Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.32035

Reasoning Concentrates Errors, and Self-Consistency Never Notices

Asaad Althoubi
View original source ↗Read source document ↗Export metadata ↓

Abstract

Self-consistency assumes that independent samples disagree when a model is unsure, so agreement is evidence of correctness. Holding weights fixed and toggling only a reasoning mode, over five benchmarks and 74,944 samples, we show that reasoning concentrates a model's errors: the probability that two independently drawn wrong answers coincide rises in all ten dataset-scale comparisons (p = 0.00098), and in nine of nine after restricting both arms to the problems each gets wrong. Where the answer space is unbounded, reasoning cuts the distinct answers produced to 0.43-0.65 of the non-reasoning count; where it is bounded, both arms hold an identical option set and reasoning concentrates mass on it instead, which no positional prior can explain at fixed weights. The aggregate cost is smaller than the mechanism predicts, because reasoning also shrinks the set of problems where answer diversity can decide anything, in ten of ten cells and by 2.7x; normalized for available headroom, both arms convert a quarter of it in domain. Confidence weighting does not recover what is left. Across 280 method-dataset-model combinations on eight models and five benchmarks, not one beats plain majority voting after correction; weighted voting agrees with it on 98.5% of problem-method pairs and is right 56.3% of the time on the rest; and a signal's direction can invert within fixed weights, with answer log-probability predicting correctness when reasoning is off and error when it is on. A learned six-signal combination gains nothing out of domain. Confidence signals should be evaluated on decisions, not on discrimination.

Explore related subjects

cs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Asaad Althoubi. 2026-09-25. Reasoning Concentrates Errors, and Self-Consistency Never Notices. https://arxiv.org/abs/2609.32035

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

KEEP EXPLORING

Related papers

arXiv2026

Hierarchical Reasoning Model

Reasoning, the process of devising and executing complex goal-oriented action sequences, remains a critical challenge in AI. Current large language models (LLMs) primarily employ Chain-of-Thought (CoT) techniques, which suffer from brittle task decomposition, extensive data requirements, and high latency. Inspired by the hierarchical and multi-timescale processing in the human brain, we propose the Hierarchical Reasoning Model (HRM), a novel recurrent architecture that attains significant computational depth while maintaining both training stability and efficiency. HRM executes sequential reasoning tasks in a single forward pass without explicit supervision of the intermediate process, through two interdependent recurrent modules: a high-level module responsible for slow, abstract planning, and a low-level module handling rapid, detailed computations. With only 27 million parameters, HRM achieves exceptional performance on complex reasoning tasks using only 1000 training samples. The model operates without pre-training or CoT data, yet achieves nearly perfect performance on challenging tasks including complex Sudoku puzzles and optimal path finding in large mazes. Furthermore, HRM outperforms much larger models with significantly longer context windows on the Abstraction and Reasoning Corpus (ARC), a key benchmark for measuring artificial general intelligence capabilities. These results underscore HRM's potential as a transformative advancement toward universal computation and general-purpose reasoning systems.

cs.AI↗
arXiv2026

A memory-based active inference model of DishBrain-like adaptive behaviour

Recent and rapid advances in artificial intelligence (AI) make it increasingly important to understand the foundations of adaptive behaviour in autonomous agents, especially for building safe and efficient systems. While artificial neural networks have dominated the development of AI, recent work has begun to explore living biological neuronal networks as an alternative substrate for computation. These systems promise remarkable data and sample efficiency and rich dynamics, and may also inspire explainable and biologically plausible models. Here, we develop an experiment-informed active inference framework to model decision-making in closed-loop agents that mirror experimental setups using biological neurons. Using a generative model whose dimensions are matched to an experiment protocol, we systematically compare three decision-making schemes within this common generative model. Under matched episode counts (i.e. total data available for learning) to the in-vitro experiment, our simulations show that agents with short memory horizons reach a level of performance close to that of mouse and human cortical cultures (DishBrain platform), whereas longer memory horizons depart from it substantially. Increasing the planning horizon, by contrast, confers no comparable benefit. Because all model parameters are explicit, we can also track the quantities in our generative model that accompany this improvement, such as the risk term and the entropy of the transition and state-action mappings. Together, these results illustrate how active inference offers a formal language for comparing decision-making schemes in similar closed-loop control environments.

cs.AI↗
arXiv2026

A Quantitative Study of Sustained Focus in Large Language Models via Repetitive Deterministic Prediction Tasks

We investigate the performance of large language models (LLMs) on repetitive deterministic prediction tasks and study how the sequence accuracy rate (SAR) scales with output length. Each such task involves the repetition of the same operation $N$ times. Examples of such tasks include letter replacement in letter strings following a given rule, integer addition, and multiplication of string operators in many-body quantum mechanics. If the LLM performs the task by a simple repetition algorithm, the success rate would follow an exponential decay with sequence length. In contrast, our experiments on leading LLMs reveal a crossover that is sharper than exponential: $-\log\mathrm{SAR}$ grows super-linearly with $N$, and accuracy collapses around a characteristic length $N_*$, the accuracy cliff that separates reliable from unreliable generation. The hypothesis of independent per-step errors is rejected for every model and task we studied. The crossover is well described by a double-exponential accumulation law, $\mathrm{SAR}=\exp(-β_0 Nα^{N-1})$, whose crossover scale $N_*$ does not depend on the functional form chosen to fit it. To interpret this behaviour we introduce a minimal effective model in which step-correctness variables interact through dense random couplings and compete with an external field set by the prompt. Solved by direct enumeration, the model reproduces the super-linear error accumulation and the accuracy cliff qualitatively, and it assigns to each model--task pair two interpretable parameters, an intrinsic error rate and an error-accumulation factor.

cs.AI↗