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The usual approach to this problem is to sample many possible inputs, run them all through the model
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Paper: Estimating the expected output of wide random MLPs more efficiently than sampling Code: mlp_cumulant_propagation GitHub repo.
Key facts
- On the other hand, using a similar number of FLOPs to Monte Carlo sampling with samples, their algorithm sometimes achieves a relative error of under 30% for probabilities 100 times lower than. [6]
- Performance of their best cumulant propagation algorithms at estimating the mean of random ReLU MLPs with 4 hidden layers and width 256
- This post covers joint work with Wilson Wu, George Robinson, Mike Winer, Victor Lecomte and Paul Christiano
- For, this is the standard He initialization, and ensures that the outputs of have variance around 1. ↩︎
Summary
This post covers joint work with Wilson Wu, George Robinson, Mike Winer, Victor Lecomte and Paul Christiano. In ARC's latest paper, they study the following problem: given a randomly initialized multilayer perceptron (MLP), produce an estimate for the expected output of the model under Gaussian input. The team are excited about this result as an early step towards their goal of producing mechanistic estimates that outperform random sampling for any trained neural network. In their paper, they consider MLPs with weights, defined by where the activation function is applied coordinatewise, and is taken to be by default. An estimation algorithm takes in and a tolerance parameter, and aims to estimate to within an error of around.