A conventional wisdom in statistical learning is that large models require strong regularization to prevent overfitting. This rule has been recently challenged by deep neural networks: despite being expressive enough to fit any training set perfectly, they still generalize well. Here we show that the same is true for linear regression in the under-determined $n\ll p$ situation, provided that one uses the minimum-norm estimator. The case of linear model with least squares loss allows full and exact mathematical analysis. We prove that augmenting a model with many random covariates with small constant variance and using minimum-norm estimator is asymptotically equivalent to adding the ridge penalty. Using toy example simulations as well as real-life high-dimensional data sets, we demonstrate that explicit ridge penalty often fails to provide any improvement over this implicit ridge regularization. In this regime, minimum-norm estimator achieves zero training error but nevertheless has low expected error.

We consider the problem of anomaly detection in images, and present a new detection technique. Given a sample of images, all known to belong to a "normal" class (e.g., dogs), we show how to train a deep neural model that can detect out-of-distribution images (i.e., non-dog objects). The main idea behind our scheme is to train a multi-class model to discriminate between dozens of geometric transformations applied on all the given images. The auxiliary expertise learned by the model generates feature detectors that effectively identify, at test time, anomalous images based on the softmax activation statistics of the model when applied on transformed images. We present extensive experiments using the proposed detector, which indicate that our algorithm improves state-of-the-art methods by a wide margin.

In this paper, we study the problem of deriving fast and accurate classification algorithms with uncertainty quantification. Gaussian process classification provides a principled approach, but the corresponding computational burden is hardly sustainable in large-scale problems and devising efficient alternatives is a challenge. In this work, we investigate if and how Gaussian process regression directly applied to the classification labels can be used to tackle this question. While in this case training time is remarkably faster, predictions need be calibrated for classification and uncertainty estimation. To this aim, we propose a novel approach based on interpreting the labels as the output of a Dirichlet distribution. Extensive experimental results show that the proposed approach provides essentially the same accuracy and uncertainty quantification of Gaussian process classification while requiring only a fraction of computational resources.

Collecting the large datasets needed to train deep neural networks can be very difficult, particularly for the many applications for which sharing and pooling data is complicated by practical, ethical, or legal concerns. However, it may be the case that derivative datasets or predictive models developed within individual sites can be shared and combined with fewer restrictions. Training on distributed datasets and combining the resulting networks is often viewed as continual learning, but these methods require networks to be trained sequentially. In this paper, we introduce parallel weight consolidation (PWC), a continual learning method to consolidate the weights of neural networks trained in parallel on independent datasets. We perform a brain segmentation case study using PWC to consolidate several dilated convolutional neural networks trained in parallel on independent structural magnetic resonance imaging (sMRI) datasets from different sites. We found that PWC led to increased performance on held-out test sets from the different sites, as well as on a very large and completely independent multi-site dataset. This demonstrates the feasibility of PWC for combining the knowledge learned by networks trained on different datasets.

The process of translation is ambiguous, in that there are typically many valid trans- lations for a given sentence. This gives rise to significant variation in parallel cor- pora, however, most current models of machine translation do not account for this variation, instead treating the prob- lem as a deterministic process. To this end, we present a deep generative model of machine translation which incorporates a chain of latent variables, in order to ac- count for local lexical and syntactic varia- tion in parallel corpora. We provide an in- depth analysis of the pitfalls encountered in variational inference for training deep generative models. Experiments on sev- eral different language pairs demonstrate that the model consistently improves over strong baselines.

Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural networks in language modeling (the softmax bottleneck). In this paper, we propose an output activation function for breaking the softmax bottleneck without additional parameters. We re-analyze the softmax bottleneck from the perspective of the output set of log-softmax and identify the cause of the softmax bottleneck. On the basis of this analysis, we propose sigsoftmax, which is composed of a multiplication of an exponential function and sigmoid function. Sigsoftmax can break the softmax bottleneck. The experiments on language modeling demonstrate that sigsoftmax and mixture of sigsoftmax outperform softmax and mixture of softmax, respectively.

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation or generalization ability of deep learning methods generated by the network architectures such as deep convolutional neural networks having convolutional structures. Here we show that a deep convolutional neural network (CNN) is universal, meaning that it can be used to approximate any continuous function to an arbitrary accuracy when the depth of the neural network is large enough. This answers an open question in learning theory. Our quantitative estimate, given tightly in terms of the number of free parameters to be computed, verifies the efficiency of deep CNNs in dealing with large dimensional data. Our study also demonstrates the role of convolutions in deep CNNs.

This paper studies the relationship between the classification performed by deep neural networks and the $k$-NN decision at the embedding space of these networks. This simple important connection shown here provides a better understanding of the relationship between the ability of neural networks to generalize and their tendency to memorize the training data, which are traditionally considered to be contradicting to each other and here shown to be compatible and complementary. Our results support the conjecture that deep neural networks approach Bayes optimal error rates.

Deep neural networks (DNNs) are vulnerable to adversarial examples, even in the black-box case, where the attacker is limited to solely query access. Existing blackbox approaches to generating adversarial examples typically require a significant amount of queries, either for training a substitute network or estimating gradients from the output scores. We introduce GenAttack, a gradient-free optimization technique which uses genetic algorithms for synthesizing adversarial examples in the black-box setting. Our experiments on the MNIST, CIFAR-10, and ImageNet datasets show that GenAttack can successfully generate visually imperceptible adversarial examples against state-of-the-art image recognition models with orders of magnitude fewer queries than existing approaches. For example, in our CIFAR-10 experiments, GenAttack required roughly 2,568 times less queries than the current state-of-the-art black-box attack. Furthermore, we show that GenAttack can successfully attack both the state-of-the-art ImageNet defense, ensemble adversarial training, and non-differentiable, randomized input transformation defenses. GenAttack's success against ensemble adversarial training demonstrates that its query efficiency enables it to exploit the defense's weakness to direct black-box attacks. GenAttack's success against non-differentiable input transformations indicates that its gradient-free nature enables it to be applicable against defenses which perform gradient masking/obfuscation to confuse the attacker. Our results suggest that population-based optimization opens up a promising area of research into effective gradient-free black-box attacks.

Attributes, such as metadata and profile, carry useful information which in principle can help improve accuracy in recommender systems. However, existing approaches have difficulty in fully leveraging attribute information due to practical challenges such as heterogeneity and sparseness. These approaches also fail to combine recurrent neural networks which have recently shown effectiveness in item recommendations in applications such as video and music browsing. To overcome the challenges and to harvest the advantages of sequence models, we present a novel approach, Heterogeneous Attribute Recurrent Neural Networks (HA-RNN), which incorporates heterogeneous attributes and captures sequential dependencies in \textit{both} items and attributes. HA-RNN extends recurrent neural networks with 1) a hierarchical attribute combination input layer and 2) an output attribute embedding layer. We conduct extensive experiments on two large-scale datasets. The new approach show significant improvements over the state-of-the-art models. Our ablation experiments demonstrate the effectiveness of the two components to address heterogeneous attribute challenges including variable lengths and attribute sparseness. We further investigate why sequence modeling works well by conducting exploratory studies and show sequence models are more effective when data scale increases.