# The Autodidactic Universe

arXiv: https://arxiv.org/abs/2104.03902 · HTML: https://mlsanity.com/paper/2104.03902/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 96 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 13 of 13)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Why does deep and cheap learning work so well?](https://mlsanity.com/paper/1608.08225/) (2016)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [An exact mapping between the Variational Renormalization Group and Deep Learning](https://mlsanity.com/paper/1410.3831/) (2014)
- [Neural Network Renormalization Group](https://mlsanity.com/paper/1802.02840/) (2018)
- [Mutual Information, Neural Networks and the Renormalization Group](https://mlsanity.com/paper/1704.06279/) (2017)
- [Network Geometry](https://mlsanity.com/paper/2001.03241/) (2020)
- [The world as a neural network](https://mlsanity.com/paper/2008.01540/) (2020)
- [A Correspondence Between Random Neural Networks and Statistical Field Theory](https://mlsanity.com/paper/1710.06570/) (2017)
- [Ollivier-Ricci curvature convergence in random geometric graphs](https://mlsanity.com/paper/2008.01209/) (2020)
- [An Infinite Restricted Boltzmann Machine](https://mlsanity.com/paper/1502.02476/) (2015)
- [Emergent Complex Network Geometry](https://mlsanity.com/paper/1412.3405/) (2014)

## Built on by (most cited first, 7 of 7)

- [Towards a theory of quantum gravity from neural networks](https://mlsanity.com/paper/2111.00903/) (2021)
- [Covariant Gradient Descent](https://mlsanity.com/paper/2504.05279/) (2025)
- [Machine-Learning the Classification of Spacetimes](https://mlsanity.com/paper/2201.01644/) (2022)
- [Molecular Learning Dynamics](https://mlsanity.com/paper/2504.10560/) (2025)
- [The Physics of Machine Learning: An Intuitive Introduction for the Physical Scientist](https://mlsanity.com/paper/2112.00851/) (2021)
- [The Universe as a Learning System](https://mlsanity.com/paper/2402.14423/) (2024)
- [Business models for the simulation hypothesis](https://mlsanity.com/paper/2404.08991/) (2024)

## Abstract (arXiv)

We present an approach to cosmology in which the Universe learns its own physical laws. It does so by exploring a landscape of possible laws, which we express as a certain class of matrix models. We discover maps that put each of these matrix models in correspondence with both a gauge/gravity theory and a mathematical model of a learning machine, such as a deep recurrent, cyclic neural network. This establishes a correspondence between each solution of the physical theory and a run of a neural network. This correspondence is not an equivalence, partly because gauge theories emerge from N rightarrow ∞  limits of the matrix models, whereas the same limits of the neural networks used here are not well-defined. We discuss in detail what it means to say that learning takes place in autodidactic systems, where there is no supervision. We propose that if the neural network model can be said to learn without supervision, the same can be said for the corresponding physical theory. We consider other protocols for autodidactic physical systems, such as optimization of graph variety, subset-replication using self-attention and look-ahead, geometrogenesis guided by reinforcement learning, structural learning using renormalization group techniques, and extensions. These protocols together provide a number of directions in which to explore the origin of physical laws based on putting machine learning architectures in correspondence with physical theories.