@conference {4699, title = {AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity}, booktitle = {Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)}, year = {2020}, month = {12/2020}, abstract = {

We present an improved method for symbolic regression that seeks to fit data toformulas that are Pareto-optimal, in the sense of having the best accuracy for a givencomplexity. It improves on the previous state-of-the-art by typically being ordersof magnitude more robust toward noise and bad data, and also by discovering manyformulas that stumped previous methods. We develop a method for discoveringgeneralized symmetries (arbitrary modularity in the computational graph of aformula) from gradient properties of a neural network fit. We use normalizingflows to generalize our symbolic regression method to probability distributionsfrom which we only have samples, and employ statistical hypothesis testing toaccelerate robust brute-force search.

GitHub:\ https://github.com/SJ001/AI-Feynman
Readthedocs: https://ai-feynman.readthedocs.io/en/latest/
Database:\ https://space.mit.edu/home/tegmark/aifeynman.html
}, author = {Silviu-Marian Udrescu and Andrew Tan and Jianhai Feng and Orisvaldo Neto and Tailin Wu and Max Tegmark} } @proceedings {2762, title = {Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNN}, volume = {70}, year = {2017}, month = {08/2017}, pages = {1733-1741 }, url = {https://arxiv.org/abs/1612.05231}, author = {Jing, Li and Shen, Yichen and Dub{\v c}ek, Tena and Peurifoi, John and Skirlo, Scott and LeCun, Yann and Max Tegmark and Solja{\v c}i{\'c}, Marin} } @article {2761, title = {Why does deep and cheap learning work so well?}, journal = {Journal of Statistical Physics}, volume = {168}, year = {2017}, month = {09/2017}, pages = {1223{\textendash}1247}, chapter = {1223}, abstract = {

We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of practical interest can frequently be approximated through {\textquotedblleft}cheap learning{\textquotedblright} with exponentially fewer parameters than generic ones. We explore how properties frequently encountered in physics such as symmetry, locality, compositionality, and polynomial log-probability translate into exceptionally simple neural networks. We further argue that when the statistical process generating the data is of a certain hierarchical form prevalent in physics and machine learning, a deep neural network can be more efficient than a shallow one. We formalize these claims using information theory and discuss the relation to the renormalization group. We prove various {\textquotedblleft}no-flattening theorems{\textquotedblright} showing when efficient linear deep networks cannot be accurately approximated by shallow ones without efficiency loss; for example, we show that n variables cannot be multiplied using fewer than 2n neurons in a single hidden layer.

}, keywords = {Artificial neural networks, deep learning, Statistical physics}, doi = {10.1007/s10955-017-1836-5}, url = {https://link.springer.com/article/10.1007/s10955-017-1836-5}, author = {Henry Lin and Max Tegmark} } @article {2760, title = {Critical Behavior from Deep Dynamics: A Hidden Dimension in Natural Language}, journal = {arXiv.org}, year = {2016}, month = {06/2016}, author = {Henry Lin and Max Tegmark} } @article {2768, title = {Improved Measures of Integrated Information}, journal = {PLOS Computational Biology}, year = {2016}, month = {11/2016}, abstract = {

Although\  there\  is\  growing\  interest\  in\  measuring\  integrated\  information\  in\  computational\  and cognitive systems, current methods for doing so in practice are computationally unfeasible.\  Existing and\  novel\  integration\  measures\  are\  investigated\  and\  classified\  by\  various\  desirable\  properties.\ \  A simple taxonomy of Φ-measures is presented where they are each characterized by their choice of factorization\  method\  (5\  options),\  choice\  of\  probability\  distributions\  to\  compare\  (3 {\texttimes} 4\  options) and choice of measure for comparing probability distributions (7 options).\  When requiring the Φ- measures to satisfy a minimum of attractive properties, these hundreds of options reduce to a mere handful, some of which turn out to be identical.\  Useful exact and approximate formulas are derived that can be applied to real-world data from laboratory experiments without posing unreasonable computational demands.

}, doi = {10.1371/journal.pcbi.100512310.1371}, url = {http://dx.plos.org/10.1371/journal.pcbi.1005123}, author = {Max Tegmark}, editor = {Seth, Anil} }