SWAMP: Sparse Weight Averaging with Multiple Particles for Iterative Magnitude Pruning

Given the ever-increasing size of modern neural networks, the significance of sparse architectures has surged due to their accelerated inference speeds and minimal memory demands. When it comes to global pruning techniques, Iterative Magnitude Pruning (IMP) still stands as a state-of-the-art algorithm despite its simple nature, particularly in extremely sparse regimes. In light of the recent finding that the two successive matching IMP solutions are linearly connected without a loss barrier, we propose Sparse Weight Averaging with Multiple Particles (SWAMP), a straightforward modification of IMP that achieves performance comparable to an ensemble of two IMP solutions. For every iteration, we concurrently train multiple sparse models, referred to as particles, using different batch orders yet the same matching ticket, and then weight average such models to produce a single mask. We demonstrate that our method consistently outperforms existing baselines across different sparsities through extensive experiments on various data and neural network structures

Linear Mode Connectivity in Sparse Neural Networks

With the rise in interest of sparse neural networks, we study how neural network pruning with synthetic data leads to sparse networks with unique training properties. We find that distilled data, a synthetic summarization of the real data, paired with Iterative Magnitude Pruning (IMP) unveils a new class of sparse networks that are more stable to SGD noise on the real data, than either the dense model, or subnetworks found with real data in IMP. That is, synthetically chosen subnetworks often train to the same minima, or exhibit linear mode connectivity. We study this through linear interpolation, loss landscape visualizations, and measuring the diagonal of the hessian. While dataset distillation as a field is still young, we find that these properties lead to synthetic subnetworks matching the performance of traditional IMP with up to 150x less training points in settings where distilled data applies.Comment: Published in NeurIPS 2023 UniReps Worksho

Lottery Tickets in Evolutionary Optimization: On Sparse Backpropagation-Free Trainability

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.Comment: 13 pages, 11 figures, International Conference on Machine Learning (ICML) 202

Random Teachers are Good Teachers

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl

Random initialisations performing above chance and how to find them

Neural networks trained with stochastic gradient descent (SGD) starting from different random initialisations typically find functionally very similar solutions, raising the question of whether there are meaningful differences between different SGD solutions. Entezari et al.\ recently conjectured that despite different initialisations, the solutions found by SGD lie in the same loss valley after taking into account the permutation invariance of neural networks. Concretely, they hypothesise that any two solutions found by SGD can be permuted such that the linear interpolation between their parameters forms a path without significant increases in loss. Here, we use a simple but powerful algorithm to find such permutations that allows us to obtain direct empirical evidence that the hypothesis is true in fully connected networks. Strikingly, we find that two networks already live in the same loss valley at the time of initialisation and averaging their random, but suitably permuted initialisation performs significantly above chance. In contrast, for convolutional architectures, our evidence suggests that the hypothesis does not hold. Especially in a large learning rate regime, SGD seems to discover diverse modes.Comment: NeurIPS 2022, 14th Annual Workshop on Optimization for Machine Learning (OPT2022

Emerging Paradigms of Neural Network Pruning

Over-parameterization of neural networks benefits the optimization and generalization yet brings cost in practice. Pruning is adopted as a post-processing solution to this problem, which aims to remove unnecessary parameters in a neural network with little performance compromised. It has been broadly believed the resulted sparse neural network cannot be trained from scratch to comparable accuracy. However, several recent works (e.g., [Frankle and Carbin, 2019a]) challenge this belief by discovering random sparse networks which can be trained to match the performance with their dense counterpart. This new pruning paradigm later inspires more new methods of pruning at initialization. In spite of the encouraging progress, how to coordinate these new pruning fashions with the traditional pruning has not been explored yet. This survey seeks to bridge the gap by proposing a general pruning framework so that the emerging pruning paradigms can be accommodated well with the traditional one. With it, we systematically reflect the major differences and new insights brought by these new pruning fashions, with representative works discussed at length. Finally, we summarize the open questions as worthy future directions