Macformer: Transformer with Random Maclaurin Feature Attention

Random feature attention (RFA) adopts random fourier feature (RFF) methods to approximate the softmax function, resulting in a linear time and space attention mechanism that enables the construction of an efficient Transformer. Inspired by RFA, we propose Macformer, a Transformer architecture that employs random Maclaurin features (RMF) to approximate various dot-product kernels, thereby accelerating attention computations for long sequence. Macformer consists of Random Maclaurin Feature Attention (RMFA) and pre-post Scaling Batch Normalization (ppSBN), the former is an unbiased approximation for dot-product kernelized attention and the later is a two-stage regularization mechanism guaranteeing the error of RMFA. We conducted toy experiments to demonstrate the efficiency of RMFA and ppSBN, and experiments on long range arena (LRA) benchmark to validate the acceleration and accuracy of Macformer with different dot-product kernels. Experiment results of Macformer are consistent with our theoretical analysis.

Self-supervised Smoothing Graph Neural Networks

This paper studies learning node representations with GNNs for unsupervised scenarios. We make a theoretical understanding and empirical demonstration about the non-steady performance of GNNs over different graph datasets, when the supervision signals are not appropriately defined. The performance of GNNs depends on both the node feature smoothness and the graph locality. To smooth the discrepancy of node proximity measured by graph topology and node feature, we proposed KS2L - a novel graph \underline{K}nowledge distillation regularized \underline{S}elf-\underline{S}upervised \underline{L}earning framework, with two complementary regularization modules, for intra-and cross-model graph knowledge distillation. We demonstrate the competitive performance of KS2L on a variety of benchmarks. Even with a single GCN layer, KS2L has consistently competitive or even better performance on various benchmark datasets.

Theoretical Analysis of Divide-and-Conquer ERM: Beyond Square Loss and RKHS

Theoretical analysis of the divide-and-conquer based distributed learning with least square loss in the reproducing kernel Hilbert space (RKHS) have recently been explored within the framework of learning theory. However, the studies on learning theory for general loss functions and hypothesis spaces remain limited. To fill the gap, we study the risk performance of distributed empirical risk minimization (ERM) for general loss functions and hypothesis spaces. The main contributions are two-fold. First, we derive two tight risk bounds under certain basic assumptions on the hypothesis space, as well as the smoothness, Lipschitz continuity, strong convexity of the loss function. Second, we further develop a more general risk bound for distributed ERM without the restriction of strong convexity.

Nearly Optimal Risk Bounds for Kernel K-Means

In this paper, we study the statistical properties of the kernel $k$-means and obtain a nearly optimal excess risk bound, substantially improving the state-of-art bounds in the existing clustering risk analyses. We further analyze the statistical effect of computational approximations of the Nystr\"{o}m kernel $k$-means, and demonstrate that it achieves the same statistical accuracy as the exact kernel $k$-means considering only $\sqrt{nk}$ Nystr\"{o}m landmark points. To the best of our knowledge, such sharp excess risk bounds for kernel (or approximate kernel) $k$-means have never been seen before.

Differentially Private ERM Based on Data Perturbation

In this paper, after observing that different training data instances affect the machine learning model to different extents, we attempt to improve the performance of differentially private empirical risk minimization (DP-ERM) from a new perspective. Specifically, we measure the contributions of various training data instances on the final machine learning model, and select some of them to add random noise. Considering that the key of our method is to measure each data instance separately, we propose a new `Data perturbation' based (DB) paradigm for DP-ERM: adding random noise to the original training data and achieving ($\epsilon,\delta$)-differential privacy on the final machine learning model, along with the preservation on the original data. By introducing the Influence Function (IF), we quantitatively measure the impact of the training data on the final model. Theoretical and experimental results show that our proposed DBDP-ERM paradigm enhances the model performance significantly.

Dynamically Visual Disambiguation of Keyword-based Image Search

Due to the high cost of manual annotation, learning directly from the web has attracted broad attention. One issue that limits their performance is the problem of visual polysemy. To address this issue, we present an adaptive multi-model framework that resolves polysemy by visual disambiguation. Compared to existing methods, the primary advantage of our approach lies in that our approach can adapt to the dynamic changes in the search results. Our proposed framework consists of two major steps: we first discover and dynamically select the text queries according to the image search results, then we employ the proposed saliency-guided deep multi-instance learning network to remove outliers and learn classification models for visual disambiguation. Extensive experiments demonstrate the superiority of our proposed approach.

Deep learning in bioinformatics: introduction, application, and perspective in big data era

Deep learning, which is especially formidable in handling big data, has achieved great success in various fields, including bioinformatics. With the advances of the big data era in biology, it is foreseeable that deep learning will become increasingly important in the field and will be incorporated in vast majorities of analysis pipelines. In this review, we provide both the exoteric introduction of deep learning, and concrete examples and implementations of its representative applications in bioinformatics. We start from the recent achievements of deep learning in the bioinformatics field, pointing out the problems which are suitable to use deep learning. After that, we introduce deep learning in an easy-to-understand fashion, from shallow neural networks to legendary convolutional neural networks, legendary recurrent neural networks, graph neural networks, generative adversarial networks, variational autoencoder, and the most recent state-of-the-art architectures. After that, we provide eight examples, covering five bioinformatics research directions and all the four kinds of data type, with the implementation written in Tensorflow and Keras. Finally, we discuss the common issues, such as overfitting and interpretability, that users will encounter when adopting deep learning methods and provide corresponding suggestions. The implementations are freely available at \url{https://github.com/lykaust15/Deep_learning_examples}.

Efficient Cross-Validation for Semi-Supervised Learning

Manifold regularization, such as laplacian regularized least squares (LapRLS) and laplacian support vector machine (LapSVM), has been widely used in semi-supervised learning, and its performance greatly depends on the choice of some hyper-parameters. Cross-validation (CV) is the most popular approach for selecting the optimal hyper-parameters, but it has high complexity due to multiple times of learner training. In this paper, we provide a method to approximate the CV for manifold regularization based on a notion of robust statistics, called Bouligand influence function (BIF). We first provide a strategy for approximating the CV via the Taylor expansion of BIF. Then, we show how to calculate the BIF for general loss function,and further give the approximate CV criteria for model selection in manifold regularization. The proposed approximate CV for manifold regularization requires training only once, hence can significantly improve the efficiency of traditional CV. Experimental results show that our approximate CV has no statistical discrepancy with the original one, but much smaller time cost.

SupportNet: solving catastrophic forgetting in class incremental learning with support data

A plain well-trained deep learning model often does not have the ability to learn new knowledge without forgetting the previously learned knowledge, which is known as the catastrophic forgetting. Here we propose a novel method, SupportNet, to solve the catastrophic forgetting problem in class incremental learning scenario efficiently and effectively. SupportNet combines the strength of deep learning and support vector machine (SVM), where SVM is used to identify the support data from the old data, which are fed to the deep learning model together with the new data for further training so that the model can review the essential information of the old data when learning the new information. Two powerful consolidation regularizers are applied to ensure the robustness of the learned model. Comprehensive experiments on various tasks, including enzyme function prediction, subcellular structure classification and breast tumor classification, show that SupportNet drastically outperforms the state-of-the-art incremental learning methods and even reaches similar performance as the deep learning model trained from scratch on both old and new data. Our program is accessible at: https://github.com/lykaust15/SupportNet

On the Decision Boundary of Deep Neural Networks

While deep learning models and techniques have achieved great empirical success, our understanding of the source of success in many aspects remains very limited. In an attempt to bridge the gap, we investigate the decision boundary of a production deep learning architecture with weak assumptions on both the training data and the model. We demonstrate, both theoretically and empirically, that the last weight layer of a neural network converges to a linear SVM trained on the output of the last hidden layer, for both the binary case and the multi-class case with the commonly used cross-entropy loss. Furthermore, we show empirically that training a neural network as a whole, instead of only fine-tuning the last weight layer, may result in better bias constant for the last weight layer, which is important for generalization. In addition to facilitating the understanding of deep learning, our result can be helpful for solving a broad range of practical problems of deep learning, such as catastrophic forgetting and adversarial attacking. The experiment codes are available at https://github.com/lykaust15/NN_decision_boundary