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REVIEW 5 major objections 6 minor 22 references

Symbolic or Numerical? Understanding Physics Problem Solving in Reasoning LLMs

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Reasoning-focused LLMs reach 75.9% zero-shot accuracy on filtered SciBench physics problems, nearly doubling the best chat-model baseline, and their correct solutions consistently favor symbolic derivation over immediate numeric…

desk verdict Useful, checkable accuracy numbers for DeepSeek-R1 on SciBench physics, but the symbolic-vs-numeric behavioral claim rests on an unvalidated LLM classifier and should be treated as preliminary. read the letter →

arxiv 2507.01334 v2 pith:6XAH2AHX submitted 2025-07-02 cs.CL

Nifu Dan , Yujun Cai , Yiwei Wang This is my paper
classification cs.CL
keywords largelanguagemodelsphysicsreasoningchain-of-thoughtpromptingsymbolicderivationSciBenchbenchmarkDeepSeek-R1few-shoterroranalysis
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

Deepseek-R1 and its distilled variants can solve most filtered textbook physics problems from the SciBench benchmark without external tools or heavy prompt engineering, reaching 75.9% average accuracy zero-shot and 81.3% with three few-shot exemplars. This is nearly double the best chat-model baseline reported in the benchmark, GPT-4-Turbo at 43.9%. The paper identifies the behavioral difference behind that gap: reasoning-specialized models tend to derive equations symbolically and substitute numbers only at the end, while chat-oriented models plug in numbers step by step, and the symbolic style appears in correct solutions far more often than in wrong ones. It also finds that few-shot prompting still buys measurable gains, especially in classical dynamics, and that a smaller distilled model can beat a larger one on several physics domains.

What carries the argument

The unit of analysis is the chain-of-thought trace, which the authors collect for every model output and then classify by resubmitting it to an LLM with a fixed prompt template listing six reasoning patterns: problem restatement and known-quantity definition, formula selection and symbolic derivation, step-by-step numeric substitution, multi-path or case enumeration, forward versus backward reasoning, and self-check and validation. The load-bearing distinction is between formula selection with symbolic derivation and step-by-step numeric substitution, because the paper's accuracy explanation is built on correct traces favoring the former. Accuracy itself is scored by comparing the parsed numeric answer to the reference under a 5% relative tolerance, using SciBench's error-categorization framework for the error analyses.

What would settle it

Re-run the pattern analysis on the same 193 problems with two independent human annotators labeling each reasoning trace as symbolic or numeric, and compare their labels with the classifier's; if agreement is near chance, or if rewording the classifier's prompt changes the labels, the reported link between symbolic derivation and correctness would not survive.

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Extended reading notes

Core claim

The paper's central claim is that instruction-tuned reasoning models, specifically Deepseek-R1 and its distilled variants, outperform chat-oriented models on physics calculation tasks because they shift toward symbolic derivation: they first write the governing equation in variables, rearrange it into a general expression, and only then substitute the numerical values. On the 193 filtered problems across fundamental physics, thermodynamics, and classical dynamics, this style is strongly associated with correct answers, whereas chat-oriented Deepseek-V3 sticks to step-by-step numeric substitution in both correct and incorrect traces. The paper treats symbolic derivation not as a stylistic side effect but as a substantive contributor to accuracy, and notes one exception, R1-distill-Qwen-32B, which favors numeric substitution yet still performs well, indicating that the style is not the only route to success.

Load-bearing premise

The paper's behavioral conclusion rests on the assumption that the classifier it uses can reliably sort the model's step-by-step written reasoning into the six named patterns, and that the symbolic-versus-numeric distinction is clean enough to be labeled consistently.

Editorial extensions

If this is right

  • Reasoning-specialized open-weight models can handle a substantial fraction of filtered textbook physics problems without external tools, retrieval, or task-specific prompt engineering.
  • Few-shot chain-of-thought prompting still provides measurable gains on top of strong zero-shot reasoning, with classical dynamics improving from 62.5% to 84.8% and overall from 75.9% to 81.3%.
  • For multi-step physics problems, a model's reasoning style, symbolic derivation versus immediate numeric substitution, is associated with correctness, meaning reasoning quality and answer accuracy are not separable in these models.
  • Distillation can preserve or even improve physics reasoning at smaller scale, since R1-distill-Qwen-32B beats R1-distill-LLaMA-70B on fundamental physics and thermodynamics, so parameter count is not the only driver of performance.
  • The average token counts reported in Table 3 imply that the accuracy gains come with high inference latency and memory load, which limits deployment in low-resource settings.

Reading between the lines

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

  • A clean way to test whether symbolic derivation is a cause rather than a correlate would be to prompt a numeric-first model such as Deepseek-V3 to derive a general expression before substituting numbers; if its accuracy rises toward the reasoning models, the style itself carries part of the advantage.
  • The same symbolic-versus-numeric distinction could plausibly extend to other quantitative STEM tasks, such as circuit analysis, stoichiometry, or geometric optics, where multi-step problems reward holding variables symbolically until the final substitution.
  • For model developers, the results suggest that training rewards for symbolic algebraic rearrangement, rather than numeric computation, could improve correctness on textbook physics, a hypothesis the paper does not directly 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

5 major / 6 minor

Summary. The paper evaluates DeepSeek-R1 and its distilled variants (R1-distill-LLaMA-70B and R1-distill-Qwen-32B) on three filtered SciBench physics subsets (fundamental physics, thermodynamics, classical dynamics) under both zero-shot and few-shot chain-of-thought prompting. It reports accuracy numbers against SciBench baselines and, using an LLM-based classifier applied to model chain-of-thought traces, categorizes reasoning into symbolic-derivation versus step-by-step numeric-substitution strategies. The paper claims that reasoning-specialized models achieve state-of-the-art accuracy, that few-shot prompting still yields measurable gains, and that reasoning-specialized models systematically shift toward symbolic derivation when producing correct answers.

Significance. If the accuracy results are valid, they provide a useful data point: reasoning-specialized LLMs can solve a substantial fraction of filtered textbook physics problems without external tools, and few-shot prompting continues to help. The reported deterministic inference protocol (temperature 1e-30, n=1, 5% relative tolerance) and the explicit prompting conditions are strengths that would make the accuracy evaluation reproducible in principle. However, the paper's more distinctive behavioral claim—that correct reasoning traces are characterized by symbolic derivation—rests on an unvalidated LLM classifier and a non-exclusive taxonomy, and the baseline comparison is potentially confounded by dataset filtering. The paper does not ship code, data, or classifier outputs, so the behavioral analysis is not reproducible as presented.

major comments (5)
  1. [§4.5, Fig. 4, App. A.5] The central behavioral claim is not supported by a validated measurement: the paper relies entirely on an LLM-based classifier prompted with the template in Fig. 5, but reports no human-LLM agreement, no inter-annotator reliability, no per-model sample sizes for the percentages in Fig. 4, and no rule for collapsing the six categories defined in App. A.5 into the binary symbolic/numeric split shown in Fig. 4. The prompt also includes the reference solution, which could bias the classifier toward stylistic similarity to a symbolic-looking reference rather than the model's own derivation strategy. As written, the reported correlation between symbolic derivation and correctness cannot be distinguished from an artifact of the labeling procedure.
  2. [§4.5, Fig. 3] The two pattern definitions are not mutually exclusive. The 'Step-by-Step Numeric Substitution' worked example in Fig. 3 itself states the symbolic work-energy relation W = ΔK + ΔEth before substituting numbers, and the 'Symbolic Derivation' example ends with numeric substitution; the real distinction is only the ordering of substitution. For traces that intermix the two styles, a forced single label is arbitrary. The paper gives no decision rule for such borderline cases and no demonstration that the taxonomy is reliable, which undermines the binary distribution in Fig. 4.
  3. [§3.2, Table 2] The comparison against baseline models is potentially confounded. The authors filter the SciBench subsets by removing problems containing visual elements and problems that 'require detailed solutions' (§3.2), yet the baseline rows in Table 2 are described simply as 'Data are taken from the SciBench benchmark,' presumably on the unfiltered sets. If the baseline numbers are on the full original SciBench sets while the R1-series numbers are on the filtered subset, the claim that DeepSeek-R1's accuracy is nearly double GPT-4-Turbo's is not a head-to-head comparison. The authors should either re-run the baselines on the exact filtered subsets or verify that the published numbers correspond to those subsets.
  4. [§4.5, Fig. 4] The paper's own reported data contradict the summary claim. The text states that R1-distill-Qwen-32B 'heavily favors numeric substitution in both incorrect (57.6%) and correct (73.6%) solutions,' meaning its correct solutions are more numeric, not more symbolic. Yet the conclusion asserts that 'reasoning-specialized models systematically shift toward symbolic derivation when producing accurate responses.' This generalization is not supported by the reported distributions and must be either qualified to exclude R1-distill-Qwen-32B or reanalyzed with a more refined claim.
  5. [§4.4, Figs. 2a/2b] The error analysis is not reproducible from the manuscript: the figure images are not legible in the provided text (they appear as garbled placeholder characters), the SciBench error categories are not defined in the paper (the prose refers to 'Logical Decomposition,' 'Calculation Skills,' and 'Assumption Identification' without giving their definitions), and the counts cited in the prose (e.g., 'from 7 to 8 errors,' '46 to 37 errors') are not tabulated. The authors should provide a readable figure, a table of error counts, and an explicit mapping from SciBench's ten error categories to the few categories highlighted in the analysis.
minor comments (6)
  1. [References] Several citations do not match the cited claims: Gao et al. (2022) is cited for physics evaluation but the reference is titled 'Evaluating large language models trained on code'; Madaan et al. (2023) is cited for decomposition prompts but the reference is 'Language models can solve computer tasks'; Zheng et al. (2024) is cited for code-generation prompt variants but the reference is 'Prompt engineering for advanced language models.' These references should be corrected.
  2. [§3.2] The sentence 'we filter out problems with detailed solutions to ensure they can be used as few-shot prompts' is contradictory: the paper should clarify whether problems with detailed solutions are used as exemplars or excluded from the evaluation set.
  3. [§3.4] The criterion for selecting the 'top three exemplars from each subset' is not defined. If the exemplars were selected by the authors based on readability or expected performance, the few-shot results may not be representative. The paper should also state whether the exemplars come from the same test set and whether test problems are excluded from the exemplar pool.
  4. [§4.3] The sentence 'The performance advantage is particularly notable given the 32B model's significantly lower computational requirements' appears verbatim twice in this section; one occurrence should be removed.
  5. [Appendix B] The token-level metrics 'average token confidence' and 'average token gap' are defined but never analyzed or discussed in the main text, and Figures 6 and 7 are not legible in the provided manuscript. The authors should either present the results with readable figures and interpretation, or remove the appendix.
  6. [Throughout] The model name is written inconsistently as 'Deepseek' and 'DeepSeek', and there are typographical errors such as 'GPT-4-T URBO' and 'identidy' in App. A.5; these should be corrected in a careful revision.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is an empirical evaluation against an external benchmark, with no fitted parameters, no self-citation chain, and no derivation that assumes its own conclusion.

full rationale

This paper is an empirical study that evaluates reasoning-focused LLMs on physics problems from the SciBench benchmark. The central accuracy claims are direct measurements against externally defined ground-truth answers with a fixed 5% relative tolerance, so the reported numbers do not reduce to any fitted parameter or to the paper's own assumptions. The few-shot exemplars are stated to be drawn from existing dataset instances with detailed solutions, which are separate from the test problems, so the few-shot improvements are not predictions of fitted values. The behavioral claim about symbolic versus numeric reasoning is produced by an LLM-based classifier described in Figure 5 and Appendix A.5; however, the reader's concern about this classifier is about validation, label noise, and category non-exclusivity, not about circularity in the sense of the target result being an input to the derivation. The paper does not fit any parameter to the reasoning-pattern data and then predict that same data; it reports observed distributions. There are no self-citations of the authors' prior work used as load-bearing evidence, no imported uniqueness theorem, and no ansatz smuggled in via citation. The manuscript even acknowledges limitations about token cost and unimodal scope, further confirming its empirical rather than circular structure. Consequently, while the reliability of the symbolic-versus-numeric finding may be open to methodological critique, no specific circular step can be exhibited, and the appropriate circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted; the paper postulates no new physical or model entities. Its claims rest on benchmark ground truth, the validity of LLM-based classifiers, and the representativeness of the filtered problem set.

assumptions (4)
  • domain assumption SciBench reference solutions are correct ground truths
    Accuracy is measured as matching these references within 5%, so any reference error propagates into all results (Section 3.5).
  • domain assumption The LLM-based error categorizer produces valid error labels
    Error-category counts in Section 4.4 rely on the SciBench automatic categorization framework, but the identity and reliability of the classifying LLM are not disclosed.
  • ad hoc to paper The reasoning-pattern classifier (prompt in Figure 5) and the human-defined six categories faithfully capture model strategies
    The symbolic-vs-numeric dichotomy in Section 4.5 is defined by the authors and classified by an unspecified LLM with no validation or inter-annotator agreement; the central behavioral claim depends on this.
  • domain assumption The filtered text-only SciBench subsets are representative of physics problem-solving skill
    The paper excludes visual and detailed-solution problems (Section 3.2), and all conclusions are limited to the remaining 193 problems.

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Cite this review

Pith. "Pith review of Symbolic or Numerical? Understanding Physics Problem Solving in Reasoning LLMs." pith.science (2026). https://pith.science/paper/6XAH2AHX

@misc{pith2026250701334,
  author       = {Pith},
  title        = {Pith review of: Symbolic or Numerical? Understanding Physics Problem Solving in Reasoning LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6XAH2AHX}},
  note         = {Machine review of arXiv:2507.01334}
}
read the original abstract

Navigating the complexities of physics reasoning has long been a difficult task for Large Language Models (LLMs), requiring a synthesis of profound conceptual understanding and adept problem-solving techniques. In this study, we investigate the application of advanced instruction-tuned reasoning models, such as Deepseek-R1, to address a diverse spectrum of physics problems curated from the challenging SciBench benchmark. Our comprehensive experimental evaluation reveals the remarkable capabilities of reasoning models. Not only do they achieve state-of-the-art accuracy in answering intricate physics questions, but they also generate distinctive reasoning patterns that emphasize on symbolic derivation. Furthermore, our findings indicate that even for these highly sophisticated reasoning models, the strategic incorporation of few-shot prompting can still yield measurable improvements in overall accuracy, highlighting the potential for continued performance gains.

Figures

Figures reproduced from arXiv: 2507.01334 by the authors.

Figure 1
Figure 1. Overview of the experimental pipeline. A diverse set of physics problems is sampled from three domains: [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Comparison of error distributions across different prompting methods, excluding near-zero categories [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Comparison of two solution strategies for finding the increase in thermal energy when a 14 kg crate is [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Distribution of reasoning patterns in (a) correct and (b) incorrect solutions across different Deepseek [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Prompt for analyzing reasoning patterns [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Average token confidence for correct vs. incorrect answers. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Average token gap for correct vs. incorrect answers. [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.