Sampling weights of deep neural networks
- URL: http://arxiv.org/abs/2306.16830v2
- Date: Sun, 12 Nov 2023 20:28:54 GMT
- Title: Sampling weights of deep neural networks
- Authors: Erik Lien Bolager and Iryna Burak and Chinmay Datar and Qing Sun and
Felix Dietrich
- Abstract summary: We introduce a probability distribution, combined with an efficient sampling algorithm, for weights and biases of fully-connected neural networks.
In a supervised learning context, no iterative optimization or gradient computations of internal network parameters are needed.
We prove that sampled networks are universal approximators.
- Score: 1.2370077627846041
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We introduce a probability distribution, combined with an efficient sampling
algorithm, for weights and biases of fully-connected neural networks. In a
supervised learning context, no iterative optimization or gradient computations
of internal network parameters are needed to obtain a trained network. The
sampling is based on the idea of random feature models. However, instead of a
data-agnostic distribution, e.g., a normal distribution, we use both the input
and the output training data to sample shallow and deep networks. We prove that
sampled networks are universal approximators. For Barron functions, we show
that the $L^2$-approximation error of sampled shallow networks decreases with
the square root of the number of neurons. Our sampling scheme is invariant to
rigid body transformations and scaling of the input data, which implies many
popular pre-processing techniques are not required. In numerical experiments,
we demonstrate that sampled networks achieve accuracy comparable to iteratively
trained ones, but can be constructed orders of magnitude faster. Our test cases
involve a classification benchmark from OpenML, sampling of neural operators to
represent maps in function spaces, and transfer learning using well-known
architectures.
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