# Probabilistic Soundness Guarantees in LLM Reasoning Chains

arXiv: https://arxiv.org/abs/2507.12948 · HTML: https://mlsanity.com/paper/2507.12948/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 3 of its 55 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 3 of 3)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Faithfulness vs. Plausibility: On the (Un)Reliability of Explanations from Large Language Models](https://mlsanity.com/paper/2402.04614/) (2024)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)

## Built on by (most cited first, 13 of 13)

- [Locate, Steer, and Improve: A Practical Survey of Actionable Mechanistic Interpretability in Large Language Models](https://mlsanity.com/paper/2601.14004/) (2026)
- [E-valuator: Reliable Agent Verifiers with Sequential Hypothesis Testing](https://mlsanity.com/paper/2512.03109/) (2025)
- [SSR: Socratic Self-Refine for Large Language Model Reasoning](https://mlsanity.com/paper/2511.10621/) (2025)
- [Interpretability Can Be Actionable](https://mlsanity.com/paper/2605.11161/) (2026)
- [Limited Reasoning Space: The cage of long-horizon reasoning in LLMs](https://mlsanity.com/paper/2602.19281/) (2026)
- [Prototyping Multimodal GenAI Real-Time Agents with Counterfactual Replays and Hybrid Wizard-of-Oz](https://mlsanity.com/paper/2510.06872/) (2025)
- [T-FIX: Text-Based Explanations with Features Interpretable to eXperts](https://mlsanity.com/paper/2511.04070/) (2025)
- [Missingness Bias Calibration in Feature Attribution Explanations](https://mlsanity.com/paper/2603.04831/) (2026)
- [Probabilistic Programs of Thought](https://mlsanity.com/paper/2604.17290/) (2026)
- [When LRP Diverges from Leave-One-Out in Transformers](https://mlsanity.com/paper/2510.18810/) (2025)
- [DanceHA: A Multi-Agent Framework for Document-Level Aspect-Based Sentiment Analysis](https://mlsanity.com/paper/2603.16546/) (2026)
- [Shattering the Autoregressive Curse: Dynamic Epistemic Entropy Orchestrated Erasable Reinforcement Learning for LLMs](https://mlsanity.com/paper/2606.17735/) (2026)
- [Online Safety Monitoring for LLMs](https://mlsanity.com/paper/2607.02510/) (2026)

## Abstract (arXiv)

In reasoning chains generated by large language models (LLMs), initial errors often propagate and undermine the reliability of the final conclusion. Current LLM-based error detection methods often fail to detect propagated errors because earlier errors can corrupt judgments of downstream reasoning. To better detect such errors, we introduce Autoregressive Reasoning Entailment Stability (ARES), a probabilistic framework that evaluates each reasoning step based solely on previously-verified premises. This inductive method yields a nuanced score for each step and provides certified statistical guarantees of its soundness, rather than a brittle binary label. ARES achieves state-of-the-art performance across four benchmarks (72.1% Macro-F1, +8.2 points) and demonstrates superior robustness on very long synthetic reasoning chains, where it excels at detecting propagated errors (90.3% F1, +27.6 points).