A Compression Perspective on Simplicity Bias

Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle, formalizing supervised learning as a problem of optimal two-part lossless compression. Our theory explains how simplicity bias governs feature selection in neural networks through a fundamental trade-off between model complexity (the cost of describing the hypothesis) and predictive power (the cost of describing the data). Our framework predicts that as the amount of available training data increases, learners transition through qualitatively different features -- from simple spurious shortcuts to complex features -- only when the reduction in data encoding cost justifies the increased model complexity. Consequently, we identify distinct data regimes where increasing data promotes robustness by ruling out trivial shortcuts, and conversely, regimes where limiting data can act as a form of complexity-based regularization, preventing the learning of unreliable complex environmental cues. We validate our theory on a semi-synthetic benchmark showing that the feature selection of neural networks follows the same trajectory of solutions as optimal two-part compressors.

In-context learning and Occam's razor

The goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees for generalization without further assumptions, in practice we observe that simple models which explain the training data generalize best: a principle called Occam's razor. Despite the need for simple models, most current approaches in machine learning only minimize the training error, and at best indirectly promote simplicity through regularization or architecture design. Here, we draw a connection between Occam's razor and in-context learning: an emergent ability of certain sequence models like Transformers to learn at inference time from past observations in a sequence. In particular, we show that the next-token prediction loss used to train in-context learners is directly equivalent to a data compression technique called prequential coding, and that minimizing this loss amounts to jointly minimizing both the training error and the complexity of the model that was implicitly learned from context. Our theory and the empirical experiments we use to support it not only provide a normative account of in-context learning, but also elucidate the shortcomings of current in-context learning methods, suggesting ways in which they can be improved. We make our code available at https://github.com/3rdCore/PrequentialCode.

Evaluating Interventional Reasoning Capabilities of Large Language Models

Numerous decision-making tasks require estimating causal effects under interventions on different parts of a system. As practitioners consider using large language models (LLMs) to automate decisions, studying their causal reasoning capabilities becomes crucial. A recent line of work evaluates LLMs ability to retrieve commonsense causal facts, but these evaluations do not sufficiently assess how LLMs reason about interventions. Motivated by the role that interventions play in causal inference, in this paper, we conduct empirical analyses to evaluate whether LLMs can accurately update their knowledge of a data-generating process in response to an intervention. We create benchmarks that span diverse causal graphs (e.g., confounding, mediation) and variable types, and enable a study of intervention-based reasoning. These benchmarks allow us to isolate the ability of LLMs to accurately predict changes resulting from their ability to memorize facts or find other shortcuts. Our analysis on four LLMs highlights that while GPT- 4 models show promising accuracy at predicting the intervention effects, they remain sensitive to distracting factors in the prompts.