Electronic Circuit Principles of Large Language Models

TL;DR

This paper introduces Electronic Circuit Principles (ECP), a novel circuit-based framework that models large language model reasoning, enabling accurate performance prediction and guiding the development of improved modular prompting strategies.

Contribution

ECP provides a new circuit-inspired model for understanding and predicting LLM reasoning performance, validated across numerous tasks and models, and enhances prompting strategies.

Findings

ECP achieves about 60% better correlation with actual performance than traditional scaling laws.

ECP explains the success of 15 prompting strategies.

ECP enables development of modular interventions surpassing top human participants.

Abstract

Large language models (LLMs) such as DeepSeek-R1 have achieved remarkable performance across diverse reasoning tasks. To uncover the principles that govern their behaviour, we introduce the Electronic Circuit Principles (ECP), which maps inference-time learning (ITL) onto a semantic electromotive force and inference-time reasoning (ITR) onto a resistive network governed by Ohm's and Faraday's laws. This circuit-based modelling yields closed-form predictions of task performance and reveals how modular prompt components interact to shape accuracy. We validated ECP on 70,000 samples spanning 350 reasoning tasks and 9 advanced LLMs, observing a about 60% improvement in Pearson correlation relative to the conventional inference-time scaling law. Moreover, ECP explains the efficacy of 15 established prompting strategies and directs the development of new modular interventions that exceed the median score of the top 80% of participants in both the International Olympiad in Informatics and the International Mathematical Olympiad. By grounding LLM reasoning in electronic-circuit principles, ECP provides a rigorous framework for predicting performance and optimising modular components.