CoNNect: Connectivity-Based Regularization for Structural Pruning

TL;DR

CoNNect is a differentiable regularizer for neural network pruning that maintains connectivity, approximates $L_0$ regularization, and improves pruning performance without causing layer collapse.

Contribution

It introduces CoNNect, a novel regularizer that ensures connectivity and integrates seamlessly with existing pruning methods, enhancing their effectiveness.

Findings

Improves classical pruning strategies.

Enhances state-of-the-art one-shot pruners.

Maintains network connectivity and avoids layer collapse.

Abstract

Pruning encompasses a range of techniques aimed at increasing the sparsity of neural networks (NNs). These techniques can generally be framed as minimizing a loss function subject to an $L_0$ norm constraint. This paper introduces CoNNect, a novel differentiable regularizer for sparse NN training that ensures connectivity between input and output layers. We prove that CoNNect approximates $L_0$ regularization, guaranteeing maximally connected network structures while avoiding issues like layer collapse. Moreover, CoNNect is easily integrated with established structural pruning strategies. Numerical experiments demonstrate that CoNNect can improve classical pruning strategies and enhance state-of-the-art one-shot pruners, such as DepGraph and LLM-pruner.