# Emergent Quantum Mechanics in an Introspective Machine Learning Architecture

## TL;DR

This paper presents an introspective neural network architecture that autonomously learns quantum concepts like the wave function and Schrödinger equation from simulated data, demonstrating potential for discovering new physics.

## Contribution

It introduces a novel machine learning framework that automatically derives quantum laws from data, bridging neural networks and fundamental physics discovery.

## Key findings

- Successfully learned the quantum wave function from data
- Discovered the Schrödinger equation through the architecture
- Demonstrated potential for autonomous physics discovery

## Abstract

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schr\"odinger equation from simulated experimental data of the potential-to-density mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schr\"odinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.