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Step-Level Sparse Autoencoder for Reasoning Process Interpretation

ICML 2026 · Large language models › Reasoning and chain of thought · approach: Search and self-correction in reasoning · 0 citations (OpenAlex)

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Proposes SSAE, a context-conditioned step-level sparse autoencoder that disentangles incremental information of each reasoning step, and uses its probed correctness for weighted self-consistency voting.

Problem

Token-level sparse autoencoders mismatch the step-level granularity needed to interpret LLM chain-of-thought reasoning, entangling incremental step information with contextual background.

Approach

A sparse autoencoder whose encoder and decoder both condition on the preceding context, with a sparsity-controlled bottleneck (dynamic lambda controller) so the sparse step feature keeps only new information; linear probes on these features predict step correctness, logicality, length and first token.

Key results

• SSAE-Llama sparse features reach 80.55% correctness accuracy on GSM8K and 2.02 step-length error, versus 70.49% and 28.04 for the naive baseline; Token-SAE-agg reaches 74.38%.
• Probe-Guided voting with SSAE-Qwen improves Qwen2.5-0.5B GSM8K accuracy from 46.20% (SC@16) to 46.80% and Llama-3.2-1B from 16.60% to 19.40%.
• On DeepSeek-R1-Distill-Qwen-32B, PG@16 raises AIME 2024 accuracy from 86.67% (SC@16) to 90.00%, with no gain on MATH-500 (95.60%) or AIME 2025.

Surprising findings

• Step correctness is linearly decodable from the sparse step features, suggesting LLMs partly know step correctness before generating the step.
• Probe-guided voting gives no gain over self-consistency on AIME 2025 and saturated MATH-500 for the 32B model.

Limitations

• Probe-guided gains are small and vanish on harder or saturated benchmarks (AIME 2025, MATH-500 for DeepSeek-R1-Distill-32B).
• Step correctness labels for MATH-500 come from GPT-4o-mini judgments rather than verified ground truth.
• Information-bottleneck capacity formula is heuristic and its assumptions are loosely justified.

Experimental setup

Datasets: GSM8K-Aug GSM8K NuminaMath-CoT OpenCodeInstruct MATH-500 SVAMP MultiArith AIME 2024 AIME 2025

Benchmarks: GSM8K MATH-500 SVAMP MultiArith AIME 2024 AIME 2025

Metrics: probe accuracy step length error (RMSE) first token perplexity precision/recall/F1 for N2G Gwet's AC1 observed agreement accuracy (Avg@16, SC@16)

Baselines: Token-SAE-last Token-SAE-agg Naive statistical baseline Avg@16 SC@16

Builds on: sparse autoencoder Neuron to Graph (N2G) Self-Consistency

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