Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.38107

Correct Answers, Invalid Traces: What Verifiable Grade-School Math Reveals About Chain-of-Thought Traces

Ratish Puduppully·Pranabendu Misra·Paarth Iyer·Durgesh Kalwar·Vardhan Palod·Subbarao Kambhampati
View original source ↗Read source document ↗Export metadata ↓

Abstract

Chain-of-thought traces are widely read as records of how models reach their answers, informing debugging, agent auditing, and claims about reasoning. Testing this interpretation is difficult because natural-language thinking traces are rarely mechanically verifiable. We revisit it in iGSM, a synthetic grade-school mathematics benchmark designed to study thinking traces and used to support claims of learned reasoning and planning. Crucially, iGSM exposes the exact quantities and dependencies that a correct solution should use, allowing generated traces to be checked programmatically step by step and enabling us to test whether correct answers are reliably accompanied by valid traces. We first evaluate models trained exclusively on valid, minimal traces. Answer correctness and trace validity nearly coincide in distribution but decouple out of distribution: on the hardest instances, 31.6% of correct answers have invalid traces, over half of which pass all syntactic and arithmetic checks but fail semantic dependency checks. We then intervene on trace supervision. Non-minimal training traces induce non-minimal outputs, while re-asking the same problem with a different query reveals computations inherited from the original query, weakening minimality as evidence of selective planning. Shuffling tokens in 10% of training trace sentences preserves near-clean accuracy even out of distribution despite no trace passing verification. Swapped training traces likewise retain high in-distribution accuracy. We discuss the implications of these findings for chain-of-thought monitoring and interpretation in the context of AI safety.

Explore related subjects

cs.CLcs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ratish Puduppully, Pranabendu Misra, Paarth Iyer, Durgesh Kalwar, Vardhan Palod, Subbarao Kambhampati. 2026-09-29. Correct Answers, Invalid Traces: What Verifiable Grade-School Math Reveals About Chain-of-Thought Traces. https://arxiv.org/abs/2609.38107

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

NMIXX: Domain-Adapted Neural Embeddings for Cross-Lingual eXploration of Finance

Financial text embeddings must distinguish changes in event status, perspective, and obligations even when passages share similar wording. NMIXX adapts existing encoders through 18.8k source-linked triplets: paraphrases and Korean-English translations preserve meaning, while targeted financial rewrites introduce semantic contrasts. We examine this recipe across seven backbones on English and Korean financial and general-domain semantic textual similarity (STS), and analyze the composition and passage lengths of KorFinSTS. BGE-M3 attains the highest adapted financial correlations in this comparison, improving from 0.1969 to 0.2967 on FinSTS and from 0.0512 to 0.2732 on KorFinSTS. Its general English and Korean correlations decrease by 0.0391 and 0.0463. Across the seven models, five improve their mean financial correlation, but all reduce their mean general-domain correlation. Per-language comparisons and benchmark-weight sensitivity analysis reveal differences obscured by a single aggregate score. The study contributes a finance-specific supervision design and evidence for evaluating adaptation jointly with retained general semantic capability; direct cross-language retrieval remains outside its evaluation scope.

cs.CL↗
arXiv2026

Sequential Bayesian Evaluation of Large Language Model Behavior

It is increasingly important to evaluate the characteristics of systems based on large language models (LLMs). Evaluations in this context often rely on a curated benchmark set of input prompts provided to the LLM, where the output for each prompt may be assigned a binary or ordinal score and the aggregation of scores across prompts is then used as a summary evaluation. In this paper, we develop a Bayesian approach for quantifying the uncertainty that arises in such evaluation metrics as a result of the stochasticity of the LLM-based systems; the same prompt may exhibit different outcomes on repeated runs. Our framework leads naturally to a sequential evaluation, in which we leverage the Bayesian model to preferentially select which prompts in the benchmark to use next, enabling more cost-effective LLM evaluations. We demonstrate this approach through four case studies: pairwise LLM preferences in interactive dialogue (MT-Bench), refusal rates on adversarial inputs (JailbreakBench), embodied agentic reasoning (ALFWorld), and agentic web-search Q&A (GAIA). Our results illustrate how a Bayesian approach can provide insightful uncertainty quantification about the behavior of blackbox LLM-based systems in a manner that is not accessible via deterministic or single-run evaluations.

cs.CL↗
arXiv2026

ResidualKV: Residual-Based KV Cache Compression for Efficient Long-Context Inference

Efficient long-context inference faces two coupled bottlenecks: KV-cache memory grows linearly with context length, while attention computation grows quadratically. Existing approaches typically address one at the expense of irreversible token eviction, full-cache retention, or full-history reconstruction, limiting their effectiveness for multi-turn interaction and long-form reasoning. Motivated by two empirical properties, Long-Range Inter-Token Similarity and Smooth Residual Distribution, we propose ResidualKV, which factorizes the KV cache into a sparse set of globally retrieved references and compact, quantized residual codes for the remaining tokens. This representation preserves token-specific information without permanent eviction and, when combined with sparse attention, reconstructs only the selected states on demand. Dynamic-stride scheduling further reduces reference growth from linear to approximately logarithmic at ultra-long contexts. Across Llama, Qwen, LLaVA-OV, and Qwen3-VL backbones, ResidualKV maintains near-full-cache performance using only 13%-16% KV storage and 30% attention computation on LongBench, and 8%-10% storage and 10% computation in matched-budget multimodal evaluation. It also accelerates decoding by up to $1.5\times$ with KV-cache quantization and $3.4\times$ without it. These results show that global cross-token redundancy supports accurate, memory-efficient, and computation-efficient long-context inference. The source code is available at https://github.com/CURRENTF/ResidualKV.

cs.CL↗