcase the good performance of our approach when used to perform CFL in an automated manner without the need to adjust hyperparameters. We also revisit the practical feasibility of CFL algorithms based on the gradients of the clients, providing firm evidence of the high efficiency of density-based clustering methods when used to differentiate between the loss surfaces of neural networks trained on different distributions. Moreover, by inspecting the feasibility of local explanations generated with the help of GradCAM, we can provide more insights into the relationship between personalisation and the explainability of local predictions.

Despite the popularity of explainable AI, there is limited work on effective methods for unsupervised learning. We study algorithms for k-means clustering, focusing on a trade-off between explainability and accuracy. Following prior work, we use a small decision tree to partition a dataset into k clusters. This enables us to explain each cluster assignment by a short sequence of single-feature thresholds. While larger trees produce more accurate clusterings, they also require more complex explanations. To allow flexibility, we develop a new explainable k-means clustering algorithm, ExKMC, that takes an additional parameter k' geq k and outputs a decision tree with k' leaves. We use a new surrogate cost to efficiently expand the tree and to label the leaves with one of k clusters. We prove that as k' increases, the surrogate cost is non-increasing, and hence, we trade explainability for accuracy. Empirically, we validate that ExKMC produces a low cost clustering, outperforming both standard decision tree methods and other algorithms for explainable clustering. Implementation of ExKMC available at https://github.com/navefr/ExKMC.

Mixture of Experts (MoE) offers remarkable performance and computational efficiency by selectively activating subsets of model parameters. Traditionally, MoE models use homogeneous experts, each with identical capacity. However, varying complexity in input data necessitates experts with diverse capabilities, while homogeneous MoE hinders effective expert specialization and efficient parameter utilization. In this study, we propose a novel Heterogeneous Mixture of Experts (HMoE), where experts differ in size and thus possess diverse capacities. This heterogeneity allows for more specialized experts to handle varying token complexities more effectively. To address the imbalance in expert activation, we propose a novel training objective that encourages the frequent activation of smaller experts, enhancing computational efficiency and parameter utilization. Extensive experiments demonstrate that HMoE achieves lower loss with fewer activated parameters and outperforms conventional homogeneous MoE models on various pre-training evaluation benchmarks. Codes will be released upon acceptance.

Pre-training convolutional neural networks with weakly-supervised and self-supervised strategies is becoming increasingly popular for several computer vision tasks. However, due to the lack of strong discriminative signals, these learned representations may overfit to the pre-training objective (e.g., hashtag prediction) and not generalize well to downstream tasks. In this work, we present a simple strategy - ClusterFit (CF) to improve the robustness of the visual representations learned during pre-training. Given a dataset, we (a) cluster its features extracted from a pre-trained network using k-means and (b) re-train a new network from scratch on this dataset using cluster assignments as pseudo-labels. We empirically show that clustering helps reduce the pre-training task-specific information from the extracted features thereby minimizing overfitting to the same. Our approach is extensible to different pre-training frameworks -- weak- and self-supervised, modalities -- images and videos, and pre-training tasks -- object and action classification. Through extensive transfer learning experiments on 11 different target datasets of varied vocabularies and granularities, we show that ClusterFit significantly improves the representation quality compared to the state-of-the-art large-scale (millions / billions) weakly-supervised image and video models and self-supervised image models.

Sparsely activated Mixture-of-Experts (SMoE) has shown promise to scale up the learning capacity of neural networks, however, they have issues like (a) High Memory Usage, due to duplication of the network layers into multiple copies as experts; and (b) Redundancy in Experts, as common learning-based routing policies suffer from representational collapse. Therefore, vanilla SMoE models are memory inefficient and non-scalable, especially for resource-constrained downstream scenarios. In this paper, we ask: Can we craft a compact SMoE model by consolidating expert information? What is the best recipe to merge multiple experts into fewer but more knowledgeable experts? Our pilot investigation reveals that conventional model merging methods fail to be effective in such expert merging for SMoE. The potential reasons are: (1) redundant information overshadows critical experts; (2) appropriate neuron permutation for each expert is missing to bring all of them in alignment. To address this, we propose M-SMoE, which leverages routing statistics to guide expert merging. Specifically, it starts with neuron permutation alignment for experts; then, dominant experts and their "group members" are formed; lastly, every expert group is merged into a single expert by utilizing each expert's activation frequency as their weight for merging, thus diminishing the impact of insignificant experts. Moreover, we observed that our proposed merging promotes a low dimensionality in the merged expert's weight space, naturally paving the way for additional compression. Hence, our final method, MC-SMoE (i.e., Merge, then Compress SMoE), further decomposes the merged experts into low-rank and structural sparse alternatives. Extensive experiments across 8 benchmarks validate the effectiveness of MC-SMoE. For instance, our MC-SMoE achieves up to 80% memory and a 20% FLOPs reduction, with virtually no loss in performance.

The rapid advancements in computing dramatically increase the scale and cost of training Large Language Models (LLMs). Accurately predicting downstream task performance prior to model training is crucial for efficient resource allocation, yet remains challenging due to two primary constraints: (1) the "emergence phenomenon", wherein downstream performance metrics become meaningful only after extensive training, which limits the ability to use smaller models for prediction; (2) Uneven task difficulty distributions and the absence of consistent scaling laws, resulting in substantial metric variability. Existing performance prediction methods suffer from limited accuracy and reliability, thereby impeding the assessment of potential LLM capabilities. To address these challenges, we propose a Clustering-On-Difficulty (COD) downstream performance prediction framework. COD first constructs a predictable support subset by clustering tasks based on difficulty features, strategically excluding non-emergent and non-scalable clusters. The scores on the selected subset serve as effective intermediate predictors of downstream performance on the full evaluation set. With theoretical support, we derive a mapping function that transforms performance metrics from the predictable subset to the full evaluation set, thereby ensuring accurate extrapolation of LLM downstream performance. The proposed method has been applied to predict performance scaling for a 70B LLM, providing actionable insights for training resource allocation and assisting in monitoring the training process. Notably, COD achieves remarkable predictive accuracy on the 70B LLM by leveraging an ensemble of small models, demonstrating an absolute mean deviation of 1.36% across eight important LLM evaluation benchmarks.

Diffusion-based generative models have achieved remarkable success in various domains. It trains a shared model on denoising tasks that encompass different noise levels simultaneously, representing a form of multi-task learning (MTL). However, analyzing and improving diffusion models from an MTL perspective remains under-explored. In particular, MTL can sometimes lead to the well-known phenomenon of negative transfer, which results in the performance degradation of certain tasks due to conflicts between tasks. In this paper, we first aim to analyze diffusion training from an MTL standpoint, presenting two key observations: (O1) the task affinity between denoising tasks diminishes as the gap between noise levels widens, and (O2) negative transfer can arise even in diffusion training. Building upon these observations, we aim to enhance diffusion training by mitigating negative transfer. To achieve this, we propose leveraging existing MTL methods, but the presence of a huge number of denoising tasks makes this computationally expensive to calculate the necessary per-task loss or gradient. To address this challenge, we propose clustering the denoising tasks into small task clusters and applying MTL methods to them. Specifically, based on (O2), we employ interval clustering to enforce temporal proximity among denoising tasks within clusters. We show that interval clustering can be solved using dynamic programming, utilizing signal-to-noise ratio, timestep, and task affinity for clustering objectives. Through this, our approach addresses the issue of negative transfer in diffusion models by allowing for efficient computation of MTL methods. We validate the proposed clustering and its integration with MTL methods through various experiments, demonstrating improved sample quality of diffusion models. Our project page is available at https://gohyojun15.github.io/ANT_diffusion/{url}.

Visualizations for scattered data are used to make users understand certain attributes of their data by solving different tasks, e.g. correlation estimation, outlier detection, cluster separation. In this paper, we focus on the later task, and develop a technique that is aligned to human perception, that can be used to understand how human subjects perceive clusterings in scattered data and possibly optimize for better understanding. Cluster separation in scatterplots is a task that is typically tackled by widely used clustering techniques, such as for instance k-means or DBSCAN. However, as these algorithms are based on non-perceptual metrics, we can show in our experiments, that their output do not reflect human cluster perception. We propose a learning strategy which directly operates on scattered data. To learn perceptual cluster separation on this data, we crowdsourced a large scale dataset, consisting of 7,320 point-wise cluster affiliations for bivariate data, which has been labeled by 384 human crowd workers. Based on this data, we were able to train ClusterNet, a point-based deep learning model, trained to reflect human perception of cluster separability. In order to train ClusterNet on human annotated data, we use a PointNet++ architecture enabling inference on point clouds directly. In this work, we provide details on how we collected our dataset, report statistics of the resulting annotations, and investigate perceptual agreement of cluster separation for real-world data. We further report the training and evaluation protocol of ClusterNet and introduce a novel metric, that measures the accuracy between a clustering technique and a group of human annotators. Finally, we compare our approach against existing state-of-the-art clustering techniques and can show, that ClusterNet is able to generalize to unseen and out of scope data.

With the growing prominence of the Mixture of Experts (MoE) architecture in developing large-scale foundation models, we investigate the Hierarchical Mixture of Experts (HMoE), a specialized variant of MoE that excels in handling complex inputs and improving performance on targeted tasks. Our analysis highlights the advantages of using the Laplace gating function over the traditional Softmax gating within the HMoE frameworks. We theoretically demonstrate that applying the Laplace gating function at both levels of the HMoE model helps eliminate undesirable parameter interactions caused by the Softmax gating and, therefore, accelerates the expert convergence as well as enhances the expert specialization. Empirical validation across diverse scenarios supports these theoretical claims. This includes large-scale multimodal tasks, image classification, and latent domain discovery and prediction tasks, where our modified HMoE models show great performance improvements compared to the conventional HMoE models.

This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities between data points, but extensions to vector data are also discussed (2) the output is a "stepwise dendrogram", a data structure which is shared by all implementations in current standard software. We present algorithms (old and new) which perform clustering in this setting efficiently, both in an asymptotic worst-case analysis and from a practical point of view. The main contributions of this paper are: (1) We present a new algorithm which is suitable for any distance update scheme and performs significantly better than the existing algorithms. (2) We prove the correctness of two algorithms by Rohlf and Murtagh, which is necessary in each case for different reasons. (3) We give well-founded recommendations for the best current algorithms for the various agglomerative clustering schemes.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

Recent advancements in large language model (LLM) unlearning have shown remarkable success in removing unwanted data-model influences while preserving the model's utility for legitimate knowledge. However, despite these strides, sparse Mixture-of-Experts (MoE) LLMs--a key subset of the LLM family--have received little attention and remain largely unexplored in the context of unlearning. As MoE LLMs are celebrated for their exceptional performance and highly efficient inference processes, we ask: How can unlearning be performed effectively and efficiently on MoE LLMs? And will traditional unlearning methods be applicable to MoE architectures? Our pilot study shows that the dynamic routing nature of MoE LLMs introduces unique challenges, leading to substantial utility drops when existing unlearning methods are applied. Specifically, unlearning disrupts the router's expert selection, causing significant selection shift from the most unlearning target-related experts to irrelevant ones. As a result, more experts than necessary are affected, leading to excessive forgetting and loss of control over which knowledge is erased. To address this, we propose a novel single-expert unlearning framework, referred to as UOE, for MoE LLMs. Through expert attribution, unlearning is concentrated on the most actively engaged expert for the specified knowledge. Concurrently, an anchor loss is applied to the router to stabilize the active state of this targeted expert, ensuring focused and controlled unlearning that preserves model utility. The proposed UOE framework is also compatible with various unlearning algorithms. Extensive experiments demonstrate that UOE enhances both forget quality up to 5% and model utility by 35% on MoE LLMs across various benchmarks, LLM architectures, while only unlearning 0.06% of the model parameters.

Despite MoE models leading many benchmarks, supervised fine-tuning (SFT) for the MoE architectures remains difficult because its router layers are fragile. Methods such as DenseMixer and ESFT mitigate router collapse with dense mixing or auxiliary load-balancing losses, but these introduce noisy gradients that often degrade performance. In preliminary experiments, we systematically pruned experts and observed that while certain super experts are activated far more frequently, discarding less used experts still leads to notable performance degradation. This suggests that even rarely activated experts encode non-trivial knowledge useful for downstream tasks. Motivated by this, we propose an auxiliary-loss-free MoE SFT framework that combines bias-driven sparsification with always-active gated condenser experts. Rather than enforcing balanced activation across all experts, our method encourages task-relevant experts to remain active while pushing long-tailed experts toward inactivity. The condenser experts provide a persistent, learnable pathway that alleviates gradient starvation and facilitates consolidation of information that would otherwise remain fragmented across sparsely activated experts. Analysis further suggest that this design better preserves long-tailed expert information under sparse routing. Experiments on large-scale MoE models demonstrate that our approach outperforms state-of-the-art SFT baselines such as DenseMixer and ESFT, achieving average gain of 2.5%+ on both mathematical reasoning and commonsenseQA benchmarks.

Can we automatically group images into semantically meaningful clusters when ground-truth annotations are absent? The task of unsupervised image classification remains an important, and open challenge in computer vision. Several recent approaches have tried to tackle this problem in an end-to-end fashion. In this paper, we deviate from recent works, and advocate a two-step approach where feature learning and clustering are decoupled. First, a self-supervised task from representation learning is employed to obtain semantically meaningful features. Second, we use the obtained features as a prior in a learnable clustering approach. In doing so, we remove the ability for cluster learning to depend on low-level features, which is present in current end-to-end learning approaches. Experimental evaluation shows that we outperform state-of-the-art methods by large margins, in particular +26.6% on CIFAR10, +25.0% on CIFAR100-20 and +21.3% on STL10 in terms of classification accuracy. Furthermore, our method is the first to perform well on a large-scale dataset for image classification. In particular, we obtain promising results on ImageNet, and outperform several semi-supervised learning methods in the low-data regime without the use of any ground-truth annotations. The code is made publicly available at https://github.com/wvangansbeke/Unsupervised-Classification.

Mixture of Experts (MoE) LLMs face significant obstacles due to their massive parameter scale, which imposes memory, storage, and deployment challenges. Although recent expert merging methods promise greater efficiency by consolidating multiple experts, they are fundamentally hindered by parameter conflicts arising from expert specialization. In this paper, we present Sub-MoE, a novel MoE compression framework via Subspace Expert Merging. Our key insight is to perform joint Singular Value Decomposition (SVD) on concatenated expert weights, reducing conflicting parameters by extracting shared U-matrices while enabling effective merging of the expert-specific V components. Specifically, Sub-MoE consists of two innovative phases: (1) Adaptive Expert Clustering, which groups functionally coherent experts via K-means clustering based on cosine similarity of expert outputs; and (2) Subspace Expert Merging, which first enforces Experts Union Decomposition to derive the shared U-matrix across experts in the same group, then pursues frequency-based merging for individual V-matrices, and finalizes expert reconstruction using the merged V-matrix. In this way, we align and fuse experts in a shared subspace, and can be extended with intra-expert compression for further inference optimization. Extensive experiments on Mixtral, DeepSeek, and Qwen-1.5|3 MoE LLMs demonstrate that our Sub-MoE significantly outperforms existing expert pruning and merging methods. Notably, our Sub-MoE maintains 96\%|86\% of original performance with 25\%|50\% expert reduction on Mixtral-8x7B in zero-shot benchmarks. Code will be released at https://github.com/lliai/MoERazor.

Self-supervised learning excels at learning representations from large amounts of data. At the same time, generative models offer the complementary property of learning information about the underlying data generation process. In this study, we aim at establishing a principled connection between these two paradigms and highlight the benefits of their complementarity. In particular, we perform an analysis of self-supervised learning objectives, elucidating the underlying probabilistic graphical models and presenting a standardized methodology for their derivation from first principles. The analysis suggests a natural means of integrating self-supervised learning with likelihood-based generative models. We instantiate this concept within the realm of cluster-based self-supervised learning and energy models, introducing a lower bound proven to reliably penalize the most important failure modes and unlocking full unification. Our theoretical findings are substantiated through experiments on synthetic and real-world data, including SVHN, CIFAR10, and CIFAR100, demonstrating that our objective function allows to jointly train a backbone network in a discriminative and generative fashion, consequently outperforming existing self-supervised learning strategies in terms of clustering, generation and out-of-distribution detection performance by a wide margin. We also demonstrate that the solution can be integrated into a neuro-symbolic framework to tackle a simple yet non-trivial instantiation of the symbol grounding problem. The code is publicly available at https://github.com/emsansone/GEDI.

The problem of Novel Class Discovery (NCD) consists in extracting knowledge from a labeled set of known classes to accurately partition an unlabeled set of novel classes. While NCD has recently received a lot of attention from the community, it is often solved on computer vision problems and under unrealistic conditions. In particular, the number of novel classes is usually assumed to be known in advance, and their labels are sometimes used to tune hyperparameters. Methods that rely on these assumptions are not applicable in real-world scenarios. In this work, we focus on solving NCD in tabular data when no prior knowledge of the novel classes is available. To this end, we propose to tune the hyperparameters of NCD methods by adapting the k-fold cross-validation process and hiding some of the known classes in each fold. Since we have found that methods with too many hyperparameters are likely to overfit these hidden classes, we define a simple deep NCD model. This method is composed of only the essential elements necessary for the NCD problem and performs impressively well under realistic conditions. Furthermore, we find that the latent space of this method can be used to reliably estimate the number of novel classes. Additionally, we adapt two unsupervised clustering algorithms (k-means and Spectral Clustering) to leverage the knowledge of the known classes. Extensive experiments are conducted on 7 tabular datasets and demonstrate the effectiveness of the proposed method and hyperparameter tuning process, and show that the NCD problem can be solved without relying on knowledge from the novel classes.

Unsupervised clustering is widely used to explore large corpora, but existing formulations neither consider the users' goals nor explain clusters' meanings. We propose a new task formulation, "Goal-Driven Clustering with Explanations" (GoalEx), which represents both the goal and the explanations as free-form language descriptions. For example, to categorize the errors made by a summarization system, the input to GoalEx is a corpus of annotator-written comments for system-generated summaries and a goal description "cluster the comments based on why the annotators think the summary is imperfect.''; the outputs are text clusters each with an explanation ("this cluster mentions that the summary misses important context information."), which relates to the goal and precisely explain which comments should (not) belong to a cluster. To tackle GoalEx, we prompt a language model with "[corpus subset] + [goal] + Brainstorm a list of explanations each representing a cluster."; then we classify whether each sample belongs to a cluster based on its explanation; finally, we use integer linear programming to select a subset of candidate clusters to cover most samples while minimizing overlaps. Under both automatic and human evaluation on corpora with or without labels, our method produces more accurate and goal-related explanations than prior methods. We release our data and implementation at https://github.com/ZihanWangKi/GoalEx.

Mixture-of-Experts (MoE) has emerged as a promising paradigm for foundation models due to its efficient and powerful scalability. In this work, we present Sigma-MoE-Tiny, an MoE language model that achieves the highest sparsity compared to existing open-source models. Sigma-MoE-Tiny employs fine-grained expert segmentation with up to 96 experts per layer, while activating only one expert for each token, resulting in 20B total parameters with just 0.5B activated. The major challenge introduced by such extreme sparsity lies in expert load balancing. We find that the widely-used load balancing loss tends to become ineffective in the lower layers under this setting. To address this issue, we propose a progressive sparsification schedule aiming to balance expert utilization and training stability. Sigma-MoE-Tiny is pre-trained on a diverse and high-quality corpus, followed by post-training to further unlock its capabilities. The entire training process remains remarkably stable, with no occurrence of irrecoverable loss spikes. Comprehensive evaluations reveal that, despite activating only 0.5B parameters, Sigma-MoE-Tiny achieves top-tier performance among counterparts of comparable or significantly larger scale. In addition, we provide an in-depth discussion of load balancing in highly sparse MoE models, offering insights for advancing sparsity in future MoE architectures. Project page: https://qghuxmu.github.io/Sigma-MoE-Tiny Code: https://github.com/microsoft/ltp-megatron-lm

Mixture-of-Experts (MoE) models achieve a favorable trade-off between performance and inference efficiency by activating only a subset of experts. However, the memory overhead of storing all experts remains a major limitation, especially in large-scale MoE models such as DeepSeek-R1(671B). In this study, we investigate domain specialization and expert redundancy in large-scale MoE models and uncover a consistent behavior we term few-shot expert localization, with only a few in-domain demonstrations, the model consistently activates a sparse and stable subset of experts on tasks within the same domain. Building on this observation, we propose a simple yet effective pruning framework, EASY-EP, that leverages a few domain-specific demonstrations to identify and retain only the most relevant experts. EASY-EP comprises two key components: output-aware expert importance assessment and expert-level token contribution estimation. The former evaluates the importance of each expert for the current token by considering the gating scores and L2 norm of the outputs of activated experts, while the latter assesses the contribution of tokens based on representation similarities before and after routed experts. Experiments on DeepSeek-R1 and DeepSeek-V3-0324 show that our method can achieve comparable performances and 2.99times throughput under the same memory budget with full model with only half the experts.

Recently, deep clustering methods have gained momentum because of the high representational power of deep neural networks (DNNs) such as autoencoder. The key idea is that representation learning and clustering can reinforce each other: Good representations lead to good clustering while good clustering provides good supervisory signals to representation learning. Critical questions include: 1) How to optimize representation learning and clustering? 2) Should the reconstruction loss of autoencoder be considered always? In this paper, we propose DEKM (for Deep Embedded K-Means) to answer these two questions. Since the embedding space generated by autoencoder may have no obvious cluster structures, we propose to further transform the embedding space to a new space that reveals the cluster-structure information. This is achieved by an orthonormal transformation matrix, which contains the eigenvectors of the within-class scatter matrix of K-means. The eigenvalues indicate the importance of the eigenvectors' contributions to the cluster-structure information in the new space. Our goal is to increase the cluster-structure information. To this end, we discard the decoder and propose a greedy method to optimize the representation. Representation learning and clustering are alternately optimized by DEKM. Experimental results on the real-world datasets demonstrate that DEKM achieves state-of-the-art performance.

In the era of large language models, Mixture-of-Experts (MoE) is a promising architecture for managing computational costs when scaling up model parameters. However, conventional MoE architectures like GShard, which activate the top-K out of N experts, face challenges in ensuring expert specialization, i.e. each expert acquires non-overlapping and focused knowledge. In response, we propose the DeepSeekMoE architecture towards ultimate expert specialization. It involves two principal strategies: (1) finely segmenting the experts into mN ones and activating mK from them, allowing for a more flexible combination of activated experts; (2) isolating K_s experts as shared ones, aiming at capturing common knowledge and mitigating redundancy in routed experts. Starting from a modest scale with 2B parameters, we demonstrate that DeepSeekMoE 2B achieves comparable performance with GShard 2.9B, which has 1.5 times the expert parameters and computation. In addition, DeepSeekMoE 2B nearly approaches the performance of its dense counterpart with the same number of total parameters, which set the upper bound of MoE models. Subsequently, we scale up DeepSeekMoE to 16B parameters and show that it achieves comparable performance with LLaMA2 7B, with only about 40% of computations. Further, our preliminary efforts to scale up DeepSeekMoE to 145B parameters consistently validate its substantial advantages over the GShard architecture, and show its performance comparable with DeepSeek 67B, using only 28.5% (maybe even 18.2%) of computations.

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

Clustering using neural networks has recently demonstrated promising performance in machine learning and computer vision applications. However, the performance of current approaches is limited either by unsupervised learning or their dependence on large set of labeled data samples. In this paper, we propose ClusterNet that uses pairwise semantic constraints from very few labeled data samples (<5% of total data) and exploits the abundant unlabeled data to drive the clustering approach. We define a new loss function that uses pairwise semantic similarity between objects combined with constrained k-means clustering to efficiently utilize both labeled and unlabeled data in the same framework. The proposed network uses convolution autoencoder to learn a latent representation that groups data into k specified clusters, while also learning the cluster centers simultaneously. We evaluate and compare the performance of ClusterNet on several datasets and state of the art deep clustering approaches.

In recent years, much of the research on clustering algorithms has primarily focused on enhancing their accuracy and efficiency, frequently at the expense of interpretability. However, as these methods are increasingly being applied in high-stakes domains such as healthcare, finance, and autonomous systems, the need for transparent and interpretable clustering outcomes has become a critical concern. This is not only necessary for gaining user trust but also for satisfying the growing ethical and regulatory demands in these fields. Ensuring that decisions derived from clustering algorithms can be clearly understood and justified is now a fundamental requirement. To address this need, this paper provides a comprehensive and structured review of the current state of explainable clustering algorithms, identifying key criteria to distinguish between various methods. These insights can effectively assist researchers in making informed decisions about the most suitable explainable clustering methods for specific application contexts, while also promoting the development and adoption of clustering algorithms that are both efficient and transparent. For convenient access and reference, an open repository organizes representative and emerging interpretable clustering methods under the taxonomy proposed in this survey, available at https://github.com/hulianyu/Awesome-Interpretable-Clustering

Deep clustering has exhibited remarkable performance; however, the overconfidence problem, i.e., the estimated confidence for a sample belonging to a particular cluster greatly exceeds its actual prediction accuracy, has been overlooked in prior research. To tackle this critical issue, we pioneer the development of a calibrated deep clustering framework. Specifically, we propose a novel dual-head deep clustering pipeline that can effectively calibrate the estimated confidence and the actual accuracy. The calibration head adjusts the overconfident predictions of the clustering head using regularization methods, generating prediction confidence and pseudo-labels that match the model learning status. This calibration process also guides the clustering head in dynamically selecting reliable high-confidence samples for training. Additionally, we introduce an effective network initialization strategy that enhances both training speed and network robustness. Extensive experiments demonstrate the proposed calibrated deep clustering framework not only surpasses state-of-the-art deep clustering methods by approximately 10 times in terms of expected calibration error but also significantly outperforms them in terms of clustering accuracy.

Mixture-of-Experts (MoE) enables efficient scaling of large language models (LLMs) with sparsely activated experts during inference. To effectively deploy large MoE models on memory-constrained devices, many systems introduce *expert offloading* that caches a subset of experts in fast memory, leaving others on slow memory to run on CPU or load on demand. While some research has exploited the locality of expert activations, where consecutive tokens activate similar experts, the degree of this **local routing consistency** varies across models and remains understudied. In this paper, we propose two metrics to measure local routing consistency of MoE models: (1) **Segment Routing Best Performance (SRP)**, which evaluates how well a fixed group of experts can cover the needs of a segment of tokens, and (2) **Segment Cache Best Hit Rate (SCH)**, which measures the optimal segment-level cache hit rate under a given cache size limit. We analyzed 20 MoE LLMs with diverse sizes and architectures and found that models that apply MoE on every layer and do not use shared experts exhibit the highest local routing consistency. We further showed that domain-specialized experts contribute more to routing consistency than vocabulary-specialized ones, and that most models can balance between cache effectiveness and efficiency with cache sizes approximately 2x the active experts. These findings pave the way for memory-efficient MoE design and deployment without compromising inference speed. We publish the code for replicating experiments at https://github.com/ljcleo/moe-lrc .

In recent years, concept-based approaches have emerged as some of the most promising explainability methods to help us interpret the decisions of Artificial Neural Networks (ANNs). These methods seek to discover intelligible visual 'concepts' buried within the complex patterns of ANN activations in two key steps: (1) concept extraction followed by (2) importance estimation. While these two steps are shared across methods, they all differ in their specific implementations. Here, we introduce a unifying theoretical framework that comprehensively defines and clarifies these two steps. This framework offers several advantages as it allows us: (i) to propose new evaluation metrics for comparing different concept extraction approaches; (ii) to leverage modern attribution methods and evaluation metrics to extend and systematically evaluate state-of-the-art concept-based approaches and importance estimation techniques; (iii) to derive theoretical guarantees regarding the optimality of such methods. We further leverage our framework to try to tackle a crucial question in explainability: how to efficiently identify clusters of data points that are classified based on a similar shared strategy. To illustrate these findings and to highlight the main strategies of a model, we introduce a visual representation called the strategic cluster graph. Finally, we present https://serre-lab.github.io/Lens, a dedicated website that offers a complete compilation of these visualizations for all classes of the ImageNet dataset.

An approach to improve neural network interpretability is via clusterability, i.e., splitting a model into disjoint clusters that can be studied independently. We define a measure for clusterability and show that pre-trained models form highly enmeshed clusters via spectral graph clustering. We thus train models to be more modular using a "clusterability loss" function that encourages the formation of non-interacting clusters. Using automated interpretability techniques, we show that our method can help train models that are more modular and learn different, disjoint, and smaller circuits. We investigate CNNs trained on MNIST and CIFAR, small transformers trained on modular addition, and language models. Our approach provides a promising direction for training neural networks that learn simpler functions and are easier to interpret.

A modified LAB algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

We introduce ClusterLLM, a novel text clustering framework that leverages feedback from an instruction-tuned large language model, such as ChatGPT. Compared with traditional unsupervised methods that builds upon "small" embedders, ClusterLLM exhibits two intriguing advantages: (1) it enjoys the emergent capability of LLM even if its embeddings are inaccessible; and (2) it understands the user's preference on clustering through textual instruction and/or a few annotated data. First, we prompt ChatGPT for insights on clustering perspective by constructing hard triplet questions <does A better correspond to B than C>, where A, B and C are similar data points that belong to different clusters according to small embedder. We empirically show that this strategy is both effective for fine-tuning small embedder and cost-efficient to query ChatGPT. Second, we prompt ChatGPT for helps on clustering granularity by carefully designed pairwise questions <do A and B belong to the same category>, and tune the granularity from cluster hierarchies that is the most consistent with the ChatGPT answers. Extensive experiments on 14 datasets show that ClusterLLM consistently improves clustering quality, at an average cost of ~$0.6 per dataset.

Continual learning (CL) with large pre-trained models is challenged by catastrophic forgetting and task interference. Existing LoRA-based Mixture-of-Experts (MoE) approaches mitigate forgetting by assigning and freezing task-specific adapters, but suffer from interference, redundancy, and ambiguous routing due to coarse adapter-level selection. However, this design introduces three key challenges: 1) Interference: Activating full LoRA experts per input leads to subspace interference and prevents selective reuse of useful components across tasks. 2) Redundancy: Newly added experts often duplicate or contradict existing knowledge due to unnecessary activation of unrelated ranks and insufficient reuse of relevant ones. 3) Ambiguity: Overlapping features across tasks confuse the router, resulting in unstable expert assignments. As more experts accumulate, earlier task routing degrades, accelerating forgetting. We propose MoRA, a Mixture-of-Rank Adaptive learning approach with self-activated and sparse rank activation for CL. Unlike mixing multiple low-rank matrices, MoRA decomposes each rank-r update into r rank-1 components, each treated as an independent expert, enabling fine-grained mixture of rank-1 expert utilization while mitigating interference and redundancy. To avoid ambiguous routing, we propose that each rank-1 expert can infer its own relevance via intermediate activations. Coupled with our proposed rank pruning and activation budgets, MoRA adaptively selects a sparse mixture of ranks per input. We validate MoRA on continual learning tasks with CLIP and large language models (LLMs), analyzing both in-domain learning and out-of-domain forgetting/generalization during fine-tuning. MoRA shows significant effectiveness on enhancing CL with PTMs, and improving generalization while mitigating forgetting.

Can pretrained models generalize to new datasets without any retraining? We deploy pretrained image models on datasets they were not trained for, and investigate whether their embeddings form meaningful clusters. Our suite of benchmarking experiments use encoders pretrained solely on ImageNet-1k with either supervised or self-supervised training techniques, deployed on image datasets that were not seen during training, and clustered with conventional clustering algorithms. This evaluation provides new insights into the embeddings of self-supervised models, which prioritize different features to supervised models. Supervised encoders typically offer more utility than SSL encoders within the training domain, and vice-versa far outside of it, however, fine-tuned encoders demonstrate the opposite trend. Clustering provides a way to evaluate the utility of self-supervised learned representations orthogonal to existing methods such as kNN. Additionally, we find the silhouette score when measured in a UMAP-reduced space is highly correlated with clustering performance, and can therefore be used as a proxy for clustering performance on data with no ground truth labels. Our code implementation is available at https://github.com/scottclowe/zs-ssl-clustering/.

Query clustering organizes queries into groups that reflect shared latent capability demands, enabling capability-aware LLM evaluation. Existing clustering methods, which primarily rely on semantic taxonomies or embeddings, often fail to capture such latent capability requirements due to a misalignment between surface-level semantics and actual model performance. We propose ECC, an algorithm that calibrates prior semantic embeddings using limited posterior model comparisons to bridge the gap between surface-level semantics and latent capability requirements. ECC characterizes each cluster through a capability profile parameterized by a Bradley-Terry model and uses trainable mixture weights to accommodate queries with mixed capability demands, jointly learning a flexible, capability-aware clustering structure that supports query-specific inference of LLM capabilities. Extensive quantitative and qualitative evaluations demonstrate that ECC significantly improves LLM capability ranking quality, outperforming human-labeled and embedding-based baselines by an average of 17.64 and 18.02 percentage points, respectively, and proves effective in downstream tasks such as query routing.

Machine unlearning (MU) for large language models has become critical for AI safety, yet existing methods fail to generalize to Mixture-of-Experts (MoE) architectures. We identify that traditional unlearning methods exploit MoE's architectural vulnerability: they manipulate routers to redirect queries away from knowledgeable experts rather than erasing knowledge, causing a loss of model utility and superficial forgetting. We propose Geometric Routing Invariance Preservation (GRIP), an algorithm-agnostic framework for unlearning for MoE. Our core contribution is a geometric constraint, implemented by projecting router gradient updates into an expert-specific null-space. Crucially, this decouples routing stability from parameter rigidity: while discrete expert selections remain stable for retained knowledge, the continuous router parameters remain plastic within the null space, allowing the model to undergo necessary internal reconfiguration to satisfy unlearning objectives. This forces the unlearning optimization to erase knowledge directly from expert parameters rather than exploiting the superficial router manipulation shortcut. GRIP functions as an adapter, constraining router parameter updates without modifying the underlying unlearning algorithm. Extensive experiments on large-scale MoE models demonstrate that our adapter eliminates expert selection shift (achieving over 95% routing stability) across all tested unlearning methods while preserving their utility. By preventing existing algorithms from exploiting MoE model's router vulnerability, GRIP adapts existing unlearning research from dense architectures to MoEs.

In large organisations, identifying experts on a given topic is crucial in leveraging the internal knowledge spread across teams and departments. So-called enterprise expert retrieval systems automatically discover and structure employees' expertise based on the vast amount of heterogeneous data available about them and the work they perform. Evaluating these systems requires comprehensive ground truth expert annotations, which are hard to obtain. Therefore, the annotation process typically relies on automated recommendations of knowledge areas to validate. This case study provides an analysis of how these recommendations can impact the evaluation of expert finding systems. We demonstrate on a popular benchmark that system-validated annotations lead to overestimated performance of traditional term-based retrieval models and even invalidate comparisons with more recent neural methods. We also augment knowledge areas with synonyms to uncover a strong bias towards literal mentions of their constituent words. Finally, we propose constraints to the annotation process to prevent these biased evaluations, and show that this still allows annotation suggestions of high utility. These findings should inform benchmark creation or selection for expert finding, to guarantee meaningful comparison of methods.

Despite their remarkable achievement, gigantic transformers encounter significant drawbacks, including exorbitant computational and memory footprints during training, as well as severe collapse evidenced by a high degree of parameter redundancy. Sparsely-activated Mixture-of-Experts (SMoEs) have shown promise to mitigate the issue of training efficiency, yet they are prone to (1) redundant experts due to representational collapse; and (2) poor expert scalability for inference and downstream fine-tuning, primarily due to overfitting of the learned routing policy to the number of activated experts during training. As recent research efforts are predominantly focused on improving routing policies to encourage expert specializations, this work focuses on exploring the overlooked scalability bottleneck of SMoEs and leveraging it to effectively scale dense transformers. To this end, we propose a new plug-and-play training framework, SMoE-Dropout, to enable scaling transformers to better accuracy in their full capacity without collapse. Specifically, SMoE-Dropout consists of a randomly initialized and fixed router network to activate experts and gradually increases the activated expert number as training progresses over time. Transformers trained by SMoE-Dropout naturally exhibit a self-slimmable property subject to resource availability, offering smooth and consistent performance boosts with an increase in activated experts during inference or fine-tuning. Our extensive experiments demonstrate the superior performance and substantial computation savings of SMoE-Dropout, compared to dense training baselines with equivalent parameter counts. In particular, our trained BERT outperforms its densely trained counterpart with consistent improvements of {1.03%, 0.78%, 1.09%} on challenging reasoning tasks {ASDiv-A, MAWPS, SVAMP}, respectively.

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed K-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including K-means, SDP and EM algorithms.

Mixture-of-Experts (MoE) architectures employ sparse activation to deliver faster training and inference with higher accuracy than dense LLMs. However, in production serving, MoE models require batch inference to optimize hardware efficiency, which may cause excessive expert activation and thus slow the memory-bound decoding stage. To address the fundamental tension between batch decoding and expert sparsity, we present SERE, a Similarity-based Expert Re-routing method for Efficient batch decoding in MoE models. SERE dynamically reduces the number of active experts in an input-aware manner by re-routing tokens from secondary experts to their most similar primary counterparts. It also leverages similarity patterns to identify and preserve critical experts, thereby preventing capability loss. Notably, SERE avoids static expert pruning or merging, instead enabling dynamic expert skipping based on batch-level expert redundancy. Additionally, we provide an efficient custom CUDA kernel for SERE, enabling plug-and-play use in vLLM with only a single-line code change. Extensive experiments on various complex reasoning benchmarks demonstrate that SERE achieves up to 2.0x speedup with minimal quality loss, providing a practical solution for cost-efficient and latency-sensitive large-scale MoE deployment. Code implementation of SERE can be found in https://github.com/JL-Cheng/SERE.

Joint clustering and feature learning methods have shown remarkable performance in unsupervised representation learning. However, the training schedule alternating between feature clustering and network parameters update leads to unstable learning of visual representations. To overcome this challenge, we propose Online Deep Clustering (ODC) that performs clustering and network update simultaneously rather than alternatingly. Our key insight is that the cluster centroids should evolve steadily in keeping the classifier stably updated. Specifically, we design and maintain two dynamic memory modules, i.e., samples memory to store samples labels and features, and centroids memory for centroids evolution. We break down the abrupt global clustering into steady memory update and batch-wise label re-assignment. The process is integrated into network update iterations. In this way, labels and the network evolve shoulder-to-shoulder rather than alternatingly. Extensive experiments demonstrate that ODC stabilizes the training process and boosts the performance effectively. Code: https://github.com/open-mmlab/OpenSelfSup.

Machine unlearning has emerged as a prevalent technical solution for selectively removing unwanted knowledge absorbed during pre-training, without requiring full retraining. While recent unlearning techniques can effectively remove undesirable content without severely compromising performance on standard benchmarks, we find that they may inadvertently create ``knowledge holes'' -- unintended losses of benign knowledge that standard benchmarks fail to capture. To probe where unlearned models reveal knowledge holes, we propose a test case generation framework that explores both immediate neighbors of unlearned content and broader areas of potential failures. Our evaluation demonstrates significant hidden costs of unlearning: up to 98.7\% of the test cases yield irrelevant or nonsensical responses from unlearned models, despite being answerable by the pretrained model. These findings necessitate rethinking the conventional approach to evaluating knowledge preservation in unlearning, moving beyond standard, static benchmarks.

We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and because it is a natural companion to dropout) designed to both facilitate optimization by dropout and improve the accuracy of dropout's fast approximate model averaging technique. We empirically verify that the model successfully accomplishes both of these tasks. We use maxout and dropout to demonstrate state of the art classification performance on four benchmark datasets: MNIST, CIFAR-10, CIFAR-100, and SVHN.

With the emergence of Mixture-of-Experts (MoE), the efficient scaling of model size has accelerated the development of large language models in recent years. However, their high memory requirements prevent their use in resource-constrained environments. While knowledge distillation (KD) has been a proven method for model compression, its application to MoE teacher models remains underexplored. Through our investigation, we discover that non-activated experts in MoE models possess valuable knowledge that benefits student models. We further demonstrate that existing KD methods are not optimal for compressing MoE models, as they fail to leverage this knowledge effectively. To address this, we propose two intuitive MoE-specific KD methods for the first time: Knowledge Augmentation (KA) and Student-Aware Router (SAR), both designed to effectively extract knowledge from all experts. Specifically, KA augments knowledge by sampling experts multiple times, while SAR uses all experts and adjusts the expert weights through router training to provide optimal knowledge. Extensive experiments show that our methods outperform conventional KD methods, demonstrating their effectiveness for MoE teacher models.

This work investigates an important phenomenon in centroid-based deep clustering (DC) algorithms: Performance quickly saturates after a period of rapid early gains. Practitioners commonly address early saturation with periodic reclustering, which we demonstrate to be insufficient to address performance plateaus. We call this phenomenon the "reclustering barrier" and empirically show when the reclustering barrier occurs, what its underlying mechanisms are, and how it is possible to Break the Reclustering Barrier with our algorithm BRB. BRB avoids early over-commitment to initial clusterings and enables continuous adaptation to reinitialized clustering targets while remaining conceptually simple. Applying our algorithm to widely-used centroid-based DC algorithms, we show that (1) BRB consistently improves performance across a wide range of clustering benchmarks, (2) BRB enables training from scratch, and (3) BRB performs competitively against state-of-the-art DC algorithms when combined with a contrastive loss. We release our code and pre-trained models at https://github.com/Probabilistic-and-Interactive-ML/breaking-the-reclustering-barrier .

Mixture of Experts models are widely assumed to achieve domain specialization through sparse routing. In this work, we question this assumption by introducing COMMITTEEAUDIT, a post hoc framework that analyzes routing behavior at the level of expert groups rather than individual experts. Across three representative models and the MMLU benchmark, we uncover a domain-invariant Standing Committee. This is a compact coalition of routed experts that consistently captures the majority of routing mass across domains, layers, and routing budgets, even when architectures already include shared experts. Qualitative analysis further shows that Standing Committees anchor reasoning structure and syntax, while peripheral experts handle domain-specific knowledge. These findings reveal a strong structural bias toward centralized computation, suggesting that specialization in Mixture of Experts models is far less pervasive than commonly believed. This inherent bias also indicates that current training objectives, such as load-balancing losses that enforce uniform expert utilization, may be working against the model's natural optimization path, thereby limiting training efficiency and performance.

Self-supervised features are the cornerstone of modern machine learning systems. They are typically pre-trained on data collections whose construction and curation typically require extensive human effort. This manual process has some limitations similar to those encountered in supervised learning, e.g., the crowd-sourced selection of data is costly and time-consuming, preventing scaling the dataset size. In this work, we consider the problem of automatic curation of high-quality datasets for self-supervised pre-training. We posit that such datasets should be large, diverse and balanced, and propose a clustering-based approach for building ones satisfying all these criteria. Our method involves successive and hierarchical applications of k-means on a large and diverse data repository to obtain clusters that distribute uniformly among data concepts, followed by a hierarchical, balanced sampling step from these clusters. Extensive experiments on three different data domains including web-based images, satellite images and text show that features trained on our automatically curated datasets outperform those trained on uncurated data while being on par or better than ones trained on manually curated data.

Mixture-of-experts (MoE) is gaining increasing attention due to its unique properties and remarkable performance, especially for language tasks. By sparsely activating a subset of parameters for each token, MoE architecture could increase the model size without sacrificing computational efficiency, achieving a better trade-off between performance and training costs. However, the underlying mechanism of MoE still lacks further exploration, and its modularization degree remains questionable. In this paper, we make an initial attempt to understand the inner workings of MoE-based large language models. Concretely, we comprehensively study the parametric and behavioral features of three recent MoE-based models and reveal some intriguing observations, including (1) Neurons act like fine-grained experts. (2) The router of MoE usually selects experts with larger output norms. (3) The expert diversity increases as the layer increases, while the last layer is an outlier. Based on the observations, we also provide suggestions for a broad spectrum of MoE practitioners, such as router design and expert allocation. We hope this work could shed light on future research on the MoE framework and other modular architectures. Code is available at https://github.com/kamanphoebe/Look-into-MoEs.

Existing long-tailed recognition methods, aiming to train class-balanced models from long-tailed data, generally assume the models would be evaluated on the uniform test class distribution. However, practical test class distributions often violate this assumption (e.g., being either long-tailed or even inversely long-tailed), which may lead existing methods to fail in real applications. In this paper, we study a more practical yet challenging task, called test-agnostic long-tailed recognition, where the training class distribution is long-tailed while the test class distribution is agnostic and not necessarily uniform. In addition to the issue of class imbalance, this task poses another challenge: the class distribution shift between the training and test data is unknown. To tackle this task, we propose a novel approach, called Self-supervised Aggregation of Diverse Experts, which consists of two strategies: (i) a new skill-diverse expert learning strategy that trains multiple experts from a single and stationary long-tailed dataset to separately handle different class distributions; (ii) a novel test-time expert aggregation strategy that leverages self-supervision to aggregate the learned multiple experts for handling unknown test class distributions. We theoretically show that our self-supervised strategy has a provable ability to simulate test-agnostic class distributions. Promising empirical results demonstrate the effectiveness of our method on both vanilla and test-agnostic long-tailed recognition. Code is available at https://github.com/Vanint/SADE-AgnosticLT.

The Mixture-of-Experts (MoE) architecture has become a predominant paradigm for scaling large language models (LLMs). Despite offering strong performance and computational efficiency, large MoE-based LLMs like DeepSeek-V3-0324 and Kimi-K2-Instruct present serious challenges due to substantial memory requirements in deployment. While recent works have explored MoE compression to address this issue, existing methods often suffer from considerable accuracy drops (e.g., 7-14% relatively) even at modest compression rates. This paper introduces a novel Mixture-of-Basis-Experts (MoBE) method that achieves model compression while incurring minimal accuracy drops. Specifically, each up/gate matrix in an expert is decomposed via a rank decomposition as W = AB, where matrix A is unique to each expert. The relatively larger matrix B is further re-parameterized as a linear combination of basis matrices {Bi} shared across all experts within a given MoE layer. The factorization is learned by minimizing the reconstruction error relative to the original weight matrices. Experiments demonstrate that MoBE achieves notably lower accuracy drops compared to prior works. For instance, MoBE can reduce the parameter counts of Qwen3-235B-A22B-2507, DeepSeek-V3-0324 (671B) and Kimi-K2-Instruct (1T) by 24%-30% with only 1%-2% accuracy drop (about 2% drops when measured relatively).

We introduce LM-Lexicon, an innovative definition modeling approach that incorporates data clustering, semantic expert learning, and model merging using a sparse mixture-of-experts architecture. By decomposing the definition modeling task into specialized semantic domains, where small language models are trained as domain experts, LM-Lexicon achieves substantial improvements (+7% BLEU score compared with the prior state-of-the-art model) over existing methods on five widely used benchmarks. Empirically, we demonstrate that 1) the clustering strategy enables fine-grained expert specialization with nearly 10% improvement in definition quality; 2) the semantic-aware domain-level routing mechanism achieves higher expert efficacy (+1%) than conventional token-level routing; and 3) further performance gains can be obtained through test-time compute and semantic expert scaling. Our work advances definition modeling while providing insights into the development of efficient language models for semantic-intensive applications.

This paper presents MoE-Infinity, a cost-efficient mixture-of-expert (MoE) serving system that realizes activation-aware expert offloading. MoE-Infinity features sequence-level expert activation tracing, a new approach adept at identifying sparse activations and capturing the temporal locality of MoE inference. By analyzing these traces, MoE-Infinity performs novel activation-aware expert prefetching and caching, substantially reducing the latency overheads usually associated with offloading experts for improved cost performance. Extensive experiments in a cluster show that MoE-Infinity outperforms numerous existing systems and approaches, reducing latency by 4 - 20X and decreasing deployment costs by over 8X for various MoEs. MoE-Infinity's source code is publicly available at https://github.com/TorchMoE/MoE-Infinity

We propose Chain-of-Experts (CoE), a new Mixture-of-Experts (MoE) architecture that introduces sequential expert communication within each layer. Unlike traditional MoE models, where experts operate independently in parallel, CoE processes tokens iteratively across a chain of experts inside a layer. To support dynamic expert selection across iterations, CoE employs a dedicated router at each iteration step within a layer. This design allows tokens to re-evaluate and select different experts during each iteration, rather than being statically assigned. As a result, CoE introduces a flexible routing mechanism that increases the diversity of expert combinations and enriches the model's representational capacity. CoE demonstrates improved performance under fixed compute: on math reasoning tasks, it reduces validation loss from 1.20 to 1.12 compared to a standard MoE. Beyond performance, CoE offers a new scaling axis: depth through expert iteration, which complements conventional width/depth scaling. For example, using 2x iterations matches the performance of 3x expert selections (in width), while reducing memory usage by 17.6-42% relative to other scaling strategies. Our analysis reveals that CoE's benefits stem from its iterative residual structure and enhanced expert specialization empowered by iterative routing, which together unlock more expressive representations. Code is available at https://github.com/ZihanWang314/coe.

Selecting an appropriate clustering method as well as an optimal number of clusters in road accident data is at times confusing and difficult. This paper analyzes shortcomings of different existing techniques applied to cluster accident-prone areas and recommends using Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Ordering Points To Identify the Clustering Structure (OPTICS) to overcome them. Comparative performance analysis based on real-life data on the recorded cases of road accidents in North Carolina also show more effectiveness and efficiency achieved by these algorithms.

Learning from non-stationary data streams subject to concept drift requires models that can adapt on-the-fly while remaining resource-efficient. Existing adaptive ensemble methods often rely on coarse-grained adaptation mechanisms or simple voting schemes that fail to optimally leverage specialized knowledge. This paper introduces DriftMoE, an online Mixture-of-Experts (MoE) architecture that addresses these limitations through a novel co-training framework. DriftMoE features a compact neural router that is co-trained alongside a pool of incremental Hoeffding tree experts. The key innovation lies in a symbiotic learning loop that enables expert specialization: the router selects the most suitable expert for prediction, the relevant experts update incrementally with the true label, and the router refines its parameters using a multi-hot correctness mask that reinforces every accurate expert. This feedback loop provides the router with a clear training signal while accelerating expert specialization. We evaluate DriftMoE's performance across nine state-of-the-art data stream learning benchmarks spanning abrupt, gradual, and real-world drifts testing two distinct configurations: one where experts specialize on data regimes (multi-class variant), and another where they focus on single-class specialization (task-based variant). Our results demonstrate that DriftMoE achieves competitive results with state-of-the-art stream learning adaptive ensembles, offering a principled and efficient approach to concept drift adaptation. All code, data pipelines, and reproducibility scripts are available in our public GitHub repository: https://github.com/miguel-ceadar/drift-moe.

Federated Learning (FL) is a machine learning paradigm that safeguards privacy by retaining client data on edge devices. However, optimizing FL in practice can be challenging due to the diverse and heterogeneous nature of the learning system. Though recent research has focused on improving the optimization of FL when distribution shifts occur among clients, ensuring global performance when multiple types of distribution shifts occur simultaneously among clients -- such as feature distribution shift, label distribution shift, and concept shift -- remain under-explored. In this paper, we identify the learning challenges posed by the simultaneous occurrence of diverse distribution shifts and propose a clustering principle to overcome these challenges. Through our research, we find that existing methods fail to address the clustering principle. Therefore, we propose a novel clustering algorithm framework, dubbed as FedRC, which adheres to our proposed clustering principle by incorporating a bi-level optimization problem and a novel objective function. Extensive experiments demonstrate that FedRC significantly outperforms other SOTA cluster-based FL methods. Our code is available at https://github.com/LINs-lab/FedRC.

Mixture-of-Experts (MoE) Multimodal large language models (MLLMs) excel at vision-language tasks, but they suffer from high computational inefficiency. To reduce inference overhead, expert skipping methods have been proposed to deactivate redundant experts based on the current input tokens. However, we find that applying these methods-originally designed for unimodal large language models (LLMs)-to MLLMs results in considerable performance degradation. This is primarily because such methods fail to account for the heterogeneous contributions of experts across MoE layers and modality-specific behaviors of tokens within these layers. Motivated by these findings, we propose MoDES, the first training-free framework that adaptively skips experts to enable efficient and accurate MoE MLLM inference. It incorporates a globally-modulated local gating (GMLG) mechanism that integrates global layer-wise importance into local routing probabilities to accurately estimate per-token expert importance. A dual-modality thresholding (DMT) method is then applied, which processes tokens from each modality separately, to derive the skipping schedule. To set the optimal thresholds, we introduce a frontier search algorithm that exploits monotonicity properties, cutting convergence time from several days to a few hours. Extensive experiments for 3 model series across 13 benchmarks demonstrate that MoDES far outperforms previous approaches. For instance, when skipping 88% experts for Qwen3-VL-MoE-30B-A3B-Instruct, the performance boost is up to 10.67% (97.33% vs. 86.66%). Furthermore, MoDES significantly enhances inference speed, improving the prefilling time by 2.16times and the decoding time by 1.26times.

Mixture-of-Experts (MoE) has emerged as a prominent architecture for scaling model size while maintaining computational efficiency. In MoE, each token in the input sequence activates a different subset of experts determined by a routing mechanism. However, the unchosen experts in MoE models do not contribute to the output, potentially leading to underutilization of the model's capacity. In this work, we first conduct exploratory studies to demonstrate that increasing the number of activated experts does not necessarily improve and can even degrade the output quality. Then, we show that output distributions from an MoE model using different routing strategies substantially differ, indicating that different experts do not always act synergistically. Motivated by these findings, we propose Self-Contrast Mixture-of-Experts (SCMoE), a training-free strategy that utilizes unchosen experts in a self-contrast manner during inference. In SCMoE, the next-token probabilities are determined by contrasting the outputs from strong and weak activation using the same MoE model. Our method is conceptually simple and computationally lightweight, as it incurs minimal latency compared to greedy decoding. Experiments on several benchmarks (GSM8K, StrategyQA, MBPP and HumanEval) demonstrate that SCMoE can consistently enhance Mixtral 8x7B's reasoning capability across various domains. For example, it improves the accuracy on GSM8K from 61.79 to 66.94. Moreover, combining SCMoE with self-consistency yields additional gains, increasing major@20 accuracy from 75.59 to 78.31.

In this paper, we introduce a novel dynamic expert selection framework for Mixture of Experts (MoE) models, aiming to enhance computational efficiency and model performance by adjusting the number of activated experts based on input difficulty. Unlike traditional MoE approaches that rely on fixed Top-K routing, which activates a predetermined number of experts regardless of the input's complexity, our method dynamically selects experts based on the confidence level in expert selection for each input. This allows for a more efficient utilization of computational resources, activating more experts for complex tasks requiring advanced reasoning and fewer for simpler tasks. Through extensive evaluations, our dynamic routing method demonstrates substantial improvements over conventional Top-2 routing across various benchmarks, achieving an average improvement of 0.7% with less than 90% activated parameters. Further analysis shows our model dispatches more experts to tasks requiring complex reasoning skills, like BBH, confirming its ability to dynamically allocate computational resources in alignment with the input's complexity. Our findings also highlight a variation in the number of experts needed across different layers of the transformer model, offering insights into the potential for designing heterogeneous MoE frameworks. The code and models are available at https://github.com/ZhenweiAn/Dynamic_MoE.

The rapid growth of dataset scales has been a key driver in advancing deep learning research. However, as dataset scale increases, the training process becomes increasingly inefficient due to the presence of low-value samples, including excessive redundant samples, overly challenging samples, and inefficient easy samples that contribute little to model improvement.To address this challenge, we propose Scale Efficient Training (SeTa) for large datasets, a dynamic sample pruning approach that losslessly reduces training time. To remove low-value samples, SeTa first performs random pruning to eliminate redundant samples, then clusters the remaining samples according to their learning difficulty measured by loss. Building upon this clustering, a sliding window strategy is employed to progressively remove both overly challenging and inefficient easy clusters following an easy-to-hard curriculum.We conduct extensive experiments on large-scale synthetic datasets, including ToCa, SS1M, and ST+MJ, each containing over 3 million samples.SeTa reduces training costs by up to 50\% while maintaining or improving performance, with minimal degradation even at 70\% cost reduction. Furthermore, experiments on various scale real datasets across various backbones (CNNs, Transformers, and Mambas) and diverse tasks (instruction tuning, multi-view stereo, geo-localization, composed image retrieval, referring image segmentation) demonstrate the powerful effectiveness and universality of our approach. Code is available at https://github.com/mrazhou/SeTa.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

Classification on long-tailed distributed data is a challenging problem, which suffers from serious class-imbalance and accordingly unpromising performance especially on tail classes. Recently, the ensembling based methods achieve the state-of-the-art performance and show great potential. However, there are two limitations for current methods. First, their predictions are not trustworthy for failure-sensitive applications. This is especially harmful for the tail classes where the wrong predictions is basically frequent. Second, they assign unified numbers of experts to all samples, which is redundant for easy samples with excessive computational cost. To address these issues, we propose a Trustworthy Long-tailed Classification (TLC) method to jointly conduct classification and uncertainty estimation to identify hard samples in a multi-expert framework. Our TLC obtains the evidence-based uncertainty (EvU) and evidence for each expert, and then combines these uncertainties and evidences under the Dempster-Shafer Evidence Theory (DST). Moreover, we propose a dynamic expert engagement to reduce the number of engaged experts for easy samples and achieve efficiency while maintaining promising performances. Finally, we conduct comprehensive experiments on the tasks of classification, tail detection, OOD detection and failure prediction. The experimental results show that the proposed TLC outperforms existing methods and is trustworthy with reliable uncertainty.

Recent advances in mixture-of-experts architectures have shown that individual experts models can be trained federatedly, i.e., in isolation from other experts by using a common base model to facilitate coordination. However, we hypothesize that full-sized experts may not be necessary for all domains and that instead low-rank adapters may be sufficient. Here, we introduce FlexMoRE, a Flexible Mixture of Rank-heterogenous Experts, which may be either full-sized experts or adapters of a suitable rank. We systematically investigate the trade-off between expert rank and downstream task performance by evaluating 6 experts with ranks 2^0 to 2^{14} resulting in experiments covering 150 mixtures (96 with 2 experts, 54 with 7 experts) that are evaluated across 120 tasks. For our experiments, we build on FlexOlmo and turn its pre-trained experts into low-rank versions. Our regression analysis from expert rank to downstream task performance reveals that the best-performing rank is substantially higher for reasoning-heavy benchmarks than for knowledge-heavy benchmarks. These findings on rank sensitivity come with direct implications for memory efficiency: Using optimal ranks, FlexMoRE yields improved downstream task performance (average score 47.18) compared to the baseline FlexOlmo-style mixture of full-sized experts (average score 45.46) at less than one third the parameters (10.75B for FlexMoRE vs. 33.27B for FlexOlmo). All code will be made available.

The training and fine-tuning of large language models (LLMs) often involve diverse textual data from multiple sources, which poses challenges due to conflicting gradient directions, hindering optimization and specialization. These challenges can undermine model generalization across tasks, resulting in reduced downstream performance. Recent research suggests that fine-tuning LLMs on carefully selected, task-specific subsets of data can match or even surpass the performance of using the entire dataset. Building on these insights, we propose the Ensembles of Low-Rank Expert Adapters (ELREA) framework to improve the model's capability to handle diverse tasks. ELREA clusters the training instructions based on their gradient directions, representing different areas of expertise and thereby reducing conflicts during optimization. Expert adapters are then trained on these clusters, utilizing the low-rank adaptation (LoRA) technique to ensure training efficiency and model scalability. During inference, ELREA combines predictions from the most relevant expert adapters based on the input data's gradient similarity to the training clusters, ensuring optimal adapter selection for each task. Experiments show that our method outperforms baseline LoRA adapters trained on the full dataset and other ensemble approaches with similar training and inference complexity across a range of domain-specific tasks.

The cultivation of expertise for large language models (LLMs) to solve tasks of specific areas often requires special-purpose tuning with calibrated behaviors on the expected stable outputs. To avoid huge cost brought by manual preparation of instruction datasets and training resources up to hundreds of hours, the exploitation of open knowledge including a wealth of low rank adaptation (LoRA) models and instruction datasets serves as a good starting point. However, existing methods on model and data selection focus on the performance of general-purpose capabilities while neglecting the knowledge gap exposed in domain-specific deployment. In the present study, we propose to bridge such gap by introducing few human-annotated samples (i.e., K-shot) for advancing task expertise of LLMs with open knowledge. Specifically, we develop an efficient and scalable pipeline to cost-efficiently produce task experts where K-shot data intervene in selecting the most promising expert candidates and the task-relevant instructions. A mixture-of-expert (MoE) system is built to make the best use of individual-yet-complementary knowledge between multiple experts. We unveil the two keys to the success of a MoE system, 1) the abidance by K-shot, and 2) the insistence on diversity. For the former, we ensure that models that truly possess problem-solving abilities on K-shot are selected rather than those blind guessers. Besides, during data selection, instructions that share task-relevant contexts with K-shot are prioritized. For the latter, we highlight the diversity of constituting experts and that of the fine-tuning instructions throughout the model and data selection process. Extensive experimental results confirm the superiority of our approach over existing methods on utilization of open knowledge across various tasks. Codes and models will be released later.

The application of mixture-of-experts (MoE) is gaining popularity due to its ability to improve model's performance. In an MoE structure, the gate layer plays a significant role in distinguishing and routing input features to different experts. This enables each expert to specialize in processing their corresponding sub-tasks. However, the gate's routing mechanism also gives rise to narrow vision: the individual MoE's expert fails to use more samples in learning the allocated sub-task, which in turn limits the MoE to further improve its generalization ability. To effectively address this, we propose a method called Mixture-of-Distilled-Expert (MoDE), which applies moderate mutual distillation among experts to enable each expert to pick up more features learned by other experts and gain more accurate perceptions on their original allocated sub-tasks. We conduct plenty experiments including tabular, NLP and CV datasets, which shows MoDE's effectiveness, universality and robustness. Furthermore, we develop a parallel study through innovatively constructing "expert probing", to experimentally prove why MoDE works: moderate distilling knowledge can improve each individual expert's test performances on their assigned tasks, leading to MoE's overall performance improvement.

For Mixture-of-Experts (MoE) models, an unbalanced expert load will lead to routing collapse or increased computational overhead. Existing methods commonly employ an auxiliary loss to encourage load balance, but a large auxiliary loss will introduce non-negligible interference gradients into training and thus impair the model performance. In order to control load balance while not producing undesired gradients during training, we propose Loss-Free Balancing, featured by an auxiliary-loss-free load balancing strategy. To be specific, before the top-K routing decision, Loss-Free Balancing will first apply an expert-wise bias to the routing scores of each expert. By dynamically updating the bias of each expert according to its recent load, Loss-Free Balancing can consistently maintain a balanced distribution of expert load. In addition, since Loss-Free Balancing does not produce any interference gradients, it also elevates the upper bound of model performance gained from MoE training. We validate the performance of Loss-Free Balancing on MoE models with up to 3B parameters trained on up to 200B tokens. Experimental results show that Loss-Free Balancing achieves both better performance and better load balance compared with traditional auxiliary-loss-controlled load balancing strategies.

Mixture of experts (MoE) has become the standard for constructing production-level large language models (LLMs) due to its promise to boost model capacity without causing significant overheads. Nevertheless, existing MoE methods usually enforce a constant top-k routing for all tokens, which is arguably restrictive because various tokens (e.g., "<EOS>" vs. "apple") may require various numbers of experts for feature abstraction. Lifting such a constraint can help make the most of limited resources and unleash the potential of the model for downstream tasks. In this sense, we introduce AdaMoE to realize token-adaptive routing for MoE, where different tokens are permitted to select a various number of experts. AdaMoE makes minimal modifications to the vanilla MoE with top-k routing -- it simply introduces a fixed number of null experts, which do not consume any FLOPs, to the expert set and increases the value of k. AdaMoE does not force each token to occupy a fixed number of null experts but ensures the average usage of the null experts with a load-balancing loss, leading to an adaptive number of null/true experts used by each token. AdaMoE exhibits a strong resemblance to MoEs with expert choice routing while allowing for trivial auto-regressive modeling. AdaMoE is easy to implement and can be effectively applied to pre-trained (MoE-)LLMs. Extensive studies show that AdaMoE can reduce average expert load (FLOPs) while achieving superior performance. For example, on the ARC-C dataset, applying our method to fine-tuning Mixtral-8x7B can reduce FLOPs by 14.5% while increasing accuracy by 1.69%.

Continual learning (CL) has garnered significant attention because of its ability to adapt to new tasks that arrive over time. Catastrophic forgetting (of old tasks) has been identified as a major issue in CL, as the model adapts to new tasks. The Mixture-of-Experts (MoE) model has recently been shown to effectively mitigate catastrophic forgetting in CL, by employing a gating network to sparsify and distribute diverse tasks among multiple experts. However, there is a lack of theoretical analysis of MoE and its impact on the learning performance in CL. This paper provides the first theoretical results to characterize the impact of MoE in CL via the lens of overparameterized linear regression tasks. We establish the benefit of MoE over a single expert by proving that the MoE model can diversify its experts to specialize in different tasks, while its router learns to select the right expert for each task and balance the loads across all experts. Our study further suggests an intriguing fact that the MoE in CL needs to terminate the update of the gating network after sufficient training rounds to attain system convergence, which is not needed in the existing MoE studies that do not consider the continual task arrival. Furthermore, we provide explicit expressions for the expected forgetting and overall generalization error to characterize the benefit of MoE in the learning performance in CL. Interestingly, adding more experts requires additional rounds before convergence, which may not enhance the learning performance. Finally, we conduct experiments on both synthetic and real datasets to extend these insights from linear models to deep neural networks (DNNs), which also shed light on the practical algorithm design for MoE in CL.

The advent of large pre-trained models has brought about a paradigm shift in both visual representation learning and natural language processing. However, clustering unlabeled images, as a fundamental and classic machine learning problem, still lacks an effective solution, particularly for large-scale datasets. In this paper, we propose a novel image clustering pipeline that leverages the powerful feature representation of large pre-trained models such as CLIP and cluster images effectively and efficiently at scale. We first developed a novel algorithm to estimate the number of clusters in a given dataset. We then show that the pre-trained features are significantly more structured by further optimizing the rate reduction objective. The resulting features may significantly improve the clustering accuracy, e.g., from 57% to 66% on ImageNet-1k. Furthermore, by leveraging CLIP's multimodality bridge between image and text, we develop a simple yet effective self-labeling algorithm that produces meaningful text labels for the clusters. Through extensive experiments, we show that our pipeline works well on standard datasets such as CIFAR-10, CIFAR-100, and ImageNet-1k. It also extends to datasets without predefined labels, such as LAION-Aesthetics and WikiArts. We released the code in https://github.com/LeslieTrue/CPP.

Large Language Models (LLMs) have demonstrated significant potential in performing multiple tasks in multimedia applications, ranging from content generation to interactive entertainment, and artistic creation. However, the diversity of downstream tasks in multitask scenarios presents substantial adaptation challenges for LLMs. While traditional methods often succumb to knowledge confusion on their monolithic dense models, Mixture-of-Experts (MoE) has been emerged as a promising solution with its sparse architecture for effective task decoupling. Inspired by the principles of human cognitive neuroscience, we design a novel framework Intuition-MoR1E that leverages the inherent semantic clustering of instances to mimic the human brain to deal with multitask, offering implicit guidance to router for optimized feature allocation. Moreover, we introduce cutting-edge Rank-1 Experts formulation designed to manage a spectrum of intuitions, demonstrating enhanced parameter efficiency and effectiveness in multitask LLM finetuning. Extensive experiments demonstrate that Intuition-MoR1E achieves superior efficiency and 2.15\% overall accuracy improvement across 14 public datasets against other state-of-the-art baselines.

Object-centric architectures usually apply a differentiable module to the entire feature map to decompose it into sets of entity representations called slots. Some of these methods structurally resemble clustering algorithms, where the cluster's center in latent space serves as a slot representation. Slot Attention is an example of such a method, acting as a learnable analog of the soft k-means algorithm. Our work employs a learnable clustering method based on the Gaussian Mixture Model. Unlike other approaches, we represent slots not only as centers of clusters but also incorporate information about the distance between clusters and assigned vectors, leading to more expressive slot representations. Our experiments demonstrate that using this approach instead of Slot Attention improves performance in object-centric scenarios, achieving state-of-the-art results in the set property prediction task.

Pretraining large language models (LLMs) typically requires centralized clusters with thousands of high-memory GPUs (e.g., H100/A100). Recent decentralized training methods reduce communication overhead by employing federated optimization; however, they still need to train the entire model on each node, remaining constrained by GPU memory limitations. In this work, we propose SParse Expert Synchronization (SPES), a memory-efficient decentralized framework for pretraining mixture-of-experts (MoE) LLMs. SPES trains only a subset of experts per node, substantially lowering the memory footprint. Each node updates its local experts and periodically synchronizes with other nodes, eliminating full-parameter transmission while ensuring efficient knowledge sharing. To accelerate convergence, we introduce an expert-merging warm-up strategy, where experts exchange knowledge early in training, to rapidly establish foundational capabilities. With SPES, we train a 2B-parameter MoE LLM using 16 standalone 48GB GPUs over internet connections, which achieves competitive performance with centrally trained LLMs under similar computational budgets. We further demonstrate scalability by training a 7B model from scratch and a 9B model upcycled from a dense checkpoint, both of which match prior centralized baselines. Our code is available at https://github.com/zjr2000/SPES.

Sparsely activated Mixture-of-Experts (MoE) models have shown promise in enhancing the learning capacity of large language models (LLMs). Leveraging the intrinsic importance differences among experts, recent research has explored expert-level compression techniques to improve the efficiency of MoE LLMs. However, existing approaches often rely on empirical criteria to identify critical experts, lacking a deeper exploration and understanding of the heterogeneous importance of experts. In this study, we present the first discovery and investigation of a distinct subset of experts that play a crucial role in the underlying mechanisms during the model's forward inference. These experts are prevalent in open-source MoE LLMs, and despite their limited number, pruning them leads to a significant decline in model performance (e.g., pruning three causes Qwen3-30B-A3B to produce repetitive and uninformative outputs). We refer to these experts as Super Experts (SEs). Our comprehensive analysis provides progressively deeper insights into SEs. (i) SEs are characterized by rare but extreme activation outliers in the output of the down_proj, which give rise to massive activations in the hidden states between decoder layers. Moreover, the distribution of SEs remains model-specific and is unaffected by post-training processes. (ii) By pruning SEs, we assess their significance across a variety of tasks, revealing their considerable impact on the model's overall performance, particularly in mathematical reasoning. (iii) We further enhance our understanding of the influence of SEs compression. Our findings confirm that MoE LLMs rely on SEs to induce attention sinks, which are crucial for the distribution of attention scores but are significantly disrupted by SE pruning. The code is available at https://github.com/ZunhaiSu/Super-Experts-Profilling.

Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.

TeleChat3-MoE is the latest series of TeleChat large language models, featuring a Mixture-of-Experts (MoE) architecture with parameter counts ranging from 105 billion to over one trillion,trained end-to-end on Ascend NPU cluster. This technical report mainly presents the underlying training infrastructure that enables reliable and efficient scaling to frontier model sizes. We detail systematic methodologies for operator-level and end-to-end numerical accuracy verification, ensuring consistency across hardware platforms and distributed parallelism strategies. Furthermore, we introduce a suite of performance optimizations, including interleaved pipeline scheduling, attention-aware data scheduling for long-sequence training,hierarchical and overlapped communication for expert parallelism, and DVM-based operator fusion. A systematic parallelization framework, leveraging analytical estimation and integer linear programming, is also proposed to optimize multi-dimensional parallelism configurations. Additionally, we present methodological approaches to cluster-level optimizations, addressing host- and device-bound bottlenecks during large-scale training tasks. These infrastructure advancements yield significant throughput improvements and near-linear scaling on clusters comprising thousands of devices, providing a robust foundation for large-scale language model development on hardware ecosystems.

Mixture of experts (MoE) methods are a key component in most large language model architectures, including the recent series of DeepSeek models. Compared to other MoE implementations, DeepSeekMoE stands out because of two unique features: the deployment of a shared expert strategy and of the normalized sigmoid gating mechanism. Despite the prominent role of DeepSeekMoE in the success of the DeepSeek series of models, there have been only a few attempts to justify theoretically the value of the shared expert strategy, while its normalized sigmoid gating has remained unexplored. To bridge this gap, we undertake a comprehensive theoretical study of these two features of DeepSeekMoE from a statistical perspective. We perform a convergence analysis of the expert estimation task to highlight the gains in sample efficiency for both the shared expert strategy and the normalized sigmoid gating, offering useful insights into the design of expert and gating structures. To verify empirically our theoretical findings, we carry out several experiments on both synthetic data and real-world datasets for (vision) language modeling tasks. Finally, we conduct an extensive empirical analysis of the router behaviors, ranging from router saturation, router change rate, to expert utilization.

As deep learning continues to advance, the transparency of neural network decision-making remains a critical challenge, limiting trust and applicability in high-stakes domains. Class Activation Mapping (CAM) techniques have emerged as a key approach toward visualizing model decisions, yet existing methods face inherent trade-offs. Gradient-based CAM variants suffer from sensitivity to gradient perturbations due to gradient noise, leading to unstable and unreliable explanations. Conversely, gradient-free approaches mitigate gradient instability but incur significant computational overhead and inference latency. To address these limitations, we propose a Cluster Filter Class Activation Map (CF-CAM) technique, a novel framework that reintroduces gradient-based weighting while enhancing robustness against gradient noise. CF-CAM utilizes hierarchical importance weighting strategy to balance discriminative feature preservation and noise elimination. A density-aware channel clustering method via Density-Based Spatial Clustering of Applications with Noise (DBSCAN) groups semantically relevant feature channels and discard noise-prone activations. Additionally, cluster-conditioned gradient filtering leverages Gaussian filters to refine gradient signals, preserving edge-aware localization while suppressing noise impact. Experiment results demonstrate that CF-CAM achieves superior interpretability performance while enhancing computational efficiency, outperforming state-of-the-art CAM methods in faithfulness and robustness. By effectively mitigating gradient instability without excessive computational cost, CF-CAM provides a competitive solution for enhancing the interpretability of deep neural networks in critical applications such as autonomous driving and medical diagnosis.

Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby boosting expressivity and accuracy but at the same time resulting in a multiplicative increase in parameters and memory. We propose MetaCluster, a framework that makes KANs highly compressible without sacrificing accuracy. Specifically, a lightweight meta-learner, trained jointly with the KAN, is used to map low-dimensional embedding to coefficient vectors, shaping them to lie on a low-dimensional manifold that is amenable to clustering. We then run K-means in coefficient space and replace per-edge vectors with shared centroids. Afterwards, the meta-learner can be discarded, and a brief fine-tuning of the centroid codebook recovers any residual accuracy loss. The resulting model stores only a small codebook and per-edge indices, exploiting the vector nature of KAN parameters to amortize storage across multiple coefficients. On MNIST, CIFAR-10, and CIFAR-100, across standard KANs and ConvKANs using multiple basis functions, MetaCluster achieves a reduction of up to 80times in parameter storage, with no loss in accuracy. Code will be released upon publication.

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling neural networks while maintaining computational efficiency. However, standard MoE implementations rely on two rigid design assumptions: (1) fixed Top-K routing where exactly K experts are activated per token, and (2) uniform expert allocation across all layers. This paper introduces DynaMoE, a novel MoE framework that relaxes both constraints through dynamic token-level expert activation and layer-wise adaptive capacity allocation. DynaMoE introduces a principled routing mechanism where the number of active experts per token varies based on input complexity. Concurrently, the framework implements six distinct scheduling strategies for distributing expert capacity across network depth, including descending, ascending, pyramid, and wave patterns. We theoretically analyze the expressivity gains of dynamic routing and derive bounds on computational efficiency. Through extensive experiments on MNIST, Fashion-MNIST, CIFAR-10 (image classification), and Recycling-the-Web (language modeling) across multiple model scales, we demonstrate that DynaMoE achieves superior parameter efficiency compared to static baselines. Our key finding is that optimal expert schedules are task- and scale-dependent: descending schedules (concentrating capacity in early layers) outperform uniform baselines on image classification. For language modeling, optimal schedules vary by model size, descending for Tiny, ascending for Small, and uniform for Medium. Furthermore, dynamic routing reduces gradient variance during training, leading to improved convergence stability. DynaMoE establishes a new framework for adaptive computation in neural networks, providing principled guidance for MoE architecture design.

Retrieval-Augmented Generation (RAG) often relies on large vector databases and cross-encoders tuned for large-scale corpora, which can be excessive for small, domain-specific collections. We present MODE (Mixture of Document Experts), a lightweight alternative that replaces fine-grained nearest-neighbor search with cluster-and-route retrieval. Documents are embedded, grouped into semantically coherent clusters, and represented by cached centroids. At query time, we route to the top centroid(s) and retrieve context only within those clusters, eliminating external vector-database infrastructure and reranking while keeping latency low. On HotpotQA and SQuAD corpora with 100-500 chunks, MODE matches or exceeds a dense-retrieval baseline in answer quality while reducing end-to-end retrieval time. Ablations show that cluster granularity and multi-cluster routing control the recall/precision trade-off, and that tighter clusters improve downstream accuracy. MODE offers a practical recipe for small and medium corpora where simplicity, speed, and topical focus matter.

The sparse Mixture-of-Experts (MoE) model is powerful for large-scale pre-training and has achieved promising results due to its model capacity. However, with trillions of parameters, MoE is hard to be deployed on cloud or mobile environment. The inference of MoE requires expert parallelism, which is not hardware-friendly and communication expensive. Especially for resource-limited downstream tasks, such sparse structure has to sacrifice a lot of computing efficiency for limited performance gains. In this work, we observe most experts contribute scarcely little to the MoE fine-tuning and inference. We further propose a general method to progressively drop the non-professional experts for the target downstream task, which preserves the benefits of MoE while reducing the MoE model into one single-expert dense model. Our experiments reveal that the fine-tuned single-expert model could preserve 99.3% benefits from MoE across six different types of tasks while enjoying 2x inference speed with free communication cost.

Large language Models (LLMs) have demonstrated remarkable skills across various domains. Understanding the mechanisms behind their abilities and implementing controls over them is becoming increasingly important for developing better models. In this paper, we focus on skill unlearning in LLMs, specifically unlearning a particular skill while retaining their overall capabilities. We introduce two lightweight, training-free machine skill unlearning techniques for LLMs. First, we observe that the pre-activation distribution of neurons in each Feed-Forward Layer (FFL) differs when the model demonstrates different skills. Additionally, we find that queries triggering the same skill cluster within the FFL key space and can be separated from other queries using a hypercube. Based on these observations, we propose two lightweight, training-free skill unlearning methods via intervention and abstention respectively: Neuron Adjust and Key Space Detection. We evaluate our methods on unlearning math-solving, Python-coding, and comprehension skills across seven different languages. The results demonstrate their strong unlearning capabilities for the designated skills. Specifically, Key Space Detection achieves over 80\% relative performance drop on the forgetting skill and less than 10\% relative performance drop on other skills and the model's general knowledge (MMLU) for most unlearning tasks. Our code is available at https://github.com/Trustworthy-ML-Lab/effective_skill_unlearning

Enabling large language models (LLMs) to unlearn knowledge and capabilities acquired during training has proven vital for ensuring compliance with data regulations and promoting ethical practices in generative AI. Although there are growing interests in developing various unlearning algorithms, it remains unclear how to best formulate the unlearning problem. The most popular formulation uses a weighted sum of forget and retain loss, but it often leads to performance degradation due to the inherent trade-off between forget and retain losses. In this work, we argue that it is important to model the hierarchical structure of the unlearning problem, where the forget problem (which unlearns certain knowledge and/or capabilities) takes priority over the retain problem (which preserves model utility). This hierarchical structure naturally leads to a bi-level optimization formulation where the lower-level objective focuses on minimizing the forget loss, while the upper-level objective aims to maintain the model's utility. Based on this new formulation, we propose a novel algorithm, termed Bi-Level UnleaRning (BLUR), which not only possesses strong theoretical guarantees but more importantly, delivers superior performance. In particular, our extensive experiments demonstrate that BLUR consistently outperforms all the state-of-the-art algorithms across various unlearning tasks, models, and metrics. Codes are available at https://github.com/OptimAI-Lab/BLURLLMUnlearning.

A large language model (LLM) with knowledge in both scientific and general tasks is the foundation of science general intelligence. However, directly continued pretraining an LLM using science data usually leads to catastrophic forgetting, which indicates severe degradation in general ability. In this report, we present Innovator, which solves this problem by upcycling a pre-trained dense LLM into a fine-grained Mixtures-of-Experts model during continued pretraining, where different experts are expected to learn science knowledge in different disciplines, and a shared expert is utilized for general tasks. Innovator introduces a four-stage upcycle training paradigm: (1) Scientific Expert Induction on discipline-specific data, (2) Fine-grained Expert Splitting via FFN dimension decomposition, (3) Science-Aware Routing warmup, and (4) Generalist-Scientist Integration training on hybrid datasets. Such a paradigm enables knowledge in the general domain, and different scientific disciplines can be decoupled, avoiding the negative influence among knowledge in different domains. With 53.3B total parameters and 13.3B activated, Innovator extends Qwen2.5-7B using a shared general expert and 64 specialized scientific experts with 8 activated. Trained on 300B tokens with tri-level quality-controlled data, Innovator achieves 25% average improvement across 30 scientific tasks with a win rate as 70%, while retaining 99% performance in general tasks. Furthermore, Innovator-Reason, which is post-trained from Innovator for reasoning boosting, exhibits excellent reasoning performance in solving complex scientific problems with improvements over 30%.

Classical clustering methods do not provide users with direct control of the clustering results, and the clustering results may not be consistent with the relevant criterion that a user has in mind. In this work, we present a new methodology for performing image clustering based on user-specified text criteria by leveraging modern vision-language models and large language models. We call our method Image Clustering Conditioned on Text Criteria (IC|TC), and it represents a different paradigm of image clustering. IC|TC requires a minimal and practical degree of human intervention and grants the user significant control over the clustering results in return. Our experiments show that IC|TC can effectively cluster images with various criteria, such as human action, physical location, or the person's mood, while significantly outperforming baselines.

We study the ability of foundation models to learn representations for classification that are transferable to new, unseen classes. Recent results in the literature show that representations learned by a single classifier over many classes are competitive on few-shot learning problems with representations learned by special-purpose algorithms designed for such problems. In this paper we provide an explanation for this behavior based on the recently observed phenomenon that the features learned by overparameterized classification networks show an interesting clustering property, called neural collapse. We demonstrate both theoretically and empirically that neural collapse generalizes to new samples from the training classes, and -- more importantly -- to new classes as well, allowing foundation models to provide feature maps that work well in transfer learning and, specifically, in the few-shot setting.

Multimodal Continual Instruction Tuning aims to continually enhance Large Vision Language Models (LVLMs) by learning from new data without forgetting previously acquired knowledge. Mixture of Experts (MoE) architectures naturally facilitate this by incrementally adding new experts and expanding routers while keeping the existing ones frozen. However, despite expert isolation, MoE-based continual learners still suffer from forgetting due to routing-drift: old-task tokens become mistakenly attracted to newly added experts, degrading performance on prior tasks. We analyze the failure mode at the token level and reveal the token's dilemma: ambiguous and old tokens in new-task data offer minimal learning benefit yet induce forgetting when routed to new experts, due to their ambiguous routing assignment during training. Motivated by this, we propose LLaVA-DyMoE, a dynamic MoE framework that incrementally expands the MoE with drift-aware token assignment. We characterize token types via their routing score distributions and apply targeted regularization. Specifically, a token-level assignment guidance steers ambiguous and old tokens away from new experts to preserve established routing patterns and alleviate routing-drift, while complementary routing score regularizations enforce expert-group separation and promote new-expert specialization. Extensive experiments demonstrate that our LLaVA-DyMoE effectively mitigates routing-drift-induced forgetting, achieving over a 7% gain in mean final accuracy and a 12% reduction in forgetting compared to baselines. The project page is https://zhaoc5.github.io/DyMoE.

Sparse Mixture-of-Experts (SMoE) has gained prominence as a scalable and computationally efficient architecture, enabling significant growth in model capacity without incurring additional inference costs. However, existing SMoE models often rely on auxiliary losses (e.g., z-loss, load balancing) and additional trainable parameters (e.g., noisy gating) to encourage expert diversity, leading to objective misalignment and increased model complexity. Moreover, existing Sinkhorn-based methods suffer from significant training overhead due to their heavy reliance on the computationally expensive Sinkhorn algorithm. In this work, we formulate token-to-expert assignment as an optimal transport problem, incorporating constraints to ensure balanced expert utilization. We demonstrate that introducing a minimal degree of optimal transport-based routing enhances SMoE performance without requiring auxiliary balancing losses. Unlike previous methods, our approach derives gating scores directly from the transport map, enabling more effective token-to-expert balancing, supported by both theoretical analysis and empirical results. Building on these insights, we propose Selective Sinkhorn Routing (SSR), a routing mechanism that replaces auxiliary loss with lightweight Sinkhorn-based routing. SSR promotes balanced token assignments while preserving flexibility in expert selection. Across both language modeling and image classification tasks, SSR achieves faster training, higher accuracy, and greater robustness to input corruption.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.