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Reasoning-Finetuning Repurposes Latent Representations in Base Models

Jake Ward, Chuqiao Lin, Constantin Venhoff, Neel Nanda

arXiv:2507.12638v1cs.LG

TL;DR

Prior work showed that steering vectors can manipulate backtracking, but the mechanism behind this behavior remains poorly understood. This paper investigates whether base-model activations contain a direction that can induce backtracking after reasoning finetuning. It finds that such a direction is present in the base model and induces backtracking in the reasoning model, but not in the base model itself.

  • Problem

    Prior work showed that steering vectors can induce backtracking, but the underlying mechanism remains poorly understood; backtracking accounts for a substantial fraction of the accuracy gap between base and reasoning-fine-tuned models.

    Source: §1 · p. 1

  • Method

    The study derives steering vectors from base and reasoning model activations, including activations at token positions preceding backtracking events, and evaluates their effects on generated traces.

    Source: §3 · p. 2, §2.2 · p. 2

  • Results

    Base-derived steering vectors reliably induce backtracking in the reasoning model but not the base model, supporting the interpretation that finetuning repurposes a pre-existing representation.

    Source: §1 · p. 1, §3.2 · p. 3, §5 · p. 5

  • Takeaways & Limitations

    The findings suggest reasoning-fine-tuned models can repurpose signals already present in base models rather than learn reasoning behavior entirely from scratch.

    Source: §1 · p. 1

    The study examines one reasoning model and identifies only one component of the backtracking mechanism, so the findings are an existence proof rather than a comprehensive explanation.

    Source: §5 · p. 5

Abstract

from arXiv · show

Backtracking, an emergent behavior elicited by reasoning fine-tuning, has been shown to be a key mechanism in reasoning models' enhanced capabilities. Prior work has succeeded in manipulating this behavior via steering vectors, but the underlying mechanism remains poorly understood. In this work, we show that the emergence of backtracking in DeepSeek-R1-Distill-Llama-8B is in part driven by a repurposed direction already present in base model activations. Specifically, we identify a direction in base Llama-3.1-8B's residual stream which systematically induces backtracking when used to steer the distilled reasoning model, and find that the effects of steering with this direction cannot be trivially explained by token-level attributes. We further find that this direction does not induce backtracking in the base model, suggesting that the reasoning finetuning process repurposes pre-existing representations to form new behavioral circuits. Additionally, we hypothesize that this direction is one of several which may work together to mediate backtracking. Our findings offer a compelling picture that reasoning-finetuned models repurpose pre-existing base model representations, rather than learn new capabilities from scratch.

1. Introduction

Backtracking contributes to the accuracy gap between base and reasoning-fine-tuned models, but how steering induces it is poorly understood. The paper finds that base-model representations can be repurposed to induce backtracking in the reasoning model.

1. Introduction

  • Backtracking accounts for a substantial fraction of the accuracy gap between base models and reasoning-fine-tuned counterparts.The passage attributes this finding to Niklas Muennighoff (2025).Source: §1 · p. 1
  • Prior work induced backtracking with steering vectors, while the mechanism underlying the behavior remained poorly understood.The prior steering vectors were derived from activation differences at sentences classified as backtracking.Source: §1 · p. 1
  • A direction present in base-model activations induces backtracking in the reasoning model, suggesting finetuning repurposes a pre-existing representation.The figure marks the tokens used to compute the steering vector in green and the start of backtracking in red.Source: §1 · p. 1, Figure 1 · p. 2
  • Base-derived steering reliably invokes backtracking in the reasoning model, and the direction is not a direct boost to backtracking-keyword logits.The direction is densely present across contexts, suggesting it is not the sole factor mediating backtracking.Source: §1 · p. 1
  • The findings suggest reasoning-fine-tuned models repurpose base-model signals rather than learn reasoning behavior entirely from scratch.The authors suggest base models may possess latent reasoning capabilities that finetuning extracts.Source: §1 · p. 1

2. Preliminaries

The paper derives steering vectors using Difference-of-Means and detects backtracking with a keyword-based proxy, supported by comparisons with judge-based classifications.

2.1. Deriving steering vectors

  • Steering vectors are derived using the Difference-of-Means method.The full derivation is provided in Appendix A.Source: §2.1 · p. 2

2.2. Detection of backtracking

  • Backtracking events are identified with a GPT-4o judge on 300 reasoning-model output traces.This follows Venhoff et al. (2025).Source: §2.2 · p. 2
  • The keyword proxy measures the fraction of output tokens matching a predefined set, including “Wait” or “But”; the supplied symbol definitions specify N as trace word count and B as {wait, hmm}.The authors report that the keyword metric is an acceptable indicator for their purposes.Source: §2.2 · p. 2

3. Steering vector analysis

The analysis finds that base-derived vectors can induce backtracking in the reasoning model, while neither base- nor reasoning-derived vectors do so in the base model. It also identifies an effective preceding-token window and finds the steering vector outperforms tested baselines.

3.1. Deriving steering vectors with a negative offset

  • At layer 10, offsets around −13 to −8 are optimal and outperform the no-offset baseline.This window usually covers the beginning of the sentence preceding backtracking; the figure maps offset and steering magnitude to the averaged metric.Source: §3.1 · p. 2, Figure 2 · p. 3

3.2. Using base model activations

  • Base-derived vectors reliably induce backtracking in the reasoning model, comparable to reasoning-derived vectors, but neither vector type induces it in the base model.The two vector types have cosine similarity of approximately 0.74, suggesting they capture the same representation.Source: §3.2 · p. 3, Figure 3 · p. 3
  • Both base- and reasoning-derived vectors are most effective around layer 10 among the 32 layers examined.The detailed layer comparisons are presented in Appendix B.1 and Fig. B.1.Source: §3.2 · p. 3

3.3. Validation against baselines

  • The backtracking vector significantly outperforms the tested mean, noise, self-amplification, deduction, and problem-initialization baselines.These comparisons test whether the effect is merely an arbitrary activation perturbation.Source: §3.3 · p. 3
  • Gaussian noise also nontrivially increases the fraction of output words that are “Wait,” and its coherent, backtracking-prone outputs are reported anecdotally.The authors leave investigation of this effect for future work.Source: §3.3 · p. 3

4. Steering vector directions represent nontrivial concepts

The section finds that the layer-10 base-derived steering direction is not explained by direct boosts to backtracking keywords. Probing suggests it is only one component of the behavior.

4. Steering vector directions represent nontrivial concepts

  • The base-derived, negative-offset steering vector has a significant effect in Figure 4’s comparison of baselines on the “Wait” metric.Source: Figure 4 · p. 4
  • The steering vectors encode more than direct trigger-token boosts, and the identified direction alone is not sufficient to explain backtracking.Source: §4 · pp. 3–4

4.1. Logit lens

  • The layer-10 base-derived vector does not decode to backtracking keywords yet elicits backtracking; later-layer vectors show token-level boosts but steer less effectively.The figure compares backtracking scores across layers and model unembedding matrices.Source: §4.1 · p. 4, Figure 5 · p. 4

4.2. Probing

  • The direction is densely present in activations but does not cleanly correlate with backtracking; moderate-strength efficacy supports a hypothesis that multiple heuristics may combine.The authors note that the direction is less effective at small steering strengths and leave this hypothesis for future work.Source: §4.2 · p. 4

5. Conclusion and Outlook

The conclusion presents evidence that reasoning fine-tuning may repurpose base-model representations to elicit backtracking, rather than learning the entire mechanism from scratch. It frames the findings as an existence proof, not a comprehensive explanation.

5. Conclusion and Outlook

  • Figure 6 shows an unsteered reasoning-model output, highlighting positive layer-10 vector projections in green and outlining “Wait” tokens in red.Source: Figure 6 · p. 5
  • A direction present in Llama-3.1-8B residual-stream activations systematically induces backtracking when added to DeepSeek-R1-Distill-Llama-8B activations, but not in the base model.The authors suggest reasoning fine-tuning may repurpose this pre-existing representation.Source: §5 · p. 5
  • The analysis covers one reasoning model, so generalization across model families and scales remains unvalidated.Source: §5 · p. 5
  • The identified direction is only one component of the backtracking mechanism; the remainder is unknown, making the findings an existence proof rather than a comprehensive explanation.Source: §5 · p. 5
  • The authors highlight interpretability tools as a way to uncover nuanced insights into mechanisms underlying emergent LLM capabilities.Source: §5 · p. 5

A. Deriving steering vectors

The paper derives backtracking steering vectors with Difference-of-Means from reasoning-trace activations, contrasting traces with and without backtracking-related tokens at selected positions.

A. Deriving steering vectors

  • The steering vector is the Difference-of-Means between activations from backtracking-labeled positions and the full selected-position dataset.The target hidden state is taken at a chosen layer, and the selected sequence positions are accessed for each tokenized prompt.Source: A. Deriving steering vectors · p. 7
  • The dataset uses 300 prompts across 10 categories, with Claude Sonnet 3.7 generating prompts and DeepSeek-R1-Distill-Llama-8B generating reasoning traces.The prompts and traces follow the cited prior methodology.Source: A. Deriving steering vectors · p. 7
  • GPT-4o classifies trace sentences as backtracking or otherwise to identify the backtracking-related subset used for vector derivation.Source: A. Deriving steering vectors · p. 7

B.1. Base-derived and reasoning-derived steering vectors from all hidden layers

Figure B.1 compares steering effectiveness when vectors are trained on base-model versus fine-tuned-model activations.

B.1. Base-derived and reasoning-derived steering vectors from all hidden layers

  • Figure B.1 compares steering effectiveness for vectors trained on base-model versus fine-tuned-model activations.Source: Figure B.1 · p. 7

C. Consistency between human, LLM and keyword judges for backtracking detection

The section assesses agreement between LLM and keyword-based backtracking judgments, then uses human judgments to examine their discrepancies. Both automated measures are treated as proxies, with more sophisticated metrics needed where high precision and accuracy are critical.

C. Consistency between human, LLM and keyword judges for backtracking detection

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