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REVIEW 5 major objections 7 minor 66 references

Decoupling Knowledge and Reasoning in LLMs: An Exploration Using Cognitive Dual-System Theory

T0 review · 5 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A dual-system framework claims that the accuracy gap between slow and fast LLM thinking measures reasoning adjustment, enabling knowledge and reasoning to be decoupled, and uses that gap to report where each lives and how scaling affects…

desk verdict The fast-slow accuracy gap is a clever and clean decomposition, but the paper's central interpretation of it as 'reasoning adjustment capability' is undermined by ceiling effects and an inconsistent evaluation protocol. read the letter →

arxiv 2507.18178 v1 pith:W3452QNA submitted 2025-07-24 cs.AI

Mutian Yang , Jiandong Gao , Ji Wu This is my paper · ORCID
classification cs.AI
keywords largelanguagemodelsknowledgeretrievalreasoningadjustmentdual-systemtheorychain-of-thoughtoverthinkingparameterscalingCKArepresentationsimilarity
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

Drawing on dual-system cognitive theory, the paper separates an LLM's answer into a fast knowledge-retrieval phase and a slow reasoning-adjustment phase. It defines knowledge retrieval capability as fast-thinking accuracy and reasoning adjustment capability as the accuracy gap $\delta = A_{\text{slow}} - A_{\text{fast}}$ between the two modes. Testing 15 LLMs on MMLU, MathQA, and MedQA, the paper reports that reasoning adjustment helps mathematics, physics, and chemistry, that it can hurt political science and history, and that parameter scaling improves knowledge more than reasoning, mainly by reducing overthinking rather than improving correction. It also reports that layer-activation similarity between the two modes stays high in lower layers and drops in higher layers, which it reads as knowledge residing low and reasoning high.

What carries the argument

The central object is the fast/slow cognitive-mode pair and the accuracy gap between them. The load-bearing identity is Equation 9, $\delta = \delta_c - \delta_o = \frac{1}{|D|}\left(r_c |D^{\text{false}}_{\text{fast}}| - r_o |D^{\text{true}}_{\text{fast}}|\right)$, which converts a behavioral accuracy difference into two rates: correction and overthinking. This identity carries the domain-specificity and scaling arguments. The layer-localization claim is carried by CKA, a similarity score between the same network layer's activations under the two modes, where lower layers stay similar and higher layers diverge.

What would settle it

Grade the same slow-thinking answers two ways — with the paper's external-judge prompt and with a direct match to the answer key — while keeping fast and slow prompts as parallel as possible, and compare the resulting $\delta$ values and their domain rankings. If the sign or ranking changes materially, the gap is partly an evaluation artifact rather than a pure measure of reasoning adjustment.

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Extended reading notes

Core claim

The central claim is that the gap between slow and fast thinking, $\delta$ in Equation 5, is a capability, $C_{\text{RA}}$, that can be cleanly separated from knowledge retrieval, $C_{\text{KR}} = A_{\text{fast}}$. The paper then decomposes $\delta$ into correction $\delta_c$ — cases where slow thinking fixes a fast error — and overthinking $\delta_o$ — cases where slow thinking overturns a fast correct answer — and explains the sign and size of $\delta$ as the trade-off between those two terms. On this basis it claims three empirical findings: reasoning adjustment is domain-specific; scaling adds more knowledge than reasoning and mostly makes models more prudent rather than more intelligent; and knowledge retrieval and reasoning adjustment occupy lower and higher network layers respectively.

Load-bearing premise

The load-bearing premise is that the accuracy gap between slow and fast thinking is caused by reasoning adjustment alone, and not by the two modes' different prompts, output lengths, or the fact that slow answers are graded by an external judge while fast answers are matched directly to the answer key; if any of those confounds contributes to the gap, the paper's conclusions about domain specificity, scaling, and layer localization do not follow.

Editorial extensions

If this is right

  • Slow thinking should be deployed selectively: in knowledge-intensive domains, chain-of-thought can reduce accuracy, so routing questions by domain could improve average performance.
  • Scaling laws hide a knowledge/reasoning split: larger models gain mostly memorized knowledge, while reasoning gains saturate once overthinking is controlled, so further reasoning gains require targeted training rather than scale alone.
  • Because overthinking, not weak correction, dominates small-model reasoning failure, small models need prudence-style training or shorter reasoning chains, not simply more parameters.
  • If knowledge sits in lower layers and reasoning in higher layers, knowledge editing and reasoning interventions target disjoint places, and the paper's CKA curves provide a map for choosing intervention layers.

Reading between the lines

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

  • Editorial inference: the same $\delta$ decomposition could be run on open-ended generation, where the evaluator confound is harder to control; one testable prediction is that the domain ranking of $\delta$ will shift when slow answers are graded by exact-match instead of by an external judge.
  • Editorial inference: the localization claim implies a testable intervention — perturbing higher layers during slow thinking should change reasoning gain more than perturbing lower layers, while the reverse should hold for factual recall.
  • Editorial inference: the overthinking rate may respond to inference-time controls, so capping chain-of-thought length or adding a decide-whether-to-revise step could selectively reduce $\delta_o$ in small models, which would support the noise interpretation.
  • Editorial inference: the anchoring result suggests a cheap prudence probe — measuring fast and slow accuracy after injecting a wrong hint; the increase in $\delta$ under anchoring would quantify how much reasoning compensates when retrieval is misled.
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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

5 major / 7 minor

Summary. The paper proposes a 'cognition attribution architecture' inspired by dual-system cognitive theory. It defines two phases of LLM inference, knowledge retrieval (fast thinking) and reasoning adjustment (slow thinking), and measures each through prompted accuracy on multiple-choice QA. The central quantity is the accuracy difference δ = Aslow − Afast (Eq. 5), which the paper identifies as the reasoning adjustment capability CRA. The paper then decomposes δ into a correction component δc and an overthinking component δo (Eq. 9). Experiments are run on 15 LLMs over MMLU, MathQA, and MedQA, with domain-level analyses on MMLU. The reported findings are: reasoning adjustment is domain-specific (benefiting mathematics, physics, and chemistry while harming knowledge-intensive domains); parameter scaling improves knowledge more than reasoning and mainly reduces overthinking; and CKA-based representational similarity indicates that knowledge retrieval is localized in lower layers while reasoning adjustment is localized in higher layers.

Significance. If the identification of δ with reasoning adjustment capability were valid, the framework would provide a cheap, model-agnostic tool for decomposing accuracy gains into knowledge and reasoning components, with potential implications for scaling laws, knowledge editing, and small-model reasoning. The paper's strengths include a transparent experimental setup, a broad span of 15 models across three datasets, the useful descriptive decomposition of δ into correction and overthinking rates, and an explicit acknowledgment of limitations. The algebraic identities in Eqs. (3)-(9) are correct. However, the significance is conditional: the headline conclusions are all phrased in terms of δ as a causal capability, and the paper does not establish that δ isolates reasoning adjustment from confounded differences between the fast and slow conditions. The descriptive accuracy-difference results are still of some value, but the claims about 'knowledge' and 'reasoning' as separable cognitive faculties do not currently follow.

major comments (5)
  1. [§3.1 and Appendix D.2] The identification CRA := δ in Eq. (5) is mechanically bounded by the fast-accuracy ceiling: δ ≤ 1 − Afast. Since Afast varies across domains and model sizes, the cross-domain and scaling conclusions may reflect base rates rather than reasoning adjustment. For example, from Table 1, Qwen 1.5B has Afast = 53.9 and Qwen 32B has Afast = 79.5, so the maximum possible positive δ for Qwen 32B is about 20.5% versus about 46.1% for Qwen 1.5B. The same mechanism affects the domain rankings in Table 2, where knowledge-intensive domains tend to have high fast accuracy and thus little room for positive δ, while math and physics have low fast accuracy and ample room for correction gains. Eq. (9) shows this directly: δ = (rc·|Dfalse_fast| − ro·|Dtrue_fast|)/|D|, so δ depends on the sizes of the correct and incorrect fast-answer sets. I request a normalization or a control for Afast, for example reporting δ on accuracy-matched subsets, or reporting confidence intervals on rc and ro, or an external validation of δ against an independent reasoning benchmark.
  2. [§3.1 and Appendix D.2] The fast and slow conditions differ in several dimensions beyond the presence of reasoning: the prompts are worded differently (Figures 5 and 6), slow answers are much longer and consume more tokens (Table 6), and the evaluation protocols differ — fast answers are compared directly to the answer key while slow answers are judged by the external model GLM-4-PLUS using a separate prompt (Figure 7). Any of these differences can produce a nonzero δ, so attributing δ to a 'reasoning adjustment capability' is not identified. I ask the authors to run a control where the same evaluator judges both conditions, and ideally also a condition with a matched-length but non-reasoning slow prompt, to isolate the effect of adding reasoning rather than the effect of changing the prompt, output length, or grader.
  3. [§2 (Eq. 5) and §5] There is a circularity in the central claims: CRA is defined as δ in Eq. (5), and then statements such as 'reasoning adjustment is domain-specific' and 'parameter scaling improves knowledge more than reasoning' are restatements of aggregate properties of the measured accuracy difference. The decomposition in Eq. (9) is descriptive and useful, but the abstract and conclusion present δ as a measure of a capability. The Limitations paragraph in Section 5 says the method is 'simplified,' but Equations 3–9 require the interpretation of δ as CRA to support the headline findings. I recommend either validating δ against an external reasoning measure (e.g., correlation with performance on held-out reasoning tasks after controlling for Afast) or rewriting the claims to be explicitly descriptive of accuracy differences under the two prompt conditions.
  4. [§3.6 and Appendix H] The 'cognitive hierarchy' claim that knowledge retrieval resides in lower layers and reasoning adjustment in higher layers is based on CKA between fast and slow activations for only two models (Qwen 7B and LLaMA 8B, Figure 4). The fast and slow conditions have different prompts and generate very different numbers of tokens; even though CKA is computed only on question-part tokens, the prompts themselves differ at the input, so the representations may diverge for reasons unrelated to reasoning, such as instruction-following or response format. No significance tests or additional models are reported. Please include more models, use a minimal prompt difference, and add a control with length-matched outputs or identical prompts under different sampling settings.
  5. [Tables 1–2] No uncertainty quantification is provided for any of the reported accuracies, δ values, or rates. Many per-domain δ entries in Table 2 are within 1–2 percentage points (e.g., several values between −1 and +1), and the domain sample sizes range from about 100 to several hundred questions (Table 4). The top-3 rankings used to support the domain-specificity claim could be unstable under this noise. I request bootstrap confidence intervals or standard errors for δ, and ideally for δc and δo, so that the reader can judge whether differences of a few percentage points are meaningful.
minor comments (7)
  1. [§3.3] Please fix the typo 'reasnong-intensive' to 'reasoning-intensive'.
  2. [§5] The Conclusion says 'parameter scaling primarily enhances both knowledge retrieval and reasoning adjustment, with reasoning adjustment more significant,' which contradicts the Abstract's statement that 'knowledge improvements are more pronounced.' Please correct the wording to be consistent.
  3. [Table 2] The table header says 'δ of 19 LLMs' but the paper reports 15 models; please correct the count.
  4. [§3.2] The sentence 'the variation in ro across model sizes is more prominent than that in ro' appears to have a typo; it should likely compare ro and rc.
  5. [§2 (Eq. 2)] Equation (2) uses the notation Cknowledge and Creasoning, while Equations (3)–(5) use CKR and CRA; please align the notation.
  6. [Appendix F.2] The statement that for MathQA 'one wrong option is randomly removed to reduce the choices from five to four' introduces a stochastic element; please specify the random seed or describe how the removal was fixed across runs.
  7. [Abstract and Appendix] The abstract promises that datasets and code will be publicly released, but no repository link is provided; please include the link in the final version.

Circularity Check

1 steps flagged · score 4.0 of 10

The central construct 'reasoning adjustment capability' is stipulated as the fast/slow accuracy difference δ (Eq. 5), so the headline conclusions about reasoning are restatements of δ; the CKA layer-localization result is independent and the δ decomposition is algebraic.

  1. self definitional [Section 2, Step 3, Eqs. (3)-(5); interpreted in Sections 3.3-3.5]
    "CRA :=δ =Aslow−Afast = 1 |D| Σ_{x∈D} I(yslow =y∗)− 1 |D| Σ_{x∈D} I(yfast =y∗) (5) This equation shows that the accuracy difference between slow and fast thinking, referred to as the reasoning gainδ, reflects the capability of reasoning adjustmentCRA. Ultimately, we decouple the knowledge and reasoning capabilities in Equation 3 and Equation 5."

    CRA is stipulated as δ, so conclusions about 'reasoning adjustment' are statements about the measured accuracy difference. 'Domain-specific reasoning' (Sec. 3.3) reduces to 'δ varies by domain'; 'scaling improves knowledge more than reasoning' (Sec. 3.4) compares ΔAfast with Δδ; 'prudent/intelligent' (Sec. 3.5) labels δo/δc from Eq. (9). The decomposition in Eqs. (6)-(9) is exact and not circular, but the cognitive labels are attached to defined quantities, so the headline results are true by construction. Ceiling effects and the differing slow/fast evaluation protocols are validity confounds, not circularity, but they underscore that δ is not validated as 'reasoning' beyond its definition.

full rationale

The paper's measurement chain is internally consistent: Afast and Aslow are directly evaluated accuracies, and δc/δo are exact algebraic decompositions of δ. The CKA experiments in Sec. 3.6 provide an independent empirical observation (lower cross-mode similarity in higher layers) that does not reduce to Eq. (5). No parameter is fitted and then renamed as a prediction, and no load-bearing uniqueness theorem is imported. The only same-author citation, [19], supports the layer-localization claim but is not load-bearing because the CKA measurement is the paper's own evidence. The central circularity is at the construct-label level: CRA is stipulated as δ (Eq. 5), and the paper then reports properties of CRA as findings about reasoning. This is partial self-definition rather than fabricated data. The Limitations section concedes the method is 'simplified and may not fully capture the underlying mechanisms,' which acknowledges the gap between the definitional measure and the latent construct. Score 4 reflects partial definitional circularity in the central claims, with the layer-localization result and exact decomposition providing independent content.

Assumptions & free parameters 0 free parameters · 5 assumptions · 1 invented entities

The framework introduces no fitted parameters. It rests on a series of domain assumptions that map prompting conditions to cognitive phases, assume additivity of accuracy contributions, control for confounds, and interpret CKA divergence as reasoning. The only invented construct is the reasoning adjustment capability itself, which is defined as the measured accuracy gap.

assumptions (5)
  • domain assumption Fast thinking prompt elicits knowledge retrieval without any reasoning adjustment.
    The entire framework relies on this mapping from a prompting condition to a cognitive phase; if fast thinking still involves implicit reasoning, CKR is not a pure knowledge measure. Invoked in Section 2, Step 2, Eq. 1.
  • domain assumption Slow thinking prompt elicits knowledge retrieval plus a reasoning adjustment, and the two phases are additive in accuracy.
    Eq. 2 and Eq. 4 assume the slow accuracy is the sum of knowledge and reasoning contributions; any non-additive interaction would break the subtraction in Eq. 5.
  • domain assumption The accuracy difference δ is attributable to reasoning adjustment rather than to prompt format, output length, token budget, or the external judge model.
    Section 2, Step 3 implicitly assumes all other factors are controlled; no ablation is provided to isolate the reasoning component.
  • domain assumption CKA divergence between slow and fast thinking at a layer indicates that reasoning operates there.
    Section 3.6 interprets lower CKA as evidence of reasoning; the paper does not rule out token divergence or other processing differences.
  • domain assumption Dual-system cognitive theory from humans transfers to LLM inference.
    Section 2, Step 1 adopts Kahneman's two-system theory as the basis for the two-phase decomposition without justification for why LLMs should exhibit the same dichotomy.
invented entities (1)
  • Reasoning adjustment capability CRA
    purpose: Quantifies the contribution of reasoning by the accuracy gap δ between slow and fast thinking.
    CRA is defined directly as δ in Eq. 5; the paper provides no external, falsifiable handle that would validate this statistic as a measure of reasoning rather than some other effect.

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Pith. "Pith review of Decoupling Knowledge and Reasoning in LLMs: An Exploration Using Cognitive Dual-System Theory." pith.science (2026). https://pith.science/paper/W3452QNA

@misc{pith2026250718178,
  author       = {Pith},
  title        = {Pith review of: Decoupling Knowledge and Reasoning in LLMs: An Exploration Using Cognitive Dual-System Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W3452QNA}},
  note         = {Machine review of arXiv:2507.18178}
}
read the original abstract

While large language models (LLMs) leverage both knowledge and reasoning during inference, the capacity to distinguish between them plays a pivotal role in model analysis, interpretability, and development. Inspired by dual-system cognitive theory, we propose a cognition attribution framework to decouple the contribution of knowledge and reasoning. In particular, the cognition of LLMs is decomposed into two distinct yet complementary phases: knowledge retrieval (Phase 1) and reasoning adjustment (Phase 2). To separate these phases, LLMs are prompted to generate answers under two different cognitive modes, fast thinking and slow thinking, respectively. The performance under different cognitive modes is analyzed to quantify the contribution of knowledge and reasoning. This architecture is employed to 15 LLMs across 3 datasets. Results reveal: (1) reasoning adjustment is domain-specific, benefiting reasoning-intensive domains (e.g., mathematics, physics, and chemistry) and potentially imparing knowledge-intensive domains. (2) Parameter scaling improves both knowledge and reasoning, with knowledge improvements being more pronounced. Additionally, parameter scaling make LLMs reasoning significantly more prudent, while moderately more intelligent. (3) Knowledge primarily resides in lower network layers, while reasoning operates in higher layers. Our framework not only helps understand LLMs from a "decoupling" perspective, but also provides new insights into existing research, including scaling laws, hierarchical knowledge editing, and limitations of small-model reasoning.

Figures

Figures reproduced from arXiv: 2507.18178 by the authors.

Figure 1
Figure 1. The schema of the cognition attribution architecture, supposing the cognitive process of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Improvement of knowledge retrieval and reasoning adjustment with parameter scaling. The [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Impact of parameter scaling on overthinking rate [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: CKA between corresponding layers under slow and fast thinking. Lower CKA indicates [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Fast thinking prompt A.2 Fast thinking example Question: A university’s mathematics department has 10 professors and will offer 20 different courses next semester. Each professor will be assigned to teach exactly 2 of the courses, and each course will have exactly one …
Figure 6
Figure 6. Figure 6: Slow thinking prompt Slow thinking answer: ### Thought 1. **Analyzing the Question:** - The problem involves assigning 10 professors to 20 courses, with each professor teaching exactly 2 courses and each course being taught by exactly one professor. - The key is to und…
Figure 7
Figure 7. Figure 7: Evaluation prompt E Results of Token consumption [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: The accuracy of fast and slow thinking on (a) MathQA and (b) MedQA. The results [PITH_FULL_IMAGE:figures/full_fig_p025_8.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.