Stochastic gradient descent (SGD) has become the most attractive optimization method in training large-scale deep neural networks due to its simplicity, low computational cost in each updating step, and good performance. Standard excess risk bounds show that SGD only needs to take one pass over the training data and more passes could not help to improve the performance. Empirically, it has been observed that SGD taking more than one pass over the training data (multi-pass SGD) has much better excess risk bound performance than the SGD only taking one pass over the training data (one-pass SGD). However, it is not very clear that how to explain this phenomenon in theory. In this paper, we provide some theoretical evidences for explaining why multiple passes over the training data can help improve performance under certain circumstance. Specifically, we consider smooth risk minimization problems whose objective function is non-convex least squared loss. Under Polyak-Lojasiewicz (PL) condition, we establish faster convergence rate of excess risk bound for multi-pass SGD than that for one-pass SGD.
Multi-epoch, small-batch, Stochastic Gradient Descent (SGD) has been the method of choice for learning with large over-parameterized models. A popular theory for explaining why SGD works well in practice is that the algorithm has an implicit regularization that biases its output towards a good solution. Perhaps the theoretically most well understood learning setting for SGD is that of Stochastic Convex Optimization (SCO), where it is well known that SGD learns at a rate of $O(1/\sqrt{n})$, where $n$ is the number of samples. In this paper, we consider the problem of SCO and explore the role of…
Knowledge distillation is a technique for improving the performance of a simple "student" model by replacing its one-hot training labels with a distribution over labels obtained from a complex "teacher" model. While this simple approach has proven widely effective, a basic question remains unresolved: why does distillation help? In this paper, we present a statistical perspective on distillation which addresses this question, and provides a novel connection to extreme multiclass retrieval techniques. Our core observation is that the teacher seeks to estimate the underlying (Bayes) class-probab…
Sea AI Lab（Sea人工智能实验室）；National University of Singapore（新加坡国立大学）
For unsupervised pretraining, mask-reconstruction pretraining (MRP) approaches, e.g. MAE and data2vec, randomly mask input patches and then reconstruct the pixels or semantic features of these masked patches via an auto-encoder. Then for a downstream task, supervised fine-tuning the pretrained encoder remarkably surpasses the conventional ``supervised learning'' (SL) trained from scratch. However, it is still unclear 1) how MRP performs semantic feature learning in the pretraining phase and 2) why it helps in downstream tasks. To solve these problems, we first theoretically show that on an aut…
Pretrained language models have achieved state-of-the-art performance when adapted to a downstream NLP task. However, theoretical analysis of these models is scarce and challenging since the pretraining and downstream tasks can be very different. We propose an analysis framework that links the pretraining and downstream tasks with an underlying latent variable generative model of text -- the downstream classifier must recover a function of the posterior distribution over the latent variables. We analyze head tuning (learning a classifier on top of the frozen pretrained model) and prompt tuning…
Mixup is a popular data augmentation technique based on taking convex combinations of pairs of examples and their labels. This simple technique has been shown to substantially improve both the robustness and the generalization of the trained model. However, it is not well-understood why such improvement occurs. In this paper, we provide theoretical analysis to demonstrate how using Mixup in training helps model robustness and generalization. For robustness, we show that minimizing the Mixup loss corresponds to approximately minimizing an upper bound of the adversarial loss. This explains why m…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks, even with zero-shot usage. However, there is little theoretical understanding of this success. This paper initiates a mathematical study of this phenomenon for the downstream task of text classification by considering the following questions: (1) What is the intuitive connection between the pretraining task of next word prediction and text classification? (2) How can we mathematically formalize this connection and quantify the benefit of…
Vision transformer (ViT) is an attention neural network architecture that is shown to be effective for computer vision tasks. However, compared to ResNet-18 with a similar number of parameters, ViT has a significantly lower evaluation accuracy when trained on small datasets. To facilitate studies in related fields, we provide a visual intuition to help understand why it is the case. We first compare the performance of the two models and confirm that ViT has less accuracy than ResNet-18 when trained on small datasets. We then interpret the results by showing attention map visualization for ViT …
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the estimates of mean and standard deviation of input (distribution) to hidden layers inaccurate due to shifting parameter values (especially during initial training epochs). Another fundamental problem with BN is that it cannot be used with batch-size $ 1 $ during training. We address t…
School of Computer Science (National Pilot Software Engineering School)（计算机科学学院（国家示范性软件工程学院））；Beijing University of Posts and Telecommunications（北京邮电大学）
As student failure rates continue to increase in higher education, predicting student performance in the following semester has become a significant demand. Personalized student performance prediction helps educators gain a comprehensive view of student status and effectively intervene in advance. However, existing works scarcely consider the explainability of student performance prediction, which educators are most concerned about. In this paper, we propose a novel Explainable Student performance prediction method with Personalized Attention (ESPA) by utilizing relationships in student profil…
Machine learning classifiers with high test accuracy often perform poorly under adversarial attacks. It is commonly believed that adversarial training alleviates this issue. In this paper, we demonstrate that, surprisingly, the opposite may be true -- Even though adversarial training helps when enough data is available, it may hurt robust generalization in the small sample size regime. We first prove this phenomenon for a high-dimensional linear classification setting with noiseless observations. Our proof provides explanatory insights that may also transfer to feature learning models. Further…
Spectral normalization (SN) is a widely-used technique for improving the stability and sample quality of Generative Adversarial Networks (GANs). However, there is currently limited understanding of why SN is effective. In this work, we show that SN controls two important failure modes of GAN training: exploding and vanishing gradients. Our proofs illustrate a (perhaps unintentional) connection with the successful LeCun initialization. This connection helps to explain why the most popular implementation of SN for GANs requires no hyper-parameter tuning, whereas stricter implementations of SN ha…
Why Does Little Robustness Help? A Further Step Towards Understanding Adversarial Transferability
School of Cyber Science and Engineering, Huazhong University of Science and Technology（电子科学与工程学院，华中科技大学）；School of Software Engineering, Huazhong University of Science and Technology（软件工程学院，华中科技大学）；School of Information and Communication Technology, Griffith University（信息与通信技术学院，格里菲斯大学）；School of Computer Science and Technology, Huazhong University of Science and Technology（计算机科学与技术学院，华中科技大学）
