An important development in deep learning from the earliest MLPs has been a move towards architectures with structural inductive biases which enable the model to keep distinct sources of information and routes of processing well-separated. This structure is linked to the notion of independent mechanisms from the causality literature, in which a mechanism is able to retain the same processing as irrelevant aspects of the world are changed. For example, convnets enable separation over positions, while attention-based architectures (especially Transformers) learn which combination of positions to process dynamically. In this work we explore a way in which the Transformer architecture is deficient: it represents each position with a large monolithic hidden representation and a single set of parameters which are applied over the entire hidden representation. This potentially throws unrelated sources of information together, and limits the Transformer's ability to capture independent mechanisms. To address this, we propose Transformers with Independent Mechanisms (TIM), a new Transformer layer which divides the hidden representation and parameters into multiple mechanisms, which only exchange information through attention. Additionally, we propose a competition mechanism which encourages these mechanisms to specialize over time steps, and thus be more independent. We study TIM on a large-scale BERT model, on the Image Transformer, and on speech enhancement and find evidence for semantically meaningful specialization as well as improved performance.

Improving the efficiency of Transformer-based language pre-training is an important task in NLP, especially for the self-attention module, which is computationally expensive. In this paper, we propose a simple but effective solution, called \emph{LazyFormer}, which computes the self-attention distribution infrequently. LazyFormer composes of multiple lazy blocks, each of which contains multiple Transformer layers. In each lazy block, the self-attention distribution is only computed once in the first layer and then is reused in all upper layers. In this way, the cost of computation could be largely saved. We also provide several training tricks for LazyFormer. Extensive experiments demonstrate the effectiveness of the proposed method.

It is well-known that standard neural networks, even with a high classification accuracy, are vulnerable to small $\ell_\infty$-norm bounded adversarial perturbations. Although many attempts have been made, most previous works either can only provide empirical verification of the defense to a particular attack method, or can only develop a certified guarantee of the model robustness in limited scenarios. In this paper, we seek for a new approach to develop a theoretically principled neural network that inherently resists $\ell_\infty$ perturbations. In particular, we design a novel neuron that uses $\ell_\infty$-distance as its basic operation (which we call $\ell_\infty$-dist neuron), and show that any neural network constructed with $\ell_\infty$-dist neurons (called $\ell_{\infty}$-dist net) is naturally a 1-Lipschitz function with respect to $\ell_\infty$-norm. This directly provides a rigorous guarantee of the certified robustness based on the margin of prediction outputs. We also prove that such networks have enough expressive power to approximate any 1-Lipschitz function with robust generalization guarantee. Our experimental results show that the proposed network is promising. Using $\ell_{\infty}$-dist nets as the basic building blocks, we consistently achieve state-of-the-art performance on commonly used datasets: 93.09% certified accuracy on MNIST ($\epsilon=0.3$), 79.23% on Fashion MNIST ($\epsilon=0.1$) and 35.10% on CIFAR-10 ($\epsilon=8/255$).

Normalization plays an important role in the optimization of deep neural networks. While there are standard normalization methods in computer vision and natural language processing, there is limited understanding of how to effectively normalize neural networks for graph representation learning. In this paper, we propose a principled normalization method, Graph Normalization (GraphNorm), where the key idea is to normalize the feature values across all nodes for each individual graph with a learnable shift. Theoretically, we show that GraphNorm serves as a preconditioner that smooths the distribution of the graph aggregation's spectrum, leading to faster optimization. Such an improvement cannot be well obtained if we use currently popular normalization methods, such as BatchNorm, which normalizes the nodes in a batch rather than in individual graphs, due to heavy batch noises. Moreover, we show that for some highly regular graphs, the mean of the feature values contains graph structural information, and directly subtracting the mean may lead to an expressiveness degradation. The learnable shift in GraphNorm enables the model to learn to avoid such degradation for those cases. Empirically, Graph neural networks (GNNs) with GraphNorm converge much faster compared to GNNs with other normalization methods, e.g., BatchNorm. GraphNorm also improves generalization of GNNs, achieving better performance on graph classification benchmarks.

Understanding what information neural networks capture is an essential problem in deep learning, and studying whether different models capture similar features is an initial step to achieve this goal. Previous works sought to define metrics over the feature matrices to measure the difference between two models. However, different metrics sometimes lead to contradictory conclusions, and there has been no consensus on which metric is suitable to use in practice. In this work, we propose a novel metric that goes beyond previous approaches. Recall that one of the most practical scenarios of using the learned representations is to apply them to downstream tasks. We argue that we should design the metric based on a similar principle. For that, we introduce the transferred discrepancy (TD), a new metric that defines the difference between two representations based on their downstream-task performance. Through an asymptotic analysis, we show how TD correlates with downstream tasks and the necessity to define metrics in such a task-dependent fashion. In particular, we also show that under specific conditions, the TD metric is closely related to previous metrics. Our experiments show that TD can provide fine-grained information for varied downstream tasks, and for the models trained from different initializations, the learned features are not the same in terms of downstream-task predictions. We find that TD may also be used to evaluate the effectiveness of different training strategies. For example, we demonstrate that the models trained with proper data augmentations that improve the generalization capture more similar features in terms of TD, while those with data augmentations that hurt the generalization will not. This suggests a training strategy that leads to more robust representation also trains models that generalize better.

Autoregressive sequence models achieve state-of-the-art performance in domains like machine translation. However, due to the autoregressive factorization nature, these models suffer from heavy latency during inference. Recently, non-autoregressive sequence models were proposed to speed up the inference time. However, these models assume that the decoding process of each token is conditionally independent of others. Such a generation process sometimes makes the output sentence inconsistent, and thus the learned non-autoregressive models could only achieve inferior accuracy compared to their autoregressive counterparts. To improve then decoding consistency and reduce the inference cost at the same time, we propose to incorporate a structured inference module into the non-autoregressive models. Specifically, we design an efficient approximation for Conditional Random Fields (CRF) for non-autoregressive sequence models, and further propose a dynamic transition technique to model positional contexts in the CRF. Experiments in machine translation show that while increasing little latency (8~14ms), our model could achieve significantly better translation performance than previous non-autoregressive models on different translation datasets. In particular, for the WMT14 En-De dataset, our model obtains a BLEU score of 26.80, which largely outperforms the previous non-autoregressive baselines and is only 0.61 lower in BLEU than purely autoregressive models.

Due to the unparallelizable nature of the autoregressive factorization, AutoRegressive Translation (ART) models have to generate tokens sequentially during decoding and thus suffer from high inference latency. Non-AutoRegressive Translation (NART) models were proposed to reduce the inference time, but could only achieve inferior translation accuracy. In this paper, we proposed a novel approach to leveraging the hints from hidden states and word alignments to help the training of NART models. The results achieve significant improvement over previous NART models for the WMT14 En-De and De-En datasets and are even comparable to a strong LSTM-based ART baseline but one order of magnitude faster in inference.

The Transformer architecture is widely used in natural language processing. Despite its success, the design principle of the Transformer remains elusive. In this paper, we provide a novel perspective towards understanding the architecture: we show that the Transformer can be mathematically interpreted as a numerical Ordinary Differential Equation (ODE) solver for a convection-diffusion equation in a multi-particle dynamic system. In particular, how words in a sentence are abstracted into contexts by passing through the layers of the Transformer can be interpreted as approximating multiple particles' movement in the space using the Lie-Trotter splitting scheme and the Euler's method. Given this ODE's perspective, the rich literature of numerical analysis can be brought to guide us in designing effective structures beyond the Transformer. As an example, we propose to replace the Lie-Trotter splitting scheme by the Strang-Marchuk splitting scheme, a scheme that is more commonly used and with much lower local truncation errors. The Strang-Marchuk splitting scheme suggests that the self-attention and position-wise feed-forward network (FFN) sub-layers should not be treated equally. Instead, in each layer, two position-wise FFN sub-layers should be used, and the self-attention sub-layer is placed in between. This leads to a brand new architecture. Such an FFN-attention-FFN layer is "Macaron-like", and thus we call the network with this new architecture the Macaron Net. Through extensive experiments, we show that the Macaron Net is superior to the Transformer on both supervised and unsupervised learning tasks. The reproducible codes and pretrained models can be found at https://github.com/zhuohan123/macaron-net

Neural network robustness has recently been highlighted by the existence of adversarial examples. Many previous works show that the learned networks do not perform well on perturbed test data, and significantly more labeled data is required to achieve adversarially robust generalization. In this paper, we theoretically and empirically show that with just more unlabeled data, we can learn a model with better adversarially robust generalization. The key insight of our results is based on a risk decomposition theorem, in which the expected robust risk is separated into two parts: the stability part which measures the prediction stability in the presence of perturbations, and the accuracy part which evaluates the standard classification accuracy. As the stability part does not depend on any label information, we can optimize this part using unlabeled data. We further prove that for a specific Gaussian mixture problem illustrated by [35], adversarially robust generalization can be almost as easy as the standard generalization in supervised learning if a sufficiently large amount of unlabeled data is provided. Inspired by the theoretical findings, we propose a new algorithm called PASS by leveraging unlabeled data during adversarial training. We show that in the transductive and semi-supervised settings, PASS achieves higher robust accuracy and defense success rate on the Cifar-10 task.

First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the prohibitive computational cost in calculating the second order information. In this paper, we propose a novel Gram-Gauss-Newton (GGN) algorithm to train deep neural networks for regression problems with square loss. Different from typical second-order methods that have heavy computational cost in each iteration, our proposed GGN only has minor overhead compared to first-order methods such as SGD. We also provide theoretical results to show that for sufficiently wide neural networks, the convergence rate of the GGN algorithm is quadratic. Preliminary experiments on regression tasks demonstrate that for training standard networks, the GGN algorithm converges faster and achieves better performance than SGD.