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Two Experts Are All You Need for Steering Thinking: Reinforcing Cognitive Effort in MoE Reasoning Models Without Additional Training

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Multiplying the routing weights of two identified "cognitive experts" by 64 raises DeepSeek-R1's AIME24 accuracy from 73.3% to 83.3% and its AIME25 accuracy from 63.3% to 73.3%, with no additional training.

desk verdict Cheap and potentially useful inference-time MoE steering, but the headline gain is partly in-sample and the 'cognitive expert' interpretation needs a token-matched control. read the letter →

arxiv 2505.14681 v2 pith:IREKU4KR submitted 2025-05-20 cs.AI cs.CLcs.CVcs.IRcs.LG

Mengru Wang , Xingyu Chen , Yue Wang , Zhiwei He , Jiahao Xu , Tian Liang , Qiuzhi Liu , Yunzhi Yao
show 7 more authors
Wenxuan Wang Ruotian Ma Haitao Mi Ningyu Zhang Zhaopeng Tu Xiaolong Li Dong Yu
This is my paper · ORCID
classification cs.AIcs.CLcs.CVcs.IRcs.LG
keywords mixture-of-expertscognitiveexpertsexpertsteeringnPMIreasoningefficiencytest-timeinterventionDeepSeek-R1underthinking
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

Multiplying the routing weight of just two experts, identified by their co-occurrence with `` tokens, at inference time improves both accuracy and token efficiency in DeepSeek-R1 and Qwen3-235B. On AIME24, DeepSeek-R1 rises from 73.3% to 83.3%; on the unseen AIME25, from 63.3% to 73.3%, and the same recipe transfers to Qwen3-235B. The method needs no gradient updates, no prompt changes, and only a single forward pass to identify the experts. If the empirical claim holds, reasoning quality in MoE models can be steered cheaply by modulating a tiny expert subset rather than retraining or constraining decoding.

What carries the argument

The nPMI selection score given in Eq. 6: for each expert, compute the normalized pointwise mutual information between its activation and a set of thinking tokens, weighted by coefficients c_<think> = 1, c_</think> = -1, and c_Alternatively = -1, then select the top-l experts as the cognitive expert set. The steering operation is a simple weight multiplication w_i <- w_i * beta for experts in that set, with beta = 64 and l = 2. nPMI marks experts whose activation co-occurs almost exclusively with the start-of-think token and not with end-of-think or alternative-branch tokens.

What would settle it

Run the same nPMI identification and weight amplification on a model whose thinking tokens are renamed without retraining, for instance replace `<think>` with `[reason]`: if the identified cognitive experts change completely and the accuracy gain disappears, the effect depends on token-format artifacts rather than reasoning substance. Alternatively, set the two identified experts' weights to zero and check whether accuracy stays unchanged.

Watch

Extended reading notes

Core claim

The central claim is that two experts per model, namely DeepSeek-R1's (39,182) and (29,126) and Qwen3-235B's (70,47) and (23,115), act as cognitive experts: they fire disproportionately on reasoning-marker tokens, and when their gating weights are multiplied by 64, they shift the model toward committing to correct reasoning paths. The paper reports accuracy gains on AIME24 and AIME25 while reducing thought count and tokens on several benchmarks, and shows that the same experts transfer across math, physics, and the aggregated "All" condition. The authors are explicit that the "cognitive expert" is a hypothetical construct with no theoretical justification; the case is empirical.

Load-bearing premise

The load-bearing premise is that which experts fire alongside the literal `<think>` token is a reliable sign of which experts actually do the reasoning, and not just a quirk of how that special-format token is processed; the paper itself labels the "cognitive expert" a hypothetical construct.

Editorial extensions

If this is right

  • Boosting two cognitive experts improves DeepSeek-R1's AIME24 accuracy by 10 points and AIME25 accuracy by 10 points without additional training.
  • The gains come with fewer or comparable tokens, with AIME24 thoughts dropping from 12.0 to 10.2 and tokens from 9,219 to 8,317, so the effect is not simply longer output.
  • The same two-expert intervention generalizes across math, physics, and chemistry and to an unseen harder exam set.
  • The method outperforms prompt placement and thinking-token decoding constraints by 2.0 average points on the AIME benchmarks.
  • General instruction-following on ArenaHard is maintained or slightly improved, from 91.0% to 92.0% with the aggregated "All" experts.

Reading between the lines

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

  • If the effect is real, it suggests that a model's overt reasoning format is controlled by a sparse, stable set of routing units, so other meta-cognitive behaviors such as verification, backtracking, and confidence might each have their own small expert sets addressable by the same nPMI scan.
  • The nPMI selector could be repurposed as a diagnostic for whether a reasoning model's "thinking" is semantically grounded or merely token-format-triggered; comparing cognitive experts found on formal symbolic reasoning versus natural-language puzzles would test that.
  • A practical implication is that cheap inference-time steering could be deployed in production without changing weights, but only if the identified experts are stable across prompts, seeds, and model checkpoints, which the paper does not fully establish.
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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

4 major / 7 minor

Summary. The paper proposes RICE, an inference-time method that identifies 'cognitive experts' in MoE reasoning models by computing nPMI between expert activations and the tokens <think>, </think>, and Alternatively, then amplifies the top-l such experts' router weights by a multiplier beta. The method requires no training. Experiments on DeepSeek-R1 and Qwen3-235B report accuracy gains on AIME24 (73.3 to 83.3 for DeepSeek-R1), AIME25 (63.3 to 73.3), mixed GPQA-domain changes, and neutral-to-positive ArenaHard instruction-following results. The authors explicitly state that the 'cognitive expert' is a hypothetical construct and that their conclusions are purely empirical.

Significance. If the central claim holds, the paper contributes an unusually lightweight and interpretable steering mechanism for large MoE reasoning models, with potential practical value and a concrete hypothesis about expert semantic specialization. The authors should be credited for a simple identification procedure requiring a single forward pass, useful controls (random expert selection, renormalization, pass@k), and a transparent limitations statement. However, the headline effect is partly in-sample, the independent evidence is based on very small benchmarks, and no control rules out selection by token-format association rather than by causal reasoning relevance. These issues currently prevent the paper from supporting its causal 'cognitive expert' interpretation.

major comments (4)
  1. [Section 3.2, Tables 2 and 3] The headline AIME24 result (73.3 to 83.3) is partly in-sample: expert identification, the choice of l=2, and the multiplier beta=64 are all selected by grid search on AIME24, and the same benchmark is then reported as the main gain. The only fully independent evidence is AIME25, which contains 30 questions, so the 10-point improvement corresponds to three additional solved problems; no confidence intervals or significance tests are provided. Please evaluate on a disjoint validation set for hyperparameter selection, and report binomial or McNemar intervals for AIME24, AIME25, and the GPQA domains.
  2. [Section 2.1 and 'On the Cognitive Expert'] The paper states that the 'cognitive expert' is a hypothetical construct with no theoretical justification. Because the nPMI scores are computed against the format tokens <think>, </think>, and Alternatively, the procedure may select experts that fire on special tokens rather than experts causally involved in reasoning. The random-expert baseline in Table 2 does not address this, since random experts are not matched on nPMI or token association. Please add a token-matched control: select experts by the same nPMI procedure using control tokens (e.g., 'Therefore', 'However', or non-reasoning special tokens) and show that boosting them does not reproduce the AIME24/AIME25 gains; also report whether the same experts are selected when identification is performed on held-out problems.
  3. [Table 8 and Table 3] The appendix reports Qwen3-235B math cognitive experts as (39, 182), (29, 126), etc., identical to the DeepSeek-R1 entries in Table 1, yet the main Qwen3 experiments in Table 3 use {(70,47), (23,115)}. Since Section 3.1 states Qwen3-235B selects 8 experts from a total of 128, entries such as (39,182) are not valid expert IDs for that model. This inconsistency must be corrected; as written, it undermines the Qwen3 generalization claims.
  4. [Section 3.3, Table 4] The claim of 'consistent improvements' across domains is not supported by Table 4: math-selected experts reduce Physics from 91.9 to 89.5, and biology-selected experts reduce the average relative to baseline (71.9 vs. 73.4). The aggregated 'All' improvement of 75.6 vs. 73.4 is driven mostly by Math. Please provide per-domain significance tests or a corrected formulation of the claim, and avoid interpreting a 2.2-point average gain on the combined AIME24 and GPQA mix as robust given the small AIME24 sample.
minor comments (7)
  1. [Eq. (4)-(5)] The definition of kn is ambiguous for tokens where multiple experts are selected; please specify whether counts are per (token position, expert) pair and how the gating weights enter the counts.
  2. [Section 3.2 and title] The text contains 'these cognitive cognitive experts' (duplicated word) and the title has an unusual spacing in 'Y ou'; both should be corrected.
  3. [Table 6] The claimed 2.0-point average gain over TIPt is driven by AIME24; on AIME25 both methods achieve 73.3, so the comparison should be described as AIME24-specific.
  4. [Section 3.4] The ArenaHard evaluation uses 50 randomly selected queries and GPT-4-Turbo pairwise judgments; please state the number of comparisons, agreement or variance, and why 50 queries are sufficient to support the neutral-impact conclusion.
  5. [Appendix B.2] The pass@1 result on AIME25 for DeepSeek-R1 decreases from 68.5 to 67.7 under RICE, which contradicts the text claiming consistent improvements; please reconcile this with the pass@8 discussion.
  6. [Appendix B.3 and main text] It is not clear whether the main paper results (Tables 2-4) use renormalization; please state this explicitly in the setup, since Table 11 shows that renormalization changes qualitative conclusions, including AIME25 (63.3 vs. 73.3).
  7. [Section 5] The Conclusion is followed by a truncated duplicate paragraph beginning 'itive experts" within MoE...', which should be removed.

Circularity Check

1 steps flagged · score 4.0 of 10

AIME24 headline gain is an in-sample tuning result; out-of-sample AIME25 support is independent but small.

  1. fitted input called prediction [Section 3.2, Tables 2-3 (with Eq. 6-7 in Section 2.2)]
    "Once identified, we reinforce the cognitive experts identified from the Math domain (AIME24) and evaluate their performance under different reinforcement configurations on the same benchmark AIME24 (Table 2). The optimal hyperparameters – the number of cognitive experts l and the steering multiplier β—are selected based on this evaluation and used in all subsequent experiments. ..."

    The expert identities P are derived from nPMI scores computed on AIME24 responses, and the number of experts l and multiplier β are chosen by maximizing AIME24 accuracy in Table 2. The reported 73.3% to 83.3% AIME24 result is therefore the best configuration selected on the same 30-problem benchmark, not an out-of-sample prediction; the abstract's claim of 'consistent improvements' leans in part on this in-sample optimum. AIME25 and the GPQA cross-domain evaluations are genuinely held out and mitigate the issue, so the circularity is partial rather than total.

full rationale

The paper makes no pretense of a theoretical derivation: it explicitly labels the 'cognitive expert' a hypothetical construct and states that conclusions are purely empirical. The nPMI selection is a correlational definition, and the AIME25 and GPQA results are real out-of-sample evaluations, so the central accuracy claim is not equivalent to its inputs by construction. The main circularity concern is that expert identification, hyperparameter tuning, and the flagship AIME24 evaluation all use the same 30-problem set; the paper discloses this in Section 3.2, but the abstract-level phrasing 'noticeable and consistent improvements' leans on that in-sample result. The self-citations to the authors' prior work on underthinking (Wang et al., 2025a) are used for the Thoughts metric and the TIPt baseline, but they are not load-bearing for the accuracy claim. Overall score 4 reflects partial, selection-based circularity rather than definitional equivalence.

Assumptions & free parameters 4 free parameters · 3 assumptions · 1 invented entities

The method's central claim rests on several hand-chosen components: the set of thinking tokens, the coefficient signs in Eq. 6, the number of experts, and the multiplier beta. The only invented entity is the 'cognitive expert', which the paper itself labels hypothetical. No theory links nPMI co-occurrence to causal reasoning function.

free parameters (4)
  • Reinforcement multiplier beta = 64 (peak also at 4, 32, 128 on AIME24; 83.3%)
    Grid-searched on AIME24 in Table 2 and fixed for all later experiments (Section 3.2). This is a free parameter fitted to the same set used for the headline result.
  • Number of cognitive experts l = 2 (Top2)
    Selected by comparing Top1-Top5 on AIME24 (Table 2); l=2 is most robust. Sensitivity is high: Top3-Top5 collapse at large multipliers (e.g., Top5 13.3% at beta=128).
  • nPMI token coefficients (c_think, c_endthink, c_Alternatively) = 1, -1, -1
    Hand-assigned in Eq. 6 to favor initiation over termination, based on observed bimodal association; no ablation or theoretical justification.
  • Thinking token set Pi = {<think>, </think>, Alternatively}
    Chosen by authors as markers of reasoning; results depend on this choice and no sensitivity analysis is given (Eq. 6).
assumptions (3)
  • domain assumption MoE routing in DeepSeek-R1 and Qwen3 exhibits semantic expert specialization, so nPMI with surface markers reveals functional roles.
    Invoked in Section 2.1 via Olson et al. (2025); if routing is token-dependent, the identified experts are artifacts of <think> token formatting.
  • domain assumption The tokens <think>, </think>, and 'Alternatively' are reliable indicators of cognitive deliberation, and expert co-occurrence with them measures reasoning-related function.
    Used in Eq. 5-6; not validated, and the paper calls the construct hypothetical (Section 1).
  • domain assumption Multiplying the router weight of selected experts by beta preserves model behavior enough to evaluate the intervention.
    Eq. 7; Appendix B.3 shows without renormalization, high beta degrades outputs (3.3% accuracy at 2048), so the safe operating range is a fragile assumption.
invented entities (1)
  • Cognitive experts (e.g., DeepSeek-R1 (39,182) and (29,126))
    purpose: Posited to orchestrate meta-level reasoning operations tied to thinking tokens; used to justify why boosting two experts improves accuracy.
    The paper explicitly states 'the cognitive expert proposed in this work is a hypothetical construct' with no theoretical justification (Section 1, footnote 1). The only support is the paper's own empirical steering results; no external mechanistic evidence is provided.

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Cite this review

Pith. "Pith review of Two Experts Are All You Need for Steering Thinking: Reinforcing Cognitive Effort in MoE Reasoning Models Without Additional Training." pith.science (2026). https://pith.science/paper/IREKU4KR

@misc{pith2026250514681,
  author       = {Pith},
  title        = {Pith review of: Two Experts Are All You Need for Steering Thinking: Reinforcing Cognitive Effort in MoE Reasoning Models Without Additional Training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IREKU4KR}},
  note         = {Machine review of arXiv:2505.14681}
}
read the original abstract

Mixture-of-Experts (MoE) architectures within Large Reasoning Models (LRMs) have achieved impressive reasoning capabilities by selectively activating experts to facilitate structured cognitive processes. Despite notable advances, existing reasoning models often suffer from cognitive inefficiencies like overthinking and underthinking. To address these limitations, we introduce a novel inference-time steering methodology called Reinforcing Cognitive Experts (RICE), designed to improve reasoning performance without additional training or complex heuristics. Leveraging normalized Pointwise Mutual Information (nPMI), we systematically identify specialized experts, termed ''cognitive experts'' that orchestrate meta-level reasoning operations characterized by tokens like ''<think>''. Empirical evaluations with leading MoE-based LRMs (DeepSeek-R1 and Qwen3-235B) on rigorous quantitative and scientific reasoning benchmarks demonstrate noticeable and consistent improvements in reasoning accuracy, cognitive efficiency, and cross-domain generalization. Crucially, our lightweight approach substantially outperforms prevalent reasoning-steering techniques, such as prompt design and decoding constraints, while preserving the model's general instruction-following skills. These results highlight reinforcing cognitive experts as a promising, practical, and interpretable direction to enhance cognitive efficiency within advanced reasoning models.

Figures

Figures reproduced from arXiv: 2505.14681 by the authors.

Figure 1
Figure 1. (a) Illustration of cognitive experts identified across domains. (b) Reinforcing only the top [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗

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Forward citations

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Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.