A model of errors in transformers

TL;DR

This paper presents a simplified two-parameter model inspired by effective field theory to analyze and predict error rates in large language models on deterministic tasks, supported by extensive empirical validation.

Contribution

It introduces a novel two-parameter quantitative relationship for LLM errors, offering insights into error accumulation and methods to reduce errors through prompt design.

Findings

Excellent agreement between model predictions and empirical data.

Identification of deviations indicating limits of the model.

Demonstration of prompt construction to lower error rates.

Abstract

We study the error rate of LLMs on tasks like arithmetic that require a deterministic output, and repetitive processing of tokens drawn from a small set of alternatives. We argue that incorrect predictions arise when small errors in the attention mechanism accumulate to cross a threshold, and use this insight to derive a quantitative two-parameter relationship between the accuracy and the complexity of the task. The two parameters vary with the prompt and the model; they can be interpreted in terms of an elementary noise rate, and the number of plausible erroneous tokens that can be predicted. Our analysis is inspired by an ``effective field theory'' perspective: the LLM's many raw parameters can be reorganized into just two parameters that govern the error rate. We perform extensive empirical tests, using Gemini 2.5 Flash, Gemini 2.5 Pro and DeepSeek R1, and find excellent agreement between the predicted and observed accuracy for a variety of tasks, although we also identify deviations in some cases. Our model provides an alternative to suggestions that errors made by LLMs on long repetitive tasks indicate the ``collapse of reasoning'', or an inability to express ``compositional'' functions. Finally, we show how to construct prompts to reduce the error rate.