Neural networks tend to achieve better accuracy with training if they are larger -- even if the resulting models are overparameterized. Nevertheless, carefully removing such excess parameters before, during, or after training may also produce models with similar or even improved accuracy. In many cases, that can be curiously achieved by heuristics as simple as removing a percentage of the weights with the smallest absolute value — even though magnitude is not a perfect proxy for weight relevance. With the premise that obtaining significantly better performance from pruning depends on accounting for the combined effect of removing multiple weights, we revisit one of the classic approaches for impact-based pruning: the Optimal Brain Surgeon(OBS). We propose a tractable heuristic for solving the combinatorial extension of OBS, in which we select weights for simultaneous removal, as well as a systematic update of the remaining weights. Our selection method outperforms other methods under high sparsity, and the weight update is advantageous even when combined with the other methods.
more »
« less
The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks
Neural networks tend to achieve better accuracy with training if they are larger — even if the resulting models are overparameterized. Nevertheless, carefully removing such excess of parameters before, during, or after training may also produce models with similar or even improved accuracy. In many cases, that can be curiously achieved by heuristics as simple as removing a percentage of the weights with the smallest absolute value — even though absolute value is not a perfect proxy for weight relevance. With the premise that obtaining significantly better performance from pruning depends on accounting for the combined effect of removing multiple weights, we revisit one of the classic approaches for impact-based pruning: the Optimal Brain Surgeon (OBS). We propose a tractable heuristic for solving the combinatorial extension of OBS, in which we select weights for simultaneous removal, and we combine it with a single-pass systematic update of unpruned weights. Our selection method outperforms other methods for high sparsity, and the single-pass weight update is also advantageous if applied after those methods.
more »
« less
- Award ID(s):
- 1764071
- NSF-PAR ID:
- 10382618
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 162
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 25668 - 25683
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Incremental Task learning (ITL) is a category of continual learning that seeks to train a single network for multiple tasks (one after another), where training data for each task is only available during the training of that task. Neural networks tend to forget older tasks when they are trained for the newer tasks; this property is often known as catastrophic forgetting. To address this issue, ITL methods use episodic memory, parameter regularization, masking and pruning, or extensible network structures. In this paper, we propose a new incremental task learning framework based on low-rank factorization. In particular, we represent the network weights for each layer as a linear combination of several rank-1 matrices. To update the network for a new task, we learn a rank-1 (or low-rank) matrix and add that to the weights of every layer. We also introduce an additional selector vector that assigns different weights to the low-rank matrices learned for the previous tasks. We show that our approach performs better than the current state-of-the-art methods in terms of accuracy and forgetting. Our method also offers better memory efficiency compared to episodic memory- and mask-based approaches. Our code will be available at https://github.com/CSIPlab/task-increment-rank-update.gitmore » « less
-
Reducing the model redundancy is an important task to deploy complex deep learning models to resource-limited or time-sensitive devices. Directly regularizing or modifying weight values makes pruning procedure less robust and sensitive to the choice of hyperparameters, and it also requires prior knowledge to tune different hyperparameters for different models. To build a better generalized and easy-to-use pruning method, we propose AutoPrune, which prunes the network through optimizing a set of trainable auxiliary parameters instead of original weights. The instability and noise during training on auxiliary parameters will not directly affect weight values, which makes pruning process more robust to noise and less sensitive to hyperparameters. Moreover, we design gradient update rules for auxiliary parameters to keep them consistent with pruning tasks. Our method can automatically eliminate network redundancy with recoverability, relieving the complicated prior knowledge required to design thresholding functions, and reducing the time for trial and error. We evaluate our method with LeNet and VGGlike on MNIST and CIFAR-10 datasets, and with AlexNet, ResNet and MobileNet on ImageNet to establish the scalability of our work. Results show that our model achieves state-of-the-art sparsity, e.g. 7%, 23% FLOPs and 310x, 75x compression ratio for LeNet5 and VGG-like structure without accuracy drop, and 200M and 100M FLOPs for MobileNet V2 with accuracy 73.32% and 66.83% respectively.more » « less
-
Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. We add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to explicitly reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods.more » « less
-
The memristor crossbar array has emerged as an intrinsically suitable matrix computation and low-power acceleration framework for DNN applications. Many techniques such as memristor-based weight pruning and memristor-based quantization have been studied. However, the high accuracy solution for the above techniques is still waiting for unraveling. In this paper, we propose a memristor-based DNN framework which combines both structured weight pruning and quantization by incorporating ADMM algorithm for better pruning and quantization performance. We also discover the non-optimality of the ADMM solution in weight pruning and the unused data path in a structured pruned model. We design a software-hardware co-optimization framework which contains the first proposed Network Purification and Unused Path Removal algorithms targeting on post-processing a structured pruned model after ADMM steps. By taking memristor hardware constraints into our whole framework, we achieve extreme high compression rate with minimum accuracy loss. For quantizing structured pruned model, our framework achieves nearly no accuracy loss after quantizing weights to 8-bit memristor weight representation. We share our models at anonymous link https://bit.ly/2VnMUy0.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
