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REVIEW 4 major objections 6 minor 65 references

Learning Composable Chains-of-Thought

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A simple format change to chain-of-thought training data enables zero-shot composition of atomic reasoning skills in language models.

desk verdict Useful empirical paper with a clever format change that genuinely helps zero-shot composition, but the claimed chaining mechanism is untested and the 'zero-shot' label is a bit generous; needs revision, not rejection. read the letter →

arxiv 2505.22635 v1 pith:WIUE2X76 submitted 2025-05-28 cs.CL cs.AI

Fangcong Yin , Zeyu Leo Liu , Liu Leqi , Xi Ye , Greg Durrett This is my paper
classification cs.CLcs.AI
keywords chain-of-thoughtcompositionalgeneralizationmodelmergingmultitasklearningrejectionsamplingfine-tuningzero-shotreasoning
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

The paper tries to establish that training large language models on chain-of-thought traces of individual reasoning skills can support later composition, provided the traces are formatted so that one skill's trace can serve as an arbitrary prefix for another's. It calls this format Composable CoT: each atomic trace is trained either as a prefix (wrapped in tags) or as a suffix that follows a random proxy prefix (wrapped in tags). Combining two such atomic models by model merging or multitask learning yields zero-shot performance on unseen compositional tasks that beats combining standard CoT models, sometimes matching supervised fine-tuning on compositional data. A small amount of answer-only compositional data can then be harvested through rejection sampling fine-tuning to improve the combined model further. If correct, the insight is that a format change to atomic data, not additional compositional supervision, is what unlocks skill composition.

What carries the argument

The central mechanism is the Composable CoT data format. For each atomic task, training examples are split into two types: prefix examples of the form $(q, t^{\text{pre}})$ where $t^{\text{pre}} = <\text{prefix}> t a<\text{/prefix}>$, and suffix examples of the form $(q, t'_1 \ldots t'_{k-1}, t^{\text{suf}})$ where $t^{\text{suf}} = <\text{suffix}> t a<\text{/suffix}>$ and the $t'_i$ are random-letter proxy prefixes. The training objective maximizes $\log p_\theta(t^{\text{pre}}|q)$ on prefix examples and $\log p_\theta(t^{\text{suf}}|q, t'_{\text{pre}})$ on suffix examples, teaching the model to continue after an arbitrary preceding trace. At inference, the combined model generates a prefix trace, the pipeline appends a <suffix> tag, and generation continues, producing two atomic CoTs in one sequence.

What would settle it

Train a Composable CoT model on two atomic skills whose composition genuinely requires the output of the first skill as input to the second, then evaluate on test items where applying only the first skill yields a wrong answer; if the model's accuracy on those items is no higher than a standard CoT model trained with the same atomic data, the central claim is false.

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Extended reading notes

Core claim

The paper claims that the standard CoT format teaches models to reproduce atomic reasoning patterns rather than to chain them, and that this can be fixed without compositional CoT annotations. By reformatting each atomic CoT example as either a prefix trace or a suffix trace that follows a random proxy prefix, the model learns to treat whatever trace precedes it as context and to continue with its own skill. When two such atomic models are combined via task-arithmetic merging or multitask learning, the combined model can at zero-shot produce one skill's trace followed by the other's, and rejection sampling fine-tuning on a small answer-only compositional set improves it further. The paper demonstrates this on string-operation compositions and on literary-plus-rhetorical language skill compositions.

Load-bearing premise

The approach assumes a compositional reasoning step can be represented as two independently learned CoT segments concatenated in a fixed order, with the second segment conditioned on the first only through the text that precedes it; the paper's own limitations note that only pairwise compositions are tested.

Editorial extensions

If this is right

  • Within the same training-data budget, Composable CoT combined by model merging or multitask learning outperforms the corresponding standard CoT combinations on zero-shot compositional tasks.
  • Zero-shot Composable CoT models sometimes match or beat supervised fine-tuning on compositional answer data, meaning the format itself, not compositional supervision, carries much of the benefit.
  • Adding a small amount of answer-only compositional data through rejection sampling fine-tuning improves the combined model further and beats continued fine-tuning and multitask-learning baselines.
  • Intrinsic evaluation shows Composable CoT models generate both atomic CoT patterns in a single response more often than standard CoT models, indicating the format increases genuine skill use rather than shortcut answers.
  • The method requires only atomic CoT data and a small set of compositional answers, reducing the need for expensive compositional CoT annotations.

Reading between the lines

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

  • An implication the paper leaves implicit is that the same prefix–suffix data augmentation could apply to any task pair with existing atomic CoT data, including code and symbolic reasoning, as long as the composition is sequential or pipeline-like.
  • A natural extension is n-way composition, since the construction supports more than two tags; because the paper only tests pairs, whether the benefit persists with longer chains is an open empirical question.
  • The random-letter proxy prefixes likely teach the model to ignore the content of the preceding trace, so the format may help with compositions where the second skill only needs the first skill's answer, not its intermediate reasoning, and may be less suited to compositions requiring joint planning or backtracking.
  • The instability of model merging on one setting (Concat + Mult) suggests that routing-based or sampling-based combination methods could preserve the format benefit more reliably than fixed linear merging.
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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 / 6 minor

Summary. The paper proposes Composable CoT, a modification of the chain-of-thought format used when fine-tuning LLMs on atomic reasoning tasks. Each atomic CoT is split into a ``<prefix>'' segment conditioned only on the question and a ``<suffix>'' segment trained to follow a proxy prefix, which in the main implementation is a string of random letters. The resulting atomic CoT models are combined either by task-arithmetic model merging or by multitask learning, and are evaluated zero-shot on compositional tasks that combine two atomic skills. The paper reports that these combined Composable CoT models outperform standard-CoT baselines on string operations and Skill-Mix, and that further rejection-sampling fine-tuning on a limited amount of answer-only compositional data improves performance beyond continued fine-tuning baselines. The central claim is that the Composable CoT format change, rather than additional compositional CoT supervision, enables zero-shot skill composition.

Significance. If validated, the paper would make a useful empirical contribution: it suggests a lightweight, format-level intervention that improves compositional generalization without compositional CoT labels, and it demonstrates that model merging and multitask learning are viable ways to combine atomic reasoning skills. The experiments are controlled, use two 7B base models and multiple tasks, include ablations, and the authors release code and data, which strengthens reproducibility. However, the significance is tempered by two unresolved issues: the proposed training construction does not clearly teach the suffix model to consume the prefix's intermediate output, and the zero-shot evaluation is partly undermined by validation-set tuning of merge weights. Both issues bear directly on the paper's central mechanism and on the strength of the zero-shot claim, so the current evidence is suggestive rather than conclusive.

major comments (4)
  1. [Section 3.1 and Appendix B] The suffix training objective in Section 3.1 optimizes p_theta(t_suf | q, t'_pre), but t'_pre is a random-letter proxy prefix that is independent of q and of the intermediate result needed for the composition. Because the model can minimize the suffix loss by simply ignoring t'_pre, the training procedure does not actually teach output-to-output chaining from the prefix to the suffix. The paper's central claim that Composable CoT ``enables'' compositional reasoning at inference time therefore needs stronger support. Concretely, the authors should provide an intervention experiment that verifies whether the suffix's generated output depends on the content of the prefix, for example by corrupting, removing, or replacing the generated prefix at inference time and measuring the resulting change in suffix accuracy. Without such a test, the observed gains could be attributed to the two-block tag structure prompting two consecutive CoT segments, rather than to genuine composition of the intermediate result.
  2. [Appendix F.4 and Table 1] The zero-shot claim is weakened by the hyperparameter selection procedure. For all model-merging methods, the scaling factors alpha and beta are chosen by sweeping over alpha in {0.1,...,0.9} with beta = 1 - alpha on a validation set for each task. If that validation set contains examples from the compositional task distribution, then the 'zero-shot' methods in Table 1 are not actually zero-shot with respect to compositional supervision, since the merge weights are tuned to the target task. The authors should clarify what the validation set contains, report the selected alpha/beta values, and provide an ablation with a fixed default (e.g., alpha=beta=1) to show that the conclusions are not an artifact of validation-set tuning.
  3. [Table 1 and Section 5.1] The claim that Composable CoT variants 'outperform all baselines on a range of settings' is too strong given the data in Table 1. In the Qwen 2.5-7B results, ComposableCoT-Merge obtains 19.2 EM on Concat + Last Letter while StandardCoT-Merge obtains 54.8, and on Concat + Mult ComposableCoT-Merge obtains 75.4 versus StandardCoT-Merge's 77.0. The paper does acknowledge one of these as an error case, but the accompanying text should systematically qualify the settings where the proposed method improves and where it does not, and the discussion should address why the format transfer fails in the Concat + Last Letter case beyond 'model merging can be unstable.'
  4. [Section 5.3 and Appendix H] The intrinsic evaluation in Table 3 only checks whether both atomic CoT patterns appear somewhere in the generated response; it does not check whether the suffix uses the prefix's result. The error cases in Appendix H.1 and H.3 are examples where the suffix repeats the prefix's computation or recomputes from the original question, which is exactly the failure mode the intrinsic metric cannot detect. The authors should add a quantitative measure of information flow, such as a masked-prefix evaluation or a test of whether the suffix's answer changes when the prefix's content is altered, to distinguish genuine chaining from two independent atomic computations in the same response.
minor comments (6)
  1. [Section 4] The atomic task name 'Letter concentation' contains a typo; it should be 'Letter concatenation.'
  2. [Appendix D.1] The text says 'the rhetorical and literay skills' with a typo; 'literay' should be 'literary.'
  3. [Table 8] The formatting of Table 8 is confusing: the first row appears to read 'StandardCoT-Merge 0 0' before the task labels in the following rows, making it unclear whether these are zero-training entries or a layout artifact. Please reformat the table so that the task names are clearly associated with each row.
  4. [Appendix G.1] The compositional training set size for Concat + Mult differs between Llama 2-7B (N=500) and Qwen 2.5-7B (N=100). This is explained in the text, but the cross-model comparison in Table 2 would be cleaner if the same data budget were used for both models.
  5. [Appendix D.2] The Skill-Mix evaluation relies entirely on GPT-4o-mini as a judge, but no agreement analysis with human raters or error analysis of the judge is reported. A small validation of the judge's reliability would strengthen the Skill-Mix results.
  6. [Section 7 and Limitations] The limitations paragraph appropriately notes that only pairwise compositions are tested, but given the method's motivating narrative of composing chains of arbitrary length, the paper should state more explicitly that the n>2 extension in Section 3.1 has not been empirically validated.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claims are empirical comparisons with controlled data budgets; RFT is filtered by external answer labels, and the only tuned quantities are hyperparameters selected on validation sets.

full rationale

The paper's contribution is a data-format modification and an empirical evaluation, not a derivation that reduces to its inputs. Composable CoT training constructs prefix and suffix objectives (Section 3.1) from the same atomic CoT data used by the standard-CoT baselines, and the compositional evaluation is on held-out tasks; the reported gains are comparative measurements rather than consequences of a fitted parameter being renamed a prediction. The rejection-sampling fine-tuning stage uses self-generated CoTs, but only those verified against external direct-answer labels are retained, so the bootstrap is anchored by outside supervision rather than by the model's own outputs being treated as ground truth. Model merging weights and learning rates are tuned on validation sets for each method, which is standard model selection and does not make the test predictions equal to training inputs. The paper contains several citations to the authors' prior work, but these appear in related-work or methodological references (e.g., LoFiT as an example of modular updates, CoT/no-CoT as an analysis) and are not load-bearing for the central claim. The reviewer's mechanistic concern about whether the suffix is ever trained to consume the prefix's output is a validity/falsifiability issue about the method's proposed mechanism, not a circularity: the paper's empirical comparisons would still be meaningful (or not) independently of that mechanism. No step in the paper's chain of reasoning equates a predicted quantity to an input quantity by construction.

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

The central method rests on a set of modeling choices: the decomposition of composition into sequential atomic steps, the use of random-letters proxy prefixes, the choice of tag count, and validation-based hyperparameter selection. None of these is derived; all are empirical choices. No new physical entities are posited.

free parameters (5)
  • merge scale alpha = varies per task; swept over {0.1,...,0.9}
    Task Arithmetic coefficient for the first atomic model, with beta = 1 - alpha. Chosen on a compositional validation set per task, so it is fitted to the evaluation target. Appears in theta_comb = alpha(theta_i - theta_0) + beta(theta_j - theta_0) + theta_0.
  • learning rate = per method and task, from {5e-3,1e-3,5e-4,1e-4,5e-5}
    Swept on validation sets for every experiment; Table 6 reports optimal values. This is standard hyperparameter selection but is part of the per-setting tuning.
  • number of CoT tags n = 2
    Set for simplicity; Section 3.1 focuses on n=2 and does not test n greater than 2 in experiments.
  • proxy prefix content = random letters
    Selected over three variants (random letters, random from prompt, random text) based on out-of-domain prefix accuracy in Appendix B, Table 4.
  • RFT sample count and temperature = 10 samples, T=0.9
    Chosen for rejection sampling in Section 4; no ablation on these values is reported.
assumptions (5)
  • domain assumption Atomic tasks are basic: each cannot be reduced into a combination of others.
    Section 2 defines 'basic' this way but does not prove it for the chosen tasks. It is plausible for the synthetic string tasks but less clearly true for Skill-Mix categories.
  • domain assumption A compositional task T(i,j) is a simple function g(Ti,Tj), either composite (Ti composed with Tj) or concatenation (Ti plus Tj).
    Appendix A restricts g to these two forms; this excludes tasks needing interleaved or joint planning of more than two skills.
  • ad hoc to paper Training on random-letter proxy prefixes teaches the model to continue from arbitrary real prefix CoTs.
    This is the core mechanism of Composable CoT. It is supported only by the ablation in Appendix B, not by an independent theory of distribution shift.
  • domain assumption GPT-4o-mini grades Skill-Mix sentences consistently with the original rubric.
    Section D.2 uses an LLM-as-a-judge for evaluation; no human agreement study is reported.
  • domain assumption CoT traces of each atomic task come from a distribution distinct to that dataset.
    Section 3.1 assumes this to motivate why standard fine-tuned models cannot easily compose traces; the paper provides some empirical support via intrinsic evaluation in Section 5.3.

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Cite this review

Pith. "Pith review of Learning Composable Chains-of-Thought." pith.science (2026). https://pith.science/paper/WIUE2X76

@misc{pith2026250522635,
  author       = {Pith},
  title        = {Pith review of: Learning Composable Chains-of-Thought},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WIUE2X76}},
  note         = {Machine review of arXiv:2505.22635}
}
read the original abstract

A common approach for teaching large language models (LLMs) to reason is to train on chain-of-thought (CoT) traces of in-distribution reasoning problems, but such annotated data is costly to obtain for every problem of interest. We want reasoning models to generalize beyond their training distribution, and ideally to generalize compositionally: combine atomic reasoning skills to solve harder, unseen reasoning tasks. We take a step towards compositional generalization of reasoning skills when addressing a target compositional task that has no labeled CoT data. We find that simply training models on CoT data of atomic tasks leads to limited generalization, but minimally modifying CoT formats of constituent atomic tasks to be composable can lead to improvements. We can train "atomic CoT" models on the atomic tasks with Composable CoT data and combine them with multitask learning or model merging for better zero-shot performance on the target compositional task. Such a combined model can be further bootstrapped on a small amount of compositional data using rejection sampling fine-tuning (RFT). Results on string operations and natural language skill compositions show that training LLMs on Composable CoT outperforms multitask learning and continued fine-tuning baselines within a given training data budget.

Figures

Figures reproduced from arXiv: 2505.22635 by the authors.

Figure 1
Figure 1. (a) Composable Chain-of-thought (left): A compositional task involves two separate atomic capabilities. We use a data augmentation scheme to teach LLMs CoT formats that can be combined at inference time to address compositional tasks. (b) Pipeline for learning Composable CoT (right): Models trained on composable CoT data of atomic skills can be combined with multitask learning or model merging for zero-shot composit… view at source ↗
Figure 2
Figure 2. Construction of Composable CoT data with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Summary of settings for methods evaluated. Names in the results table reference [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Pith tools

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