Algorithmic Compression via Pretrained Neural Networks

Area of Science:

• Artificial Intelligence
• Machine Learning Theory
• Algorithmic Information Theory

Background:

• Large neural networks trained on vast datasets exhibit complex reasoning, resembling planning and search.
• This emergent behavior challenges traditional computational and intelligence theories.
• Bridging the gap between practical Large Language Models (LLMs) and formal theories is crucial.

Purpose of the Study:

• To review theoretical and empirical work connecting LLM success to formal computation and intelligence theories.
• To propose a framework where next-token prediction meta-trains models for algorithmic compression and Bayesian inference.
• To explore the implications of algorithmic information theory for understanding modern AI.

Main Methods:

• Grounded in memory-based meta-learning, the study analyzes how sequence models perform implicit meta-training.
• The core argument posits that predicting the next token across diverse tasks leads to algorithmic compression.
• Theoretical and empirical evidence is reviewed to support the connection to Solomonoff induction and Bayesian inference.

Main Results:

• Pretrained neural networks infer generative algorithms from data, effectively compressing information.
• The approach approximates Solomonoff induction and matches exact Bayesian inference on complex data.
• Models demonstrate strong compression on out-of-distribution data and synthesize complex algorithms like chessboard evaluations.

Conclusions:

• Understanding LLMs through algorithmic information theory provides insights into their capabilities and limitations.
• As models advance, theoretical grounding in algorithmic information theory becomes increasingly vital.
• Open research questions are outlined to connect theoretical understanding with practical machine learning advancements.