Pruning neural networks without any data by iteratively conserving synaptic flow

TL;DR

This paper introduces SynFlow, a data-agnostic pruning algorithm that preserves synaptic flow at initialization, enabling highly sparse neural networks without training data and outperforming existing methods across various models and datasets.

Contribution

The paper presents a novel theory and algorithm for data-free neural network pruning at initialization, avoiding layer-collapse and matching or exceeding state-of-the-art performance.

Findings

SynFlow outperforms existing pruning algorithms at initialization.

The conservation law explains layer-collapse and guides the new pruning method.

SynFlow works across multiple models and datasets with high sparsity levels.

Abstract

Pruning the parameters of deep neural networks has generated intense interest due to potential savings in time, memory and energy both during training and at test time. Recent works have identified, through an expensive sequence of training and pruning cycles, the existence of winning lottery tickets or sparse trainable subnetworks at initialization. This raises a foundational question: can we identify highly sparse trainable subnetworks at initialization, without ever training, or indeed without ever looking at the data? We provide an affirmative answer to this question through theory driven algorithm design. We first mathematically formulate and experimentally verify a conservation law that explains why existing gradient-based pruning algorithms at initialization suffer from layer-collapse, the premature pruning of an entire layer rendering a network untrainable. This theory also elucidates how layer-collapse can be entirely avoided, motivating a novel pruning algorithm Iterative Synaptic Flow Pruning (SynFlow). This algorithm can be interpreted as preserving the total flow of synaptic strengths through the network at initialization subject to a sparsity constraint. Notably, this algorithm makes no reference to the training data and consistently competes with or outperforms existing state-of-the-art pruning algorithms at initialization over a range of models (VGG and ResNet), datasets (CIFAR-10/100 and Tiny ImageNet), and sparsity constraints (up to 99.99 percent). Thus our data-agnostic pruning algorithm challenges the existing paradigm that, at initialization, data must be used to quantify which synapses are important.