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High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models which allow sum of any number of component parameters, and each component structure can be characterized by any norm. We present a simple estimator for such models, give a geometric condition under which the components can be accurately estimated, characterize sample complexity of the estimator, and give high probability nonasymptotic bounds on the componentwise estimation error. We use tools from empirical processes and generic chaining for the statistical analysis, and our results, which substantially generalize prior work on superposition models, are in terms of Gaussian widths of suitable sets.

Behavioral experiments on humans and animals suggest that the brain performs probabilistic inference to interpret its environment. Here we present a new generalpurpose, biologically-plausible neural implementation of approximate inference. The neural network represents uncertainty using Probabilistic Population Codes (PPCs), which are distributed neural representations that naturally encode probability distributions, and support marginalization and evidence integration in a biologically-plausible manner. By connecting multiple PPCs together as a probabilistic graphical model, we represent multivariate probability distributions. Approximate inference in graphical models can be accomplished by message-passing algorithms that disseminate local information throughout the graph. An attractive and often accurate example of such an algorithm is Loopy Belief Propagation (LBP), which uses local marginalization and evidence integration operations to perform approximate inference efficiently even for complex models.

Rapid categorization paradigms have a long history in experimental psychology: Characterized by short presentation times and speeded behavioral responses, these tasks highlight the efficiency with which our visual system processes natural object categories. Previous studies have shown that feed-forward hierarchical models of the visual cortex provide a good fit to human visual decisions. At the same time, recent work in computer vision has demonstrated significant gains in object recognition accuracy with increasingly deep hierarchical architectures. But it is unclear how well these models account for human visual decisions and what they may reveal about the underlying brain processes. We have conducted a large-scale psychophysics study to assess the correlation between computational models and human behavioral responses on a rapid animal vs. non-animal categorization task. We considered visual representations of varying complexity by analyzing the output of different stages of processing in three stateof-the-art deep networks. We found that recognition accuracy increases with higher stages of visual processing (higher level stages indeed outperforming human participants on the same task) but that human decisions agree best with predictions from intermediate stages. Overall, these results suggest that human participants may rely on visual features of intermediate complexity and that the complexity of visual representations afforded by modern deep network models may exceed the complexity of those used by human participants during rapid categorization.

This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling.

Online allocation problems have been widely studied due to their numerous practical applications (particularly to Internet advertising), as well as considerable theoretical interest. The main challenge in such problems is making assignment decisions in the face of uncertainty about future input; effective algorithms need to predict which constraints are most likely to bind, and learn the balance between short-term gain and the value of long-term resource availability. In many important applications, the algorithm designer is faced with multiple objectives to optimize. In particular, in online advertising it is fairly common to optimize multiple metrics, such as clicks, conversions, and impressions, as well as other metrics which may be largely uncorrelated such as'share of voice', and'buyer surplus'. While there has been considerable work on multi-objective offline optimization (when the entire input is known in advance), very little is known about the online case, particularly in the case of adversarial input. In this paper, we give the first results for bi-objective online submodular optimization, providing almost matching upper and lower bounds for allocating items to agents with two submodular value functions. We also study practically relevant special cases of this problem related to Internet advertising, and obtain improved results. All our algorithms are nearly best possible, as well as being efficient and easy to implement in practice.

While progress has been made in understanding the robustness of machine learning classifiers to test-time adversaries (evasion attacks), fundamental questions remain unresolved. In this paper, we use optimal transport to characterize the minimum possible loss in an adversarial classification scenario. In this setting, an adversary receives a random labeled example from one of two classes, perturbs the example subject to a neighborhood constraint, and presents the modified example to the classifier. We define an appropriate cost function such that the minimum transportation cost between the distributions of the two classes determines the minimum 0 1 loss for any classifier. When the classifier comes from a restricted hypothesis class, the optimal transportation cost provides a lower bound. We apply our framework to the case of Gaussian data with norm-bounded adversaries and explicitly show matching bounds for the classification and transport problems as well as the optimality of linear classifiers. We also characterize the sample complexity of learning in this setting, deriving and extending previously known results as a special case. Finally, we use our framework to study the gap between the optimal classification performance possible and that currently achieved by state-of-the-art robustly trained neural networks for datasets of interest, namely, MNIST, Fashion MNIST and CIFAR-10.

At least nine people, including two children, were killed in Israeli strikes in southern Lebanon on Thursday, the health ministry said, as violence continues despite a ceasefire now in its second week. The strikes - which Israel said were targeting Hezbollah infrastructure - also wounded 23 people, among them eight children and seven women, the ministry said. Separately, Hezbollah said it had carried out attacks on Israeli forces in the south, including a drone strike targeting soldiers in the Bint Jbeil district. The violence comes as Israel presses ahead with military operations in Lebanon despite the ceasefire announced on 16 April, after direct talks between Lebanese and Israeli ambassadors in Washington. Lebanese President Joseph Aoun criticised what he described as continuing Israeli violations of the truce, saying strikes and demolitions of homes and places of worship were ongoing despite the ceasefire.