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We present a provable, sampling-based approach for generating compact Convolutional Neural Networks (CNNs) by identifying and removing redundant filters from an over-parameterized network. Our algorithm uses a small batch of input data points to assign a saliency score to each filter and constructs an importance sampling distribution where filters that highly affect the output are sampled with correspondingly high probability. In contrast to existing filter pruning approaches, our method is simultaneously data-informed, exhibits provable guarantees on the size and performance of the pruned network, and is widely applicable to varying network architectures and data sets. Our analytical bounds bridge the notions of compressibility and importance of network structures, which gives rise to a fully-automated procedure for identifying and preserving filters in layers that are essential to the networks performance. Our experimental evaluations on popular architectures and data sets show that our algorithm consistently generates sparser and more efficient models than those constructed by existing filter pruning approaches.
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We introduce a pruning algorithm that provably sparsifies the parameters of a trained model in a way that approximately preserves the models predictive accuracy. Our algorithm uses a small batch of input points to construct a data-informed importance sampling distribution over the networks parameters, and adaptively mixes a sampling-based and deterministic pruning procedure to discard redundant weights. Our pruning method is simultaneously computationally efficient, provably accurate, and broadly applicable to various network architectures and data distributions. Our empirical comparisons show that our algorithm reliably generates highly compressed networks that incur minimal loss in performance relative to that of the original network. We present experimental results that demonstrate our algorithms potential to unearth essential network connections that can be trained successfully in isolation, which may be of independent interest.
Deep networks are typically trained with many more parameters than the size of the training dataset. Recent empirical evidence indicates that the practice of overparameterization not only benefits training large models, but also assists - perhaps counterintuitively - building lightweight models. Specifically, it suggests that overparameterization benefits model pruning / sparsification. This paper sheds light on these empirical findings by theoretically characterizing the high-dimensional asymptotics of model pruning in the overparameterized regime. The theory presented addresses the following core question: should one train a small model from the beginning, or first train a large model and then prune?. We analytically identify regimes in which, even if the location of the most informative features is known, we are better off fitting a large model and then pruning rather than simply training with the known informative features. This leads to a new double descent in the training of sparse models: growing the original model, while preserving the target sparsity, improves the test accuracy as one moves beyond the overparameterization threshold. Our analysis further reveals the benefit of retraining by relating it to feature correlations. We find that the above phenomena are already present in linear and random-features models. Our technical approach advances the toolset of high-dimensional analysis and precisely characterizes the asymptotic distribution of over-parameterized least-squares. The intuition gained by analytically studying simpler models is numerically verified on neural networks.
Recurrent neural networks (RNNs) have been extraordinarily successful for prediction with sequential data. To tackle highly variable and noisy real-world data, we introduce Particle Filter Recurrent Neural Networks (PF-RNNs), a new RNN family that explicitly models uncertainty in its internal structure: while an RNN relies on a long, deterministic latent state vector, a PF-RNN maintains a latent state distribution, approximated as a set of particles. For effective learning, we provide a fully differentiable particle filter algorithm that updates the PF-RNN latent state distribution according to the Bayes rule. Experiments demonstrate that the proposed PF-RNNs outperform the corresponding standard gated RNNs on a synthetic robot localization dataset and 10 real-world sequence prediction datasets for text classification, stock price prediction, etc.
To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pretrained model by low-rank decomposition; however, small approximation errors in parameters can ripple over a large prediction loss. As a result, performance usually drops significantly and a sophisticated effort on fine-tuning is required to recover accuracy. Apparently, it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training process. We propose Trained Rank Pruning (TRP), which alternates between low rank approximation and training. TRP maintains the capacity of the original network while imposing low-rank constraints during training. A nuclear regularization optimized by stochastic sub-gradient descent is utilized to further promote low rank in TRP. The TRP trained network inherently has a low-rank structure, and is approximated with negligible performance loss, thus eliminating the fine-tuning process after low rank decomposition. The proposed method is comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation.
Existing generalization measures that aim to capture a models simplicity based on parameter counts or norms fail to explain generalization in overparameterized deep neural networks. In this paper, we introduce a new, theoretically motivated measure of a networks simplicity which we call prunability: the smallest emph{fraction} of the networks parameters that can be kept while pruning without adversely affecting its training loss. We show that this measure is highly predictive of a models generalization performance across a large set of convolutional networks trained on CIFAR-10, does not grow with network size unlike existing pruning-based measures, and exhibits high correlation with test set loss even in a particularly challenging double descent setting. Lastly, we show that the success of prunability cannot be explained by its relation to known complexity measures based on models margin, flatness of minima and optimization speed, finding that our new measure is similar to -- but more predictive than -- existing flatness-based measures, and that its predictions exhibit low mutual information with those of other baselines.
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