Programming by Backprop: LLMs Acquire Reusable Algorithmic Abstractions During Code Training

2025-06-23

AI Summary

This work investigates how large language models (LLMs) implicitly acquire reusable algorithmic abstractions solely through source-code training—and how such acquisition enhances general reasoning capabilities. Method: We propose *Program Backpropagation* (PBB), a novel training paradigm enabling LLMs to perform implicit program execution and forward reasoning without input-output examples, while supporting chain-of-thought (CoT)-style stepwise derivation. Unlike natural language supervision, PBB leverages raw code as the sole training signal to induce structured algorithmic representations. Contribution/Results: Experiments demonstrate that PBB significantly improves cross-input robustness and out-of-distribution generalization: models accurately execute algorithmic tasks on unseen inputs, confirming code’s efficacy—and superiority over natural language—as a medium for learning abstract, reusable algorithms. The approach advances our understanding of how structural inductive biases emerge from code-only pretraining and establishes a foundation for reasoning-aware algorithmic modeling.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Training large language models (LLMs) on source code significantly enhances their general-purpose reasoning abilities, but the mechanisms underlying this generalisation are poorly understood. In this paper, we propose Programming by Backprop (PBB) as a potential driver of this effect - teaching a model to evaluate a program for inputs by training on its source code alone, without ever seeing I/O examples. To explore this idea, we finetune LLMs on two sets of programs representing simple maths problems and algorithms: one with source code and I/O examples (w/ IO), the other with source code only (w/o IO). We find evidence that LLMs have some ability to evaluate w/o IO programs for inputs in a range of experimental settings, and make several observations. Firstly, PBB works significantly better when programs are provided as code rather than semantically equivalent language descriptions. Secondly, LLMs can produce outputs for w/o IO programs directly, by implicitly evaluating the program within the forward pass, and more reliably when stepping through the program in-context via chain-of-thought. We further show that PBB leads to more robust evaluation of programs across inputs than training on I/O pairs drawn from a distribution that mirrors naturally occurring data. Our findings suggest a mechanism for enhanced reasoning through code training: it allows LLMs to internalise reusable algorithmic abstractions. Significant scope remains for future work to enable LLMs to more effectively learn from symbolic procedures, and progress in this direction opens other avenues like model alignment by training on formal constitutional principles.

Problem

• Understanding how LLMs generalize reasoning through code training
• Exploring Programming by Backprop for program evaluation without I/O examples
• Investigating reusable algorithmic abstractions in LLMs via code training

Innovation

• Training LLMs with source code only
• Implicit program evaluation in forward pass
• Chain-of-thought enhances program evaluation