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.

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.

Weaknesses: Method: - Theorem 1 is not new, and similar results were already presented in previous work [Liang et al., 2019]. For the proof of Theorem 1, In L171, there are no bias terms that appeared in computing z_j. However, for ResNet and VGGNet they all have bias terms at each layer, so this theorem does not apply for them. For example, when the input data is very sparse and most of its dimensions are not correlated with the prediction, then you can probably prune a lot at the input layer. Therefore, I am not convinced with the motivation of data-independent pruning.

This paper introduces synaptic saliency for deep network pruning which does not require any dataset. While there is overall appreciation of the results theoretically there are some concerns about the experiments. The authors have addressed some of the issues and contingent on their addressing the concerns one can recommend acceptance.

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.