For fixed-depth mean-field Bayesian nets on the Boolean cube, poly-sample learnability at infinite width equals poly-width learnability equals poly-bounded reduced entropy.
Summary statistics of learning link changing neural representations to behavior
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How can we make sense of large-scale recordings of neural activity across learning? Theories of neural network learning with their origins in statistical physics offer a potential answer: for a given task, there are often a small set of summary statistics that are sufficient to predict performance as the network learns. Here, we review recent advances in how summary statistics can be used to build theoretical understanding of neural network learning. We then argue for how this perspective can inform the analysis of neural data, enabling better understanding of learning in biological and artificial neural networks.
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Width-Robust Learnability in Mean-Field Bayesian Neural Networks
For fixed-depth mean-field Bayesian nets on the Boolean cube, poly-sample learnability at infinite width equals poly-width learnability equals poly-bounded reduced entropy.