Daily Papers

This paper proposes a new loss function for adversarial training. Since adversarial training has difficulties, e.g., necessity of high model capacity, focusing on important data points by weighting cross-entropy loss has attracted much attention. However, they are vulnerable to sophisticated attacks, e.g., Auto-Attack. This paper experimentally reveals that the cause of their vulnerability is their small margins between logits for the true label and the other labels. Since neural networks classify the data points based on the logits, logit margins should be large enough to avoid flipping the largest logit by the attacks. Importance-aware methods do not increase logit margins of important samples but decrease those of less-important samples compared with cross-entropy loss. To increase logit margins of important samples, we propose switching one-vs-the-rest loss (SOVR), which switches from cross-entropy to one-vs-the-rest loss for important samples that have small logit margins. We prove that one-vs-the-rest loss increases logit margins two times larger than the weighted cross-entropy loss for a simple problem. We experimentally confirm that SOVR increases logit margins of important samples unlike existing methods and achieves better robustness against Auto-Attack than importance-aware methods.

Breaking down a document or a conversation into multiple contiguous segments based on its semantic structure is an important and challenging problem in NLP, which can assist many downstream tasks. However, current works on topic segmentation often focus on segmentation of structured texts. In this paper, we comprehensively analyze the generalization capabilities of state-of-the-art topic segmentation models on unstructured texts. We find that: (a) Current strategies of pre-training on a large corpus of structured text such as Wiki-727K do not help in transferability to unstructured conversational data. (b) Training from scratch with only a relatively small-sized dataset of the target unstructured domain improves the segmentation results by a significant margin. We stress-test our proposed Topic Segmentation approach by experimenting with multiple loss functions, in order to mitigate effects of imbalance in unstructured conversational datasets. Our empirical evaluation indicates that Focal Loss function is a robust alternative to Cross-Entropy and re-weighted Cross-Entropy loss function when segmenting unstructured and semi-structured chats.

In this paper, we introduce SalsaNext for the uncertainty-aware semantic segmentation of a full 3D LiDAR point cloud in real-time. SalsaNext is the next version of SalsaNet [1] which has an encoder-decoder architecture where the encoder unit has a set of ResNet blocks and the decoder part combines upsampled features from the residual blocks. In contrast to SalsaNet, we introduce a new context module, replace the ResNet encoder blocks with a new residual dilated convolution stack with gradually increasing receptive fields and add the pixel-shuffle layer in the decoder. Additionally, we switch from stride convolution to average pooling and also apply central dropout treatment. To directly optimize the Jaccard index, we further combine the weighted cross-entropy loss with Lovasz-Softmax loss [2]. We finally inject a Bayesian treatment to compute the epistemic and aleatoric uncertainties for each point in the cloud. We provide a thorough quantitative evaluation on the Semantic-KITTI dataset [3], which demonstrates that the proposed SalsaNext outperforms other state-of-the-art semantic segmentation networks and ranks first on the Semantic-KITTI leaderboard. We also release our source code https://github.com/TiagoCortinhal/SalsaNext.

Recently, zero-shot image captioning has gained increasing attention, where only text data is available for training. The remarkable progress in text-to-image diffusion model presents the potential to resolve this task by employing synthetic image-caption pairs generated by this pre-trained prior. Nonetheless, the defective details in the salient regions of the synthetic images introduce semantic misalignment between the synthetic image and text, leading to compromised results. To address this challenge, we propose a novel Patch-wise Cross-modal feature Mix-up (PCM) mechanism to adaptively mitigate the unfaithful contents in a fine-grained manner during training, which can be integrated into most of encoder-decoder frameworks, introducing our PCM-Net. Specifically, for each input image, salient visual concepts in the image are first detected considering the image-text similarity in CLIP space. Next, the patch-wise visual features of the input image are selectively fused with the textual features of the salient visual concepts, leading to a mixed-up feature map with less defective content. Finally, a visual-semantic encoder is exploited to refine the derived feature map, which is further incorporated into the sentence decoder for caption generation. Additionally, to facilitate the model training with synthetic data, a novel CLIP-weighted cross-entropy loss is devised to prioritize the high-quality image-text pairs over the low-quality counterparts. Extensive experiments on MSCOCO and Flickr30k datasets demonstrate the superiority of our PCM-Net compared with state-of-the-art VLMs-based approaches. It is noteworthy that our PCM-Net ranks first in both in-domain and cross-domain zero-shot image captioning. The synthetic dataset SynthImgCap and code are available at https://jianjieluo.github.io/SynthImgCap.

We propose a novel TACLE (TAsk and CLass-awarE) framework to address the relatively unexplored and challenging problem of exemplar-free semi-supervised class incremental learning. In this scenario, at each new task, the model has to learn new classes from both (few) labeled and unlabeled data without access to exemplars from previous classes. In addition to leveraging the capabilities of pre-trained models, TACLE proposes a novel task-adaptive threshold, thereby maximizing the utilization of the available unlabeled data as incremental learning progresses. Additionally, to enhance the performance of the under-represented classes within each task, we propose a class-aware weighted cross-entropy loss. We also exploit the unlabeled data for classifier alignment, which further enhances the model performance. Extensive experiments on benchmark datasets, namely CIFAR10, CIFAR100, and ImageNet-Subset100 demonstrate the effectiveness of the proposed TACLE framework. We further showcase its effectiveness when the unlabeled data is imbalanced and also for the extreme case of one labeled example per class.

Large Language Models (LLMs) have quickly become an invaluable assistant for a variety of tasks. However, their effectiveness is constrained by their ability to tailor responses to human preferences and behaviors via personalization. Prior work in LLM personalization has largely focused on style transfer or incorporating small factoids about the user, as knowledge injection remains an open challenge. In this paper, we explore injecting knowledge of prior conversations into LLMs to enable future work on less redundant, personalized conversations. We identify two real-world constraints: (1) conversations are sequential in time and must be treated as such during training, and (2) per-user personalization is only viable in parameter-efficient settings. To this aim, we propose PLUM, a pipeline performing data augmentation for up-sampling conversations as question-answer pairs, that are then used to finetune a low-rank adaptation adapter with a weighted cross entropy loss. Even in this first exploration of the problem, we perform competitively with baselines such as RAG, attaining an accuracy of 81.5% across 100 conversations.

We introduce Bielik 7B v0.1, a 7-billion-parameter generative text model for Polish language processing. Trained on curated Polish corpora, this model addresses key challenges in language model development through innovative techniques. These include Weighted Instruction Cross-Entropy Loss, which balances the learning of different instruction types, and Adaptive Learning Rate, which dynamically adjusts the learning rate based on training progress. To evaluate performance, we created the Open PL LLM Leaderboard and Polish MT-Bench, novel frameworks assessing various NLP tasks and conversational abilities. Bielik 7B v0.1 demonstrates significant improvements, achieving a 9 percentage point increase in average score compared to Mistral-7B-v0.1 on the RAG Reader task. It also excels in the Polish MT-Bench, particularly in Reasoning (6.15/10) and Role-playing (7.83/10) categories. This model represents a substantial advancement in Polish language AI, offering a powerful tool for diverse linguistic applications and setting new benchmarks in the field.

We present Bielik 11B v2, a state-of-the-art language model optimized for Polish text processing. Built on the Mistral 7B v0.2 architecture and scaled to 11B parameters using depth up-scaling, this model demonstrates exceptional performance across Polish language benchmarks while maintaining strong cross-lingual capabilities. We introduce two key technical innovations: Weighted Instruction Cross-Entropy Loss, which optimizes learning across diverse instruction types by assigning quality-based weights to training examples, and Adaptive Learning Rate, which dynamically adjusts based on context length. Comprehensive evaluation across multiple benchmarks demonstrates that Bielik 11B v2 outperforms many larger models, including those with 2-6 times more parameters, and significantly surpasses other specialized Polish language models on tasks ranging from linguistic understanding to complex reasoning. The model's parameter efficiency and extensive quantization options enable deployment across various hardware configurations, advancing Polish language AI capabilities and establishing new benchmarks for resource-efficient language modeling in less-represented languages.

We introduce Bielik v3, a series of parameter-efficient generative text models (1.5B and 4.5B) optimized for Polish language processing. These models demonstrate that smaller, well-optimized architectures can achieve performance comparable to much larger counterparts while requiring substantially fewer computational resources. Our approach incorporates several key innovations: a custom Polish tokenizer (APT4) that significantly improves token efficiency, Weighted Instruction Cross-Entropy Loss to balance learning across instruction types, and Adaptive Learning Rate that dynamically adjusts based on training progress. Trained on a meticulously curated corpus of 292 billion tokens spanning 303 million documents, these models excel across multiple benchmarks, including the Open PL LLM Leaderboard, Complex Polish Text Understanding Benchmark, Polish EQ-Bench, and Polish Medical Leaderboard. The 4.5B parameter model achieves results competitive with models 2-3 times its size, while the 1.5B model delivers strong performance despite its extremely compact profile. These advances establish new benchmarks for parameter-efficient language modeling in less-represented languages, making high-quality Polish language AI more accessible for resource-constrained applications.

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.78~(CIFAR-10) and 3.42 (ImageNet 64times64) bits per dimension that are comparable or better than autoregressive models of similar sizes.

Consistency learning using input image, feature, or network perturbations has shown remarkable results in semi-supervised semantic segmentation, but this approach can be seriously affected by inaccurate predictions of unlabelled training images. There are two consequences of these inaccurate predictions: 1) the training based on the "strict" cross-entropy (CE) loss can easily overfit prediction mistakes, leading to confirmation bias; and 2) the perturbations applied to these inaccurate predictions will use potentially erroneous predictions as training signals, degrading consistency learning. In this paper, we address the prediction accuracy problem of consistency learning methods with novel extensions of the mean-teacher (MT) model, which include a new auxiliary teacher, and the replacement of MT's mean square error (MSE) by a stricter confidence-weighted cross-entropy (Conf-CE) loss. The accurate prediction by this model allows us to use a challenging combination of network, input data and feature perturbations to improve the consistency learning generalisation, where the feature perturbations consist of a new adversarial perturbation. Results on public benchmarks show that our approach achieves remarkable improvements over the previous SOTA methods in the field. Our code is available at https://github.com/yyliu01/PS-MT.

Deep-learning has proved in recent years to be a powerful tool for image analysis and is now widely used to segment both 2D and 3D medical images. Deep-learning segmentation frameworks rely not only on the choice of network architecture but also on the choice of loss function. When the segmentation process targets rare observations, a severe class imbalance is likely to occur between candidate labels, thus resulting in sub-optimal performance. In order to mitigate this issue, strategies such as the weighted cross-entropy function, the sensitivity function or the Dice loss function, have been proposed. In this work, we investigate the behavior of these loss functions and their sensitivity to learning rate tuning in the presence of different rates of label imbalance across 2D and 3D segmentation tasks. We also propose to use the class re-balancing properties of the Generalized Dice overlap, a known metric for segmentation assessment, as a robust and accurate deep-learning loss function for unbalanced tasks.

Many approximate machine unlearning methods demonstrate strong logit-level forgetting -- such as near-zero accuracy on the forget set -- yet continue to preserve substantial information within their internal feature representations. We refer to this discrepancy as superficial forgetting. Recent studies indicate that most existing unlearning approaches primarily alter the final classifier, leaving intermediate representations largely unchanged and highly similar to those of the original model. To address this limitation, we introduce the Erase at the Core (EC), a framework designed to enforce forgetting throughout the entire network hierarchy. EC integrates multi-layer contrastive unlearning on the forget set with retain set preservation through deeply supervised learning. Concretely, EC attaches auxiliary modules to intermediate layers and applies both contrastive unlearning and cross-entropy losses at each supervision point, with layer-wise weighted losses. Experimental results show that EC not only achieves effective logit-level forgetting, but also substantially reduces representational similarity to the original model across intermediate layers. Furthermore, EC is model-agnostic and can be incorporated as a plug-in module into existing unlearning methods, improving representation-level forgetting while maintaining performance on the retain set.

Face recognition technology has become an integral part of modern security systems and user authentication processes. However, these systems are vulnerable to spoofing attacks and can easily be circumvented. Most prior research in face anti-spoofing (FAS) approaches it as a two-class classification task where models are trained on real samples and known spoof attacks and tested for detection performance on unknown spoof attacks. However, in practice, FAS should be treated as a one-class classification task where, while training, one cannot assume any knowledge regarding the spoof samples a priori. In this paper, we reformulate the face anti-spoofing task from a one-class perspective and propose a novel hyperbolic one-class classification framework. To train our network, we use a pseudo-negative class sampled from the Gaussian distribution with a weighted running mean and propose two novel loss functions: (1) Hyp-PC: Hyperbolic Pairwise Confusion loss, and (2) Hyp-CE: Hyperbolic Cross Entropy loss, which operate in the hyperbolic space. Additionally, we employ Euclidean feature clipping and gradient clipping to stabilize the training in the hyperbolic space. To the best of our knowledge, this is the first work extending hyperbolic embeddings for face anti-spoofing in a one-class manner. With extensive experiments on five benchmark datasets: Rose-Youtu, MSU-MFSD, CASIA-MFSD, Idiap Replay-Attack, and OULU-NPU, we demonstrate that our method significantly outperforms the state-of-the-art, achieving better spoof detection performance.

We present MERaLiON-SER, a robust speech emotion recognition model de- signed for English and Southeast Asian languages. The model is trained using a hybrid objective combining weighted categorical cross-entropy and Concordance Correlation Coefficient (CCC) losses for joint discrete and dimensional emotion modelling. This dual approach enables the model to capture both the distinct categories of emotion (like happy or angry) and the fine-grained, such as arousal (intensity), valence (positivity/negativity), and dominance (sense of control), lead- ing to a more comprehensive and robust representation of human affect. Extensive evaluations across multilingual Singaporean languages (English, Chinese, Malay, and Tamil ) and other public benchmarks show that MERaLiON-SER consistently surpasses both open-source speech encoders and large Audio-LLMs. These results underscore the importance of specialised speech-only models for accurate paralin- guistic understanding and cross-lingual generalisation. Furthermore, the proposed framework provides a foundation for integrating emotion-aware perception into future agentic audio systems, enabling more empathetic and contextually adaptive multimodal reasoning.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

Inspired by recent advancements in large language models (LLMs) for Natural Language Processing (NLP), there has been a surge in research focused on developing foundational models for time series forecasting. One approach involves training LLM architectures on tokenized time series data using cross-entropy loss. Although this method has demonstrated promising results, cross-entropy loss is primarily designed for classification tasks and does not account for the distance between classes. To address this limitation, we propose using the Wasserstein loss for such architectures. To validate our approach, we fine-tuned a foundational time series model on 22 zero-shot datasets, comparing the performance of cross-entropy loss with that of Wasserstein loss. Our results demonstrate that replacing cross-entropy loss with Wasserstein loss significantly improves point estimation.

Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised deep-learning applications, these methods tend to be less adequate when there is large intra-class variance and low inter-class variance in input data distribution. Deep Metric Learning seeks to develop methods that aim to measure the similarity between data samples by learning a representation function that maps these data samples into a representative embedding space. It leverages carefully designed sampling strategies and loss functions that aid in optimizing the generation of a discriminative embedding space even for distributions having low inter-class and high intra-class variances. In this chapter, we will provide an overview of recent progress in this area and discuss state-of-the-art Deep Metric Learning approaches.

Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The harmonic loss is a distance-based alternative grounded in Euclidean geometry that improves interpretability and mitigates phenomena such as grokking, or delayed generalization on the test set. However, the study of harmonic loss remains narrow: only Euclidean distance is explored, and no systematic evaluation of computational efficiency or sustainability was conducted. We extend harmonic loss by systematically investigating a broad spectrum of distance metrics as replacements for the Euclidean distance. We comprehensively evaluate distance-tailored harmonic losses on both vision backbones and large language models. Our analysis is framed around a three-way evaluation of model performance, interpretability, and sustainability. On vision tasks, cosine distances provide the most favorable trade-off, consistently improving accuracy while lowering carbon emissions, whereas Bray-Curtis and Mahalanobis further enhance interpretability at varying efficiency costs. On language models, cosine-based harmonic losses improve gradient and learning stability, strengthen representation structure, and reduce emissions relative to cross-entropy and Euclidean heads. Our code is available at: https://anonymous.4open.science/r/rethinking-harmonic-loss-5BAB/.

Nearly all practical neural models for classification are trained using cross-entropy loss. Yet this ubiquitous choice is supported by little theoretical or empirical evidence. Recent work (Hui & Belkin, 2020) suggests that training using the (rescaled) square loss is often superior in terms of the classification accuracy. In this paper we propose the "squentropy" loss, which is the sum of two terms: the cross-entropy loss and the average square loss over the incorrect classes. We provide an extensive set of experiments on multi-class classification problems showing that the squentropy loss outperforms both the pure cross entropy and rescaled square losses in terms of the classification accuracy. We also demonstrate that it provides significantly better model calibration than either of these alternative losses and, furthermore, has less variance with respect to the random initialization. Additionally, in contrast to the square loss, squentropy loss can typically be trained using exactly the same optimization parameters, including the learning rate, as the standard cross-entropy loss, making it a true "plug-and-play" replacement. Finally, unlike the rescaled square loss, multiclass squentropy contains no parameters that need to be adjusted.

Training vision-language models (VLMs) for medical report generation is often hindered by the scarcity of high-quality annotated data. This work evaluates the use of a weighted loss function to improve data efficiency. Compared to standard cross-entropy loss, which treats all token prediction errors equally, the reweighted loss shifts the focus to semantically salient tokens with outsized clinical importance. In experiments on ophthalmological report generation, we show that this simple method improves efficiency across multiple data scales, achieving similar report quality with up to ten times less training data.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.

Progress in language model development is often driven by comparative decisions: which architecture to adopt, which pretraining corpus to use, or which training recipe to apply. Making these decisions well requires reliable performance forecasts, yet the two commonly used signals are fundamentally limited. Cross-entropy loss is poorly aligned with downstream capabilities, and direct downstream evaluation is expensive, sparse, and often uninformative at early training stages. Instead, we propose to construct proxy metrics by aggregating token-level statistics, such as entropy, top-k accuracy, and expert token rank, from a candidate model's next token distribution over expert-written solutions. Across three settings, our proxies consistently outperform loss- and compute-based baselines: 1) For cross-family model selection, they rank a heterogeneous population of reasoning models with mean Spearman Rho = 0.81 (vs. Rho = 0.36 for cross-entropy loss); 2) For pretraining data selection, they reliably rank 25 candidate corpora for a target model at roughly 10{,}000times less compute than direct evaluation, pushing the Pareto frontier beyond existing methods; and 3) for training-time forecasting, they extrapolate downstream accuracy across an 18times compute horizon with roughly half the error of existing alternatives. Together, these results suggest that expert trajectories are a broadly useful source of signal for assessing model capabilities, enabling reliable performance forecasting throughout the model development life cycle.

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal imageleftrightarrowtext models, and mathematical problem solving. In all cases autoregressive Transformers smoothly improve in performance as model size and compute budgets increase, following a power-law plus constant scaling law. The optimal model size also depends on the compute budget through a power-law, with exponents that are nearly universal across all data domains. The cross-entropy loss has an information theoretic interpretation as S(True) + D_{KL}(True||Model), and the empirical scaling laws suggest a prediction for both the true data distribution's entropy and the KL divergence between the true and model distributions. With this interpretation, billion-parameter Transformers are nearly perfect models of the YFCC100M image distribution downsampled to an 8times 8 resolution, and we can forecast the model size needed to achieve any given reducible loss (ie D_{KL}) in nats/image for other resolutions. We find a number of additional scaling laws in specific domains: (a) we identify a scaling relation for the mutual information between captions and images in multimodal models, and show how to answer the question "Is a picture worth a thousand words?"; (b) in the case of mathematical problem solving, we identify scaling laws for model performance when extrapolating beyond the training distribution; (c) we finetune generative image models for ImageNet classification and find smooth scaling of the classification loss and error rate, even as the generative loss levels off. Taken together, these results strengthen the case that scaling laws have important implications for neural network performance, including on downstream tasks.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

This paper analyzes Cross-Entropy (CE) loss in knowledge distillation (KD) for recommender systems. KD for recommender systems targets at distilling rankings, especially among items most likely to be preferred, and can only be computed on a small subset of items. Considering these features, we reveal the connection between CE loss and NDCG in the field of KD. We prove that when performing KD on an item subset, minimizing CE loss maximizes the lower bound of NDCG, only if an assumption of closure is satisfied. It requires that the item subset consists of the student's top items. However, this contradicts our goal of distilling rankings of the teacher's top items. We empirically demonstrate the vast gap between these two kinds of top items. To bridge the gap between our goal and theoretical support, we propose Rejuvenated Cross-Entropy for Knowledge Distillation (RCE-KD). It splits the top items given by the teacher into two subsets based on whether they are highly ranked by the student. For the subset that defies the condition, a sampling strategy is devised to use teacher-student collaboration to approximate our assumption of closure. We also combine the losses on the two subsets adaptively. Extensive experiments demonstrate the effectiveness of our method. Our code is available at https://github.com/BDML-lab/RCE-KD.

Optimization analyses for cross-entropy training rely on local Taylor models of the loss to predict whether a proposed step will decrease the objective. These surrogates are reliable only inside the Taylor convergence radius of the true loss along the update direction. That radius is set not by real-line curvature alone but by the nearest complex singularity. For cross-entropy, the softmax partition function F=sum_j exp(z_j) has complex zeros -- ``ghosts of softmax'' -- that induce logarithmic singularities in the loss and cap this radius. To make this geometry usable, we derive closed-form expressions under logit linearization along the proposed update direction. In the binary case, the exact radius is ρ^*=δ^2+ π^2/Δ_a. In the multiclass case, we obtain the lower bound ρ_a=π/Δ_a, where Δ_a=max_k a_k-min_k a_k is the spread of directional logit derivatives a_k=nabla z_kcdot v. This bound costs one Jacobian-vector product and reveals what makes a step fragile: samples that are both near a decision flip and highly sensitive to the proposed direction tighten the radius. The normalized step size r=τ/ρ_a separates safe from dangerous updates. Across six tested architectures and multiple step directions, no model fails for r<1, yet collapse appears once rge 1. Temperature scaling confirms the mechanism: normalizing by ρ_a shrinks the onset-threshold spread from standard deviation 0.992 to 0.164. A controller that enforces τleρ_a survives learning-rate spikes up to 10{,} 000times in our tests, where gradient clipping still collapses. Together, these results identify a geometric constraint on cross-entropy optimization that operates through Taylor convergence rather than Hessian curvature.

As language models grow ever larger, so do their vocabularies. This has shifted the memory footprint of LLMs during training disproportionately to one single layer: the cross-entropy in the loss computation. Cross-entropy builds up a logit matrix with entries for each pair of input tokens and vocabulary items and, for small models, consumes an order of magnitude more memory than the rest of the LLM combined. We propose Cut Cross-Entropy (CCE), a method that computes the cross-entropy loss without materializing the logits for all tokens into global memory. Rather, CCE only computes the logit for the correct token and evaluates the log-sum-exp over all logits on the fly. We implement a custom kernel that performs the matrix multiplications and the log-sum-exp reduction over the vocabulary in flash memory, making global memory consumption for the cross-entropy computation negligible. This has a dramatic effect. Taking the Gemma 2 (2B) model as an example, CCE reduces the memory footprint of the loss computation from 24 GB to 1 MB, and the total training-time memory consumption of the classifier head from 28 GB to 1 GB. To improve the throughput of CCE, we leverage the inherent sparsity of softmax and propose to skip elements of the gradient computation that have a negligible (i.e., below numerical precision) contribution to the gradient. Experiments demonstrate that the dramatic reduction in memory consumption is accomplished without sacrificing training speed or convergence.

Deep learning algorithms can fare poorly when the training dataset suffers from heavy class-imbalance but the testing criterion requires good generalization on less frequent classes. We design two novel methods to improve performance in such scenarios. First, we propose a theoretically-principled label-distribution-aware margin (LDAM) loss motivated by minimizing a margin-based generalization bound. This loss replaces the standard cross-entropy objective during training and can be applied with prior strategies for training with class-imbalance such as re-weighting or re-sampling. Second, we propose a simple, yet effective, training schedule that defers re-weighting until after the initial stage, allowing the model to learn an initial representation while avoiding some of the complications associated with re-weighting or re-sampling. We test our methods on several benchmark vision tasks including the real-world imbalanced dataset iNaturalist 2018. Our experiments show that either of these methods alone can already improve over existing techniques and their combination achieves even better performance gains.

Dual-encoder retrievers depend on the principle that relevant documents should score higher than irrelevant ones for a given query. Yet the dominant Noise Contrastive Estimation (NCE) objective, which underpins Contrastive Loss, optimizes a softened ranking surrogate that we rigorously prove is fundamentally oblivious to score separation quality and unrelated to AUC. This mismatch leads to poor calibration and suboptimal performance in downstream tasks like retrieval-augmented generation (RAG). To address this fundamental limitation, we introduce the MW loss, a new training objective that maximizes the Mann-Whitney U statistic, which is mathematically equivalent to the Area under the ROC Curve (AUC). MW loss encourages each positive-negative pair to be correctly ranked by minimizing binary cross entropy over score differences. We provide theoretical guarantees that MW loss directly upper-bounds the AoC, better aligning optimization with retrieval goals. We further promote ROC curves and AUC as natural threshold free diagnostics for evaluating retriever calibration and ranking quality. Empirically, retrievers trained with MW loss consistently outperform contrastive counterparts in AUC and standard retrieval metrics. Our experiments show that MW loss is an empirically superior alternative to Contrastive Loss, yielding better-calibrated and more discriminative retrievers for high-stakes applications like RAG.

Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and does not explicitly force different class features to be well-separated. Motivated by the observation that ground-truth class representations in CE loss are orthogonal (one-hot encoded vectors), we develop a novel loss function termed `Orthogonal Projection Loss' (OPL) which imposes orthogonality in the feature space. OPL augments the properties of CE loss and directly enforces inter-class separation alongside intra-class clustering in the feature space through orthogonality constraints on the mini-batch level. As compared to other alternatives of CE, OPL offers unique advantages e.g., no additional learnable parameters, does not require careful negative mining and is not sensitive to the batch size. Given the plug-and-play nature of OPL, we evaluate it on a diverse range of tasks including image recognition (CIFAR-100), large-scale classification (ImageNet), domain generalization (PACS) and few-shot learning (miniImageNet, CIFAR-FS, tiered-ImageNet and Meta-dataset) and demonstrate its effectiveness across the board. Furthermore, OPL offers better robustness against practical nuisances such as adversarial attacks and label noise. Code is available at: https://github.com/kahnchana/opl.

We study a family of loss functions named label-distributionally robust (LDR) losses for multi-class classification that are formulated from distributionally robust optimization (DRO) perspective, where the uncertainty in the given label information are modeled and captured by taking the worse case of distributional weights. The benefits of this perspective are several fold: (i) it provides a unified framework to explain the classical cross-entropy (CE) loss and SVM loss and their variants, (ii) it includes a special family corresponding to the temperature-scaled CE loss, which is widely adopted but poorly understood; (iii) it allows us to achieve adaptivity to the uncertainty degree of label information at an instance level. Our contributions include: (1) we study both consistency and robustness by establishing top-k (forall kgeq 1) consistency of LDR losses for multi-class classification, and a negative result that a top-1 consistent and symmetric robust loss cannot achieve top-k consistency simultaneously for all kgeq 2; (2) we propose a new adaptive LDR loss that automatically adapts the individualized temperature parameter to the noise degree of class label of each instance; (3) we demonstrate stable and competitive performance for the proposed adaptive LDR loss on 7 benchmark datasets under 6 noisy label and 1 clean settings against 13 loss functions, and on one real-world noisy dataset. The code is open-sourced at https://github.com/Optimization-AI/ICML2023_LDR.

Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: any loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of underfitting. To address this, we propose a framework to build robust loss functions called Active Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

In the presence of noisy labels, designing robust loss functions is critical for securing the generalization performance of deep neural networks. Cross Entropy (CE) loss has been shown to be not robust to noisy labels due to its unboundedness. To alleviate this issue, existing works typically design specialized robust losses with the symmetric condition, which usually lead to the underfitting issue. In this paper, our key idea is to induce a loss bound at the logit level, thus universally enhancing the noise robustness of existing losses. Specifically, we propose logit clipping (LogitClip), which clamps the norm of the logit vector to ensure that it is upper bounded by a constant. In this manner, CE loss equipped with our LogitClip method is effectively bounded, mitigating the overfitting to examples with noisy labels. Moreover, we present theoretical analyses to certify the noise-tolerant ability of LogitClip. Extensive experiments show that LogitClip not only significantly improves the noise robustness of CE loss, but also broadly enhances the generalization performance of popular robust losses.

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

IoU losses are surrogates that directly optimize the Jaccard index. In semantic segmentation, leveraging IoU losses as part of the loss function is shown to perform better with respect to the Jaccard index measure than optimizing pixel-wise losses such as the cross-entropy loss alone. The most notable IoU losses are the soft Jaccard loss and the Lovasz-Softmax loss. However, these losses are incompatible with soft labels which are ubiquitous in machine learning. In this paper, we propose Jaccard metric losses (JMLs), which are identical to the soft Jaccard loss in a standard setting with hard labels, but are compatible with soft labels. With JMLs, we study two of the most popular use cases of soft labels: label smoothing and knowledge distillation. With a variety of architectures, our experiments show significant improvements over the cross-entropy loss on three semantic segmentation datasets (Cityscapes, PASCAL VOC and DeepGlobe Land), and our simple approach outperforms state-of-the-art knowledge distillation methods by a large margin. Code is available at: https://github.com/zifuwanggg/JDTLosses{https://github.com/zifuwanggg/JDTLosses}.

During the finetuning stage of text generation tasks, standard cross-entropy loss treats all tokens equally. This can lead models to overemphasize high-frequency, low-information tokens, neglecting lower-frequency tokens crucial for specificity and informativeness in generated content. This paper introduces a novel loss function, Power-Law Decay Loss (PDL), specifically designed to optimize the finetuning process for text generation. The core motivation for PDL stems from observations in information theory and linguistics: the informativeness of a token is often inversely proportional to its frequency of occurrence. PDL re-weights the contribution of each token in the standard cross-entropy loss based on its frequency in the training corpus, following a power-law decay. Specifically, the weights for high-frequency tokens are reduced, while low-frequency, information-dense tokens are assigned higher weights. This mechanism guides the model during finetuning to focus more on learning and generating tokens that convey specific and unique information, thereby enhancing the quality, diversity, and informativeness of the generated text. We theoretically elaborate on the motivation and construction of PDL and discuss its potential applications and advantages across various text generation finetuning tasks, such as abstractive summarization, dialogue systems, and style transfer.

Many NLP tasks such as tagging and machine reading comprehension are faced with the severe data imbalance issue: negative examples significantly outnumber positive examples, and the huge number of background examples (or easy-negative examples) overwhelms the training. The most commonly used cross entropy (CE) criteria is actually an accuracy-oriented objective, and thus creates a discrepancy between training and test: at training time, each training instance contributes equally to the objective function, while at test time F1 score concerns more about positive examples. In this paper, we propose to use dice loss in replacement of the standard cross-entropy objective for data-imbalanced NLP tasks. Dice loss is based on the Sorensen-Dice coefficient or Tversky index, which attaches similar importance to false positives and false negatives, and is more immune to the data-imbalance issue. To further alleviate the dominating influence from easy-negative examples in training, we propose to associate training examples with dynamically adjusted weights to deemphasize easy-negative examples.Theoretical analysis shows that this strategy narrows down the gap between the F1 score in evaluation and the dice loss in training. With the proposed training objective, we observe significant performance boost on a wide range of data imbalanced NLP tasks. Notably, we are able to achieve SOTA results on CTB5, CTB6 and UD1.4 for the part of speech tagging task; SOTA results on CoNLL03, OntoNotes5.0, MSRA and OntoNotes4.0 for the named entity recognition task; along with competitive results on the tasks of machine reading comprehension and paraphrase identification.

The design of modern neural architectures has converged through incremental empirical choices, yet the mechanisms governing their training dynamics remain only partially understood. We identify and analyze a negative weight drift induced by the interaction between standard losses and positively biased activation functions. We prove that under MSE or cross-entropy loss, the gradient with respect to positive pre-activations is non-negative in expectation at initialization, driving downstream weights toward negative values during early training. The drift is intrinsic to optimization rather than data, and persists across architectures (MLP, ResNet, ViT, GPT-nano, MP-SENe) and asymmetric activation functions (ReLU, GELU, SiLU). Coupled with ReLU, weight drift produces activation sparsity reaching up to 90\% in GPT-nano. We characterize the sparsity-accuracy tradeoff across 79 configurations and identify a sharp accuracy cliff above sim70\% activation sparsity. While ReLU^2 achieves a good sparsity--accuracy ratio in GPT-nano, it pathologically amplifies identified activation spikes in intermediate transformer layers. Clipping resolves this while preserving the representational benefits of squaring: clipped ReLU^2 outperforms its unclipped version, and GELU^2 achieves the lowest validation loss on GPT-nano. Code is available at https://github.com/On-Point-RND/BugOrFeature.

Recent advancements in deep learning have significantly improved performance on computer vision tasks. Previous image classification methods primarily modify model architectures or add features, and they optimize models using cross-entropy loss on class logits. Since they focus on classifying images with considering class labels, these methods may struggle to learn various aspects of classes (e.g., natural positions and shape changes). Rethinking the previous approach from a novel view, we propose a multi-aspect knowledge distillation method using Multimodal Large Language Models (MLLMs). Our approach involves: 1) querying Large Language Model with multi-aspect questions relevant to the knowledge we want to transfer to the model, 2) extracting corresponding logits from MLLM, and 3) expanding the model's output dimensions to distill these multi-aspect logits. We then apply cross-entropy loss to class logits and binary cross-entropy loss to multi-aspect logits. Through our method, the model can learn not only the knowledge about visual aspects but also the abstract and complex aspects that require a deeper understanding. We primarily apply our method to image classification, and to explore the potential for extending our model, we expand it to other tasks, such as object detection. In all experimental results, our method improves the performance of the baselines. Additionally, we analyze the effect of multi-aspect knowledge distillation. These results demonstrate that our method can transfer knowledge about various aspects to the model and the aspect knowledge can enhance model performance in computer vision tasks. This paper demonstrates the great potential of multi-aspect knowledge distillation, and we believe it offers a promising direction for future research in computer vision and beyond.

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

In this work, we have worked towards two major goals. Firstly, we have investigated the importance of Batch Normalisation (BN) layers in a non-contrastive representation learning framework called Bootstrap Your Own Latent (BYOL). We conducted several experiments to conclude that BN layers are not necessary for representation learning in BYOL. Moreover, BYOL only learns from the positive pairs of images but ignores other semantically similar images in the same input batch. For the second goal, we have introduced two new loss functions to determine the semantically similar pairs in the same input batch of images and reduce the distance between their representations. These loss functions are Cross-Cosine Similarity Loss (CCSL) and Cross-Sigmoid Similarity Loss (CSSL). Using the proposed loss functions, we are able to surpass the performance of Vanilla BYOL (71.04%) by training the BYOL framework using CCSL loss (76.87%) on the STL10 dataset. BYOL trained using CSSL loss performs comparably with Vanilla BYOL.

Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model size compression. However, these studies often approach various lossy and lossless compression methods in isolation, leading to challenges in achieving high compression ratios efficiently. This work proposes a post-training model size compression method that combines lossy and lossless compression in a unified way. We first propose a unified parametric weight transformation, which ensures different lossy compression methods can be performed jointly in a post-training manner. Then, a dedicated differentiable counter is introduced to guide the optimization of lossy compression to arrive at a more suitable point for later lossless compression. Additionally, our method can easily control a desired global compression ratio and allocate adaptive ratios for different layers. Finally, our method can achieve a stable 10times compression ratio without sacrificing accuracy and a 20times compression ratio with minor accuracy loss in a short time. Our code is available at https://github.com/ModelTC/L2_Compression .

We propose a method to optimize language model pre-training data mixtures through efficient approximation of the cross-entropy loss corresponding to each candidate mixture via a Mixture of Data Experts (MDE). We use this approximation as a source of additional features in a regression model, trained from observations of model loss for a small number of mixtures. Experiments with Transformer decoder-only language models in the range of 70M to 1B parameters on the SlimPajama dataset show that our method achieves significantly better performance than approaches that train regression models using only the mixture rates as input features. Combining this improved optimization method with an objective that takes into account cross-entropy on end task data leads to superior performance on few-shot downstream evaluations. We also provide theoretical insights on why aggregation of data expert predictions can provide good approximations to model losses for data mixtures.

Exemplar-free class-incremental learning (EFCIL) presents a significant challenge as the old class samples are absent for new task learning. Due to the severe imbalance between old and new class samples, the learned classifiers can be easily biased toward the new ones. Moreover, continually updating the feature extractor under EFCIL can compromise the discriminative power of old class features, e.g., leading to less compact and more overlapping distributions across classes. Existing methods mainly focus on handling biased classifier learning. In this work, both cases are considered using the proposed method. Specifically, we first introduce a Distribution-Based Global Classifier (DBGC) to avoid bias factors in existing methods, such as data imbalance and sampling. More importantly, the compromised distributions of old classes are simulated via a simple operation, variance enlarging (VE). Incorporating VE based on DBGC results in a novel classification loss for EFCIL. This loss is proven equivalent to an Adaptive Margin Softmax Cross Entropy (AMarX). The proposed method is thus called Adaptive Margin Global Classifier (AMGC). AMGC is simple yet effective. Extensive experiments show that AMGC achieves superior image classification results on its own under a challenging EFCIL setting. Detailed analysis is also provided for further demonstration.

In most machine learning tasks, we evaluate a model M on a given data population S by measuring a population-level metric F(S;M). Examples of such evaluation metric F include precision/recall for (binary) recognition, the F1 score for multi-class classification, and the BLEU metric for language generation. On the other hand, the model M is trained by optimizing a sample-level loss G(S_t;M) at each learning step t, where S_t is a subset of S (a.k.a. the mini-batch). Popular choices of G include cross-entropy loss, the Dice loss, and sentence-level BLEU scores. A fundamental assumption behind this paradigm is that the mean value of the sample-level loss G, if averaged over all possible samples, should effectively represent the population-level metric F of the task, such as, that E[ G(S_t;M) ] approx F(S;M). In this paper, we systematically investigate the above assumption in several NLP tasks. We show, both theoretically and experimentally, that some popular designs of the sample-level loss G may be inconsistent with the true population-level metric F of the task, so that models trained to optimize the former can be substantially sub-optimal to the latter, a phenomenon we call it, Simpson's bias, due to its deep connections with the classic paradox known as Simpson's reversal paradox in statistics and social sciences.

This paper provides a pair similarity optimization viewpoint on deep feature learning, aiming to maximize the within-class similarity s_p and minimize the between-class similarity s_n. We find a majority of loss functions, including the triplet loss and the softmax plus cross-entropy loss, embed s_n and s_p into similarity pairs and seek to reduce (s_n-s_p). Such an optimization manner is inflexible, because the penalty strength on every single similarity score is restricted to be equal. Our intuition is that if a similarity score deviates far from the optimum, it should be emphasized. To this end, we simply re-weight each similarity to highlight the less-optimized similarity scores. It results in a Circle loss, which is named due to its circular decision boundary. The Circle loss has a unified formula for two elemental deep feature learning approaches, i.e. learning with class-level labels and pair-wise labels. Analytically, we show that the Circle loss offers a more flexible optimization approach towards a more definite convergence target, compared with the loss functions optimizing (s_n-s_p). Experimentally, we demonstrate the superiority of the Circle loss on a variety of deep feature learning tasks. On face recognition, person re-identification, as well as several fine-grained image retrieval datasets, the achieved performance is on par with the state of the art.

Estimating the test performance of a model, possibly under distribution shift, without having access to the ground-truth labels is a challenging, yet very important problem for the safe deployment of machine learning algorithms in the wild. Existing works mostly rely on information from either the outputs or the extracted features of neural networks to estimate a score that correlates with the ground-truth test accuracy. In this paper, we investigate -- both empirically and theoretically -- how the information provided by the gradients can be predictive of the ground-truth test accuracy even under distribution shifts. More specifically, we use the norm of classification-layer gradients, backpropagated from the cross-entropy loss after only one gradient step over test data. Our intuition is that these gradients should be of higher magnitude when the model generalizes poorly. We provide the theoretical insights behind our approach and the key ingredients that ensure its empirical success. Extensive experiments conducted with various architectures on diverse distribution shifts demonstrate that our method significantly outperforms current state-of-the-art approaches. The code is available at https://github.com/Renchunzi-Xie/GdScore

Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in accelerating MILP solvers by predicting high-quality solutions. However, we identify that existing methods misalign with the intrinsic structure of MILP problems at two levels. At the leaning objective level, the Binary Cross-Entropy (BCE) loss treats variables independently, neglecting their relative priority and yielding plausible logits. At the model architecture level, standard GNN message passing inherently smooths the representations across variables, missing the natural competitive relationships within constraints. To address these challenges, we propose CoCo-MILP, which explicitly models inter-variable Contrast and intra-constraint Competition for advanced MILP solution prediction. At the objective level, CoCo-MILP introduces the Inter-Variable Contrastive Loss (VCL), which explicitly maximizes the embedding margin between variables assigned one versus zero. At the architectural level, we design an Intra-Constraint Competitive GNN layer that, instead of homogenizing features, learns to differentiate representations of competing variables within a constraint, capturing their exclusionary nature. Experimental results on standard benchmarks demonstrate that CoCo-MILP significantly outperforms existing learning-based approaches, reducing the solution gap by up to 68.12% compared to traditional solvers. Our code is available at https://github.com/happypu326/CoCo-MILP.

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

When training or evaluating deep learning models, two essential parts are picking the proper loss function and deciding on performance metrics. In this paper, we provide a comprehensive overview of the most common loss functions and metrics used across many different types of deep learning tasks, from general tasks such as regression and classification to more specific tasks in Computer Vision and Natural Language Processing. We introduce the formula for each loss and metric, discuss their strengths and limitations, and describe how these methods can be applied to various problems within deep learning. This work can serve as a reference for researchers and practitioners in the field, helping them make informed decisions when selecting the most appropriate loss function and performance metrics for their deep learning projects.

A family of loss functions built on pair-based computation have been proposed in the literature which provide a myriad of solutions for deep metric learning. In this paper, we provide a general weighting framework for understanding recent pair-based loss functions. Our contributions are three-fold: (1) we establish a General Pair Weighting (GPW) framework, which casts the sampling problem of deep metric learning into a unified view of pair weighting through gradient analysis, providing a powerful tool for understanding recent pair-based loss functions; (2) we show that with GPW, various existing pair-based methods can be compared and discussed comprehensively, with clear differences and key limitations identified; (3) we propose a new loss called multi-similarity loss (MS loss) under the GPW, which is implemented in two iterative steps (i.e., mining and weighting). This allows it to fully consider three similarities for pair weighting, providing a more principled approach for collecting and weighting informative pairs. Finally, the proposed MS loss obtains new state-of-the-art performance on four image retrieval benchmarks, where it outperforms the most recent approaches, such as ABEKim_2018_ECCV and HTL by a large margin: 60.6% to 65.7% on CUB200, and 80.9% to 88.0% on In-Shop Clothes Retrieval dataset at Recall@1. Code is available at https://github.com/MalongTech/research-ms-loss.

Deep embeddings answer one simple question: How similar are two images? Learning these embeddings is the bedrock of verification, zero-shot learning, and visual search. The most prominent approaches optimize a deep convolutional network with a suitable loss function, such as contrastive loss or triplet loss. While a rich line of work focuses solely on the loss functions, we show in this paper that selecting training examples plays an equally important role. We propose distance weighted sampling, which selects more informative and stable examples than traditional approaches. In addition, we show that a simple margin based loss is sufficient to outperform all other loss functions. We evaluate our approach on the Stanford Online Products, CAR196, and the CUB200-2011 datasets for image retrieval and clustering, and on the LFW dataset for face verification. Our method achieves state-of-the-art performance on all of them.

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

Scaling limits, such as infinite-width limits, serve as promising theoretical tools to study large-scale models. However, it is widely believed that existing infinite-width theory does not faithfully explain the behavior of practical networks, especially those trained in standard parameterization (SP) meaning He initialization with a global learning rate. For instance, existing theory for SP predicts instability at large learning rates and vanishing feature learning at stable ones. In practice, however, optimal learning rates decay slower than theoretically predicted and networks exhibit both stable training and non-trivial feature learning, even at very large widths. Here, we show that this discrepancy is not fully explained by finite-width phenomena. Instead, we find a resolution through a finer-grained analysis of the regime previously considered unstable and therefore uninteresting. In particular, we show that, under cross-entropy (CE) loss, the unstable regime comprises two distinct sub-regimes: a catastrophically unstable regime and a more benign controlled divergence regime, where logits diverge but gradients and activations remain stable. Moreover, under large learning rates at the edge of the controlled divergence regime, there exists a well-defined infinite width limit where features continue to evolve in all the hidden layers. In experiments across optimizers, architectures, and data modalities, we validate that neural networks operate in this controlled divergence regime under CE loss but not under MSE loss. Our empirical evidence suggests that width-scaling considerations are surprisingly useful for predicting empirically maximal stable learning rate exponents which provide useful guidance on optimal learning rate exponents. Finally, our analysis clarifies the effectiveness and limitations of recently proposed layerwise learning rate scaling for standard initialization.

We study empirical scaling laws for language model performance on the cross-entropy loss. The loss scales as a power-law with model size, dataset size, and the amount of compute used for training, with some trends spanning more than seven orders of magnitude. Other architectural details such as network width or depth have minimal effects within a wide range. Simple equations govern the dependence of overfitting on model/dataset size and the dependence of training speed on model size. These relationships allow us to determine the optimal allocation of a fixed compute budget. Larger models are significantly more sample-efficient, such that optimally compute-efficient training involves training very large models on a relatively modest amount of data and stopping significantly before convergence.

Many evaluation metrics can be used to assess the performance of models in binary classification tasks. However, most of them are derived from a confusion matrix in a non-differentiable form, making it very difficult to generate a differentiable loss function that could directly optimize them. The lack of solutions to bridge this challenge not only hinders our ability to solve difficult tasks, such as imbalanced learning, but also requires the deployment of computationally expensive hyperparameter search processes in model selection. In this paper, we propose a general-purpose approach that transforms any confusion matrix-based metric into a loss function, AnyLoss, that is available in optimization processes. To this end, we use an approximation function to make a confusion matrix represented in a differentiable form, and this approach enables any confusion matrix-based metric to be directly used as a loss function. The mechanism of the approximation function is provided to ensure its operability and the differentiability of our loss functions is proved by suggesting their derivatives. We conduct extensive experiments under diverse neural networks with many datasets, and we demonstrate their general availability to target any confusion matrix-based metrics. Our method, especially, shows outstanding achievements in dealing with imbalanced datasets, and its competitive learning speed, compared to multiple baseline models, underscores its efficiency.

In this paper, we introduce **harmonic loss** as an alternative to the standard cross-entropy loss for training neural networks and large language models (LLMs). Harmonic loss enables improved interpretability and faster convergence, owing to its scale invariance and finite convergence point by design, which can be interpreted as a class center. We first validate the performance of harmonic models across algorithmic, vision, and language datasets. Through extensive experiments, we demonstrate that models trained with harmonic loss outperform standard models by: (a) enhancing interpretability, (b) requiring less data for generalization, and (c) reducing grokking. Moreover, we compare a GPT-2 model trained with harmonic loss to the standard GPT-2, illustrating that the harmonic model develops more interpretable representations. Looking forward, we believe harmonic loss has the potential to become a valuable tool in domains with limited data availability or in high-stakes applications where interpretability and reliability are paramount, paving the way for more robust and efficient neural network models.

The highest accuracy object detectors to date are based on a two-stage approach popularized by R-CNN, where a classifier is applied to a sparse set of candidate object locations. In contrast, one-stage detectors that are applied over a regular, dense sampling of possible object locations have the potential to be faster and simpler, but have trailed the accuracy of two-stage detectors thus far. In this paper, we investigate why this is the case. We discover that the extreme foreground-background class imbalance encountered during training of dense detectors is the central cause. We propose to address this class imbalance by reshaping the standard cross entropy loss such that it down-weights the loss assigned to well-classified examples. Our novel Focal Loss focuses training on a sparse set of hard examples and prevents the vast number of easy negatives from overwhelming the detector during training. To evaluate the effectiveness of our loss, we design and train a simple dense detector we call RetinaNet. Our results show that when trained with the focal loss, RetinaNet is able to match the speed of previous one-stage detectors while surpassing the accuracy of all existing state-of-the-art two-stage detectors. Code is at: https://github.com/facebookresearch/Detectron.

We propose a novel scaling law for general-purpose decoder-only language models (LMs) trained on multilingual data, tackling the problem of balancing languages during multilingual pretraining. A primary challenge in studying multilingual scaling is the difficulty of analyzing individual language performance due to cross-lingual transfer. To address this, we shift the focus from individual languages to language families. We introduce and validate a hypothesis that the test cross-entropy loss for each language family is determined solely by its own sampling ratio, independent of other languages in the mixture. This insight simplifies the complexity of multilingual scaling and make the analysis scalable to an arbitrary number of languages. Building on this hypothesis, we derive a power-law relationship that links performance with dataset size, model size and sampling ratios. This relationship enables us to predict performance across various combinations of the above three quantities, and derive the optimal sampling ratios at different model scales. To demonstrate the effectiveness and accuracy of our proposed scaling law, we perform a large-scale empirical study, training more than 100 models on 23 languages spanning 5 language families. Our experiments show that the optimal sampling ratios derived from small models (85M parameters) generalize effectively to models that are several orders of magnitude larger (1.2B parameters), offering a resource-efficient approach for multilingual LM training at scale.

The conventional wisdom behind learning deep classification models is to focus on bad-classified examples and ignore well-classified examples that are far from the decision boundary. For instance, when training with cross-entropy loss, examples with higher likelihoods (i.e., well-classified examples) contribute smaller gradients in back-propagation. However, we theoretically show that this common practice hinders representation learning, energy optimization, and margin growth. To counteract this deficiency, we propose to reward well-classified examples with additive bonuses to revive their contribution to the learning process. This counterexample theoretically addresses these three issues. We empirically support this claim by directly verifying the theoretical results or significant performance improvement with our counterexample on diverse tasks, including image classification, graph classification, and machine translation. Furthermore, this paper shows that we can deal with complex scenarios, such as imbalanced classification, OOD detection, and applications under adversarial attacks because our idea can solve these three issues. Code is available at: https://github.com/lancopku/well-classified-examples-are-underestimated.

We find that the cross-entropy loss curves of neural language models empirically adhere to a scaling law with learning rate (LR) annealing over training steps (s): $L(s) = L_0 + Acdot S_1^{-alpha} - Ccdot S_2 Where S_1 is forward area and S_2$ is learning rate annealing area. This formulation takes into account two factors: (1) The forward scaling defined as typical scaling law, and (2) the additional loss drop brought by LR annealing. Therefore, this formulation can describe the full loss curve at each step, rather than the single loss point at the end of training. Applying the scaling law with LR annealing and fitting only one or two training curves, we can accurately predict the loss of language model training at any given step and across any learning rate scheduler (LRS). Furthermore, this equation accurately describes the dynamics during training process, and provides a theoretical verification and explanation for numerous experimental findings of previous studies, particularly those focusing on LR schedule and LR annealing. The resulting insights, also serve as a guide for researchers to select critical LRS in advance by prediction using our equation. Most significantly, since all the points in a full training curve follow the equation, we can achieve accurate loss prediction at any given step across any learning rate scheduler, while expending less than 1\% of the computational cost required by the chinchilla scaling law to fit language modeling loss. This approach extremely democratizes scaling law fitting and predicting in developing large language models.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

Dominant dual-encoder models enable efficient image-text retrieval but suffer from limited accuracy while the cross-encoder models offer higher accuracy at the expense of efficiency. Distilling cross-modality matching knowledge from cross-encoder to dual-encoder provides a natural approach to harness their strengths. Thus we investigate the following valuable question: how to make cross-encoder a good teacher for dual-encoder? Our findings are threefold:(1) Cross-modal similarity score distribution of cross-encoder is more concentrated while the result of dual-encoder is nearly normal making vanilla logit distillation less effective. However ranking distillation remains practical as it is not affected by the score distribution.(2) Only the relative order between hard negatives conveys valid knowledge while the order information between easy negatives has little significance.(3) Maintaining the coordination between distillation loss and dual-encoder training loss is beneficial for knowledge transfer. Based on these findings we propose a novel Contrastive Partial Ranking Distillation (CPRD) method which implements the objective of mimicking relative order between hard negative samples with contrastive learning. This approach coordinates with the training of the dual-encoder effectively transferring valid knowledge from the cross-encoder to the dual-encoder. Extensive experiments on image-text retrieval and ranking tasks show that our method surpasses other distillation methods and significantly improves the accuracy of dual-encoder.

Softmax Loss (SL) is widely applied in recommender systems (RS) and has demonstrated effectiveness. This work analyzes SL from a pairwise perspective, revealing two significant limitations: 1) the relationship between SL and conventional ranking metrics like DCG is not sufficiently tight; 2) SL is highly sensitive to false negative instances. Our analysis indicates that these limitations are primarily due to the use of the exponential function. To address these issues, this work extends SL to a new family of loss functions, termed Pairwise Softmax Loss (PSL), which replaces the exponential function in SL with other appropriate activation functions. While the revision is minimal, we highlight three merits of PSL: 1) it serves as a tighter surrogate for DCG with suitable activation functions; 2) it better balances data contributions; and 3) it acts as a specific BPR loss enhanced by Distributionally Robust Optimization (DRO). We further validate the effectiveness and robustness of PSL through empirical experiments. The code is available at https://github.com/Tiny-Snow/IR-Benchmark.

Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on items' ranks), their derivatives are either undefined or zero everywhere. This makes them unsuitable for gradient-based optimisation, which is the usual method of learning appropriate scoring functions. Commonly used LTR loss functions are only loosely related to the evaluation metrics, causing a mismatch between the optimisation objective and the evaluation criterion. In this paper, we address this mismatch by proposing NeuralNDCG, a novel differentiable approximation to NDCG. Since NDCG relies on the non-differentiable sorting operator, we obtain NeuralNDCG by relaxing that operator using NeuralSort, a differentiable approximation of sorting. As a result, we obtain a new ranking loss function which is an arbitrarily accurate approximation to the evaluation metric, thus closing the gap between the training and the evaluation of LTR models. We introduce two variants of the proposed loss function. Finally, the empirical evaluation shows that our proposed method outperforms previous work aimed at direct optimisation of NDCG and is competitive with the state-of-the-art methods.

Assigning importance weights to adversarial data has achieved great success in training adversarially robust networks under limited model capacity. However, existing instance-reweighted adversarial training (AT) methods heavily depend on heuristics and/or geometric interpretations to determine those importance weights, making these algorithms lack rigorous theoretical justification/guarantee. Moreover, recent research has shown that adversarial training suffers from a severe non-uniform robust performance across the training distribution, e.g., data points belonging to some classes can be much more vulnerable to adversarial attacks than others. To address both issues, in this paper, we propose a novel doubly-robust instance reweighted AT framework, which allows to obtain the importance weights via exploring distributionally robust optimization (DRO) techniques, and at the same time boosts the robustness on the most vulnerable examples. In particular, our importance weights are obtained by optimizing the KL-divergence regularized loss function, which allows us to devise new algorithms with a theoretical convergence guarantee. Experiments on standard classification datasets demonstrate that our proposed approach outperforms related state-of-the-art baseline methods in terms of average robust performance, and at the same time improves the robustness against attacks on the weakest data points. Codes will be available soon.

Machine unlearning in foundation models (e.g., language and vision transformers) is essential for privacy and safety; however, existing approaches are unstable and unreliable. A widely used strategy, the gradient difference method, applies gradient descent to retained data while performing gradient ascent on forgotten data. When combined with cross-entropy, this procedure can trigger the unbounded growth of weights and gradients, degrading both forgetting and retention. We provide a theoretical framework that explains this failure by showing how ascent destabilizes optimization in transformer feedforward MLP layers. Guided by this insight, we propose *Bounded Parameter-Efficient Unlearning*, which stabilizes LoRA-based fine-tuning by applying bounded functions to MLP adapters. This controls the weight dynamics during ascent and enables reliable convergence. We validate the approach on Vision Transformer class deletion on CIFAR-100, where GD+Sine is the only evaluated method to achieve both high forget quality and model utility across ViT-B/16, ViT-L/14, and DeiT-S architectures, and demonstrate generality on language-model benchmarks (TOFU, TDEC, MUSE) across architectures from 22M to 8B parameters, achieving improved forgetting while preserving utility.

Loss reweighting has shown significant benefits for machine unlearning with large language models (LLMs). However, their exact functionalities are left unclear and the optimal strategy remains an open question, thus impeding the understanding and improvement of existing methodologies. In this paper, we identify two distinct goals of loss reweighting, namely, Saturation and Importance -- the former indicates that those insufficiently optimized data should be emphasized, while the latter stresses some critical data that are most influential for loss minimization. To study their usefulness, we design specific reweighting strategies for each goal and evaluate their respective effects on unlearning. We conduct extensive empirical analyses on well-established benchmarks, and summarize some important observations as follows: (i) Saturation enhances efficacy more than importance-based reweighting, and their combination can yield additional improvements. (ii) Saturation typically allocates lower weights to data with lower likelihoods, whereas importance-based reweighting does the opposite. (iii) The efficacy of unlearning is also largely influenced by the smoothness and granularity of the weight distributions. Based on these findings, we propose SatImp, a simple reweighting method that combines the advantages of both saturation and importance. Empirical results on extensive datasets validate the efficacy of our method, potentially bridging existing research gaps and indicating directions for future research. Our code is available at https://github.com/tmlr-group/SatImp.

Autoregressive language models are trained by minimizing the cross-entropy of the model distribution Q relative to the data distribution P -- that is, minimizing the forward cross-entropy, which is equivalent to maximum likelihood estimation (MLE). We have observed that models trained in this way may "over-generalize", in the sense that they produce non-human-like text. Moreover, we believe that reverse cross-entropy, i.e., the cross-entropy of P relative to Q, is a better reflection of how a human would evaluate text generated by a model. Hence, we propose learning with MixCE, an objective that mixes the forward and reverse cross-entropies. We evaluate models trained with this objective on synthetic data settings (where P is known) and real data, and show that the resulting models yield better generated text without complex decoding strategies. Our code and models are publicly available at https://github.com/bloomberg/mixce-acl2023

Adam has been shown to outperform gradient descent on large language models by a larger margin than on other tasks, but it is unclear why. We show that a key factor in this performance gap is the heavy-tailed class imbalance found in language tasks. When trained with gradient descent, the loss of infrequent words decreases more slowly than the loss of frequent ones. This leads to a slow decrease on the average loss as most samples come from infrequent words. On the other hand, Adam and sign-based methods are less sensitive to this problem. To establish that this behavior is caused by class imbalance, we show empirically that it can be reproduced across architectures and data types, on language transformers, vision CNNs, and linear models. On a linear model with cross-entropy loss, we show that class imbalance leads to imbalanced, correlated gradients and Hessians that have been hypothesized to benefit Adam. We also prove that, in continuous time, gradient descent converges slowly on low-frequency classes while sign descent does not.

Large Language Models (LLMs) typically rely on Supervised Fine-Tuning (SFT) to specialize in downstream tasks, with the Cross Entropy (CE) loss being the de facto choice. However, CE maximizes the likelihood of observed data without accounting for alternative possibilities. As such, CE usually leads to reduced diversity in the model's outputs, which hinders further development that requires sampling to explore better responses. To address this limitation, this paper introduces a new game-theoretic formulation for SFT. In this framework, an auxiliary variable is introduced to regulate the learning process. We prove that the proposed game-theoretic approach connects to the problem of reverse KL minimization with entropy regularization. This regularization prevents over-memorization of training data and promotes output diversity. To implement this framework, we develop GEM, a new training algorithm that is computationally efficient as CE by leveraging some unique properties of LLMs. Empirical studies of pre-trained models from 3B to 70B parameters show that GEM achieves comparable downstream performance to CE while significantly enhancing output diversity. This increased diversity translates to performance gains in test-time compute scaling for chat and code generation tasks. Moreover, we observe that preserving output diversity has the added benefit of mitigating forgetting, as maintaining diverse outputs encourages models to retain pre-trained knowledge throughout the training process.

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on volumetric overlap, often at the expense of preserving structural connectivity or topology. This can lead to segmentation errors that adversely affect downstream tasks, including flow calculation, navigation, and structural inspection. Although current topology-focused losses mark an improvement, they introduce significant computational and memory overheads. This is particularly relevant for 3D data, rendering these losses infeasible for larger volumes as well as increasingly important multi-class segmentation problems. To mitigate this, we propose a novel Skeleton Recall Loss, which effectively addresses these challenges by circumventing intensive GPU-based calculations with inexpensive CPU operations. It demonstrates overall superior performance to current state-of-the-art approaches on five public datasets for topology-preserving segmentation, while substantially reducing computational overheads by more than 90%. In doing so, we introduce the first multi-class capable loss function for thin structure segmentation, excelling in both efficiency and efficacy for topology-preservation.

We investigate cross-lingual sentiment analysis, which has attracted significant attention due to its applications in various areas including market research, politics and social sciences. In particular, we introduce a sentiment analysis framework in multi-label setting as it obeys Plutchik wheel of emotions. We introduce a novel dynamic weighting method that balances the contribution from each class during training, unlike previous static weighting methods that assign non-changing weights based on their class frequency. Moreover, we adapt the focal loss that favors harder instances from single-label object recognition literature to our multi-label setting. Furthermore, we derive a method to choose optimal class-specific thresholds that maximize the macro-f1 score in linear time complexity. Through an extensive set of experiments, we show that our method obtains the state-of-the-art performance in 7 of 9 metrics in 3 different languages using a single model compared to the common baselines and the best-performing methods in the SemEval competition. We publicly share our code for our model, which can perform sentiment analysis in 100 languages, to facilitate further research.

In a typical multi-label setting, a picture contains on average few positive labels, and many negative ones. This positive-negative imbalance dominates the optimization process, and can lead to under-emphasizing gradients from positive labels during training, resulting in poor accuracy. In this paper, we introduce a novel asymmetric loss ("ASL"), which operates differently on positive and negative samples. The loss enables to dynamically down-weights and hard-thresholds easy negative samples, while also discarding possibly mislabeled samples. We demonstrate how ASL can balance the probabilities of different samples, and how this balancing is translated to better mAP scores. With ASL, we reach state-of-the-art results on multiple popular multi-label datasets: MS-COCO, Pascal-VOC, NUS-WIDE and Open Images. We also demonstrate ASL applicability for other tasks, such as single-label classification and object detection. ASL is effective, easy to implement, and does not increase the training time or complexity. Implementation is available at: https://github.com/Alibaba-MIIL/ASL.

In this report, we present our champion solution for EPIC-KITCHENS-100 Multi-Instance Retrieval Challenge in CVPR 2024. Essentially, this challenge differs from traditional visual-text retrieval tasks by providing a correlation matrix that acts as a set of soft labels for video-text clip combinations. However, existing loss functions have not fully exploited this information. Motivated by this, we propose a novel loss function, Symmetric Multi-Similarity Loss, which offers a more precise learning objective. Together with tricks and ensemble learning, the model achieves 63.76% average mAP and 74.25% average nDCG on the public leaderboard, demonstrating the effectiveness of our approach. Our code will be released at: https://github.com/xqwang14/SMS-Loss/tree/main

Metric learning involves learning a discriminative representation such that embeddings of similar classes are encouraged to be close, while embeddings of dissimilar classes are pushed far apart. State-of-the-art methods focus mostly on sophisticated loss functions or mining strategies. On the one hand, metric learning losses consider two or more examples at a time. On the other hand, modern data augmentation methods for classification consider two or more examples at a time. The combination of the two ideas is under-studied. In this work, we aim to bridge this gap and improve representations using mixup, which is a powerful data augmentation approach interpolating two or more examples and corresponding target labels at a time. This task is challenging because unlike classification, the loss functions used in metric learning are not additive over examples, so the idea of interpolating target labels is not straightforward. To the best of our knowledge, we are the first to investigate mixing both examples and target labels for deep metric learning. We develop a generalized formulation that encompasses existing metric learning loss functions and modify it to accommodate for mixup, introducing Metric Mix, or Metrix. We also introduce a new metric - utilization, to demonstrate that by mixing examples during training, we are exploring areas of the embedding space beyond the training classes, thereby improving representations. To validate the effect of improved representations, we show that mixing inputs, intermediate representations or embeddings along with target labels significantly outperforms state-of-the-art metric learning methods on four benchmark deep metric learning datasets.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

Self-distillation (SD) is the process of first training a teacher model and then using its predictions to train a student model with the same architecture. Specifically, the student's objective function is big(xi*ell(teacher's predictions, student's predictions) + (1-xi)*ell(given labels, student's predictions)big), where ell is some loss function and xi is some parameter in [0,1]. Empirically, SD has been observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with noisy labels. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of xi that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that xi > 1 works better than xi leq 1 even with the cross-entropy loss for several classification datasets when 50\% or 30\% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher in terms of accuracy. To our knowledge, this is the first result of its kind for the cross-entropy loss.

The cross-entropy objective has proved to be an all-purpose training objective for autoregressive language models (LMs). However, without considering the penalization of problematic tokens, LMs trained using cross-entropy exhibit text degeneration. To address this, unlikelihood training has been proposed to reduce the probability of unlikely tokens predicted by LMs. But unlikelihood does not consider the relationship between the label tokens and unlikely token candidates, thus showing marginal improvements in degeneration. We propose a new contrastive token learning objective that inherits the advantages of cross-entropy and unlikelihood training and avoids their limitations. The key idea is to teach a LM to generate high probabilities for label tokens and low probabilities of negative candidates. Comprehensive experiments on language modeling and open-domain dialogue generation tasks show that the proposed contrastive token objective yields much less repetitive texts, with a higher generation quality than baseline approaches, achieving the new state-of-the-art performance on text degeneration.

The representation degeneration problem is a phenomenon that is widely observed among self-supervised learning methods based on Transformers. In NLP, it takes the form of anisotropy, a singular property of hidden representations which makes them unexpectedly close to each other in terms of angular distance (cosine-similarity). Some recent works tend to show that anisotropy is a consequence of optimizing the cross-entropy loss on long-tailed distributions of tokens. We show in this paper that anisotropy can also be observed empirically in language models with specific objectives that should not suffer directly from the same consequences. We also show that the anisotropy problem extends to Transformers trained on other modalities. Our observations suggest that anisotropy is actually inherent to Transformers-based models.

Cross-entropy (CE) training provides dense and scalable supervision for language models, but it optimizes next-token prediction under teacher forcing rather than sequence-level behavior under model rollouts. We introduce a feature-matching objective for language-model fine-tuning that targets sequence-level statistics of the completion distribution, providing dense semantic feedback without requiring a task-specific verifier or preference model. To optimize this objective efficiently, we propose energy-based fine-tuning (EBFT), which uses strided block-parallel sampling to generate multiple rollouts from nested prefixes concurrently, batches feature extraction over these rollouts, and uses the resulting embeddings to perform an on-policy policy-gradient update. We present a theoretical perspective connecting EBFT to KL-regularized feature-matching and energy-based modeling. Empirically, across Q&A coding, unstructured coding, and translation, EBFT matches RLVR and outperforms SFT on downstream accuracy while achieving a lower validation cross-entropy than both methods.

The goal of face recognition (FR) can be viewed as a pair similarity optimization problem, maximizing a similarity set S^p over positive pairs, while minimizing similarity set S^n over negative pairs. Ideally, it is expected that FR models form a well-discriminative feature space (WDFS) that satisfies mathcal{S^p} > mathcal{S^n}. With regard to WDFS, the existing deep feature learning paradigms (i.e., metric and classification losses) can be expressed as a unified perspective on different pair generation (PG) strategies. Unfortunately, in the metric loss (ML), it is infeasible to generate negative pairs taking all classes into account in each iteration because of the limited mini-batch size. In contrast, in classification loss (CL), it is difficult to generate extremely hard negative pairs owing to the convergence of the class weight vectors to their center. This leads to a mismatch between the two similarity distributions of the sampled pairs and all negative pairs. Thus, this paper proposes a unified negative pair generation (UNPG) by combining two PG strategies (i.e., MLPG and CLPG) from a unified perspective to alleviate the mismatch. UNPG introduces useful information about negative pairs using MLPG to overcome the CLPG deficiency. Moreover, it includes filtering the similarities of noisy negative pairs to guarantee reliable convergence and improved performance. Exhaustive experiments show the superiority of UNPG by achieving state-of-the-art performance across recent loss functions on public benchmark datasets. Our code and pretrained models are publicly available.

We propose a new regularization method based on virtual adversarial loss: a new measure of local smoothness of the conditional label distribution given input. Virtual adversarial loss is defined as the robustness of the conditional label distribution around each input data point against local perturbation. Unlike adversarial training, our method defines the adversarial direction without label information and is hence applicable to semi-supervised learning. Because the directions in which we smooth the model are only "virtually" adversarial, we call our method virtual adversarial training (VAT). The computational cost of VAT is relatively low. For neural networks, the approximated gradient of virtual adversarial loss can be computed with no more than two pairs of forward- and back-propagations. In our experiments, we applied VAT to supervised and semi-supervised learning tasks on multiple benchmark datasets. With a simple enhancement of the algorithm based on the entropy minimization principle, our VAT achieves state-of-the-art performance for semi-supervised learning tasks on SVHN and CIFAR-10.

In this research, I explore advanced deep learning methodologies to forecast the outcomes of the 2025 NCAA Division 1 Men's and Women's Basketball tournaments. Leveraging historical NCAA game data, I implement two sophisticated sequence-based models: Long Short-Term Memory (LSTM) and Transformer architectures. The predictive power of these models is augmented through comprehensive feature engineering, including team quality metrics derived from Generalized Linear Models (GLM), Elo ratings, seed differences, and aggregated box-score statistics. To evaluate the robustness and reliability of predictions, I train each model variant using both Binary Cross-Entropy (BCE) and Brier loss functions, providing insights into classification performance and probability calibration. My comparative analysis reveals that while the Transformer architecture optimized with BCE yields superior discriminative power (highest AUC of 0.8473), the LSTM model trained with Brier loss demonstrates superior probabilistic calibration (lowest Brier score of 0.1589). These findings underscore the importance of selecting appropriate model architectures and loss functions based on the specific requirements of forecasting tasks. The detailed analytical pipeline presented here serves as a reproducible framework for future predictive modeling tasks in sports analytics and beyond.

Convolutional neural network training can suffer from diverse issues like exploding or vanishing gradients, scaling-based weight space symmetry and covariant-shift. In order to address these issues, researchers develop weight regularization methods and activation normalization methods. In this work we propose a weight soft-regularization method based on the Oblique manifold. The proposed method uses a loss function which pushes each weight vector to have a norm close to one, i.e. the weight matrix is smoothly steered toward the so-called Oblique manifold. We evaluate our method on the very popular CIFAR-10, CIFAR-100 and ImageNet 2012 datasets using two state-of-the-art architectures, namely the ResNet and wide-ResNet. Our method introduces negligible computational overhead and the results show that it is competitive to the state-of-the-art and in some cases superior to it. Additionally, the results are less sensitive to hyperparameter settings such as batch size and regularization factor.

In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great impact on the performance of a model such as the convergence speed, the generalization performance metrics, etc. While in some cases the hyperparameters of a learning algorithm can be part of learning parameters, in other scenarios the hyperparameters of a stochastic optimization algorithm such as Adam [5] and its variants are either fixed as a constant or are kept changing in a monotonic way over time. We give an in-depth analysis of the presented method in the framework of expectation maximization (EM). The presented algorithm of cross-entropy optimization for hyperparameter optimization of a learning algorithm (CEHPO) can be equally applicable to other areas of optimization problems in deep learning. We hope that the presented methods can provide different perspectives and offer some insights for optimization problems in different areas of machine learning and beyond.

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size of problems we are able to tackle with current hardware. Second, it remains unclear how close it matches the task loss such as the top-k error rate or other non-differentiable evaluation metrics which we aim to optimize ultimately. In this paper, we introduce an alternative classification loss function, the Z-loss, which is designed to address these two issues. Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with a complexity independent of the number of output classes. We show experimentally that it significantly outperforms the other spherical loss functions previously investigated. Furthermore, we show on a word language modeling task that it also outperforms the log-softmax with respect to certain ranking scores, such as top-k scores, suggesting that the Z-loss has the flexibility to better match the task loss. These qualities thus makes the Z-loss an appealing candidate to train very efficiently large output networks such as word-language models or other extreme classification problems. On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

As the scale of training corpora for large language models (LLMs) grows, model developers become increasingly reluctant to disclose details on their data. This lack of transparency poses challenges to scientific evaluation and ethical deployment. Recently, pretraining data detection approaches, which infer whether a given text was part of an LLM's training data through black-box access, have been explored. The Min-K\% Prob method, which has achieved state-of-the-art results, assumes that a non-training example tends to contain a few outlier words with low token probabilities. However, the effectiveness may be limited as it tends to misclassify non-training texts that contain many common words with high probabilities predicted by LLMs. To address this issue, we introduce a divergence-based calibration method, inspired by the divergence-from-randomness concept, to calibrate token probabilities for pretraining data detection. We compute the cross-entropy (i.e., the divergence) between the token probability distribution and the token frequency distribution to derive a detection score. We have developed a Chinese-language benchmark, PatentMIA, to assess the performance of detection approaches for LLMs on Chinese text. Experimental results on English-language benchmarks and PatentMIA demonstrate that our proposed method significantly outperforms existing methods. Our code and PatentMIA benchmark are available at https://github.com/zhang-wei-chao/DC-PDD.

Neural text generation models are typically trained by maximizing log-likelihood with the sequence cross entropy (CE) loss, which encourages an exact token-by-token match between a target sequence with a generated sequence. Such training objective is sub-optimal when the target sequence is not perfect, e.g., when the target sequence is corrupted with noises, or when only weak sequence supervision is available. To address the challenge, we propose a novel Edit-Invariant Sequence Loss (EISL), which computes the matching loss of a target n-gram with all n-grams in the generated sequence. EISL is designed to be robust to various noises and edits in the target sequences. Moreover, the EISL computation is essentially an approximate convolution operation with target n-grams as kernels, which is easy to implement and efficient to compute with existing libraries. To demonstrate the effectiveness of EISL, we conduct experiments on a wide range of tasks, including machine translation with noisy target sequences, unsupervised text style transfer with only weak training signals, and non-autoregressive generation with non-predefined generation order. Experimental results show our method significantly outperforms the common CE loss and other strong baselines on all the tasks. EISL has a simple API that can be used as a drop-in replacement of the CE loss: https://github.com/guangyliu/EISL.

With the advent of LLMs, various tasks across the natural language processing domain have been transformed. However, their application in predictive tasks remains less researched. This study compares large language models, including GatorTron-Base (trained on clinical data), Llama 8B, and Mistral 7B, against models like BioBERT, DocBERT, BioClinicalBERT, Word2Vec, and Doc2Vec, setting benchmarks for predicting Shock in critically ill patients. Timely prediction of shock can enable early interventions, thus improving patient outcomes. Text data from 17,294 ICU stays of patients in the MIMIC III database were scored for length of stay > 24 hours and shock index (SI) > 0.7 to yield 355 and 87 patients with normal and abnormal SI-index, respectively. Both focal and cross-entropy losses were used during finetuning to address class imbalances. Our findings indicate that while GatorTron Base achieved the highest weighted recall of 80.5%, the overall performance metrics were comparable between SLMs and LLMs. This suggests that LLMs are not inherently superior to SLMs in predicting future clinical events despite their strong performance on text-based tasks. To achieve meaningful clinical outcomes, future efforts in training LLMs should prioritize developing models capable of predicting clinical trajectories rather than focusing on simpler tasks such as named entity recognition or phenotyping.

By reinterpreting a robust discriminative classifier as Energy-based Model (EBM), we offer a new take on the dynamics of adversarial training (AT). Our analysis of the energy landscape during AT reveals that untargeted attacks generate adversarial images much more in-distribution (lower energy) than the original data from the point of view of the model. Conversely, we observe the opposite for targeted attacks. On the ground of our thorough analysis, we present new theoretical and practical results that show how interpreting AT energy dynamics unlocks a better understanding: (1) AT dynamic is governed by three phases and robust overfitting occurs in the third phase with a drastic divergence between natural and adversarial energies (2) by rewriting the loss of TRadeoff-inspired Adversarial DEfense via Surrogate-loss minimization (TRADES) in terms of energies, we show that TRADES implicitly alleviates overfitting by means of aligning the natural energy with the adversarial one (3) we empirically show that all recent state-of-the-art robust classifiers are smoothing the energy landscape and we reconcile a variety of studies about understanding AT and weighting the loss function under the umbrella of EBMs. Motivated by rigorous evidence, we propose Weighted Energy Adversarial Training (WEAT), a novel sample weighting scheme that yields robust accuracy matching the state-of-the-art on multiple benchmarks such as CIFAR-10 and SVHN and going beyond in CIFAR-100 and Tiny-ImageNet. We further show that robust classifiers vary in the intensity and quality of their generative capabilities, and offer a simple method to push this capability, reaching a remarkable Inception Score (IS) and FID using a robust classifier without training for generative modeling. The code to reproduce our results is available at http://github.com/OmnAI-Lab/Robust-Classifiers-under-the-lens-of-EBM/ .

Most recent test-time adaptation methods focus on only classification tasks, use specialized network architectures, destroy model calibration or rely on lightweight information from the source domain. To tackle these issues, this paper proposes a novel Test-time Self-Learning method with automatic Adversarial augmentation dubbed TeSLA for adapting a pre-trained source model to the unlabeled streaming test data. In contrast to conventional self-learning methods based on cross-entropy, we introduce a new test-time loss function through an implicitly tight connection with the mutual information and online knowledge distillation. Furthermore, we propose a learnable efficient adversarial augmentation module that further enhances online knowledge distillation by simulating high entropy augmented images. Our method achieves state-of-the-art classification and segmentation results on several benchmarks and types of domain shifts, particularly on challenging measurement shifts of medical images. TeSLA also benefits from several desirable properties compared to competing methods in terms of calibration, uncertainty metrics, insensitivity to model architectures, and source training strategies, all supported by extensive ablations. Our code and models are available on GitHub.

A range of recent works addresses the problem of compression of sequence of tokens into a shorter sequence of real-valued vectors to be used as inputs instead of token embeddings or key-value cache. These approaches allow to reduce the amount of compute in existing language models. Despite relying on powerful models as encoders, the maximum attainable lossless compression ratio is typically not higher than x10. This fact is highly intriguing because, in theory, the maximum information capacity of large real-valued vectors is far beyond the presented rates even for 16-bit precision and a modest vector size. In this work, we explore the limits of compression by replacing the encoder with a per-sample optimization procedure. We show that vectors with compression ratios up to x1500 exist, which highlights two orders of magnitude gap between existing and practically attainable solutions. Furthermore, we empirically show that the compression limits are determined not by the length of the input but by the amount of uncertainty to be reduced, namely, the cross-entropy loss on this sequence without any conditioning. The obtained limits highlight the substantial gap between the theoretical capacity of input embeddings and their practical utilization, suggesting significant room for optimization in model design.

Language models (LMs) are often used as zero-shot or few-shot classifiers by scoring label words, but they remain fragile to adversarial prompts. Prior work typically optimizes task- or model-specific triggers, making results difficult to compare and limiting transferability. We study universal adversarial suffixes: short token sequences (4-10 tokens) that, when appended to any input, broadly reduce accuracy across tasks and models. Our approach learns the suffix in a differentiable "soft" form using Gumbel-Softmax relaxation and then discretizes it for inference. Training maximizes calibrated cross-entropy on the label region while masking gold tokens to prevent trivial leakage, with entropy regularization to avoid collapse. A single suffix trained on one model transfers effectively to others, consistently lowering both accuracy and calibrated confidence. Experiments on sentiment analysis, natural language inference, paraphrase detection, commonsense QA, and physical reasoning with Qwen2-1.5B, Phi-1.5, and TinyLlama-1.1B demonstrate consistent attack effectiveness and transfer across tasks and model families.

In federated learning (FL), weighted aggregation of local models is conducted to generate a global model, and the aggregation weights are normalized (the sum of weights is 1) and proportional to the local data sizes. In this paper, we revisit the weighted aggregation process and gain new insights into the training dynamics of FL. First, we find that the sum of weights can be smaller than 1, causing global weight shrinking effect (analogous to weight decay) and improving generalization. We explore how the optimal shrinking factor is affected by clients' data heterogeneity and local epochs. Second, we dive into the relative aggregation weights among clients to depict the clients' importance. We develop client coherence to study the learning dynamics and find a critical point that exists. Before entering the critical point, more coherent clients play more essential roles in generalization. Based on the above insights, we propose an effective method for Federated Learning with Learnable Aggregation Weights, named as FedLAW. Extensive experiments verify that our method can improve the generalization of the global model by a large margin on different datasets and models.

Pretraining large language models (LLMs) on vast and heterogeneous datasets is crucial for achieving state-of-the-art performance across diverse downstream tasks. However, current training paradigms treat all samples equally, overlooking the importance or relevance of individual samples throughout the training process. Existing reweighting strategies, which primarily focus on group-level data importance, fail to leverage fine-grained instance-level information and do not adapt dynamically to individual sample importance as training progresses. In this paper, we introduce novel algorithms for dynamic, instance-level data reweighting aimed at improving both the efficiency and effectiveness of LLM pretraining. Our methods adjust the weight of each training sample based on its loss value in an online fashion, allowing the model to dynamically focus on more informative or important samples at the current training stage. In particular, our framework allows us to systematically devise reweighting strategies deprioritizing redundant or uninformative data, which we find tend to work best. Furthermore, we develop a new theoretical framework for analyzing the impact of loss-based reweighting on the convergence of gradient-based optimization, providing the first formal characterization of how these strategies affect convergence bounds. We empirically validate our approach across a spectrum of tasks, from pretraining 7B and 1.4B parameter LLMs to smaller-scale language models and linear regression problems, demonstrating that our loss-based reweighting approach can lead to faster convergence and significantly improved performance.

In this paper we introduce the SCoRe (Submodular Combinatorial Representation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the Total Information and Total Correlation, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6\% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.

Collaborative filtering (CF) is a widely studied research topic in recommender systems. The learning of a CF model generally depends on three major components, namely interaction encoder, loss function, and negative sampling. While many existing studies focus on the design of more powerful interaction encoders, the impacts of loss functions and negative sampling ratios have not yet been well explored. In this work, we show that the choice of loss function as well as negative sampling ratio is equivalently important. More specifically, we propose the cosine contrastive loss (CCL) and further incorporate it to a simple unified CF model, dubbed SimpleX. Extensive experiments have been conducted on 11 benchmark datasets and compared with 29 existing CF models in total. Surprisingly, the results show that, under our CCL loss and a large negative sampling ratio, SimpleX can surpass most sophisticated state-of-the-art models by a large margin (e.g., max 48.5% improvement in NDCG@20 over LightGCN). We believe that SimpleX could not only serve as a simple strong baseline to foster future research on CF, but also shed light on the potential research direction towards improving loss function and negative sampling. Our source code will be available at https://reczoo.github.io/SimpleX.

Natural Language Generation (NLG) models are prone to generating repetitive utterances. In this work, we study the repetition problem for encoder-decoder models, using both recurrent neural network (RNN) and transformer architectures. To this end, we consider the chit-chat task, where the problem is more prominent than in other tasks that need encoder-decoder architectures. We first study the influence of model architectures. By using pre-attention and highway connections for RNNs, we manage to achieve lower repetition rates. However, this method does not generalize to other models such as transformers. We hypothesize that the deeper reason is that in the training corpora, there are hard tokens that are more difficult for a generative model to learn than others and, once learning has finished, hard tokens are still under-learned, so that repetitive generations are more likely to happen. Based on this hypothesis, we propose token loss dynamic reweighting (TLDR) that applies differentiable weights to individual token losses. By using higher weights for hard tokens and lower weights for easy tokens, NLG models are able to learn individual tokens at different paces. Experiments on chit-chat benchmark datasets show that TLDR is more effective in repetition reduction for both RNN and transformer architectures than baselines using different weighting functions.

Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its practical efficacy: the implicit regularization it instigates. Several studies have investigated the linear stability property of SGD in the vicinity of a stationary point as a predictive proxy for sharpness and generalization error in overparameterized neural networks (Wu et al., 2022; Jastrzebski et al., 2019; Cohen et al., 2021). In this paper, we delve deeper into the relationship between linear stability and sharpness. More specifically, we meticulously delineate the necessary and sufficient conditions for linear stability, contingent on hyperparameters of SGD and the sharpness at the optimum. Towards this end, we introduce a novel coherence measure of the loss Hessian that encapsulates pertinent geometric properties of the loss function that are relevant to the linear stability of SGD. It enables us to provide a simplified sufficient condition for identifying linear instability at an optimum. Notably, compared to previous works, our analysis relies on significantly milder assumptions and is applicable for a broader class of loss functions than known before, encompassing not only mean-squared error but also cross-entropy loss.

Neural language models are probabilistic models of human text. They are predominantly trained using maximum likelihood estimation (MLE), which is equivalent to minimizing the forward cross-entropy between the empirical data distribution and the model distribution. However, various degeneration phenomena are still widely observed when decoding from the distributions learned by such models. We establish that the forward cross-entropy is suboptimal as a distance metric for aligning human and model distribution due to its (1) recall-prioritization (2) negative diversity ignorance and (3) train-test mismatch. In this paper, we propose Earth Mover Distance Optimization (EMO) for auto-regressive language modeling. EMO capitalizes on the inherent properties of earth mover distance to address the aforementioned challenges. Due to the high complexity of direct computation, we further introduce a feasible upper bound for EMO to ease end-to-end training. Upon extensive evaluation of language models trained using EMO and MLE. We find that EMO demonstrates a consistently better language modeling performance than MLE across domains. Moreover, EMO demonstrates noteworthy enhancements in downstream performance with minimal fine-tuning on merely 25,000 sentences. This highlights the tremendous potential of EMO as a lightweight calibration method for enhancing large-scale pre-trained language models.

Dual-encoder (DE) models are widely used in retrieval tasks, most commonly studied on open QA benchmarks that are often characterized by multi-class and limited training data. In contrast, their performance in multi-label and data-rich retrieval settings like extreme multi-label classification (XMC), remains under-explored. Current empirical evidence indicates that DE models fall significantly short on XMC benchmarks, where SOTA methods linearly scale the number of learnable parameters with the total number of classes (documents in the corpus) by employing per-class classification head. To this end, we first study and highlight that existing multi-label contrastive training losses are not appropriate for training DE models on XMC tasks. We propose decoupled softmax loss - a simple modification to the InfoNCE loss - that overcomes the limitations of existing contrastive losses. We further extend our loss design to a soft top-k operator-based loss which is tailored to optimize top-k prediction performance. When trained with our proposed loss functions, standard DE models alone can match or outperform SOTA methods by up to 2% at Precision@1 even on the largest XMC datasets while being 20x smaller in terms of the number of trainable parameters. This leads to more parameter-efficient and universally applicable solutions for retrieval tasks. Our code and models are publicly available at https://github.com/nilesh2797/dexml.

Knowledge distillation compresses large teachers into smaller students, but performance saturates at a loss floor that persists across training methods and objectives. We argue this floor is geometric: neural networks represent far more features than dimensions through superposition, and a student of width d_S can encode at most d_S cdot g(α) features, where g(α) = 1/((1-α)ln1{1-α}) is a sparsity-dependent capacity function. Features beyond this budget are permanently lost, yielding an importance-weighted loss floor. We validate on a toy model (48 configurations, median accuracy >93%) and on Pythia-410M, where sparse autoencoders measure F approx 28{,}700 features at αapprox 0.992 (critical width d_S^* approx 1{,}065). Distillation into five student widths confirms the predicted monotonic floor ordering. The observed floor decomposes into a geometric component and a width-independent architectural baseline (R^2 = 0.993). Linear probing shows coarse concepts survive even 88% feature loss, revealing the floor arises from aggregate loss of fine-grained features in the importance distribution's long tail. Our results connect representation geometry to distillation limits and provide a practical tool for predicting distillation performance from SAE measurements alone.

Efficient k-nearest neighbor search is a fundamental task, foundational for many problems in NLP. When the similarity is measured by dot-product between dual-encoder vectors or ell_2-distance, there already exist many scalable and efficient search methods. But not so when similarity is measured by more accurate and expensive black-box neural similarity models, such as cross-encoders, which jointly encode the query and candidate neighbor. The cross-encoders' high computational cost typically limits their use to reranking candidates retrieved by a cheaper model, such as dual encoder or TF-IDF. However, the accuracy of such a two-stage approach is upper-bounded by the recall of the initial candidate set, and potentially requires additional training to align the auxiliary retrieval model with the cross-encoder model. In this paper, we present an approach that avoids the use of a dual-encoder for retrieval, relying solely on the cross-encoder. Retrieval is made efficient with CUR decomposition, a matrix decomposition approach that approximates all pairwise cross-encoder distances from a small subset of rows and columns of the distance matrix. Indexing items using our approach is computationally cheaper than training an auxiliary dual-encoder model through distillation. Empirically, for k > 10, our approach provides test-time recall-vs-computational cost trade-offs superior to the current widely-used methods that re-rank items retrieved using a dual-encoder or TF-IDF.

Few-shot learning is a challenging area of research that aims to learn new concepts with only a few labeled samples of data. Recent works based on metric-learning approaches leverage the meta-learning approach, which is encompassed by episodic tasks that make use a support (training) and query set (test) with the objective of learning a similarity comparison metric between those sets. Due to the lack of data, the learning process of the embedding network becomes an important part of the few-shot task. Previous works have addressed this problem using metric learning approaches, but the properties of the underlying latent space and the separability of the difference classes on it was not entirely enforced. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking at the intra-class and inter-class distance between the few data. The first loss function is the Proto-Triplet Loss, which is based on the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss function, which we dub ICNN loss is based on an inter and intra class nearest neighbors score, which help us to assess the quality of embeddings obtained from the trained network. Our results, obtained from a extensive experimental setup show a significant improvement in accuracy in the miniImagenNet benchmark compared to other metric-based few-shot learning methods by a margin of 2%, demonstrating the capability of these loss functions to allow the network to generalize better to previously unseen classes. In our experiments, we demonstrate competitive generalization capabilities to other domains, such as the Caltech CUB, Dogs and Cars datasets compared with the state of the art.

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in maximizing accuracy, thereby offering a wide range of options for surrogate losses. In this article, we propose a novel ensemble method, namely EnsLoss, which extends the ensemble learning concept to combine loss functions within the ERM framework. A key feature of our method is the consideration on preserving the "legitimacy" of the combined losses, i.e., ensuring the CC properties. Specifically, we first transform the CC conditions of losses into loss-derivatives, thereby bypassing the need for explicit loss functions and directly generating calibrated loss-derivatives. Therefore, inspired by Dropout, EnsLoss enables loss ensembles through one training process with doubly stochastic gradient descent (i.e., random batch samples and random calibrated loss-derivatives). We theoretically establish the statistical consistency of our approach and provide insights into its benefits. The numerical effectiveness of EnsLoss compared to fixed loss methods is demonstrated through experiments on a broad range of 14 OpenML tabular datasets and 46 image datasets with various deep learning architectures. Python repository and source code are available on GitHub at https://github.com/statmlben/ensloss.

Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped close to each other and dissimilar examples are mapped farther apart, have been proposed to construct effective structures for loss functions and have shown promising results. In this paper, different from the approaches on learning the loss structures, we propose a robust SNR distance metric based on Signal-to-Noise Ratio (SNR) for measuring the similarity of image pairs for deep metric learning. By exploring the properties of our SNR distance metric from the view of geometry space and statistical theory, we analyze the properties of our metric and show that it can preserve the semantic similarity between image pairs, which well justify its suitability for deep metric learning. Compared with Euclidean distance metric, our SNR distance metric can further jointly reduce the intra-class distances and enlarge the inter-class distances for learned features. Leveraging our SNR distance metric, we propose Deep SNR-based Metric Learning (DSML) to generate discriminative feature embeddings. By extensive experiments on three widely adopted benchmarks, including CARS196, CUB200-2011 and CIFAR10, our DSML has shown its superiority over other state-of-the-art methods. Additionally, we extend our SNR distance metric to deep hashing learning, and conduct experiments on two benchmarks, including CIFAR10 and NUS-WIDE, to demonstrate the effectiveness and generality of our SNR distance metric.

In this work, we propose to study the performance of a model trained with a sentence embedding regression loss component for the Automated Audio Captioning task. This task aims to build systems that can describe audio content with a single sentence written in natural language. Most systems are trained with the standard Cross-Entropy loss, which does not take into account the semantic closeness of the sentence. We found that adding a sentence embedding loss term reduces overfitting, but also increased SPIDEr from 0.397 to 0.418 in our first setting on the AudioCaps corpus. When we increased the weight decay value, we found our model to be much closer to the current state-of-the-art methods, with a SPIDEr score up to 0.444 compared to a 0.475 score. Moreover, this model uses eight times less trainable parameters. In this training setting, the sentence embedding loss has no more impact on the model performance.

Cross-encoders distilled from large language models (LLMs) are often more effective re-rankers than cross-encoders fine-tuned on manually labeled data. However, distilled models do not match the effectiveness of their teacher LLMs. We hypothesize that this effectiveness gap is due to the fact that previous work has not applied the best-suited methods for fine-tuning cross-encoders on manually labeled data (e.g., hard-negative sampling, deep sampling, and listwise loss functions). To close this gap, we create a new dataset, Rank-DistiLLM. Cross-encoders trained on Rank-DistiLLM achieve the effectiveness of LLMs while being up to 173 times faster and 24 times more memory efficient. Our code and data is available at https://github.com/webis-de/ECIR-25.

Large language models memorize sensitive data from their pretraining corpora. In this work, we propose CE-U (Cross Entropy Unlearning), a loss function for unlearning. CE-U addresses fundamental limitations of gradient ascent approaches that suffer from vanishing gradients when model confidence is high and exploding gradients when confidence is low. We also unify standard cross entropy learning and unlearning into a single framework. On the TOFU benchmark for unlearning, CE-U achieves state-of-the-art results on LLaMA2-7B models without using an extra oracle model or additional positive samples. Our analysis reveals that the problematic gradient ascent component also exists in reinforcement learning algorithms like DPO and GRPO. This suggests that applying CE-U approach to reinforcement learning could be promising to improve stability and convergence.

Gradient inversion attacks can leak data privacy when clients share weight updates with the server in federated learning (FL). Existing studies mainly use L2 or cosine distance as the loss function for gradient matching in the attack. Our empirical investigation shows that the vulnerability ranking varies with the loss function used. Gradient norm, which is commonly used as a vulnerability proxy for gradient inversion attack, cannot explain this as it remains constant regardless of the loss function for gradient matching. In this paper, we propose a loss-aware vulnerability proxy (LAVP) for the first time. LAVP refers to either the maximum or minimum eigenvalue of the Hessian with respect to gradient matching loss at ground truth. This suggestion is based on our theoretical findings regarding the local optimization of the gradient inversion in proximity to the ground truth, which corresponds to the worst case attack scenario. We demonstrate the effectiveness of LAVP on various architectures and datasets, showing its consistent superiority over the gradient norm in capturing sample vulnerabilities. The performance of each proxy is measured in terms of Spearman's rank correlation with respect to several similarity scores. This work will contribute to enhancing FL security against any potential loss functions beyond L2 or cosine distance in the future.

Video super-resolution aims to enhance low-resolution videos by leveraging both spatial and temporal information. While deep learning has led to impressive progress, it typically requires centralized data, which raises privacy concerns. Federated learning offers a privacy-friendly solution, but general FL frameworks often struggle with low-level vision tasks, resulting in blurry, low-quality outputs. To address this, we introduce FedVSR, the first FL framework specifically designed for VSR. It is model-agnostic and stateless, and introduces a lightweight loss function based on the DWT to better preserve high-frequency details during local training. Additionally, a loss-aware aggregation strategy combines both DWT-based and task-specific losses to guide global updates effectively. Extensive experiments across multiple VSR models and datasets demonstrate that FedVSR consistently outperforms existing FL methods, achieving up to 0.82 dB higher PSNR, 0.0327 higher SSIM, and 0.0251 lower LPIPS. These results underscore FedVSR's ability to bridge the gap between privacy and performance, setting a new benchmark for federated learning in low-level vision tasks. The code is available at: https://github.com/alimd94/FedVSR

Increasing the size of a Transformer model does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, improved generalization ability occurs as the model memorizes the training samples. We present a theoretical framework that sheds light on the memorization process and performance dynamics of transformer-based language models. We model the behavior of Transformers with associative memories using Hopfield networks, such that each transformer block effectively conducts an approximate nearest-neighbor search. Based on this, we design an energy function analogous to that in the modern continuous Hopfield network which provides an insightful explanation for the attention mechanism. Using the majorization-minimization technique, we construct a global energy function that captures the layered architecture of the Transformer. Under specific conditions, we show that the minimum achievable cross-entropy loss is bounded from below by a constant approximately equal to 1. We substantiate our theoretical results by conducting experiments with GPT-2 on various data sizes, as well as training vanilla Transformers on a dataset of 2M tokens.

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.