Parameter Norm Growth During Training of Transformers

The capacity of neural networks like the widely adopted transformer is known to be very high. Evidence is emerging that they learn successfully due to inductive bias in the training routine, typically some variant of gradient descent (GD). To better understand this bias, we study the tendency of transformer parameters to grow in magnitude during training. We find, both theoretically and empirically, that, in certain contexts, GD increases the parameter $L_2$ norm up to a threshold that itself increases with training-set accuracy. This means increasing training accuracy over time enables the norm to increase. Empirically, we show that the norm grows continuously over pretraining for T5 (Raffel et al., 2019). We show that pretrained T5 approximates a semi-discretized network with saturated activation functions. Such "saturated" networks are known to have a reduced capacity compared to the original network family that can be described in automata-theoretic terms. This suggests saturation is a new characterization of an inductive bias implicit in GD that is of particular interest for NLP. While our experiments focus on transformers, our theoretical analysis extends to other architectures with similar formal properties, such as feedforward ReLU networks.

Supermasks in Superposition

We present the Supermasks in Superposition (SupSup) model, capable of sequentially learning thousands of tasks without catastrophic forgetting. Our approach uses a randomly initialized, fixed base network and for each task finds a subnetwork (supermask) that achieves good performance. If task identity is given at test time, the correct subnetwork can be retrieved with minimal memory usage. If not provided, SupSup can infer the task using gradient-based optimization to find a linear superposition of learned supermasks which minimizes the output entropy. In practice we find that a single gradient step is often sufficient to identify the correct mask, even among 2500 tasks. We also showcase two promising extensions. First, SupSup models can be trained entirely without task identity information, as they may detect when they are uncertain about new data and allocate an additional supermask for the new training distribution. Finally the entire, growing set of supermasks can be stored in a constant-sized reservoir by implicitly storing them as attractors in a fixed-sized Hopfield network.

Soft Threshold Weight Reparameterization for Learnable Sparsity

Sparsity in Deep Neural Networks (DNNs) is studied extensively with the focus of maximizing prediction accuracy given an overall parameter budget. Existing methods rely on uniform or heuristic non-uniform sparsity budgets which have sub-optimal layer-wise parameter allocation resulting in a) lower prediction accuracy or b) higher inference cost (FLOPs). This work proposes Soft Threshold Reparameterization (STR), a novel use of the soft-threshold operator on DNN weights. STR smoothly induces sparsity while learning pruning thresholds thereby obtaining a non-uniform sparsity budget. Our method achieves state-of-the-art accuracy for unstructured sparsity in CNNs (ResNet50 and MobileNetV1 on ImageNet-1K), and, additionally, learns non-uniform budgets that empirically reduce the FLOPs by up to 50%. Notably, STR boosts the accuracy over existing results by up to 10% in the ultra sparse (99%) regime and can also be used to induce low-rank (structured sparsity) in RNNs. In short, STR is a simple mechanism which learns effective sparsity budgets that contrast with popular heuristics.

What's Hidden in a Randomly Weighted Neural Network?

Training a neural network is synonymous with learning the values of the weights. In contrast, we demonstrate that randomly weighted neural networks contain subnetworks which achieve impressive performance without ever training the weight values. Hidden in a randomly weighted Wide ResNet-50 we show that there is a subnetwork (with random weights) that is smaller than, but matches the performance of a ResNet-34 trained on ImageNet. Not only do these "untrained subnetworks" exist, but we provide an algorithm to effectively find them. We empirically show that as randomly weighted neural networks with fixed weights grow wider and deeper, an "untrained subnetwork" approaches a network with learned weights in accuracy.

Improving Shape Deformation in Unsupervised Image-to-Image Translation

Unsupervised image-to-image translation techniques are able to map local texture between two domains, but they are typically unsuccessful when the domains require larger shape change. Inspired by semantic segmentation, we introduce a discriminator with dilated convolutions that is able to use information from across the entire image to train a more context-aware generator. This is coupled with a multi-scale perceptual loss that is better able to represent error in the underlying shape of objects. We demonstrate that this design is more capable of representing shape deformation in a challenging toy dataset, plus in complex mappings with significant dataset variation between humans, dolls, and anime faces, and between cats and dogs.