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RAST: Reasoning Activation in LLMs via Small-model Transfer

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that the token-level probability shifts reinforcement learning induces in a small model can be transferred at decoding time to a larger base model, recovering most of the RL performance gap without running RL on the…

desk verdict RAST is a practical empirical contribution with a simple, honest method, but the size-invariance hypothesis is much thinner than the abstract implies. read the letter →

arxiv 2506.15710 v1 pith:4K5Z7M56 submitted 2025-05-30 cs.LG cs.AI

Siru Ouyang , Xinyu Zhu , Zilin Xiao , Minhao Jiang , Yu Meng , Jiawei Han This is my paper
classification cs.LGcs.AI
keywords reinforcementlearningLLMreasoningdecoding-timetransferlogit-spacecorrectionmodel-sizeinvariancezero-RLmathematicalpathcoveragerate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to prove that the reasoning gains from reinforcement learning on a language model are a transferable signal: the small set of token-level probability shifts RL induces in a small model can be added to a larger model's logits at decoding time, giving the larger model most of the reasoning improvement with none of the RL training cost. The claim matters because RL on large models currently means loading several copies of the model and running long training loops; if the signal transfers, the expensive part can be done once on a small model and replayed on any larger model that shares its vocabulary. The authors first measure how much of an RL-trained model's output path a base model already reproduces token by token and find over 95% overlap, supporting their hypothesis that RL adjusts only a sparse set of reasoning-critical tokens. They then define RAST, which decodes with the base logits plus a scaled logit difference from a small RL-trained pair, and show across six math and three code benchmarks that it consistently lifts the base model, recovering between roughly 60% and over 100% of the gap to the fully RL-trained model while using about half the GPU memory. The paper's 1.5B-transfer experiments, where the prompt template did not match, show visibly smaller gains, which marks the practical boundary of the claim.

What carries the argument

The load-bearing object is the delta-logit signal $\Delta_R(x_{<t}) = S_{\mathrm{RL}}(x_{<t}) - S_{\mathrm{base}}(x_{<t})$, the token-level difference in logits between a small RL-trained model and its own base twin, injected additively at every decoding step through $P = \mathrm{softmax}[M_{\mathrm{base}} + \lambda \Delta_R]$, which amplifies tokens tied to behaviors such as self-verification, branching, and backtracking while leaving ordinary tokens to the base model. Two diagnostics carry the empirical argument: path coverage rate (PCR), the fraction of an RL-produced trajectory that the base model regenerates token for token, which the paper measures above 95% and uses as direct evidence for the sparsity of RL-induced shifts; and cosine similarity between delta signals from different model pairs, which the paper shows correlates with recovery rate so that users can predict transferability before running experiments.

What would settle it

A concrete test: apply a delta computed from a small RL-trained model to a larger base that uses a different tokenizer or a mismatched prompt template, and measure path coverage rate plus recovery on the same benchmarks. The size-invariance hypothesis predicts PCR stays near 95% and recovery stays well above zero; the paper's own AIME24 results, where recovery is roughly 62% and the base gains are small, mark where the claim already starts to weaken, so a dataset or pairing that drives PCR below 90% with recovery near zero would falsify the transfer claim.

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Extended reading notes

Core claim

The central claim is that RL-induced probability shifts are largely model-size invariant, so the logit-space correction $\Delta_R = S_{\mathrm{RL}} - S_{\mathrm{base}}$ learned on a small model pair carries reasoning behavior that can be activated in larger models at inference. The proposed decoding rule is $P(x_t \mid x_{<t}) = \mathrm{softmax}[M_{\mathrm{base}}(x_{<t}) + \lambda(S_{\mathrm{RL}}(x_{<t}) - S_{\mathrm{base}}(x_{<t}))]$, with $\lambda = 1.0$; path coverage rate, the fraction of the RL trajectory the base regenerates greedily, stays above 95% for 7B, 14B, and 32B models, which the paper reads as evidence that RL steers a small number of reasoning-critical tokens rather than rewriting outputs. On MATH500, AIME24, AMC, Minerva, OlympiadBench, and GSM8K, adding the transferred delta lifts every base model tested, with average recovery rates of the gap to the RL-trained ceiling ranging from 63.4% to 84.8% depending on the pairing, and recovery above 100% in some cells; on Llama-3.1-70B with an 8B delta and on a 14B coding model with a 7B delta the correction transfers across families and domains. The paper also claims the correction widens the sampling search space, so RAST's pass@k reaches or exceeds the RL-trained model's, and that cosine similarity between candidate deltas predicts recovery rate, giving a cheap pre-screening signal.

Load-bearing premise

The assumption that carries the argument is that the logit-space difference measured on a small model pair transfers unchanged to a larger model's logits, which requires a shared tokenizer, comparable logit scales, and matching prompt templates; the paper's own 1.5B experiments, where the template differed from the training prompt, produced visibly smaller gains, marking where the transfer starts to break.

Editorial extensions

If this is right

  • Transplanting a 14B-trained delta into a 32B base yields an average recovery rate of 84.8% across the math benchmarks while needing roughly 160 GB of GPU memory against about 350 GB for full RL training of the 32B model, so most of the reasoning gain arrives at roughly half the memory cost.
  • Recovery rates vary with the pairing and benchmark, from 63.4% to over 100%; on Minerva the 32B base with the 14B delta exceeds the RL-trained 32B model outright, so the transferred signal can sometimes beat its own ceiling.
  • Sampling with the transferred delta yields pass@k curves that reach or exceed the RL-trained model's on all six math benchmarks, indicating the correction diversifies the search space instead of narrowing it.
  • The correction transfers across model families and domains: an 8B Llama-3.1 delta lifts Llama-3.1-70B on all six math benchmarks, and a 7B code delta lifts a 14B coding model by 4.4 points on average, so the mechanism is not specific to one architecture or task type.
  • Because recovery rate tracks the cosine similarity between candidate delta signals, a user can screen which small RL expert to train by measuring delta alignment first, without running full evaluations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial extension: if RL-induced shifts are size-invariant beyond the two families tested, the economics of reasoning RL change — one small expert's delta becomes a reusable inference-time asset for any larger model sharing its tokenizer, decoupling reasoning quality from per-model training budgets.
  • Editorial extension: the shared-tokenizer requirement is the hidden boundary of the claim, so a natural test is whether deltas survive cross-vocabulary transfer after a token-alignment or projection step, which the paper does not attempt.
  • Editorial extension: RAST is a parameter-free distillation of RL behavior into decoding; distilling the delta into a lightweight adapter (as the paper's future-work section suggests) would make the correction persistent and avoid running three models at inference.
  • Editorial extension: the fact that RAST's pass@k can exceed the RL-trained ceiling hints that the combination of base knowledge and transferred behavior searches more broadly than either alone, which suggests the enhanced sampler could itself generate training data for further RL — a loop the paper does not test.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes RAST, a decoding-time method that augments a large base model's logits with the logit difference ΔR = SRL − Sbase computed from a small RL-trained model and its base counterpart. The authors first present a hypothesis that RL-induced probability shifts are largely model-size invariant, supported by a path-coverage-rate analysis on 50 SimpleRL trajectories. They then evaluate RAST across Qwen-2.5 and Llama-3.1 math benchmarks and a code benchmark, reporting consistent pass@1 gains, a recovery-rate analysis, robustness sweeps over λ and temperature, and an estimated GPU-memory comparison with GRPO.

Significance. If the empirical results hold, RAST is a practical and inexpensive alternative to full-scale RL: it requires no RL training on the large model, only an additional forward pass through a small pair at inference time, and it is simple to implement. The paper's strongest assets are the breadth of the evaluation (three model families, nine benchmarks, multiple pass@k levels), the fixed λ=1.0 with a robustness sweep, and honest limitations. However, the paper's explanatory claim about size invariance is not yet supported by the evidence, because all alignment measurements are made on RL-expert trajectories rather than on the prefixes where RAST actually applies the delta. If the empirical gains are robust, the method could still be valuable even if the hypothesis is refined or replaced; the main contribution would then be empirical rather than mechanistic.

major comments (3)
  1. [Sections 2.1 and 4.1 (Eqs. 1-2, 6)] The size-invariance evidence is computed only on 50 trajectories generated by SimpleRL-32B. PCR measures whether Mbase can continue the RL expert's path, and AvgCosineSim is computed by feeding those same RL trajectories through Mbase and MRL. Neither measures the alignment between small-model and large-model deltas on the prefixes that RAST actually decodes from, namely prefixes generated by Mbase or by the augmented model in Eq. (3). Because SRL and Sbase may be off-distribution on those prefixes, the transferred ΔR could in principle be a fixed output bias (e.g., for longer or self-verification text) rather than a scale-invariant reasoning signal. I ask for a concrete test: compute PCR and AvgCosineSim(ΔR_small, ΔR_large) on prefixes sampled from Mbase and from RAST itself, not only from MRL, and report whether the observed alignment persists on those prefixes. This is needed to support the abstract's 'largely model-size invariant' claim.
  2. [Tables 1-3 and §3.2] The central empirical claim of consistent gains is reported without variance or significance statistics. Pass@1 is averaged over 32 runs, yet no confidence intervals, standard deviations, or paired tests are given, so several reported gains are difficult to interpret. For example, Qwen-2.5-32B on GSM8K goes from 93.1 to 93.3 with ΔR1.5B, and Llama-3.1-70B on AIME24 goes from 0.0 to 2.8; both are within the range one would expect from 32-sample sampling noise. The only error bars appear in Figure 6 for a single configuration. Please add bootstrap confidence intervals or paired significance tests for all main tables, or state explicitly which reported differences are not statistically distinguishable.
  3. [Table 1 footnote and Fig. 7] The 1.5B row is confounded with a prompt mismatch. The footnote says the prompt used for RAST does not match the one used to train the small RL-tuned model, and Appendix A.2 explains that a different template (Prompt b) is used for the 1.5B source. This means the observed smaller gains for ΔR1.5B, and the 'stronger experts yield greater gains' trend in §3.2, may be partly an artifact of prompt mismatch rather than model scale. The claim that RAST transfers across scales would be better supported by using a matched-prompt 1.5B RL model, or by an ablation in which the same mismatch is artificially applied to ΔR7B and ΔR14B.
minor comments (6)
  1. [Section 4.2] 'PRC' is used instead of 'PCR' in the sentence 'The PRC in this experiment is 96.37%'; the acronym is inconsistent with Eq. (2).
  2. [Figure 4] The figure is difficult to read as printed: the plotted points and axes are not clearly labeled, and the numbers in the caption are not mapped to visible axes. Please redraw with explicit axis labels and a legend.
  3. [Appendix E] 'MAHT500' is a typo for MATH500.
  4. [Section 3.3 and 4.2] There are several grammatical slips, including 'pass@k for MRL is large than Mbase' and 'the tn+1-th token based on the first n tokens'; these should be corrected.
  5. [Table 5] The decoding-configurations table mixes model names and hyperparameter rows; separating base-model and RAST rows would improve readability.
  6. [General] No code release is mentioned in the text beyond the project page; given the revised vLLM implementation and the reproducibility claims, an explicit code link would be valuable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: RAST's decoding rule is an empirical proposal tested on external benchmarks, and its supporting analyses do not construct the reported gains.

full rationale

RAST's central claim is an empirical one: adding ΔR = SRL − Sbase at decoding time (Eq. 3) improves a larger base model's reasoning performance. Equation 3 is a proposed decoding rule, not a consequence derived from the size-invariance hypothesis. The hypothesis is supported by PCR and cosine-similarity measurements, but neither quantity appears as a fitted parameter in Eq. 3, and the gains in Tables 1–3 are measured on MATH500, GSM8K, AIME, AMC, Minerva, OlympiadBench, and code benchmarks rather than being definitionally entailed by the delta. The PCR result quantifies how often the base model predicts the next token of an RL expert trajectory; it is evidence about the hypothesis, not a construction of the RAST output. No fitted input is renamed as a prediction: λ is fixed to 1.0 in the main experiments, with a robustness sweep reported in Fig. 6, and the paper explicitly presents the method as simple and fixed rather than optimized against the evaluation sets. The only self-citation with author overlap is [76] (Jiawei Han), which appears in a future-direction sentence about LoRA distillation and is not load-bearing. The paper's own Appendix F acknowledges the lack of theoretical understanding and the dependence on expert quality, which is consistent with an empirical, non-circular derivation chain. The skeptic concern that PCR and cosine similarity are measured on RL-expert trajectories rather than on the base/RAST prefixes where ΔR is actually applied is a correctness risk about the strength of the evidence, not a circularity, because RAST's measured improvements are not forced by those measurements. Overall, the derivation chain is self-contained: the method is defined explicitly, the hypothesis is tested separately, and the reported predictions are external to the definition.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical or theoretical entities; its free parameters reduce to the single strength knob lambda. The main load-bearing commitments are borrowed empirical claims about RL (no new knowledge), the representativeness of a 50-trajectory sample, and logit-space comparability across model scales.

free parameters (1)
  • lambda (deltaR strength) = 1.0
    Eq. 3 multiplies the logit delta by lambda; default lambda=1.0 for all experiments, with robustness sweep in Section 4.4 showing moderate sensitivity.
assumptions (3)
  • domain assumption RL-from-scratch training does not add new knowledge; it reshapes the output distribution to activate latent reasoning behaviors
    Invoked in Section 1 to motivate why deltas could transfer across scales; the paper relies on prior works [70,12,74,40,8] for this, and it is not independently proven here.
  • domain assumption The 50 sampled MATH500 trajectories from a single RL-tuned model are representative for measuring PCR and delta-logit similarity across model scales
    Sections 2.1 and 4.1 draw the main evidence for the scale-invariance hypothesis from these samples, without confidence intervals or multiple datasets.
  • domain assumption The logits of SRL, Sbase, and Mbase are directly comparable: shared tokenizer, comparable scales, and matched prompt templates
    Eq. 3 adds logits across models; the paper only uses same-family models, and the prompt-mismatched 1.5B delta shows degraded gains, indicating sensitivity to this assumption.

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Cite this review

Pith. "Pith review of RAST: Reasoning Activation in LLMs via Small-model Transfer." pith.science (2026). https://pith.science/paper/4K5Z7M56

@misc{pith2026250615710,
  author       = {Pith},
  title        = {Pith review of: RAST: Reasoning Activation in LLMs via Small-model Transfer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4K5Z7M56}},
  note         = {Machine review of arXiv:2506.15710}
}
read the original abstract

Reinforcement learning (RL) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs), as evidenced by recent successes such as OpenAI's o1 and Deepseek-R1. However, applying RL at scale remains intimidatingly resource-intensive, requiring multiple model copies and extensive GPU workloads. On the other hand, while being powerful, recent studies suggest that RL does not fundamentally endow models with new knowledge; rather, it primarily reshapes the model's output distribution to activate reasoning capabilities latent in the base model. Building on this insight, we hypothesize that the changes in output probabilities induced by RL are largely model-size invariant, opening the door to a more efficient paradigm: training a small model with RL and transferring its induced probability shifts to larger base models. To verify our hypothesis, we conduct a token-level analysis of decoding trajectories and find high alignment in RL-induced output distributions across model scales, validating our hypothesis. Motivated by this, we propose RAST, a simple yet effective method that transfers reasoning behaviors by injecting RL-induced probability adjustments from a small RL-trained model into larger models. Experiments across multiple mathematical reasoning benchmarks show that RAST substantially and consistently enhances the reasoning capabilities of base models while requiring significantly lower GPU memory than direct RL training, sometimes even yielding better performance than the RL-trained counterparts. Our findings offer new insights into the nature of RL-driven reasoning and practical strategies for scaling its benefits without incurring its full computational cost. The project page of RAST is available at https://ozyyshr.github.io/RAST/.

Figures

Figures reproduced from arXiv: 2506.15710 by the authors.

Figure 1
Figure 1. (a) PCR (path coverage rate) across different model scales. (b) A case study revealing the decoding path of Mbase and its RL-trained version MRL. Only a very small subset of tokens differ on the decoding path between Mbase and MRL, which indicates particular reasoning behaviors. 4]. It is increasingly believed that RL does not endow LLMs with fundamentally new knowledge [70, 12]. Instead, it serves to elicit and amp… view at source ↗
Figure 2
Figure 2. A concrete illustration of RAST: logit differences from a small RL-tuned model SRL guide a large base model Mbase at decoding time, amplifying reasoning-relevant predictions (e.g., “instead”) while maintaining base outputs for non-reasoning tokens (e.g., “of”). 3 Unlocking Reasoning Activation 3.1 Experimental Setup Models and Tasks We systematically evaluate model performance across a comprehensive suite of mathema… view at source ↗
Figure 3
Figure 3. The illustration of pass@k for different values of k on 6 mathematical reasoning datasets, where Mbase is Qwen-2.5-32B, RAST uses ∆R14B, and MRL is the RL-trained version of Mbase. ∆R from stronger experts yield greater gains. The effectiveness of RAST also depends on the strength of the SRL and Sbase that generates the delta logit ∆R. For each base model, using larger delta sources (e.g., base model of 32B with ∆R7… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Cosine similarity vs. re￾covery rate across delta logit pairs (∆R) from varying model scales. E.g., “∆R14B v.s. ∆R7B” denotes AvgCosineSim(∆R14B, ∆R7B). As shown in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: A case study comparing generated outputs for the same math problem sampled from [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Experiment results with varying λ (left) and τ (right) on MATH500 dataset, ⋆ denotes the peak performance. The position represents the accuracy, and the size of the circle denotes the standard deviation over 32 runs. 4.4 Robustness regarding τ and λ To evaluate the sen…
Figure 7
Figure 7. Figure 7: Prompt templates used for mathematical reasoning tasks. [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: The illustration of majority@k for different values of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: The set of manually curated reasoning tokens that corresponds to three key reasoning [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: Normalized frequencies of reasoning-related tokens across three models ( [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

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