We introduce a new notion of generalization -- Distributional Generalization -- which roughly states that outputs of a classifier at train and test time are close *as distributions*, as opposed to close in just their average error. For example, if we mislabel 30% of dogs as cats in the train set of CIFAR-10, then a ResNet trained to interpolation will in fact mislabel roughly 30% of dogs as cats on the *test set* as well, while leaving other classes unaffected. This behavior is not captured by classical generalization, which would only consider the average error and not the distribution of errors over the input domain. Our formal conjectures, which are much more general than this example, characterize the form of distributional generalization that can be expected in terms of problem parameters: model architecture, training procedure, number of samples, and data distribution. We give empirical evidence for these conjectures across a variety of domains in machine learning, including neural networks, kernel machines, and decision trees. Our results thus advance our empirical understanding of interpolating classifiers.

One of the most efficient methods to solve L2-regularized primal problems, such as logistic regression and linear support vector machine (SVM) classification, is the widely used trust region Newton algorithm, TRON. While TRON has recently been shown to enjoy substantial speedups on shared-memory multi-core systems, exploiting graphical processing units (GPUs) to speed up the method is significantly more difficult, owing to the highly complex and heavily sequential nature of the algorithm. In this work, we show that using judicious GPU-optimization principles, TRON training time for different losses and feature representations may be drastically reduced. For sparse feature sets, we show that using GPUs to train logistic regression classifiers in LIBLINEAR is up to an order-of-magnitude faster than solely using multithreading. For dense feature sets--which impose far more stringent memory constraints--we show that GPUs substantially reduce the lengthy SVM learning times required for state-of-the-art proteomics analysis, leading to dramatic improvements over recently proposed speedups. Furthermore, we show how GPU speedups may be mixed with multithreading to enable such speedups when the dataset is too large for GPU memory requirements; on a massive dense proteomics dataset of nearly a quarter-billion data instances, these mixed-architecture speedups reduce SVM analysis time from over half a week to less than a single day while using limited GPU memory.

Federated learning (FL) ameliorates privacy concerns in settings where a central server coordinates learning from data distributed across many clients. The clients train locally and communicate the models they learn to the server; aggregation of local models requires frequent communication of large amounts of information between the clients and the central server. We propose a novel, simple and efficient way of updating the central model in communication-constrained settings based on collecting models from clients with informative updates and estimating local updates that were not communicated. In particular, modeling the progression of model's weights by an Ornstein-Uhlenbeck process allows us to derive an optimal sampling strategy for selecting a subset of clients with significant weight updates. The central server collects updated local models from only the selected clients and combines them with estimated model updates of the clients that were not selected for communication. We test this policy on a synthetic dataset for logistic regression and two FL benchmarks, namely, a classification task on EMNIST and a realistic language modeling task using the Shakespeare dataset. The results demonstrate that the proposed framework provides significant reduction in communication while maintaining competitive or achieving superior performance compared to a baseline. Our method represents a new line of strategies for communication-efficient FL that is orthogonal to the existing user-local methods such as quantization or sparsification, thus complementing rather than aiming to replace those existing methods.

In this work, we analyze the role of the network architecture in shaping the inductive bias of deep classifiers. To that end, we start by focusing on a very simple problem, i.e., classifying a class of linearly separable distributions, and show that, depending on the direction of the discriminative feature of the distribution, many state-of-the-art deep convolutional neural networks (CNNs) have a surprisingly hard time solving this simple task. We then define as neural anisotropy directions (NADs) the vectors that encapsulate the directional inductive bias of an architecture. These vectors, which are specific for each architecture and hence act as a signature, encode the preference of a network to separate the input data based on some particular features. We provide an efficient method to identify NADs for several CNN architectures and thus reveal their directional inductive biases. Furthermore, we show that, for the CIFAR-10 dataset, NADs characterize the features used by CNNs to discriminate between different classes.

Recently, graph-based algorithms have drawn much attention because of their impressive success in semi-supervised setups. For better model performance, previous studies learn to transform the topology of the input graph. However, these works only focus on optimizing the original nodes and edges, leaving the direction of augmenting existing data unexplored. In this paper, by simulating the generation process of graph signals, we propose a novel heuristic pre-processing technique, namely ELectoral COllege (ELCO), which automatically expands new nodes and edges to refine the label similarity within a dense subgraph. Substantially enlarging the original training set with high-quality generated labeled data, our framework can effectively benefit downstream models. To justify the generality and practicality of ELCO, we couple it with the popular Graph Convolution Network and Graph Attention Network to perform extensive evaluations on three standard datasets. In all setups tested, our method boosts the average score of base models by a large margin of 4.7 points, as well as consistently outperforms the state-of-the-art. We release our code and data on https://github.com/RingBDStack/ELCO to guarantee reproducibility.

The quality of datasets is one of the key factors that affect the accuracy of aerodynamic data models. For example, in the uniformly sampled Burgers' dataset, the insufficient high-speed data is overwhelmed by massive low-speed data. Predicting high-speed data is more difficult than predicting low-speed data, owing to that the number of high-speed data is limited, i.e. the quality of the Burgers' dataset is not satisfactory. To improve the quality of datasets, traditional methods usually employ the data resampling technology to produce enough data for the insufficient parts in the original datasets before modeling, which increases computational costs. Recently, the mixtures of experts have been used in natural language processing to deal with different parts of sentences, which provides a solution for eliminating the need for data resampling in aerodynamic data modeling. Motivated by this, we propose the multi-task learning (MTL), a datasets quality-adaptive learning scheme, which combines task allocation and aerodynamic characteristics learning together to disperse the pressure of the entire learning task. The task allocation divides a whole learning task into several independent subtasks, while the aerodynamic characteristics learning learns these subtasks simultaneously to achieve better precision. Two experiments with poor quality datasets are conducted to verify the data quality-adaptivity of the MTL to datasets. The results show than the MTL is more accurate than FCNs and GANs in poor quality datasets.

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the computational efficiency in comparison with the existing algorithms. IRCUR achieves this acceleration by employing CUR decomposition when updating the low rank component, which allows us to obtain an accurate low rank approximation via only three small submatrices. Consequently, IRCUR is able to process only the small submatrices and avoid expensive computing on the full matrix through the entire algorithm. Numerical experiments establish the computational advantage of IRCUR over the state-of-art algorithms on both synthetic and real-world datasets.

The softmax function combined with a cross-entropy loss is a principled approach to modeling probability distributions that has become ubiquitous in deep learning. The softmax function is defined by a lone hyperparameter, the temperature, that is commonly set to one or regarded as a way to tune model confidence after training; however, less is known about how the temperature impacts training dynamics or generalization performance. In this work we develop a theory of early learning for models trained with softmax-cross-entropy loss and show that the learning dynamics depend crucially on the inverse-temperature $\beta$ as well as the magnitude of the logits at initialization, $||\beta{\bf z}||_{2}$. We follow up these analytic results with a large-scale empirical study of a variety of model architectures trained on CIFAR10, ImageNet, and IMDB sentiment analysis. We find that generalization performance depends strongly on the temperature, but only weakly on the initial logit magnitude. We provide evidence that the dependence of generalization on $\beta$ is not due to changes in model confidence, but is a dynamical phenomenon. It follows that the addition of $\beta$ as a tunable hyperparameter is key to maximizing model performance. Although we find the optimal $\beta$ to be sensitive to the architecture, our results suggest that tuning $\beta$ over the range $10^{-2}$ to $10^1$ improves performance over all architectures studied. We find that smaller $\beta$ may lead to better peak performance at the cost of learning stability.

As a result of the recent popularity of social networks and the increase in the number of research papers published across all fields, attributed networks consisting of relationships between objects, such as humans and the papers, that have attributes are becoming increasingly large. Therefore, various studies for clustering attributed networks into sub-networks are being actively conducted. When clustering attributed networks using spectral clustering, the clustering accuracy is strongly affected by the quality of the similarity matrices, which are input into spectral clustering and represent the similarities between pairs of objects. In this paper, we aim to increase the accuracy by refining the matrices before applying spectral clustering to them. We verify the practicability of our proposed method by comparing the accuracy of spectral clustering with similarity matrices before and after refining them.

While many recent works have studied the problem of algorithmic fairness from the perspective of predictions, here we investigate the fairness of recourse actions recommended to individuals to recover from an unfavourable classification. To this end, we propose two new fairness criteria at the group and individual level which---unlike prior work on equalising the average distance from the decision boundary across protected groups---are based on a causal framework that explicitly models relationships between input features, thereby allowing to capture downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We then investigate how to enforce fair recourse in the training of the classifier. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions and structural changes to the system, as opposed to constraints on the classifier.