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Register a new userKeep the Gradients Flowing: Using Gradient Flow to Study Sparse Network Optimization
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Kale-Ab Tessera
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Training sparse networks to converge to the same performance as dense neural architectures has proven to be elusive. Recent work suggests that initialization is the key. However, while this direction of research has had some success, focusing on initialization alone appears to be inadequate. In this paper, we take a broader view of training sparse networks and consider the role of regularization, optimization, and architecture choices on sparse models. We propose a simple experimental framework, Same Capacity Sparse vs Dense Comparison (SC-SDC), that allows for a fair comparison of sparse and dense networks. Furthermore, we propose a new measure of gradient flow, Effective Gradient Flow (EGF), that better correlates to performance in sparse networks. Using top-line metrics, SC-SDC and EGF, we show that default choices of optimizers, activation functions and regularizers used for dense networks can disadvantage sparse networks. Based upon these findings, we show that gradient flow in sparse networks can be improved by reconsidering aspects of the architecture design and the training regime. Our work suggests that initialization is only one piece of the puzzle and taking a wider view of tailoring optimization to sparse networks yields promising results.
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Sparse Neural Networks (NNs) can match the generalization of dense NNs using a fraction of the compute/storage for inference, and also have the potential to enable efficient training. However, naively training unstructured sparse NNs from random initialization results in significantly worse generalization, with the notable exception of Lottery Tickets (LTs) and Dynamic Sparse Training (DST). In this work, we attempt to answer: (1) why training unstructured sparse networks from random initialization performs poorly and; (2) what makes LTs and DST the exceptions? We show that sparse NNs have poor gradient flow at initialization and propose a modified initialization for unstructured connectivity. Furthermore, we find that DST methods significantly improve gradient flow during training over traditional sparse training methods. Finally, we show that LTs do not improve gradient flow, rather their success lies in re-learning the pruning solution they are derived from - however, this comes at the cost of learning novel solutions.
The compression of deep neural networks (DNNs) to reduce inference cost becomes increasingly important to meet realistic deployment requirements of various applications. There have been a significant amount of work regarding network compression, while most of them are heuristic rule-based or typically not friendly to be incorporated into varying scenarios. On the other hand, sparse optimization yielding sparse solutions naturally fits the compression requirement, but due to the limited study of sparse optimization in stochastic learning, its extension and application onto model compression is rarely well explored. In this work, we propose a model compression framework based on the recent progress on sparse stochastic optimization. Compared to existing model compression techniques, our method is effective and requires fewer extra engineering efforts to incorporate with varying applications, and has been numerically demonstrated on benchmark compression tasks. Particularly, we achieve up to 7.2 and 2.9 times FLOPs reduction with the same level of evaluation accuracy on VGG16 for CIFAR10 and ResNet50 for ImageNet compared to the baseline heavy models, respectively.
Saliency methods interpret the prediction of a neural network by showing the importance of input elements for that prediction. A popular family of saliency methods utilize gradient information. In this work, we empirically show that two approaches for handling the gradient information, namely positive aggregation, and positive propagation, break these methods. Though these methods reflect visually salient information in the input, they do not explain the model prediction anymore as the generated saliency maps are insensitive to the predicted output and are insensitive to model parameter randomization. Specifically for methods that aggregate the gradients of a chosen layer such as GradCAM++ and FullGrad, exclusively aggregating positive gradients is detrimental. We further support this by proposing several variants of aggregation methods with positive handling of gradient information. For methods that backpropagate gradient information such as LRP, RectGrad, and Guided Backpropagation, we show the destructive effect of exclusively propagating positive gradient information.
The signed volume function for polyhedra can be generalized to a mean volume function for volume elements by averaging over the triangulations of the underlying polyhedron. If we consider these up to translation and scaling, the resulting quotient space is diffeomorphic to a sphere. The mean volume function restricted to this sphere is a quality measure for volume elements. We show that, the gradient ascent of this map regularizes the building blocks of hybrid meshes consisting of tetrahedra, hexahedra, prisms, pyramids and octahedra, that is, the optimization process converges to regular polyhedra. We show that the (normalized) gradient flow of the mean volume yields a fast and efficient optimization scheme for the finite element method known as the geometric element transformation method (GETMe). Furthermore, we shed some light on the dynamics of this method and the resulting smoothing procedure both theoretically and experimentally.
Gradient-based hyperparameter optimization is an attractive way to perform meta-learning across a distribution of tasks, or improve the performance of an optimizer on a single task. However, this approach has been unpopular for tasks requiring long horizons (many gradient steps), due to memory scaling and gradient degradation issues. A common workaround is to learn hyperparameters online or split the horizon into smaller chunks. However, this introduces greediness which comes with a large performance drop, since the best local hyperparameters can make for poor global solutions. In this work, we enable non-greediness over long horizons with a two-fold solution. First, we share hyperparameters that are contiguous in time, and show that this drastically mitigates gradient degradation issues. Then, we derive a forward-mode differentiation algorithm for the popular momentum-based SGD optimizer, which allows for a memory cost that is constant with horizon size. When put together, these solutions allow us to learn hyperparameters without any prior knowledge. Compared to the baseline of hand-tuned off-the-shelf hyperparameters, our method compares favorably on simple datasets like SVHN. On CIFAR-10 we match the baseline performance, and demonstrate for the first time that learning rate, momentum and weight decay schedules can be learned with gradients on a dataset of this size. Code is available at https://github.com/polo5/NonGreedyGradientHPO
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