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Controllable LLM Reasoning via Sparse Autoencoder-Based Steering

Yi Fang, Wenjie Wang, Mingfeng Xue, Boyi Deng, Fengli Xu, Dayiheng Liu, Fuli Feng

arXiv:2601.03595v2cs.AIcs.CL

TL;DR

LRMs’ autonomous strategy selection can yield inefficient or erroneous reasoning, while existing controls struggle with entangled hidden-state concepts. This paper uses SAEs and SAE-Steering to identify disentangled strategy features for steering, achieving over 15% higher control effectiveness and a 7% absolute accuracy improvement for correcting erroneous paths.

  • Problem

    LRMs may autonomously select inefficient or erroneous reasoning paths, while existing control methods struggle with concept entanglement in hidden states.

  • Method

    The paper decomposes hidden states with SAEs and uses SAE-Steering to recall keyword-logit features before ranking candidates by control effectiveness.

  • Results

    SAE-Steering outperforms existing methods by over 15% in control effectiveness and improves absolute accuracy by 7% when correcting erroneous reasoning paths.

  • Takeaways & Limitations

    Controlling reasoning strategies can redirect LRMs from erroneous paths toward correct ones.

  • Takeaways & Limitations

    The evaluation covers five representative strategies, relies on manually specified strategy keywords, and only preliminarily studies negative steering.

Abstract

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Large Reasoning Models (LRMs) exhibit human-like cognitive reasoning strategies (\eg backtracking, cross-verification) during the reasoning process, which improves their performance on complex tasks. Currently, reasoning strategies are autonomously selected by LRMs themselves. However, such autonomous selection often produces inefficient or even erroneous reasoning paths. To make reasoning more reliable and flexible, it is important to develop methods for controlling reasoning strategies. Existing methods struggle to control fine-grained reasoning strategies due to conceptual entanglement in LRMs' hidden states. To address this, we leverage Sparse Autoencoders (SAEs) to decompose strategy-entangled hidden states into a disentangled feature space. To identify the few strategy-specific features from the vast pool of SAE features, we propose SAE-Steering, an efficient two-stage feature identification pipeline. SAE-Steering first recalls features that amplify the logits of strategy-specific keywords, filtering out over 99\% of features, and then ranks the remaining features by their control effectiveness. Using the identified strategy-specific features as control vectors, SAE-Steering outperforms existing methods by over 15\% in control effectiveness. Furthermore, controlling reasoning strategies can redirect LRMs from erroneous paths to correct ones, achieving a 7\% absolute accuracy improvement. Our code and data are available at https://github.com/Peter-Fy/SAE-Steering.

1 Introduction

LRMs use reasoning strategies that can improve challenging-task performance, but autonomous selection may produce inefficient or erroneous paths. The paper proposes SAE-Steering to disentangle strategy features and identify control vectors for more precise intervention.

  • Reasoning strategies such as self-correction and cross-verification improve LRM accuracy and robustness on challenging tasks.
  • Autonomous strategy selection can produce inefficient or erroneous reasoning paths, motivating external guidance during reasoning.
  • Prompt-based methods lack direct internal control, while activation-based methods risk concept entanglement because contrastive pairs may capture multiple strategies.
  • SAEs decompose strategy-entangled hidden states into a disentangled feature space intended to isolate strategy-specific control vectors.
  • SAE-Steering filters out over 99% of irrelevant features using keyword-logit amplification, then ranks remaining candidates by control effectiveness.
  • SAE-Steering outperforms baselines by over 15% in control effectiveness and improves absolute accuracy by 7% when correcting erroneous reasoning paths.

2 Preliminary

The paper defines reasoning-strategy control as intervening on LRM activations so generated continuations exhibit a desired strategy. Its evaluation focuses on five representative strategies and repeated activation steering across subsequent decoding steps.

  • Strategy Selection: The evaluation covers Problem Understanding, Procedural Planning, Backtracking, Multi-Perspective Verification, and Hypothesis Reasoning.
  • Strategy Selection: The selected strategies are chosen for evaluation convenience, while the method is intended to apply to other reasoning strategies.
  • Task Formulation: At each decoding step, an LRM processes the generated prefix through transformer layers to produce residual-stream activations.
  • Task Formulation: Strategy control injects a control vector into a specified layer, with the steering coefficient α determining intervention strength.
  • Task Formulation: The intervention is applied at every subsequent decoding step for T consecutive tokens, producing a steered trajectory intended to exhibit the desired strategy.

3 Method

The method uses sparse autoencoders to represent hidden states with interpretable features, then identifies strategy-specific features through keyword-logit recall and validation-based effectiveness ranking. Selected features are repeatedly injected as control vectors during generation.

  • SAE Features and Strategy Control: SAE-Steering uses SAE features as control vectors and combines feature identification with activation intervention in a two-part method.
  • SAE Features and Strategy Control: An SAE encodes an N-dimensional residual activation into a sparse M-dimensional feature vector, where M ≫ N, and reconstructs the activation.
  • SAE Features and Strategy Control: SAE training minimizes reconstruction error while enforcing sparsity, enabling reconstruction from only a few active latent directions.
  • SAE Features and Strategy Control: Each decoder column is an interpretable feature direction, and its activation value indicates the feature’s strength for the input.
  • SAE Features and Strategy Control: The selected strategy-specific feature is repeatedly injected into residual activations at the SAE-trained layer for the next T generated tokens.
  • Feature Identification: SAE-Steering first uses low-cost keyword-logit recall to filter out 99% of irrelevant features, then applies higher-cost evaluation to rank candidates.
  • Feature Identification: The first stage estimates feature contributions to vocabulary logits using a single matrix multiplication and retains features meeting keyword-count and contribution thresholds.
  • Feature Identification: The second stage compares baseline and steered continuations on a validation set, uses an LLM judge, and selects the top-ranked feature by control success rate.

4 Experiments

Experiments evaluate SAE-Steering across reasoning strategies, feature identification, layers, and erroneous-path correction. SAE-Steering generally outperforms comparison methods, supports behavior suppression, and improves correction outcomes.

  • Experiment Setup: Experiments evaluate control across five strategies using majority voting among three LLM judges, with AIME and GPQA responses as evaluation data.The strategies are Problem Understanding, Procedural Planning, Backtracking, Multi-Perspective Verification, and Hypothesis Reasoning.
  • Control Effectiveness: Activation-based methods outperform prompt-based Think Intervention except in some Hypothesis Reasoning cases.The comparison includes Vector Steering and SAE-Steering as activation-based methods.
  • Control Effectiveness: 15%: SAE-Steering’s average improvement over Vector Steering in control effectiveness.The paper attributes this advantage to SAE disentanglement, which mitigates conceptual entanglement in control vectors.
  • Control Effectiveness: Over 35%: SAE-Steering’s control-effectiveness advantage over Logit Boosting, whose keyword amplification does not genuinely change reasoning strategy.The case study contrasts keyword production with adoption of Multi-Perspective Verification.
  • Control Effectiveness: 30%: negative steering reduces the frequency of the corresponding reasoning strategy, while reasoning length decreases by 14%.The same identified features can therefore induce target strategies or inhibit specific behaviors.
  • Feature Identification: 28%: SAE-Steering’s precision advantage over ReasonScore, supporting logit-based rather than activation-based feature identification.The paper states that logits better reflect features’ actual control capability than activation strength.
  • Feature Identification and Layer Analysis: Strategy-specific features are rare in shallow layers but prevalent in deeper layers, while layers beyond 20 show strong and relatively stable control effectiveness.The layer-wise analysis was conducted on Qwen3-8B and supports applying control in middle-to-late layers.

5 Related Work

Prior work guides LRM reasoning through prompts or hidden-state interventions, while SAE-based methods seek more interpretable and disentangled control features.

  • Prompt-based methods guide reasoning by inserting instructions into initial prompts or intermediate reasoning steps.
  • Activation-based methods directly modify hidden states using control vectors derived from contrasting activations.
  • SAE-based steering uses unsupervised monosemantic features to better disentangle conceptually entangled hidden states without annotations.
  • SAEs decompose high-dimensional LRM activations into sparse latent features that often correspond to interpretable concepts.

6 Conclusion

The paper presents SAE-Steering for fine-grained control of LRM reasoning strategies by identifying and intervening on disentangled SAE features.

  • SAE-Steering identifies strategy-specific SAE features and uses them to control reasoning strategies in LRMs.
  • The two-stage pipeline recalls candidate features through strategy-keyword logit amplification, then ranks them using validation-set intervention experiments.
  • The identified features show effective and robust reasoning-strategy control, including redirecting LRMs from erroneous paths to correct ones.

Limitations

The paper’s limitations concern strategy coverage, manual keyword retrieval, application scope, and the timing of interventions used for error correction.

  • The study evaluates only five representative reasoning strategies and relies on manually specified strategy-related keywords for candidate retrieval.
  • The evaluation mainly addresses error correction, with only a preliminary study of negative steering and limited exploration of broader applications.
  • Error correction enforces continued reasoning and controls subsequent strategies, leaving earlier intervention points for future study.
  • The keyword extraction procedure samples 100 Qwen3-8B responses, collects 50 representative segments per strategy, and requires manual review.
  • Keywords are selected by removing semantically neutral frequent words and retaining terms whose contexts reflect the target strategy.

B.2 Robustness Analysis of Keyword Selection

The keyword-selection procedure transfers across a different model family and out-of-domain benchmark, while experiments indicate robustness to moderate keyword variation and reliable LLM judging.

  • Keywords extracted from Qwen3-8B on AIME transfer to DeepSeek-R1-Distill-Llama-8B and the out-of-domain GPQA benchmark.
  • Each of three evaluated LLMs recovers at least three of five human-selected Problem Understanding keywords.
  • SAE-Steering recalls target features using both overlapping human-selected keywords and alternative unseen keywords.
  • Human annotation compares 200 steered outputs with unsteered baselines across five strategies, with Krippendorff’s alpha = 0.78 among three annotators.

D Curation of Error Correction Dataset

The error-correction dataset samples multiple responses per problem and retains incorrect ones, while a contrastive router learns to select effective strategy-specific features from reasoning contexts. At inference, it scores candidate features and steers with the highest-scoring feature.

  • Eight responses are sampled for each problem from MATH500, AIME25, and GPQA, retaining only incorrect responses for the error-correction dataset.The resulting dataset statistics are reported in Table 7.
  • The strategy router uses a context encoder for the response prefix and a feature encoder for each strategy-specific feature.Both encoders map their inputs into a shared representation space.
  • The router computes context–feature scores as dot products and trains with InfoNCE to separate positive from negative context–feature pairs.Positive pairs correspond to features whose steering leads to a correct final answer; other pairings are negative.
  • At inference, the router scores all candidate features for the current reasoning context and selects the highest-scoring feature for steering.

E.2 Implementation Details

The router is trained on AIME and NUMINAMATH problems, using sampled responses and repeated steering evaluations to measure feature effectiveness. These evaluations provide the data for selecting context-dependent strategy features.

  • Three strategy-specific features are retained per reasoning strategy, yielding fifteen router candidates overall.Multiple features per strategy allow adaptation to different reasoning contexts.
  • The router training set contains 919 past AIME problems and 4,000 NUMINAMATH-1.5 aops_forum problems.Eight initial responses are sampled for each problem.
  • Each feature is evaluated on incorrect responses by applying steering, generating eight responses, and measuring the proportion that reach a correct answer.

F Preliminary Analysis of Negative Steering

Negative steering suppresses a targeted verification behavior and shortens reasoning, but the accompanying accuracy loss shows that continuously suppressing a strategy can remove beneficial reasoning steps. The analysis therefore points toward more fine-grained or dynamic intervention.

  • Negative steering reduces Multi-Perspective Verification from 13 to 9 occurrences per response, a 30% reduction.
  • Average reasoning length falls from 14k to 12k tokens, a 14% reduction, suggesting improved reasoning efficiency.
  • Accuracy drops from 0.4667 to 0.4333 when the strategy is continuously suppressed throughout reasoning.The text attributes this to potentially removing reasoning steps that are sometimes beneficial.
  • The findings motivate more fine-grained or dynamic intervention strategies to balance reasoning efficiency and accuracy.
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