When do neural networks learn world models?

2025-02-13

AI Summary

This paper investigates whether neural networks in multi-task learning can provably recover the true linear latent-variable world model underlying data generation, particularly under nonlinear observables. Method: We establish the first sufficient conditions for verifiable recovery of linear latent variables from nonlinear observations. Introducing a novel Fourier–Walsh analytic framework, we develop Boolean reversible transformations to characterize how low-degree bias and architectural sensitivity govern latent identifiability. Contribution/Results: Under mild assumptions, we prove that models exhibiting low-degree bias exactly recover the generative latent variables; moreover, architectural choices fundamentally determine success or failure in world-model learning. Our analysis provides rigorous theoretical foundations for self-supervised learning, out-of-distribution generalization, and the linear representation hypothesis in large language models.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: (Large) Language Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Humans develop world models that capture the underlying generation process of data. Whether neural networks can learn similar world models remains an open problem. In this work, we provide the first theoretical results for this problem, showing that in a multi-task setting, models with a low-degree bias provably recover latent data-generating variables under mild assumptions -- even if proxy tasks involve complex, non-linear functions of the latents. However, such recovery is also sensitive to model architecture. Our analysis leverages Boolean models of task solutions via the Fourier-Walsh transform and introduces new techniques for analyzing invertible Boolean transforms, which may be of independent interest. We illustrate the algorithmic implications of our results and connect them to related research areas, including self-supervised learning, out-of-distribution generalization, and the linear representation hypothesis in large language models.

Problem

• Neural networks learn world models
• Theoretical results for multi-task settings
• Sensitivity to model architecture

Innovation

• multi-task setting recovery
• Fourier-Walsh transform analysis
• invertible Boolean transforms