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CryptoX : Compositional Reasoning Evaluation of Large Language Models

T0 review · 4 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A benchmark that encodes prompts reveals that most LLMs are weak at compositional reasoning, with open-source models trailing closed-source ones by a large margin.

desk verdict A usable stress-test benchmark whose central 'compositional reasoning' claim is undercut by its own case studies; worth refereeing, but only after the authors reposition the claim. read the letter →

arxiv 2502.07813 v2 pith:U2YGPS47 submitted 2025-02-08 cs.CR cs.AI

Jiajun Shi , Chaoren Wei , Liqun Yang , Zekun Moore Wang , Chenghao Yang , Ge Zhang , Stephen Huang , Tao Peng
show 2 more authors
Jian Yang Zhoufutu Wen
This is my paper · ORCID
classification cs.CRcs.AI
keywords compositionalreasoningevaluationinstructionencryptioncipher-basedpromptinglargelanguagemodelsbenchmarkAUCmechanisticinterpretabilitylogitlensopen-sourcevsclosed-source
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 argues that standard reasoning benchmarks are saturated and miss a distinct ability: compositional reasoning, the capacity to combine separate subtasks in a single model run. Its proposal, CryptoX, rewrites existing benchmark questions by encoding a variable number of words with a cipher (for instance, emoji substitution) and adding answer-projection rules, so that a model must decode the prompt and then solve the original task in one pass. The resulting CryptoBench covers 21 sub-datasets and roughly 7,000 cases drawn from MATH, MMLU, BBH, MBPP, and long-context needle retrieval, tested on more than 20 models. The central finding is that accuracy falls sharply as more words are encoded, that most LLMs show weak compositional reasoning, and that open-source models score far below closed-source ones, with o1, o3-mini, and Gemini-2.0-Flash-Thinking the strongest. A sympathetic reader would care because the benchmark claims to expose a capability gap that ordinary accuracy numbers hide, and the accompanying mechanistic analyses suggest the gap reflects how models order decoding, reasoning, and answer summarization across layers.

What carries the argument

The engine of the method is instruction encryption: a codebook (base Morse, emoji Morse, or emoji shuffle) randomly replaces a chosen number of words in a prompt, and the encoding rules are explicitly included in the prompt. Instruction transformation then adds further projection steps from the decoded answer to the required output, such as mapping A–D to 1–4 or appending the first character of the option text. Performance is summarized as an area-under-curve (AUC) score computed as the number of encoded words ranges from 0 to 10, which the paper argues is more sensitive than a single accuracy value. On the mechanism side, logit lens and neuron activation analysis identify which layers track decoded words versus answer options, and reasoning-stage analysis labels layer bands as shallow (decomposition), intermediate (subtask solving), and deep (summarization).

What would settle it

The paper's own Appendix G case studies show models producing correct answers even when they fail to decode the question or skip the decoding step outright. A direct test of the central mechanism would measure, per item, whether final-answer accuracy tracks decoding accuracy (for example, ROUGE or BLEU against the true plaintext question); if many items are answered correctly despite failed decoding, the benchmark is measuring something other than decode-then-reason compositionality.

Watch

Extended reading notes

Core claim

CryptoBench quantifies compositional reasoning by forcing a model to perform two coupled subtasks in one run: decode a cipher-transformed question using rules stated in the prompt, then answer the original question under an additional output transformation (for example, convert the chosen option letter to its alphabet position). The authors report that no tested model handles this well at high encoding levels, that the gap between open-source and closed-source models is large — o1 reaches 83.7% average accuracy while the smallest open-source models fall to near zero — and that model size, instruction tuning, and architecture all shift performance. Their mechanistic experiments indicate that models decompose the problem, decode in early-to-middle layers, solve the base task, and summarize subtask answers in later layers, and that neuron activation for encoding rules precedes the logit-lens rise of decoded words. The paper's conclusion is that compositional reasoning is a measurable ability distinct from the skills tapped by vanilla benchmarks, and that CryptoBench's area-under-curve score over encoding levels is a more discriminating metric than single accuracy numbers.

Load-bearing premise

The load-bearing premise is that a model's accuracy on prompts that must be decoded before answering is a valid measure of compositional reasoning as a distinct ability, separate from instruction following, resilience to input perturbations, or memorization of benchmark answers; if that premise gives way, the scores blend unrelated capabilities.

Editorial extensions

If this is right

  • Standard benchmarks such as MMLU can be stress-tested by re-encoding prompts with a fresh codebook, yielding a difficulty curve instead of a single accuracy point.
  • Model rankings change under CryptoBench relative to vanilla accuracy, so a model's advertised reasoning skill on familiar benchmarks does not reliably predict its performance when prompts are superficially transformed.
  • The strong drop in accuracy as encoded-word count rises implies that improving compositional reasoning—not just base-task skill—could be a lever for better generalization.
  • The observed layer-level ordering (decode, then reason, then summarize) suggests that architectures or inference procedures that enforce explicit decomposition may improve CR performance.
  • AUC over encoding levels gives benchmark designers a graded metric that keeps some discrimination even when models saturate the vanilla task.

Reading between the lines

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

  • Editorial inference: Appendix G's cases where a model answers correctly despite failed or skipped decoding suggest that CryptoBench scores may partly reflect memorized or shortcut answers, so the benchmark's construct validity as a pure measure of compositional reasoning remains an open question.
  • Editorial inference: The framework is codebook-agnostic, so an immediate extension would be to test whether a model's ranking under emoji shuffle transfers to structurally different ciphers (for example, Huffman coding or RSA-style encryption), which would show whether the measured ability is generic compositionality or specific familiarity with the cipher format.
  • Editorial inference: The multi-turn versus single-turn ablation implies that decomposing a task into separate prompts is easier than composing the same subtasks in one context; a natural application is to use that gap as a diagnostic for how much context-composition overhead a model carries.
  • Editorial inference: The logit-lens finding that decoded-word probability peaks before answer-option probability suggests a testable intervention: explicitly forcing a model to output the plaintext question before answering should raise accuracy if the mechanism is causal, and should leave accuracy unchanged if decoding is epiphenomenal.
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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 / 5 minor

Summary. The paper proposes CryptoX, a framework that transforms existing benchmarks (MATH, MMLU, MBPP, BBH, Needle) by encrypting 5 or 10 words in each prompt using fixed codebooks and by adding answer-projection rules (numeric and alpha transformations). It constructs CryptoBench with 21 sub-datasets and roughly 7K cases, evaluates 20+ open- and closed-source LLMs, and reports that accuracy declines as more words are encoded, that closed-source models outperform open-source models, and that an AUC score provides a better ranking than average accuracy. The paper also presents logit-lens, neuron-activation, and reasoning-stage analyses on smaller open models to argue that models decode encoded words before solving the original problem.

Significance. If the benchmark measures a distinct compositional-reasoning ability, it would be a useful tool: it is grounded in established datasets, ships code, and the monotone accuracy decline with encoding level is a crisp and reproducible empirical finding. The paper is also transparent in providing detailed case studies in the appendix. However, the construct-validity premise is not established, and the paper's own appendix contradicts the central claim that the benchmark forces models to decode before answering. The evaluation of math answers relies on an unvalidated LLM-as-judge, and the mechanistic analyses are limited to small, low-scoring models. These issues make the headline conclusion ('most LLMs have weak compositional reasoning abilities') premature, although the benchmark itself may be salvageable with additional controls and more modest claims.

major comments (4)
  1. [Section 3.1, Appendix G (Figures 35-37)] Section 3.1 states that 'CryptoBench forces models to conduct compositional reasoning, requiring them to decode the question before answering it,' but the paper's own case studies contradict this. In Figure 35, Qwen2.5-72B-Instruct answers correctly despite mistranslating the encoded question, and on the Crypto-MMLU single-stage task it 'skipped the translation step entirely and directly answered the question.' Figure 37 reports correct answers despite incorrect decoding in both conditions. Consequently, item-level scores do not require the intended decode-then-answer chain, and the central claim that CryptoBench quantifies compositional reasoning is unsupported. Please either redesign items so that correct answers require decoding (e.g., encode all content words and the answer options, or require the decoded question to be echoed in the response), or reframe the benchmark as measuring robustness to input corruption and explicitly state that construct-validity evidence is still needed.
  2. [Algorithm 1, Table 1] With only 5 or 10 words encoded in prompts that are hundreds to thousands of characters long (e.g., Crypto-BBH average length ranges from 1585.3 to 3517.24 characters; Crypto-MMLU from 627.97 to 1333.6), most of the question and all answer options remain in plaintext. This leaves ample residual cues for models to answer correctly, especially for public benchmarks like MMLU that are likely present in pretraining corpora. The case studies in Appendix G are consistent with this alternative explanation: the model often answers correctly without decoding or after failed decoding. To support the compositional-reasoning interpretation, please add control conditions in which all content words are encoded (or a random-permutation control) and show that performance still tracks the number of encoded words; otherwise, the observed decline may reflect token-level perturbation sensitivity or partial-prompt pattern matching rather than compositional reasoning.
  3. [Section 3, 'Evaluation Metrics'] Scores for Crypto-Math and Crypto-HighResolution are obtained with an LLM-as-judge (Doubao-Pro-256K) without reporting any validation, inter-judge agreement, comparison against exact match, or human ratings. Since mathematical answers are a significant part of the reported results, please provide evidence that the judge is reliable (e.g., agreement rates on a sample, or a comparison with exact-match with tolerance), or report exact-match numbers with clearly stated normalization rules for mathematical expressions.
  4. [Section 4, Appendices D-F] The logit-lens and neuron-activation analyses are run only on Qwen2.5-3B/7B, Llama-3.1-8B, and similar small models, which are among the lowest-performing models in Table 2 (e.g., Qwen2.5-7B-Instruct has AUC 1.24). The paper draws general conclusions that 'LLMs' summarize subtask answers and that 'the layers of LLMs' exhibit a hierarchical pattern of subtask execution, but the highest-scoring models (o1, o3-mini, Gemini-2.0-Flash-Thinking) are not analyzed. Please restrict the mechanistic claims to the studied models or extend the analysis to at least one high-performing model before making claims about LLM compositional reasoning in general.
minor comments (5)
  1. [Appendix G.2] The paper uses the term 'overfitting' to describe correct answers despite decoding errors, but the evidence is equally consistent with memorization of public MMLU questions or with the model simply ignoring the encoding. Please clarify the terminology and discuss the possibility of benchmark contamination explicitly.
  2. [Section 3, 'LLMs'] The sampling parameters are given as wide ranges ('temperature T = 0.7 to 1.0 and top p = 0.75 to 1.0') without per-model values. Please report the exact settings and number of runs for each model, especially because temperature affects the variance reported in Table 5.
  3. [Throughout] There are several typos and heading errors: 'Compostional Reasoning' (Section 5.1), 'Performane' (Appendix C.2), 'Thr Effect' (Appendix C.5), 'Instrcut' (Figure 6), 'nueron' (Section 4.2), and 'chararcter' (Figure 2).
  4. [Table 2] Table 2 is visually dense and uses color coding (green/blue/orange) that may not render reliably in print or for color-blind readers; consider splitting the 0/5/10 columns into separate rows or adding explicit numeric highlighting.
  5. [Appendix C.8] The Spearman correlations with Chatbot Arena (0.61, 0.57, 0.19) are reported without the number of models or p-values; please add these statistics to make the correlation comparison interpretable.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: CryptoBench is an empirical benchmark and the CR conclusions rest on measured scores with independent mechanistic evidence; Appendix G raises construct-validity concerns but no derivation reduces to its inputs.

full rationale

The paper's central claim is an empirical evaluation result: CryptoBench scores are measured accuracies and AUC over tasks built from external datasets (MATH, MMLU, BBH, MBPP, Needle) by instruction encryption and transformation. No parameter is fitted and then renamed as a prediction; the AUC in Eq. (2) is an explicit aggregation of measured performance, not a hidden definition of compositional reasoning. The conceptual definition of CR in the introduction is independent of the benchmark score, and the mechanistic analyses (logit lens, neuron activation, reasoning stage) provide additional, though limited, evidence. Self-citations in the references are not load-bearing, and no uniqueness theorem is imported. The main weakness is construct validity, not circularity: Section 3.1 asserts that CryptoBench 'forces models to conduct compositional reasoning, requiring them to decode the question before answering it,' but Appendix G (Figures 35-37) documents cases where models answer correctly despite decoding errors or skip decoding entirely, and Algorithm 1 encodes only 5 or 10 words in long prompts, leaving much of the question and all options in plaintext. These observations undermine the inference from scores to CR ability, but they do not make the conclusion equivalent to the inputs by construction. The benchmark is self-contained as a measurement instrument; therefore the circularity score is 0.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the assumption that the decode-and-answer task isolates compositional reasoning. The paper provides some internal evidence but no external validation, so the ledger records the main design choices and assumptions.

free parameters (5)
  • Encoding levels (0, 5, 10 words) = 0, 5, 10
    Chosen by hand to define the difficulty curve and compute AUC; no justification that these levels are representative or that the resulting AUC is stable.
  • Encoding codebooks = base Morse, emoji Morse, emoji shuffle
    Three hand-designed codebooks; results may depend on the specific symbol mappings chosen.
  • Answer transformation rules = numeric (A->1), alpha (first character)
    Hand-chosen extra reasoning hops; the alpha transformation requires the first character of the answer content, which is task-specific.
  • Number of needles in Needle benchmark = 3
    Taken from the gkamradt baseline without sensitivity analysis; changing this could affect results.
  • Sampling temperature and top_p = temperature 0.7-1.0, top_p 0.75-1.0
    Non-deterministic decoding settings chosen without reporting repeated-run variance; results are not reproducible to a single number.
assumptions (3)
  • domain assumption Decoding encoded words and applying answer transformations is a valid measure of compositional reasoning.
    This is the central operationalization of compositional reasoning in the paper. No external validation is provided against other CR measures, human judgments, or controlled tasks.
  • domain assumption The LLM-as-judge (Doubao-Pro-256K) provides correct evaluations of math answers.
    Used as the metric for Crypto-Math and Crypto-BBH without human validation, agreement rates, or error analysis (Section 3, Evaluation Metrics).
  • domain assumption Logit lens probabilities and neuron activation counts reflect the model's internal reasoning stages.
    Section 4 interpretations are post-hoc and descriptive; no controls (e.g., random token sets) or statistical tests support the claimed decomposition and summarization stages.

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Cite this review

Pith. "Pith review of CryptoX : Compositional Reasoning Evaluation of Large Language Models." pith.science (2026). https://pith.science/paper/U2YGPS47

@misc{pith2026250207813,
  author       = {Pith},
  title        = {Pith review of: CryptoX : Compositional Reasoning Evaluation of Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/U2YGPS47}},
  note         = {Machine review of arXiv:2502.07813}
}
read the original abstract

The compositional reasoning capacity has long been regarded as critical to the generalization and intelligence emergence of large language models LLMs. However, despite numerous reasoning-related benchmarks, the compositional reasoning capacity of LLMs is rarely studied or quantified in the existing benchmarks. In this paper, we introduce CryptoX, an evaluation framework that, for the first time, combines existing benchmarks and cryptographic, to quantify the compositional reasoning capacity of LLMs. Building upon CryptoX, we construct CryptoBench, which integrates these principles into several benchmarks for systematic evaluation. We conduct detailed experiments on widely used open-source and closed-source LLMs using CryptoBench, revealing a huge gap between open-source and closed-source LLMs. We further conduct thorough mechanical interpretability experiments to reveal the inner mechanism of LLMs' compositional reasoning, involving subproblem decomposition, subproblem inference, and summarizing subproblem conclusions. Through analysis based on CryptoBench, we highlight the value of independently studying compositional reasoning and emphasize the need to enhance the compositional reasoning capabilities of LLMs.

Figures

Figures reproduced from arXiv: 2502.07813 by the authors.

Figure 1
Figure 1. (a) shows the concept of compositional reasoning (CR) which involves combining [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Overview of the CryptoBench Construction Process. We apply instruction encryption [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. The performance of different models on Crypto-HighResolution with 10 varying degrees of encoding. the number of subtasks or the number of encoded words increases, the model’s accuracy in answering questions decreases. This indicates that the evaluation of the model’s CR ability is influenced by the complexity of the question composition and the difficulty of the subtasks. We test the performance of Qwen2.5 models wi… view at source ↗
Figures from the paper (35 more)
Figure 4
Figure 4. Figure 4: The performance of models with different model size on Crypto-MMLU-Alpha. In [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: The comparison of the performance of multi-turn and single-turn dialogues. In [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: The performance of the Base models and the Instrcut models on Crypto-MMLU. In [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: The result of logit lens experiments. The green valid line “ [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Neuron Activation Analysis:the comparison figure of neuron activation analysis and [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Encoding rule for our experiments. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: Zero-shot prompt for Crypto-Math and Crypto-MMBP [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]
Figure 11
Figure 11. Figure 11: Three-shot prompt for Crypto-BBH 22 [PITH_FULL_IMAGE:figures/full_fig_p022_11.png]
Figure 12
Figure 12. Figure 12: Five-shot prompt for Crypto-BBH, Crypto-Math and Crypto-MMBP [PITH_FULL_IMAGE:figures/full_fig_p023_12.png]
Figure 13
Figure 13. Figure 13: Zero-shot prompt for Crypto-Math and Crypto-MMBP [PITH_FULL_IMAGE:figures/full_fig_p023_13.png]
Figure 14
Figure 14. Figure 14: Zero-shot prompt for Crypto-MMLU B.2.3. Five-Shot Prompt (a) Five-shot prompt used for non-encoded question (b) Five-shot prompt used for encoded question [PITH_FULL_IMAGE:figures/full_fig_p024_14.png]
Figure 15
Figure 15. Figure 15: Five-shot prompt for Crypto-MMLU 24 [PITH_FULL_IMAGE:figures/full_fig_p024_15.png]
Figure 16
Figure 16. Figure 16: Zero-shot prompt for Crypto-Needle-30K 25 [PITH_FULL_IMAGE:figures/full_fig_p025_16.png]
Figure 17
Figure 17. Figure 17: The performance of models with different model size. In [PITH_FULL_IMAGE:figures/full_fig_p026_17.png]
Figure 18
Figure 18. Figure 18: The performance of Doubao-Moe and Doubao-Dense. In [PITH_FULL_IMAGE:figures/full_fig_p027_18.png]
Figure 19
Figure 19. Figure 19: The performance of models with different model size. In [PITH_FULL_IMAGE:figures/full_fig_p028_19.png]
Figure 20
Figure 20. Figure 20: The performance between base models and instruct models. In [PITH_FULL_IMAGE:figures/full_fig_p029_20.png]
Figure 21
Figure 21. Figure 21: The performance of different architectural models. In [PITH_FULL_IMAGE:figures/full_fig_p030_21.png]
Figure 22
Figure 22. Figure 22: The decoding performance of different models. In [PITH_FULL_IMAGE:figures/full_fig_p031_22.png]
Figure 23
Figure 23. Figure 23: The decoding performance of different models. In [PITH_FULL_IMAGE:figures/full_fig_p032_23.png]
Figure 24
Figure 24. Figure 24: The correlation matrix for benchmarks. The closer the Spearman correlation is to 1, [PITH_FULL_IMAGE:figures/full_fig_p033_24.png]
Figure 25
Figure 25. Figure 25: The logit lens analysis on Crypto-MMLU-BaseMorse using [PITH_FULL_IMAGE:figures/full_fig_p034_25.png]
Figure 26
Figure 26. Figure 26: The logit lens analysis on Crypto-MMLU-BaseMorse using 0%/50%/100% encoding [PITH_FULL_IMAGE:figures/full_fig_p035_26.png]
Figure 27
Figure 27. Figure 27: The logit lens analysis on Crypto-MMLU-EmojiMorse using 0%/50%/100% [PITH_FULL_IMAGE:figures/full_fig_p036_27.png]
Figure 28
Figure 28. Figure 28: The logit lens analysis on Crypto-MMLU-EmojiShuffle using 0%/50%/100% [PITH_FULL_IMAGE:figures/full_fig_p037_28.png]
Figure 29
Figure 29. Figure 29: The logit lens analysis on Crypto-MMLU-BaseMorse using 0/3/5 encoding words. [PITH_FULL_IMAGE:figures/full_fig_p038_29.png]
Figure 30
Figure 30. Figure 30: The logit lens analysis on Crypto-MMLU-BaseMorse using 0/3/5 encoding words. [PITH_FULL_IMAGE:figures/full_fig_p039_30.png]
Figure 31
Figure 31. Figure 31: The logit lens analysis on Crypto-MMLU-EmojiMorse using 0/3/5 encoding words. [PITH_FULL_IMAGE:figures/full_fig_p039_31.png]
Figure 32
Figure 32. Figure 32: The logit lens analysis on Crypto-MMLU-EmojiShuffle using 0/3/5 encoding words. [PITH_FULL_IMAGE:figures/full_fig_p040_32.png]
Figure 33
Figure 33. Figure 33: The other result of Neuron Activation Analysis. [PITH_FULL_IMAGE:figures/full_fig_p040_33.png]
Figure 34
Figure 34. Figure 34: Case 1 in the Case Study: The prompts for the Crypto-MMLU-Alpha and [PITH_FULL_IMAGE:figures/full_fig_p041_34.png]
Figure 35
Figure 35. Figure 35: Case 2 in the Case Study: The prompts for the Crypto-MMLU-Alpha and [PITH_FULL_IMAGE:figures/full_fig_p041_35.png]
Figure 36
Figure 36. Figure 36: Case 3 in the Case Study: The prompts for the Crypto-MMLU-Alpha and [PITH_FULL_IMAGE:figures/full_fig_p042_36.png]
Figure 37
Figure 37. Figure 37: Case 4 in the Case Study: The prompts for the Crypto-MMLU-Alpha and [PITH_FULL_IMAGE:figures/full_fig_p042_37.png]
Figure 38
Figure 38. Figure 38: Prompt of Reasoning Stage Analysis. 44 [PITH_FULL_IMAGE:figures/full_fig_p044_38.png]

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Forward citations

Cited by 1 Pith paper

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.