caiovicentino1/Qwen3.5-4B-SAE-L18-topk

🔬 Qwen3.5-4B TopK SAE · Layer 18

The first public TopK residual-stream Sparse Autoencoder for Qwen3.5, with a labeled catalog of reasoning features and downstream RL-reward validation.

The nearest prior public SAE on the Qwen3.5 hybrid-GDN family is kroonen-ai/sae-qwen3.5-9b (ReLU SAE on layer-16 MLP output of Qwen3.5-9B, d_sae=16,384, ~50 M training tokens, March 2026). Ours is distinct on every axis relevant for downstream use: TopK vs ReLU, residual stream vs MLP output, 16× vs 4× expansion, 200 M vs 50 M training tokens, Qwen3.5-4B vs 9B, and the only one of the two with a validated feature-pack + RL-reward downstream pipeline (see Stage Gates below).

Trained on residual-stream activations at layer 18 of Qwen/Qwen3.5-4B using the TopK objective from Gao et al. (arxiv:2406.04093), and shipped with a ReasonScore feature catalog (arxiv:2503.18878) that identifies the directions in Qwen3.5's latent space that encode meta-cognitive reasoning.

---

🆚 Before vs. after this release

	Before	After (this SAE)
TopK residual-stream SAE for Qwen3.5	❌ None (kroonen-ai/sae-qwen3.5-9b, Mar 2026, is ReLU on layer-16 MLP — different hook + activation)	✅ 40,960 features, TopK k=128, residual stream layer 18
TransformerLens / sae_lens support	❌ No	✅ Bypassed with plain HF forward hooks
Reasoning features identified	❌ Unknown	✅ Top-25 labeled via ReasonScore
Feature catalog	❌ —	✅ reasoning_pack.json — per-word distributions + entropy
Causally validated features	❌ None	✅ #11424 verified via activation steering — see steering_validation.json
Reconstruction on out-of-distribution prompts	❌ Unmeasured	✅ var_exp 0.866 on code + reasoning prompts
Usage	❌ Custom training stack needed	✅ 3 lines with mechreward, or raw PyTorch

Qwen3.5 uses a hybrid Gated Delta Networks architecture that TransformerLens and sae_lens don't yet support. This release adds a TopK residual-stream SAE to the Qwen3.5 interpretability stack (kroonen-ai's prior ReLU SAE targets layer-16 MLP output on Qwen3.5-9B — a complementary rather than competing hook), and ships with the downstream pipeline — feature catalog, causal-steering validation, and per-token RL-reward demonstration — that lets it drop into GRPO fine-tuning without needing any custom hook infrastructure.

---

⚡ 30-second quickstart

pip install mechreward

import torch
from transformers import AutoModelForCausalLM, AutoTokenizer
from mechreward.sae.topk_sae import load_topk_sae

tok = AutoTokenizer.from_pretrained("Qwen/Qwen3.5-4B")
model = AutoModelForCausalLM.from_pretrained(
    "Qwen/Qwen3.5-4B", dtype=torch.bfloat16, device_map="cuda"
).eval()

sae = load_topk_sae(
    "caiovicentino1/Qwen3.5-4B-SAE-L18-topk",
    layer=18,
    model_name="Qwen/Qwen3.5-4B",
)

ids = tok("Wait, let me think about this more carefully.",
          return_tensors="pt").input_ids.cuda()
with torch.inference_mode():
    out = model(input_ids=ids, output_hidden_states=True,
                use_cache=False, return_dict=True)
h = out.hidden_states[19].float().squeeze(0)   # layer 18 residual

features = sae.encode(h)                         # [seq_len, 40960]
active = (features > 0).sum(-1).float().mean()
print(f"L0 = {active.item():.1f}/128")           # ≈ 128 — structural
print("Top feature per token:", features.argmax(-1).tolist())

That's it. No forward-hook gymnastics, no TransformerLens, no training stack. Use hidden_states[19] because the layer index in output_hidden_states is 1-based.

---

🧠 Feature catalog — 25 reasoning directions, pre-labeled

Identified by the ReasonScore metric (Gao et al., AIRI, arxiv:2503.18878):

ReasonScore_i = p(i | D_R^W) · H_i^α − p(i | D_nR^W)

Contrastive between a reasoning corpus (300 samples from open-thoughts/OpenThoughts-114k) and a baseline corpus (300 from HuggingFaceFW/fineweb-edu sample-10BT), restricted to ±(2,3) token windows around 10 meta-cognitive trigger words: alternatively, hmm, maybe, wait, perhaps, let me, therefore, however, but, another. The entropy factor H_i^α=0.7 rewards features that fire across multiple trigger words, filtering out polysemantic or word-specific features.

Top-10 reasoning features (full top-25 with per-word breakdowns in reasoning_pack.json):

Rank	Feature	Score	Entropy (H)	Fires strongest on
1	#11424	0.0171	2.19	however / therefore / another / but
2	#22188	0.0147	1.90	let me / perhaps / maybe / wait
3	#13281	0.0131	2.13	perhaps / maybe / therefore / however
4	#33609	0.0095	2.00	however / let me / therefore / hmm
5	#23501	0.0094	1.91	however / another / therefore / hmm
6	#9639	0.0093	1.82	(see reasoning_pack.json)
7	#16924	0.0077	1.66	(see reasoning_pack.json)
8	#2015	0.0076	1.71	(see reasoning_pack.json)
9	#8097	0.0073	1.70	(see reasoning_pack.json)
10	#39743	0.0067	1.67	(see reasoning_pack.json)

Max possible entropy is log(10) ≈ 2.30 — the top features hit ≥ 2.0, confirming they fire across the full reasoning vocabulary rather than latching onto a single word.

Feature health: 24,956 / 40,960 features are alive (60.9%), 15,154 fire on ≥2 reasoning words (H > 0.1), 7,259 on ≥3 (H > 1.0). Plenty of signal left to explore beyond the top-25.

Use the catalog

import json
from huggingface_hub import hf_hub_download

pack = json.load(open(hf_hub_download(
    "caiovicentino1/Qwen3.5-4B-SAE-L18-topk", "reasoning_pack.json")))

for f in pack["top_25_features"][:5]:
    top_word = max(f["per_word_distribution"].items(), key=lambda kv: kv[1])
    print(f"#{f['feature_id']:>5}  score={f['reason_score']:.4f}  "
          f"H={f['entropy']:.2f}  top={top_word[0]} ({top_word[1]:.2f})")

---

🎯 Causal validation (feature #11424)

Top-25 ReasonScore gives you correlational evidence that a feature tracks reasoning. To get causal evidence, we intervene on the feature during generation via activation steering:

hidden_steered = hidden + (sae_decode(feats_modified) - sae_decode(feats))

This is a delta injection — we preserve the SAE reconstruction error and only perturb the direction corresponding to one feature. Scale = 1.0 gives zero delta (exact baseline); scale = 0.0 ablates the feature; scale = 10.0 amplifies it 10×.

Hook diagnostic — delta norms scale linearly

Phase	Scale 0.0 (ablate)	Scale 1.0 (baseline)	Scale 3.0	Scale 10.0
Prefill (prompt pass)	0.333	0.000	0.665	2.994
Decode (per new token)	0.045	0.000	0.083	0.428

Baseline is exactly zero (correct — scale = 1.0 cancels). Perturbation grows monotonically with amplification, confirming the steering hook works.

Text divergence vs baseline (greedy decoding, 3 prompts × 4 scales)

Prompt	Ablate	Amp × 3	Amp × 10
"Let me analyze the tradeoffs between speed and accuracy…"	16.7 %	0 %	8.0 %
"Critics argue that AI regulation slows innovation."	15.6 %	0 %	0 %
"The experiment produced mixed results. On one hand, accuracy improved."	23.2 %	0 %	0 %

Ablation produces 15–23 % text divergence on 3 / 3 prompts — removing #11424 reliably changes generation. Amplification is non-monotonic under greedy decoding: perturbations below the argmax margin don't flip tokens, so only × 10 crosses the boundary (and only on one prompt).

The smoking gun — semantic diff on prompt 1

On "Let me analyze the tradeoffs…", the character-level divergence looks small but the semantic change is unambiguous:

Intervention	Continuation snippet
Ablate (× 0)	"The key insight is… We can use a hash set to store elements…"
Amp × 10	"The key insight is… Instead of checking all pairs, we can use a hash set…"

Amplification injects the contrastive construction "Instead of X, Y" — exactly the kind of alternative-enumeration scaffold that the ReasonScore profile predicted (however / therefore / another / but). Ablation suppresses it. The feature's label is:

#11424 — alternative enumeration / contrastive structure

Full 3-prompt × 4-scale traces + delta-norm diagnostics are in steering_validation.json.

Try it yourself

target = model.get_submodule("model.language_model.layers.18")
current_scale = {"v": 1.0}

def steering_hook(module, inputs, output):
    hidden, rest = (output[0], output[1:]) if isinstance(output, tuple) else (output, None)
    flat = hidden.float().view(-1, hidden.shape[-1])
    feats = sae.encode(flat)
    feats_mod = feats.clone()
    feats_mod[:, 11424] = feats[:, 11424] * current_scale["v"]
    delta = sae.decode(feats_mod) - sae.decode(feats)
    new = (flat + delta).view_as(hidden).to(hidden.dtype)
    return (new, *rest) if rest is not None else new

handle = target.register_forward_hook(steering_hook)
for scale in [1.0, 0.0, 10.0]:
    current_scale["v"] = scale
    # model.generate(...) as usual — output changes with scale
handle.remove()

---

🧪 GSM8K reasoning experiments (honest findings)

We ran a series of interventional experiments on GSM8K (openai/gsm8k:main:test, 50 questions, Qwen3.5-4B chat-template CoT, greedy decoding) to test whether the SAE features could boost math accuracy beyond the 88 % baseline. Results are mixed and instructive — the mechanism is causally real but the net aggregate lift is sample-size-dominated at n = 50.

Experiment summary

Experiment	Features tested	Method	Net accuracy Δ	Mechanism confirmed?
ReasonScore top-5 amp	5 features by ReasonScore rank	Feature amp × 3	−8.0 pp (bundle)	❌ ReasonScore features are reasoning rhetoric, not computation
Contrastive discovery	Top-5 features by mean(correct) − mean(wrong) on 50 baseline responses	Bundle amp × 5–8 + suppress × −1 to −2	−6.0 pp to −8.0 pp	✅ Recovered 3–4 of 6 baseline failures, collateral damage on 5–6 others
CAA (no SAE) at L13	Single direction = mean(h_correct) − mean(h_wrong) at layer 13	Raw steering vector, scale +0.3	0 pp (net), +2 recovered / −2 lost	✅ Same recoverable questions as SAE bundle, lower collateral

Key findings

1. ReasonScore features do not boost GSM8K. The top-25 ReasonScore features (in reasoning_pack.json) encode discourse/hedging markers (however, let me, wait, another). They are causally validated for text-level structure (see the causal validation section above) but not for arithmetic reasoning. Amplifying them during GSM8K generation neither helps nor hurts individual questions meaningfully; a bundle of 5 at amp × 3 costs −8 pp.

2. Contrastive feature discovery finds the right features. Running mean(activations | correct) − mean(activations | wrong) on 50 baseline GSM8K responses surfaces an entirely different set of features than ReasonScore:

# Top-5 helpful (robust — high absolute mean + ratio):
[35842, 6998, 39695, 15360, 8773]
# Top-5 harmful:
[30967, 14912, 33246, 23272, 18654]

These features recover 4 of the 6 baseline failures (indices 5, 13, 14, 39 out of the full wrong set [5, 8, 12, 13, 14, 39]) when amplified/suppressed through the SAE. All 5 ReasonScore top-5 features appear as effect = neutral in this ranking (|Cohen's d| < 1, while the contrastive top-5 have |d| > 1.8). ReasonScore and GSM8K correctness select for almost disjoint feature populations.

3. Layer-wise contrastive mapping puts the peak at L13, not L18.

Multi-layer effect-size analysis (top-10 directions per layer) of mean residual activations across all 32 decoder layers of Qwen3.5-4B:

effect peak @ L13 (top-10 |d| = 1.391)
effect @ L18 (our SAE layer) = 1.289

L13 sits exactly at the transition where the logit lens first shows commitment tokens (Step, ####, <think>) in Qwen3.5-4B. L18 is ~7 % past the peak, in the post-commitment consolidation zone. This layer is not "wrong" — it still carries recoverable causal signal — but future SAE training for math-reasoning work should target L13–L15 on Qwen3.5-4B.

4. CAA at L13 matches SAE bundle without training new SAEs.

We built a single steering_vec = mean(h_13 | correct) − mean(h_13 | wrong) (norm 0.612 at L13) and applied hidden += scale · steering_vec during generation:

Scale	Accuracy	Δ	Gained / Lost
baseline	88.0 %	—	—
+0.3	88.0 %	0 pp	+2 (q5, q14) / −2 (q20, q43)
+0.5	84.0 %	−4 pp	+2 (q5, q39) / −4
+1.0	86.0 %	−2 pp	+1 (q5) / −2
−0.5 (negative control)	80.0 %	−8 pp	confirms direction is causal

The mechanism is real — positive scales recover the same baseline failures that the SAE bundle recovers, and the negative scale confirms directional causality by consistently hurting performance. The net aggregate is null at n = 50 because gains and losses cancel. At amp × 5 and above, the steering vector pushes the residual off-manifold and destroys generation entirely.

Honest limitations

• n = 50 is too small. With 88 % baseline (6 wrong), one flipped question is 2 pp of noise. We saw +13 pp at step 15 for CAA +0.3 and watched it regress to 0 pp at step 50 — that's textbook regression-to-mean. The cleanest next step is to run n = 200+ to quantify whether any scale sustains > 2 pp at statistical significance.
• Collateral damage is structural. Every intervention method we tried (ReasonScore, SAE contrastive, raw CAA) broke 2–6 questions that the baseline got right. This is the central unsolved problem — uniform magnitude steering perturbs all generations, not just the ones that needed it.
• The 4 recoverable questions are heterogeneous. Question 5 is recovered by almost every method; question 39 is recovered only by +0.5 CAA; question 13 only by SAE bundle strong amp. Different interventions find different sub-mechanisms.

Update (2026-04-16): CAA n = 100 + 55 % recovery rate

We extended the CAA scan to n = 100 held-out GSM8K questions with a fine scale sweep around the previously observed sweet spot:

Scale	Accuracy	Δ vs baseline	Baseline-failure recovery
baseline	89.0 %	—	—
+0.15	87.0 %	−2.0 pp	4/11 (36 %)
+0.20	89.0 %	0 pp	5/11 (45 %)
+0.25	90.0 %	+1.0 pp	6/11 (55 %)
+0.30	90.0 %	+1.0 pp	5/11 (45 %)

The aggregate lift is small, but the recovery rate is the real story. At scale +0.25, the contrastive direction at L13 recovers 55 % of the questions the baseline got wrong — 6 of 11 failures flipped to correct. The collateral damage falls on a consistent set of 5 questions [7, 20, 43, 58, 93] across all positive scales, which the baseline already answers with high confidence.

This is the first clean evidence in our experiments that the mechanistic signal is structured, not random: hard questions can be recovered by pushing the residual in the discovered direction, while easy questions get perturbed without benefit. The obvious follow-up — conditional / confidence-gated steering à la CAST (arxiv:2409.05907), ICLR 2025 spotlight — is on the roadmap.

🧪 Stage Gate 1: mech-reward viability check (passed)

The mechreward repo exists because the project's original thesis is not activation steering at inference time — it is using contrastive SAE features as a dense reward signal for RL fine-tuning. Before committing GPU hours to RL, we ran a passive correlation pre-test (n = 100 held-out GSM8K questions, no steering, just measuring whether the features predict baseline correctness):

Signal	Spearman ρ	Pearson r	p-value
R_mech_features (top-10 helpful − top-10 harmful, L18 SAE)	+0.540	+0.726	< 0.0001
R_mech_direction (cos-sim with L13 contrastive direction)	+0.508	+0.624	< 0.0001

Both pass the "strong correlation" threshold (ρ > 0.5). The SAE feature decomposition slightly outperforms the raw residual direction, which is additional evidence that the SAE is extracting signal beyond what is visible in the raw L13 hidden state.

Interpretation: the mechanism responsible for GSM8K correctness is readable from the SAE features — it is just not controllable via uniform additive steering (as we showed above with the collateral-damage experiments). This gap between "readable" and "controllable" is exactly what reward-based RL fine-tuning can close: let the model learn when to fire the helpful features and when to suppress the harmful ones, rather than imposing the decision uniformly at every token.

Top-10 helpful features (fire more on correct answers, Cohen's d > 1.8):

[36405, 27873, 35818, 12399, 2643, 6998, 15360, 25868, 21154, 35842]

Top-10 harmful features (fire more on wrong answers):

[18654, 36412, 15686, 23272, 13672, 14912, 5863, 29516, 30690, 40589]

🏆 Stage Gate 2: RL training with mech-reward (passed)

We ran GRPO fine-tuning on 500 GSM8K training questions (100 steps, 4 rollouts per question, LR = 1e-6, KL penalty β = 0.05) with three reward configurations on the same base model, same seed, same eval set (100 held-out questions):

Run	Reward	Final eval acc	Δ vs step 0	Δ vs R0
R0	Outcome only (binary)	74 %	+10 pp	— (baseline)
R1	Outcome + SAE features (λ = 0.1)	76 %	+12 pp	+2 pp ✅
R2	Outcome + raw L13 direction (λ = 0.1)	65 %	+1 pp	−9 pp ❌

R1 passes the +2 pp threshold over outcome-only. The convergence profile is even more striking than the final gap:

         Step 0    20     40     60     80    100
R0:       64 %   68 %   70 %   73 %   76 %   74 %  ← drops at end
R1:       64 %   70 %   74 %   75 %   75 %   76 %  ← stable at end

R1 reaches R0's final accuracy (74 %) at step 40 — 2.5× faster convergence. The mech-reward signal provides denser per-response gradient that accelerates early learning. At convergence, R0 drops from its step-80 peak (76 % → 74 %) while R1 holds or climbs (75 % → 76 %), suggesting the SAE features act as a regularizer that prevents late-training degradation.

R2 (raw direction without SAE decomposition) is actively harmful: R2 finished at 65 % (+1 pp from baseline), a full −9 pp below outcome-only R0 and −11 pp below SAE-based R1. The raw contrastive direction — which passively correlates with correctness at ρ = 0.508 — produced gradient signals that actively interfered with the outcome-driven learning. R2's eval trajectory (64 → 61 → 64 → 65 → 66 → 65) shows a model that barely learns, spending most of its budget recovering from the early damage caused by the noisy reward signal.

The 11 pp gap between R1 and R2 (76 % vs 65 %) — using the same underlying contrastive signal, same model, same training data, same seed — is the strongest evidence in our pipeline that SAE feature decomposition is the necessary processing step. The raw L13 direction is polysemantic: it correlates with correctness on average but also encodes task-irrelevant variation (difficulty, length, style) that corrupts the policy gradient. The SAE's sparse decomposition into 10 helpful + 10 harmful features acts as a denoiser — removing the polysemantic components and leaving a clean, sparse optimization target that the GRPO policy can reliably learn from.

Reproducible artifacts

All raw results are saved as JSON in this repo:

File	Content
reasoning_pack.json	ReasonScore top-25 + per-word distributions
steering_validation.json	Causal validation of feature #11424 (delta norms, traces)

Pending upload: contrastive discovery JSON, CAA sweep n = 100, Stage Gate 1 correlation, Stage Gate 2 GRPO traces.

🏔️ Stage Gate 3 Phase A: ceiling broken at scale (passed)

📖 Full write-up: Per-token SAE features as online RL reward: breaking the G2 76% ceiling on GSM8K (LessWrong, 2026-04-17)

Building on G2's C2 validation, we scaled up to test whether per-token mech-reward could break the 76 % G2 R1 ceiling. GRPO trained on 7500 GSM8K questions with Qwen3.5-4B + LoRA r=32, raw prompt Q:/A:, 4 rollouts × 4 questions/step (16 rollouts/step), max_gen_len=256, LR=3e-6, KL β=0.05, λ_mech=0.1, seed=42. Trained LoRA adapter: caiovicentino1/Qwen3.5-4B-mechreward-G3-phaseA-step400.

Step-400 eval (vs baseline with LoRA disabled via model.disable_adapter()):

Metric	Baseline	G3 @ step 400	Δ
GSM8K (500Q greedy, raw prompt)	64.00 %	83.00 %	+19 pp
MMLU (200Q raw zeroshot)	50.00 %	54.50 %	+4.50 pp
MATH-500 (500Q greedy, not trained on)	—	18.20 %	— (transfer)
Hack rate (canaries n=50)	4.0 % (2/50)	8.0 % (4/50)	+4 pp (within 95 % CI)
Correct under canary (n=50)	18.0 %	28.0 %	+10 pp
Ambiguous under canary (n=50)	78.0 %	64.0 %	−14 pp

Ceiling-break claim: G2 R1 final was 76 % in 100 steps with trajectory-level mech-reward. G3 Phase A reaches 83 % at nominal step 400, but the first 232 steps ran at the G2-documented LR=1e-6 and produced zero lift (KL stuck at 0.018, quick_gsm8k@200 = 64 % == baseline). Only after raising LR to 3e-6 at step 232 did training actually move — so the effective training budget that broke the ceiling was 168 steps at LR=3e-6 (step 232 → 400), roughly 1.68× G2 R1's 100-step budget for a +7 pp gain on GSM8K and using the same 20 contrastive features (10 helpful + 10 harmful). We stopped at step 400 of 2000 planned because the C2-extended target (≥ 80 %) was already achieved with margin.

Mech signal trajectory during training — key evidence that features drive the lift, not just outcome-only GRPO:

• Steps 1–200 at LR=1e-6 (G2's documented value): mech oscillated at −0.02, KL stuck at 0.018, quick_gsm8k=64 % (same as baseline — no lift).
• Step 232 diagnostic: gnorm was always < 0.5 throughout, so clip_grad_norm_=1.0 was inert — clipping was never the bottleneck. LR was. Raising LR to 3e-6 produced immediate learning.
• Steps 232–400 at LR=3e-6: mech rose −0.02 → +0.076 (step 250) → +0.382 (step 270) → +0.58 peak (step 330) → plateau ~+0.4-0.5. KL climbed 0.018 → 0.11. Training outcome at temp-0.9 went 0.55 → 0.75 avg.

Anti-Goodhart validation (n=50 canaries): with 10-canary measurement the hack rate read 30 % (statistical noise in a 10-point test). Expanding to 50 canaries across 5 hack patterns (repetition demands, reasoning-rhetoric abuse, forced templates, instruction bypass, chain-of-reasoning abuse), the trained policy showed hack_rate = 8 % (vs 4 % baseline, within 95 % CI), while correct-under-adversarial-prompt rose +10 pp (18 → 28 %). The policy is both more confident and more resilient to distraction — the opposite of the Goodhart failure mode.

Key lessons applied to future mechreward RL runs:

1. Verify gnorm before blaming clipping. Our gnorm≈0.3 proved clip=1.0 was inert for 200 steps while we wasted time on LR-unrelated hypotheses.
2. LR in prior work may not transfer across batch configurations. G2's 1e-6 with 4×1 rollouts needed 3e-6 here for 4×4 rollouts + per-token reward + bf16 log_softmax.
3. Prompt format must match the SAE contrastive-discovery distribution. Using a chat template when the SAE pack was discovered on raw Q:/A: outputs kept mech negative for 200 steps before we reverted.

---

📐 Specs

Base model	Qwen/Qwen3.5-4B
Hook	Residual stream, post-layer 18
d_model	2,560
d_sae	40,960 (16× expansion)
k (active features / token)	128
Training tokens	200 M (FineWeb-Edu sample-10BT, streamed)
Optimizer	Adam, peak LR 2e-4 → cosine → floor 6e-5
Aux dead-feature loss	coef = 0.125, k_aux = 512
Decoder column norm	1.0 (re-projected every 10 steps)
b_dec init	Geometric median over 16,384 samples
Precision	bf16 model, fp32 SAE
Hardware	NVIDIA RTX PRO 6000 Blackwell 96 GB

---

📊 Training + eval metrics

Metric	Training (FineWeb-Edu)	Eval (code + reasoning prompts)
Variance explained	≥ 0.87	0.866
MSE	~0.010	0.0178
L0 (active features / token)	128 / 128	127.9 / 128
Alive features	40,950 / 40,960	24,956 / 40,960 (on eval prompts)
Features with H > 1.0	—	7,259

The eval prompts are Python snippets and meta-cognitive reasoning fragments — a different distribution from the educational articles the SAE was trained on. Reconstruction holds tight and L0 stays structural (127.9/128), confirming the TopK sparsity constraint survives distribution shift.

Dead-feature revival worked as designed: the auxiliary loss kicked in at step 5,225, pulled the peak of 9,171 dead features back to 1 by step 6,400, and the SAE stayed in healthy churn (0–10 dead) for the remaining 43k steps.

Reproduce the eval numbers

import torch
from transformers import AutoModelForCausalLM, AutoTokenizer
from huggingface_hub import hf_hub_download

ckpt = torch.load(
    hf_hub_download("caiovicentino1/Qwen3.5-4B-SAE-L18-topk", "sae_final.pt"),
    map_location="cuda", weights_only=True,
)
W_enc, W_dec = ckpt["W_enc"].cuda().float(), ckpt["W_dec"].cuda().float()
b_enc, b_dec = ckpt["b_enc"].cuda().float(), ckpt["b_dec"].cuda().float()
k = int(ckpt["k"])

def encode(x):
    pre = (x - b_dec) @ W_enc + b_enc
    topv, topi = torch.topk(pre, k, dim=-1)
    out = torch.zeros_like(pre)
    out.scatter_(-1, topi, topv)
    return torch.relu(out)

def decode(f):
    return f @ W_dec + b_dec

tok = AutoTokenizer.from_pretrained("Qwen/Qwen3.5-4B")
model = AutoModelForCausalLM.from_pretrained(
    "Qwen/Qwen3.5-4B", dtype=torch.bfloat16, device_map="cuda"
).eval()

prompts = [
    "The key insight behind transformers is that attention lets every token",
    "def fibonacci(n):\n    if n < 2:\n        return n\n    return",
    "Wait, let me think about this more carefully. The problem is that",
    "import torch\nimport torch.nn as nn\n\nclass Attention(nn.Module):",
    "A sparse autoencoder decomposes neural network activations into",
]

total_var, total_mse, total_l0 = 0.0, 0.0, 0.0
with torch.inference_mode():
    for p in prompts:
        ids = tok(p, return_tensors="pt").input_ids.cuda()
        out = model(input_ids=ids, output_hidden_states=True,
                    use_cache=False, return_dict=True)
        x = out.hidden_states[19].float().squeeze(0)
        feats = encode(x)
        recon = decode(feats)
        mse = (x - recon).pow(2).mean().item()
        total_var += 1 - mse / x.var().item()
        total_mse += mse
        total_l0 += (feats > 0).float().sum(-1).mean().item()

n = len(prompts)
print(f"var_exp={total_var/n:.4f}  mse={total_mse/n:.6f}  L0={total_l0/n:.1f}/{k}")
# var_exp=0.8655  mse=0.017728  L0=127.9/128

---

📁 Files

File	Size	Purpose
sae_final.pt	839 MB	Trained weights (W_enc, W_dec, b_enc, b_dec + scalar meta)
sae_final.json	256 B	Structured metadata (d_model, d_sae, k, layer, tokens, timestamp)
reasoning_pack.json	~15 KB	Top-25 reasoning features, per-word distributions, entropy + stats
steering_validation.json	~7 KB	Causal validation of #11424 — activation steering traces, delta norms, semantic diff

---

🚀 Full usage

With mechreward (recommended)

pip install mechreward

import torch
from transformers import AutoModelForCausalLM, AutoTokenizer
from mechreward.sae.topk_sae import load_topk_sae

tok = AutoTokenizer.from_pretrained("Qwen/Qwen3.5-4B")
model = AutoModelForCausalLM.from_pretrained(
    "Qwen/Qwen3.5-4B", dtype=torch.bfloat16, device_map="cuda"
).eval()

sae = load_topk_sae(
    "caiovicentino1/Qwen3.5-4B-SAE-L18-topk",
    layer=18,
    model_name="Qwen/Qwen3.5-4B",
)

# Extract layer-18 residual and encode
ids = tok("The sparse features behind reasoning", return_tensors="pt").input_ids.cuda()
with torch.inference_mode():
    out = model(input_ids=ids, output_hidden_states=True,
                use_cache=False, return_dict=True)
h = out.hidden_states[19].float().squeeze(0)

features = sae.encode(h)
print(features.shape)                             # [seq_len, 40960]
print((features > 0).sum(-1).float().mean())      # ≈ 128 — structural L0

Raw (no mechreward dependency)

import torch
from huggingface_hub import hf_hub_download

ckpt = torch.load(
    hf_hub_download("caiovicentino1/Qwen3.5-4B-SAE-L18-topk", "sae_final.pt"),
    map_location="cuda",
    weights_only=True,
)
W_enc, W_dec = ckpt["W_enc"].cuda(), ckpt["W_dec"].cuda()
b_enc, b_dec = ckpt["b_enc"].cuda(), ckpt["b_dec"].cuda()
k = int(ckpt["k"])

def encode(x):  # x: [..., 2560]
    pre = (x - b_dec) @ W_enc + b_enc
    topv, topi = torch.topk(pre, k, dim=-1)
    out = torch.zeros_like(pre)
    out.scatter_(-1, topi, topv)
    return torch.relu(out)

def decode(f):  # f: [..., 40960]
    return f @ W_dec + b_dec

---

🧠 Training details

• Objective: MSE reconstruction of the layer-18 residual stream.
• Sparsity: hard TopK (Gao et al. 2024) — L0 = k = 128 by construction. No L1 tuning.
• Dead-feature revival: auxiliary loss on the top-512 pre-activations of dormant features, scaled by 1/8. Dead threshold: 5,000 steps without firing.
• Decoder norm constraint: each decoder column re-projected to unit norm every 10 steps, preventing the weight explosion that plagues L1 SAEs.
• b_dec initialization: geometric median of 16,384 sampled residual-stream activations — more robust than the mean for the heavy-tailed Qwen3.5 activation distribution (max|x| ≈ 38 vs std ≈ 0.28).
• LR schedule: 5k-step warmup → cosine decay from 2e-4 to 6e-5 floor. The non-zero floor sustains dead-feature revival throughout training.
• Data: HuggingFaceFW/fineweb-edu sample-10BT, streamed in 2M-token buffers. No tokenizer-specific filtering.
• Activation extraction: plain HF output_hidden_states=True — no TransformerLens, no custom hooks, ports trivially to any HF-compatible model.

---

🔧 Why a custom script?

Qwen3.5 uses a hybrid Gated Delta Networks (GDN) architecture that TransformerLens and sae_lens don't yet support — their hook infrastructure targets Gemma, Llama, and GPT-2 style attention, not hybrid state-space layers. The training script (mechreward/scripts/train_sae_qwen35.py) uses only HuggingFace's built-in output_hidden_states=True, so it ports trivially to any HF-compatible model.

---

⚠️ Limitations

• Token budget: 200 M tokens is small relative to Gemma Scope (8 B tokens on 9 B models). Feature quality is publishable but further training would likely improve coverage.
• Single layer: only layer 18 (mid-depth residual). Other depths would need separate runs.
• Feature catalog is reasoning-focused: the top-25 pack targets meta-cognitive features specifically. Math, code, multilingual, and factual feature catalogs are future work.
• Causal validation is demo-scale: only feature #11424 has been validated by activation steering so far (3 prompts × 4 scales). Scaling this to the full top-25 and testing under sampled decoding is the next step.
• Layer choice is suboptimal for math reasoning. Multi-layer effect-size analysis shows contrastive signal peaks at L13 (1.391 top-10 Cohen's d) while our SAE is at L18 (1.289). L18 still carries recoverable causal features — it's in the post-commitment consolidation zone — but a future SAE trained on L13-L15 activations would likely give cleaner GSM8K steering. Re-training is expected to cost ~9 h on an RTX PRO 6000 Blackwell.
• Token budget is small compared to Gemma Scope (200 M vs 8 B tokens on 9 B models) and to our Gemma 4 E4B companion (1 B tokens, var_exp = 0.939 vs our 0.87). Re-training this SAE with 1 B tokens would likely lift var_exp to the 0.92–0.94 range and tighten the feature catalog. ~36 h on RTX PRO 6000.
• No net GSM8K accuracy boost demonstrated at n = 50. See the experiments section — individual features and CAA directions recover specific baseline failures, but net aggregate lift is sample-size-dominated at 50 questions. n ≥ 200 needed to quantify.

---

📚 Citation

If you use this SAE, please cite the TopK SAE paper:

@article{gao2024scaling,
  title   = {Scaling and evaluating sparse autoencoders},
  author  = {Gao, Leo and Dupr{\'e} la Tour, Tom and Tillman, Henk and
             Goh, Gabriel and Troll, Rajan and Radford, Alec and
             Sutskever, Ilya and Leike, Jan and Wu, Jeffrey},
  journal = {arXiv preprint arXiv:2406.04093},
  year    = {2024}
}

And the ReasonScore metric used to build the feature catalog:

@article{gao2025reasoning,
  title   = {I Have Covered All the Bases Here: Interpreting Reasoning
             Features in Large Language Models via Sparse Autoencoders},
  author  = {AIRI Institute},
  journal = {arXiv preprint arXiv:2503.18878},
  year    = {2025}
}

And the base model:

@misc{qwen35,
  title  = {Qwen3.5 Technical Report},
  author = {Qwen Team},
  year   = {2026}
}

---

🧪 Companion releases

• caiovicentino1/Gemma-4-E4B-SAE-L21-topk — Gemma 4 E4B TopK SAE at layer 21 of 42. Trained on 1 B tokens, d_sae = 32,768, var_exp = 0.939. First public SAE for hybrid MoE reasoning research. Final n = 50 CAA sweep at L27 (peak contrastive layer) produced a null aggregate: +10 scale finished at 0 pp vs baseline while the −5 negative control finished at +2 pp — inconsistent with a directional-causality hypothesis. Both +10 and −5 recovered the same 20 % of baseline-wrong questions, but on partially disjoint subsets, indicating that moderate perturbation acts as a decision-boundary regularizer in either direction rather than encoding a "correctness direction". The monotone magnitude penalty (+15 → −12 pp) is the only directional signal that survived. This gap between readable (ρ = 0.54 correlation on the Qwen companion) and controllable (null aggregate steering on both models) is the central motivator for pivoting from inference-time steering to learned-policy reward shaping in later mechreward stages. Full honest breakdown in the Gemma README. Released 2026-04-15, analysis 2026-04-16.

Cross-architecture observations (Qwen3.5-4B GDN vs Gemma 4 E4B MoE)

Metric	Qwen3.5-4B (GDN)	Gemma 4 E4B (MoE)
Total layers	32	42
Peak contrastive effect layer	L13 (41 % depth)	L27 (64 % depth)
First English-commitment layer (logit lens)	L15 (47 %)	L30 (71 %)
GSM8K baseline accuracy (chat template CoT)	89 % (n = 100)	50 % (n = 50)
CAA best positive scale lift	+1 pp / 55 % recovery (@ +0.25)	0 pp / 20 % recovery (@ +10)
CAA negative control lift	0 pp (as expected)	+2 pp (beats positive — non-directional)
CAA overdose penalty (largest scale)	— (not tested)	−12 pp (real magnitude effect)
Top-10 feature effect size (Cohen's d)	1.391	0.896
Stage Gate 1 correlation (ρ, held-out)	0.540 (p < 0.0001)	not yet measured

Gemma 4 E4B commits to English mathematical reasoning 15 layers later than Qwen3.5-4B, consistent with extensive multilingual parallel processing in the early-middle stack of the ensemble-MoE architecture. The logit lens trajectory for Gemma shows dominant non-English token predictions across L0–L29 (mixed Chinese, Bengali, Hindi, Arabic, code-adjacent tokens) before converging on English reasoning formatting at L30+. This is a novel observation — no prior published SAE work has been performed on hybrid MoE architectures.

Hybrid architectures break the dense-transformer consensus on reasoning-feature localization. Published work on dense models (AIRI ReasonScore on DeepSeek-R1-Distill, Rimsky CAA on Llama-2, RouteSAE) converges on 50–60 % depth. Qwen3.5 GDN peaks at 41 % (earlier, consistent with linear-attention collapsing information earlier in the stack); Gemma 4 E4B MoE peaks at 64 % (later, consistent with longer distributed processing before consolidation).

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📄 License

Apache-2.0 — same as the base model Qwen/Qwen3.5-4B.