While Large Language Models (LLMs) achieve impressive performance on multi-step reasoning tasks, their reliability is persistently hindered by critical limitations such as unconstrained hallucinations and poor numerical computation. Fundamentally, these issues arise because standard models treat reasoning as a transient, one-off generation process rather than retaining and refining successful procedural logic. To address these challenges, we propose eMoT (evolving Memory-of-Thought), a unified framework that stabilizes multi-step reasoning by treating reasoning trajectories as dynamic, evolving memories rather than static templates. The framework primarily consists of three interconnected modules: (i) a memory corrosion mechanism that reinforces high-utility reasoning structures while gradually decaying less frequent ones; (ii) a symbolic anchoring engine that utilizes Python for deterministic computation, much like a human uses a calculator; and (iii) a consistency-driven refinement process that aligns neural inference with symbolic outcomes, reducing the accumulation of logical discrepancies. Across multiple reasoning benchmarks, eMoT improves accuracy and solution consistency over standard Chain-of-Thought and structured reasoning baselines.On the traditional task Game of 24, eMoT achieves 100% accuracy, surpassing the baseline by up to 17.6%. Evaluations on mathematical task GSM8K, ASDiv, SVAMP, and MGSM further show consistent gains in multi-step mathematical reasoning. In our evaluation, we achieve superior performance despite utilizing a lightweight backbone model with constrained baseline capabilities. Compared to alternative methods that rely on massively scaled models, our results demonstrate that the performance gains are fundamentally driven by the eMoT framework's reasoning control rather than sheer model size.
Large Language Models (LLMs) achieve impressive accuracy on mathematical reasoning benchmarks, yet their performance drops when problems are modified with simple changes like different names or numbers. Code execution methods, which let models generate and run Python code instead of reasoning in natural language, have been proposed as a solution, but their effect on reasoning robustness (the ability to maintain accuracy across problem variations) has not been systematically tested. This study evaluates three approaches on 1,000 problems from the GSM-Symbolic dataset: pure reasoning using chain-of-thought (CoT) prompting, single-shot code execution using Program-Aided Language models (PAL), and iterative code execution using Step-by-Step Coding (SBSC). All three were run on paired original and modified problems using Claude Haiku 4.5. CoT was the most robust method, with an accuracy drop of 1.3 percentage points and 1.8% of problems breaking under perturbation. PAL was the least robust at 1.7 percentage points and 3.1% broke, with SBSC falling in between. Although these differences were not statistically significant (p=.096), the directional trend was consistent across all measures, suggesting that code execution, whether single-shot or iterative, does not improve reasoning robustness on grade-school-level problem variations.
Large Language Models have achieved strong performance on reasoning tasks with objective answers by generating step-by-step solutions, but diagnosing where a multi-step reasoning trace might fail remains difficult. Confidence estimation offers a diagnostic signal, yet existing methods are restricted to final answers or require internal model access. In this paper, we introduce Stepwise Confidence Attribution (SCA), a framework for closed-source LLMs that assigns step-level confidence based only on generated reasoning traces. SCA applies the Information Bottleneck principle: steps aligning with consensus structures across correct solutions receive high confidence, while deviations are flagged as potentially erroneous. We propose two complementary methods: (1) NIBS, a non-parametric IB approach measuring consistency without graph structures, and (2) GIBS, a graph-based IB model that learns subgraphs through a differentiable mask to capture logical variability. Extensive experiments on mathematical reasoning and multi-hop question answering show that SCA reliably identifies low-confidence steps strongly correlated with reasoning errors. Moreover, using step-level confidence to guide self-correction improves the correction success rate by up to 13.5% over answer-level feedback.
Large language models (LLMs) demonstrate strong chain-of-thought (CoT) reasoning abilities, while smaller models (<= 3B parameters) significantly underperform on multi-step reasoning tasks. Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.