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This paper argues that thinking models primarily learn when to deploy reasoning mechanisms that already exist in their base models, and demonstrates this by recovering up to 91% of the base-to-thinking performance gap with no weight updates

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 10:57 UTC pith:CZSISG5F

load-bearing objection A useful steering/taxonomy toolkit wrapped around an unsupported headline claim about RL teaching 'when', with abstract numbers that don't appear in the body. the 4 major comments →

arxiv 2510.07364 v4 pith:CZSISG5F submitted 2025-10-08 cs.AI cs.LG

Base Models Know How to Reason, Thinking Models Learn When

Constantin Venhoff , Iv\'an Arcuschin , Philip Torr , Arthur Conmy , Neel Nanda This is my paper
classification cs.AI cs.LG
keywords activation steeringsparse autoencodersreasoning taxonomiesreinforcement learning with verifiable rewardsknowledge distillationconstructive model diffingchain-of-thoughtbase-to-thinking gap
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tries to establish that the performance gap between base models and 'thinking' models is mostly a gap in timing, not in reasoning ability. The authors build a hybrid model in which a base model generates the tokens and a classifier derived from the thinking model decides when to apply a steering vector that activates a specific reasoning mechanism, such as backtracking, verifying, or planning. To find those mechanisms they train small sparse autoencoders on sentence-level activations, producing an unsupervised taxonomy of roughly ten to twenty reasoning behaviors. Across several model pairs, the hybrid recovers up to 91 percent of the base-to-thinking performance gap on GSM8K and MATH500 while steering only about 12 percent of tokens and updating no weights. The paper also claims that on a larger set of pairs the hybrid recovers 76 percent of the gap for RL-trained thinking models but only 11 percent for SFT-distilled ones, indicating that RL primarily teaches orchestration of pre-existing skills.

Core claim

On the paper's own terms, the central claim is that thinking models do not so much acquire new reasoning operations as learn a scheduling policy over operations that already exist in their base models as activation-space directions. Supporting evidence is constructive: the authors recover most of the thinking model's advantage by 'diffing' the base-to-thinking change into category vectors (directions that induce a reasoning mechanism) plus a classifier that fires the right vector at the right time. With this hybrid, the base model produces reasoning-level chains; the best result recovers 91 percent of the gap with no parameter updates and only sparse intervention. The distillation-vs-RL comp

What carries the argument

The load-bearing object is the hybrid model built through constructive model diffing: the difference between a base model and its thinking counterpart is decomposed into (1) category vectors — directions in the base model's activation space that causally induce a named reasoning mechanism — and (2) a reasoning-heuristic classifier that chooses when a mechanism should fire. The category vectors come from an unsupervised taxonomy: a top-k sparse autoencoder trained on sentence-level activations of thinking-model traces, with a deliberately small latent dictionary (5–50 units) so that each learned feature corresponds to a cognitive function like backtracking or uncertainty estimation. Steering

Load-bearing premise

The load-bearing premise is that the thinking model's classifier is only providing the timing while the base model supplies the reasoning itself; if that external oracle is secretly contributing orchestration or content, the claim that base models already know how to reason and only lack when is not established.

What would settle it

On MATH500 with a 32B-class base model, keep the trained category-specific steering vectors fixed but replace the thinking-model activation classifier with a timing rule computed entirely from base-model features, such as firing a steering vector whenever the base model's hidden-state norm crosses a threshold. If gap recovery falls from the reported 91 percent toward the random-firing ablation's 77.8 percent, the orchestration skill does not live in the base model; if recovery stays near 84–91 percent, the base indeed contains the when-information.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Reinforcement learning with verifiable rewards should be understood primarily as shaping when to deploy existing mechanisms, so RLVR design can focus on reward shaping for orchestration rather than on teaching individual reasoning steps.
  • Distillation transfers reasoning to smaller models mostly by teaching the when-deployment policy, which helps explain why distilled small models can approach much larger base models on math benchmarks.
  • Targeted activation-space interventions may substitute for full parameter updates when the base model already contains the mechanisms, pointing toward cheaper ways to build reasoning-specialized models.
  • The unsupervised taxonomy offers a reusable decomposition of reasoning traces, so failures can be attributed to a specific missing or mistimed mechanism rather than to general model weakness.
  • Sparse steering suffices: recovering most of the gap while steering only about 12 percent of tokens indicates that reasoning orchestration is concentrated in a relatively small set of decisions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A testable extension: if a timing signal computed entirely from base-model internal features (e.g., hidden-state norm spikes) can replace the thinking-model classifier without losing most of the gap recovery, then the 'when' knowledge is also latent in the base model; if recovery collapses, the oracle is doing more than the paper credits.
  • The when-versus-how split suggests a mechanistic account of test-time scaling: extra inference compute pays off only when the scheduling policy fires the right mechanism at the right point, tying the value of longer chains directly to the quality of the timing policy.
  • The framework predicts a boundary on steerability: mechanisms that a base model has never encountered in pretraining (a genuinely novel verification strategy, for instance) should have no corresponding category vector, which is a falsifiable boundary condition for 'base models know how to reason.'

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes that pretrained base models already contain the reasoning mechanisms used by thinking models, and that post-training (especially RLVR) primarily teaches the model *when* to activate these mechanisms. To support this, the authors (1) train small Top-K SAEs on sentence-level activations of reasoning traces to derive human-interpretable taxonomies of reasoning categories; (2) optimize steering vectors in base models that reproduce thinking-model completions for each category; and (3) build a 'hybrid model' in which a thinking-model activation classifier decides when to apply each steering vector during decoding. On five base/thinking pairs (four DeepSeek-R1-Distill, one QwQ-32B) and two math benchmarks, the hybrid recovers up to 91% of the thinking-model performance gap (Qwen2.5-32B + QwQ on MATH500) while steering only ~12% of tokens on average. The authors conclude that RLVR teaches orchestration heuristics, not new reasoning skills.

Significance. If established, the distinction between 'mechanisms' (latent reasoning abilities) and 'heuristics' (when to deploy them) would be an important conceptual contribution to understanding reasoning-model training and to designing cheaper interventions. The paper is strong on engineering: it releases code, documents hyperparameters in appendices, and the headline hybrid result (91% gap recovery on MATH500 with a 32B base) is a striking demonstration of activation-level control. However, the central interpretive claim is currently underdetermined by the experimental design because the timing signal is provided by the target thinking model itself, and because the nine-pair RL-vs-SFT analysis advertised in the abstract is absent from the body. The paper's contribution in its present form is best characterized as a promising proof-of-concept for oracle-driven activation steering, not a demonstrated theory of what RLVR training teaches.

major comments (4)
  1. [§3.2, Figure 1] The hybrid model is 'driven by the thinking model': at each token position, the classifier that decides which steering vector to fire is a 'thinking model activation classifier' (§3.2, caption of Fig. 1). The paper's central claim is that thinking models learn *when* to activate pre-existing mechanisms, but the hybrid inherits the 'when' signal directly from the target thinking model. The experiment therefore shows that a base model can be steered effectively when an oracle supplies the timing, not that the base model lacks or that RL training supplies this timing. A direct test would be to compare the base model's own SAE-based classifier with the thinking model's classifier, or to ablate the source of the timing signal while keeping the same steering vectors. Without such a control, the 91% gap-recovery result conflates 'the base model contains steerable mechanisms' with 'thinking-mode
  2. [Abstract (v3) vs. §3.3, Tables 1–2] The arXiv abstract claims a nine-pair analysis with 'category vectors in the base model converge to far lower loss for taxonomies derived from purely RL-trained models' and 'hybrid models recover roughly 76% of the RL base-to-thinking gap but only 11% of the SFT gap.' The supplied manuscript body contains none of this analysis: Tables 1–2 report five base/thinking pairs, all but one of which use DeepSeek-R1-Distill (SFT-distillation) targets; QwQ-32B is the only RLVR model. There is no category-vector loss comparison and no RL-vs-SFT gap-recovery contrast. The conclusion (§5) makes the RLVR-specific claim without any RLVR-vs-SFT evidence in the results. This is a load-bearing discrepancy: the title and abstract make a much stronger claim than the experiments in the body support. The missing analysis must either be added to the main text or the claims must be appropriately scaled back.
  3. [§3.1, item 4] Each steering vector is optimized to minimize cross-entropy on the thinking model's completion tokens (§3.1, item 4: 'Optimize a steering vector in the base model that, when applied, minimizes cross-entropy on the thinking model’s completion tokens'). This means the induced 'reasoning mechanisms' are fitted to reproduce the target model's outputs, rather than being discovered independently in the base model's representation. The hybrid result thus measures how well activation-space fitting can mimic thinking-model completions, which is not equivalent to demonstrating that the base model already 'knows how' to perform those mechanisms. The random-vector ablation (§3.4) controls for direction specificity, but it does not address the fact that the fitted directions are supervised by the target outputs. An additional control—e.g., using data-independent or contrastive directions, or checking
  4. [§3.3, Tables 1–2; §3.4] The headline 'up to 91% gap recovery' rests on a single favorable pair (Qwen2.5-32B with QwQ-32B on MATH500, a 23-point gap). Across the five pairs, gap recovery varies from 0% to 91%, and the two smallest models show essentially no or negative recovery (Tables 1–2; e.g., Qwen2.5-Math-1.5B on GSM8K: 0.0%; Llama-3.1-8B on MATH500: 3.5%). The paper attributes this to 'less clean steering directions' in smaller models, but this is a post-hoc interpretation. A reader cannot conclude that 'a significant portion of the thinking model’s advantage' is generally due to 'when' on the basis of these five pairs, especially since the largest gains come from the pair where the base is already strong. The authors should report a more systematic aggregate (or discuss the ceiling effects and model-size dependence) and avoid generalizing from the single 91% result.
minor comments (4)
  1. [§2.2] The taxonomy evaluation uses LLM-as-a-judge for completeness, consistency, and independence. The authors correctly note that 'the alignment between our evaluation pipeline and true human judgment remains to be validated' (§2.2), but the main text presents the taxonomy as 'human-interpretable' without human validation. This should be flagged in the results or moved to limitations.
  2. [§3.4 / Appendix C.4] The ablations and the appendix show substantial sensitivity to the steering coefficient/window sweep: for the 14B and 8B models, the 'narrower default' results differ markedly from the swept results (e.g., Llama-3.1-8B on GSM8K drops from 63.4% to 54.6%; Qwen2.5-14B on MATH500 drops from 75.4% to 69.4%). This suggests the reported gap-recovery numbers are strongly dependent on the hyperparameter selection protocol, which itself uses the thinking model's perplexity. The paper should discuss this sensitivity in the main text and provide error bars or repeated-selection stability analyses.
  3. [Table 3 and conclusion] The abstract and conclusion state 'steering only 12% of tokens,' but Table 3 reports per-problem steered fractions ranging from 6.5% to 21.5%; the 12% figure is an average. Consider reporting the range and clarifying that the 12% is the mean across pairs.
  4. [§1 and §5] The paper uses the phrase 'reinforcement learning with verifiable rewards (RLVR) used to train thinking models' (§1) to conclude that 'RL primarily teaches heuristics.' However, the four DeepSeek-R1-Distill models in the evaluation are distillation/SFT models, not RLVR-trained models. Only QwQ-32B is RLVR-trained. This terminology is misleading and should be clarified in the introduction and conclusion.

Circularity Check

2 steps flagged

Hybrid 'when' signal is supplied by the thinking model and steering vectors are fit to thinking completions — central claim partially reduces by construction.

specific steps
  1. fitted input called prediction [Section 3.1 (Finding Steering Vectors in Base Models), item 4; see also Tables 1-2]
    "4. Optimize a steering vector in the base model that, when applied, minimizes cross-entropy on the thinking model’s completion tokens."

    The category steering vectors—the only mechanism said to 'induce' reasoning behaviors in the base model—are fit directly to the target thinking model's own completions. The later demonstration that base + steering vector reproduces thinking-level behavior (up to 91% gap recovery) therefore partly restates the training objective: the vector was optimized to make the base model imitate the thinking model. Held-out transfer to GSM8K/MATH500 gives the result some empirical content, but the core 'base models already know how' claim is not an independent discovery; it is a fitted imitation evaluated on nearby tasks.

  2. self definitional [Section 3 (Steering Base Models to Reason), opening paragraph; Section 3.2 (Hybrid Model Implementation); Figure 1B]
    "In other words, the hybrid model is powered by the base model, but driven by the thinking model. ... (B) For each token position, we evaluate the current rollout in a target thinking model and use a 'thinking model activation classifier' to detect the reasoning mechanism that should be applied next."

    The paper's central conclusion is that RL teaches thinking models 'when' to deploy pre-existing base mechanisms. But in the hybrid experiment that supports this claim, the 'when' signal is supplied by the target thinking model's own classifier, not learned or demonstrated by the base model. The gap recovery therefore measures how well the base model follows an external oracle; it cannot distinguish 'base lacks when' from 'base has when but was not asked.' The conclusion is baked into the construction: the hybrid is defined as base + thinking-model timing.

full rationale

The derivation has two partially circular hinges. First, the 'reasoning mechanism' vectors that supposedly reveal latent base-model skills are fit directly to the thinking model's completion tokens (Sec. 3.1, item 4), so the observation that they elicit thinking-like behavior is partly a restatement of the fitting objective; only the held-out transfer to GSM8K/MATH500 gives it independent content. Second, and more central, the hybrid model that supports the paper's strongest claim ('thinking models learn when') delegates the 'when' decision to the target thinking model's own activation classifier (Sec. 3.2 / Fig. 1B). The base model is never tested on the timing component, so the conclusion that RL teaches 'when' rather than 'how' is assumed by the experimental construction rather than derived from it. The v3 abstract's nine-pair 76%-vs-11% RL/SFT contrast, which would be the cleanest test of the claim, does not appear in the supplied manuscript; that is an evidentiary gap rather than circularity, and I do not score it as such. The paper does contain independent content: the unsupervised SAE taxonomy is not circular, the steering vectors do transfer to held-out benchmarks, and the ablations (random firing vs. timed firing) show timing matters. Those elements keep the paper from being fully circular, but the central attribution of the gap to 'when' is structurally guaranteed by the oracle-based design and by fitting vectors to thinking outputs, so partial circularity is real. Self-citations (Venhoff et al. 2025; Ward et al. 2025a) are present but not the main load-bearing mechanism.

Axiom & Free-Parameter Ledger

6 free parameters · 6 axioms · 2 invented entities

The central claim rests on hand-selected taxonomy hyperparameters and on the assumption that grafting a thinking-model oracle onto a base model does not change the conclusion about what thinking-model training teaches.

free parameters (6)
  • SAE dictionary size (number of reasoning categories per model) = 5-25 across models (grid 5-50, step 5; elbow selected)
    Taxonomy size set by grid-search elbow; the claim that 10-20 categories capture reasoning depends on this choice.
  • Top-k sparsity k = 3
    Assumed at most 3 mechanisms active per sentence; no sensitivity analysis shown.
  • SAE layer per model = e.g., Llama-8B layer 6, QwQ-32B layer 27
    Selected as best from 6 evenly distributed layers; taxonomies and steering vectors are layer-dependent.
  • Steering layer depth = 37% of model depth
    Chosen from prior work (Venhoff et al. 2025), not derived per base/thinking pair.
  • Steering coefficient and window per token = coefficients {0.1..1.0}, windows {0,-1,-15,-50,-100}; selected by lowest perplexity under thinking model
    Per-token hyperparameter selection partially tunes the evaluation to the target model and can inflate gap recovery.
  • Steering vector training examples and hyperparameters = 8192 top sentences -> 2048; lr=1e-2; 50 iterations; batch 6
    Hand-set by the authors; no sensitivity analysis shown.
axioms (6)
  • domain assumption Linear representation hypothesis: behaviors are directions in residual-stream activation space.
    Invoked to justify steering vectors in Section 3; if wrong, steering-vector intervention does not isolate reasoning mechanisms.
  • domain assumption Sentence-level averaging preserves reasoning categories; each sentence has at most 3 active categories.
    Section 2.1: 'We average activations over sentences under the assumption that each sentence can be primarily classified by one or, at most, three reasoning categories.'
  • domain assumption Restricted Top-K SAE (dimensions 5-50, k=3) discovers complete, independent reasoning taxonomies.
    Sections 2.1-2.2; completeness and independence are evaluated by LLM judges, not human raters.
  • domain assumption LLM-as-a-judge scores are valid proxies for interpretability and category quality.
    Sections 2.2 and Appendix B; authors explicitly note 'the alignment between our evaluation pipeline and true human judgment remains to be validated.'
  • domain assumption A classifier/SAE trained on thinking-model activations can identify when to fire reasoning mechanisms in a base model's rollout.
    Section 3.2 hybrid design; this external-oracle timing signal is what 'thinking model learns when' is supposed to explain.
  • domain assumption Recovering performance with an external oracle implies base models already contain the mechanisms and only lack orchestration.
    Sections 3.3 and 5; this is the interpretive step never tested by a control where the base model must decide when.
invented entities (2)
  • Reasoning mechanism category vectors no independent evidence
    purpose: Steering directions that induce a reasoning behavior in the base model
    Optimized to reproduce thinking-model completions; no external falsifiable handle outside this pipeline. Within-paper ablations (random vectors) are not independent evidence.
  • Reasoning heuristics (the classifier deciding when a mechanism fires) no independent evidence
    purpose: The 'when' component attributed to thinking-model training
    Constructed from SAE clusters and LLM labels on thinking-model traces; not independently validated as a real cognitive variable.

reviewed 2026-08-04 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Base Models Know How to Reason, Thinking Models Learn When." pith.science (2026). https://pith.science/paper/CZSISG5F

@misc{pith2026251007364,
  author       = {Pith},
  title        = {Pith review of: Base Models Know How to Reason, Thinking Models Learn When},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CZSISG5F}},
  note         = {Machine review of arXiv:2510.07364}
}
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read the original abstract

What do thinking language models learn during training that their base models lack? We first present an unsupervised method that discovers a model's reasoning behaviors by training small Sparse Autoencoders on sentence-level activations of reasoning traces, yielding interpretable reasoning taxonomies. Building on this, we introduce constructive model diffing, which aims to reconstruct the base-to-fine-tuned difference from interpretable components: reasoning mechanisms (category vectors that can induce a reasoning behavior in the base model) and reasoning heuristics (a classifier determining when a mechanism should fire). Across nine base/thinking pairs (four RL-trained, four SFT-distilled, one mixed), two independent findings agree: category vectors in the base model converge to far lower loss for taxonomies derived from purely RL-trained models, and hybrid models recover roughly 76% of the RL base-to-thinking gap but only 11% of the SFT gap. This indicates RL primarily teaches heuristics for orchestrating pre-existing base mechanisms, whereas SFT-distillation installs new ones, offering a new lens on what training paradigms teach, with implications for efficient reasoning-model development.

Figures

Figures reproduced from arXiv: 2510.07364 by Arthur Conmy, Constantin Venhoff, Iv\'an Arcuschin, Neel Nanda, Philip Torr.

Figure 1
Figure 1. Figure 1: Hybrid Models Unlock Reasoning Model-Level Behavior with Minimal Intervention. Overview of our approach for steering base language models to reason like thinking models. (A) We use the base model as the primary generator of tokens in the output sequence. (B) For each token position, we evaluate the current rollout in a target thinking model and use a “thinking model activation classifier” to detect the rea… view at source ↗
Figure 2
Figure 2. Figure 2: Grid search results comparing the performance of Sparse Autoencoder taxonomies across the five thinking models in our taxonomy evaluation. Each heatmap shows the combined score (average of completeness, independence, and consistency) for different combinations of layer locations (x-axis) and cluster sizes ranging from 5 to 50 with increments of 5 (y-axis). Values highlighted in blue indicate particularly s… view at source ↗
Figure 3
Figure 3. Figure 3: Hybrid model in action. Example of a hybrid model (Qwen2.5-32B as the base model with steering vectors trained on QwQ-32B thinking model) solving a MATH500 problem, showing how steering vectors are dynamically applied based on SAE activations to guide the base model’s reasoning process. The model successfully identifies and applies appropriate reasoning mechanisms at each step, demonstrating the effectiven… view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.