Deep Neural Networks as Complex Networks

• URL: http://arxiv.org/abs/2209.05488v1
• Date: Mon, 12 Sep 2022 16:26:04 GMT
• Title: Deep Neural Networks as Complex Networks
• Authors: Emanuele La Malfa, Gabriele La Malfa, Claudio Caprioli, Giuseppe Nicosia, Vito Latora
• Abstract summary: We use Complex Network Theory to represent Deep Neural Networks (DNNs) as directed weighted graphs. We introduce metrics to study DNNs as dynamical systems, with a granularity that spans from weights to layers, including neurons. We show that our metrics discriminate low vs. high performing networks.
• Score: 1.704936863091649
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed weighted graphs: within this framework, we introduce metrics to study DNNs as dynamical systems, with a granularity that spans from weights to layers, including neurons. CNT discriminates networks that differ in the number of parameters and neurons, the type of hidden layers and activations, and the objective task. We further show that our metrics discriminate low vs. high performing networks. CNT is a comprehensive method to reason about DNNs and a complementary approach to explain a model's behavior that is physically grounded to networks theory and goes beyond the well-studied input-output relation.

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