Stably unactivated neurons in ReLU neural networks

• URL: http://arxiv.org/abs/2412.06829v2
• Date: Tue, 17 Dec 2024 17:28:59 GMT
• Title: Stably unactivated neurons in ReLU neural networks
• Authors: Natalie Brownlowe, Christopher R. Cornwell, Ethan Montes, Gabriel Quijano, Grace Stulman, Na Zhang,
• Abstract summary: In ReLU neural networks, the presence of stably unactivated neurons can reduce the network's expressiveness. In this work, we investigate the probability of a neuron in the second hidden layer of such neural networks being stably unactivated.
• Score: 1.347660513756976
• License:
• Abstract: The choice of architecture of a neural network influences which functions will be realizable by that neural network and, as a result, studying the expressiveness of a chosen architecture has received much attention. In ReLU neural networks, the presence of stably unactivated neurons can reduce the network's expressiveness. In this work, we investigate the probability of a neuron in the second hidden layer of such neural networks being stably unactivated when the weights and biases are initialized from symmetric probability distributions. For networks with input dimension $n_0$, we prove that if the first hidden layer has $n_0+1$ neurons then this probability is exactly $\frac{2^{n_0}+1}{4^{n_0+1}}$, and if the first hidden layer has $n_1$ neurons, $n_1 \le n_0$, then the probability is $\frac{1}{2^{n_1+1}}$. Finally, for the case when the first hidden layer has more neurons than $n_0+1$, a conjecture is proposed along with the rationale. Computational evidence is presented to support the conjecture.

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