Variational Learning of Physical Intuition from a Few Observations

TL;DR

This paper presents a variational learning framework enabling neural networks to acquire physical intuition from minimal observations, demonstrating strong generalization across classical and quantum systems, and providing a theoretical basis for this capability.

Contribution

The work introduces a novel variational learning approach for neural networks to learn physical states from few examples, with a unified theory explaining generalization and critical network size.

Findings

Networks generalize well beyond training data

A unified theory explains the conditions for successful generalization

A critical network size threshold is identified

Abstract

Humans can often predict physical outcomes after only a few observations, a capability known as physical intuition. The mechanisms underlying this efficient learning remain elusive. Here, we introduce a variational learning framework in which small neural networks learn to discover optimal physical states from merely two or three similar examples. Demonstrating across classical and quantum systems including strongly correlated molecules, we show that networks trained this way generalize accurately across wide observation ranges, far beyond the training data. This generalization is explained by a unified theory: it arises when the network approximates a solution manifold where the Euler-Lagrange operator is stationary with respect to observation features. The theory predicts the existence of a critical network size below which robust generalization fails to emerge. Our work establishes variational learning as a principled route to acquiring artificial physical intuition and offers a theoretical perspective for understanding similar capabilities in biological intelligence.