Recent years have witnessed significant progress in understanding the relationship between the connectivity of a deep network's architecture as a graph, and the network's performance. A few prior arts connected deep architectures to expander graphs or Ramanujan graphs, and particularly,[7] demonstrated the use of such graph connectivity measures with ranking and relative performance of various obtained sparse sub-networks (i.e. models with prune masks) without the need for training. However, no prior work explicitly explores the role of parameters in the graph's connectivity, making the graph-based understanding of prune masks and the magnitude/gradient-based pruning practice isolated from one another. This paper strives to fill in this gap, by analyzing the Weighted Spectral Gap of Ramanujan structures in sparse neural networks and investigates its correlation with final performance. We specifically examine the evolution of sparse structures under a popular dynamic sparse-to-sparse network training scheme, and intriguingly find that the generated random topologies inherently maximize Ramanujan graphs. We also identify a strong correlation between masks, performance, and the weighted spectral gap. Leveraging this observation, we propose to construct a new "full-spectrum coordinate'' aiming to comprehensively characterize a sparse neural network's promise. Concretely, it consists of the classical Ramanujan's gap (structure), our proposed weighted spectral gap (parameters), and the constituent nested regular graphs within. In this new coordinate system, a sparse subnetwork's L2-distance from its original initialization is found to have nearly linear correlated with its performance. Eventually, we apply this unified perspective to develop a new actionable pruning method, by sampling sparse masks to maximize the L2-coordinate distance. Our method can be augmented with the "pruning at initialization" (PaI) method, and significantly outperforms existing PaI methods. With only a few iterations of training (e.g 500 iterations), we can get LTH-comparable performance as that yielded via "pruning after training", significantly saving pre-training costs. Codes can be found at: https://github.com/VITA-Group/FullSpectrum-PAI.
more »
« less
Training Your Sparse Neural Network Better with Any Mask
Pruning large neural networks to create high-quality, independently trainable sparse masks, which can maintain similar performance to their dense counterparts, is very desirable due to the reduced space and time complexity. As research effort is focused on increasingly sophisticated pruning methods that leads to sparse subnetworks trainable from the scratch, we argue for an orthogonal, under-explored theme: improving training techniques for pruned sub-networks, i.e. sparse training. Apart from the popular belief that only the quality of sparse masks matters for sparse training, in this paper we demonstrate an alternative opportunity: one can carefully customize the sparse training techniques to deviate from the default dense network training protocols, consisting of introducing ``ghost" neurons and skip connections at the early stage of training, and strategically modifying the initialization as well as labels. Our new sparse training recipe is generally applicable to improving training from scratch with various sparse masks. By adopting our newly curated techniques, we demonstrate significant performance gains across various popular datasets (CIFAR-10, CIFAR-100, TinyImageNet), architectures (ResNet-18/32/104, Vgg16, MobileNet), and sparse mask options (lottery ticket, SNIP/GRASP, SynFlow, or even randomly pruning), compared to the default training protocols, especially at high sparsity levels.
more »
« less
- Award ID(s):
- 2053279
- NSF-PAR ID:
- 10480987
- Publisher / Repository:
- International Conference on Machine Learning (ICML)
- Date Published:
- Journal Name:
- International Conference on Machine Learning (ICML)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
na (Ed.)Ensemble Learning is an effective method for improving gen- eralization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associ- ated with training several independent networks becomes ex- pensive. We introduce a fast, low-cost method for creating di- verse ensembles of neural networks without needing to train multiple models from scratch. We do this by first training a single parent network. We then create child networks by cloning the parent and dramatically pruning the parameters of each child to create an ensemble of members with unique and diverse topologies. We then briefly train each child net- work for a small number of epochs, which now converge significantly faster when compared to training from scratch. We explore various ways to maximize diversity in the child networks, including the use of anti-random pruning and one- cycle tuning. This diversity enables “Prune and Tune” ensem- bles to achieve results that are competitive with traditional ensembles at a fraction of the training cost. We benchmark our approach against state of the art low-cost ensemble meth- ods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100.more » « less
-
NA (Ed.)Ensemble Learning is an effective method for improving gen- eralization in machine learning. However, as state-of-the-art neural networks grow larger, the computational cost associ- ated with training several independent networks becomes ex- pensive. We introduce a fast, low-cost method for creating di- verse ensembles of neural networks without needing to train multiple models from scratch. We do this by first training a single parent network. We then create child networks by cloning the parent and dramatically pruning the parameters of each child to create an ensemble of members with unique and diverse topologies. We then briefly train each child net- work for a small number of epochs, which now converge significantly faster when compared to training from scratch. We explore various ways to maximize diversity in the child networks, including the use of anti-random pruning and one- cycle tuning. This diversity enables “Prune and Tune” ensem- bles to achieve results that are competitive with traditional ensembles at a fraction of the training cost. We benchmark our approach against state of the art low-cost ensemble meth- ods and display marked improvement in both accuracy and uncertainty estimation on CIFAR-10 and CIFAR-100.more » « less
-
null (Ed.)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.more » « less
-
We introduce Evenly Cascaded convolutional Network (ECN), a neural network taking inspiration from the cascade algorithm of wavelet analysis. ECN employs two feature streams - a low-level and high-level steam. At each layer these streams interact, such that low-level features are modulated using advanced perspectives from the high-level stream. ECN is evenly structured through resizing feature map dimensions by a consistent ratio, which removes the burden of ad-hoc specification of feature map dimensions. ECN produces easily interpretable features maps, a result whose intuition can be understood in the context of scale-space theory. We demonstrate that ECN's design facilitates the training process through providing easily trainable shortcuts. We report new state-of-the-art results for small networks, without the need for additional treatment such as pruning or compression - a consequence of ECN's simple structure and direct training. A 6-layered ECN design with under 500k parameters achieves 95.24% and 78.99% accuracy on CIFAR-10 and CIFAR-100 datasets, respectively, outperforming the current state-of-the-art on small parameter networks, and a 3 million parameter ECN produces results competitive to the state-of-the-art.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
