We investigate whether Differentially Private SGD offers better privacy in practice than what is guaranteed by its state-of-the-art analysis. We do so via novel data poisoning attacks, which we show correspond to realistic privacy attacks. While previous work (Ma et al., arXiv 2019) proposed this connection between differential privacy and data poisoning as a defense against data poisoning, our use as a tool for understanding the privacy of a specific mechanism is new. More generally, our work takes a quantitative, empirical approach to understanding the privacy afforded by specific implementations of differentially private algorithms that we believe has the potential to complement and influence analytical work on differential privacy.

Most recent self-supervised learning methods learn visual representation by contrasting different augmented views of images. Compared with supervised learning, more aggressive augmentations have been introduced to further improve the diversity of training pairs. However, aggressive augmentations may distort images' structures leading to a severe semantic shift problem that augmented views of the same image may not share the same semantics, thus degrading the transfer performance. To address this problem, we propose a new SSL paradigm, which counteracts the impact of semantic shift by balancing the role of weak and aggressively augmented pairs. Specifically, semantically inconsistent pairs are of minority, and we treat them as noisy pairs.

The brain uses population codes to form distributed, noise-tolerant representations of sensory and motor variables. Recent work has examined the theoretical optimality of such codes in order to gain insight into the principles governing population codes found in the brain. However, the majority of the population coding literature considers either conditionally independent neurons or neurons with noise governed by a stimulus-independent covariance matrix. Here we analyze population coding under a simple alternative model in which latent input noise" corrupts the stimulus before it is encoded by the population. This provides a convenient and tractable description for irreducible uncertainty that cannot be overcome by adding neurons, and induces stimulus-dependent correlations that mimic certain aspects of the correlations observed in real populations. We examine prior-dependent, Bayesian optimal coding in such populations using exact analyses of cases in which the posterior is approximately Gaussian. These analyses extend previous results on independent Poisson population codes and yield an analytic expression for squared loss and a tight upper bound for mutual information. We show that, for homogeneous populations that tile the input domain, optimal tuning curve width depends on the prior, the loss function, the resource constraint, and the amount of input noise. This framework provides a practical testbed for examining issues of optimality, noise, correlation, and coding fidelity in realistic neural populations."

Stochastic Gradient Descent (SGD) is arguably the most important single algorithm in modern machine learning. Although SGD with unbiased gradient estimators has been studied extensively over at least half a century, SGD variants relying on biased estimators are rare. Nevertheless, there has been an increased interest in this topic in recent years. However, existing literature on SGD with biased estimators lacks coherence since each new paper relies on a different set of assumptions, without any clear understanding of how they are connected, which may lead to confusion. We address this gap by establishing connections among the existing assumptions, and presenting a comprehensive map of the underlying relationships. Additionally, we introduce a new set of assumptions that is provably weaker than all previous assumptions, and use it to present a thorough analysis of BiasedSGD in both convex and non-convex settings, offering advantages over previous results.

Unsupervised learning from continuous visual streams is a challenging problem that cannot be naturally and efficiently managed in the classic batch-mode setting of computation. The information stream must be carefully processed accordingly to an appropriate spatio-temporal distribution of the visual data, while most approaches of learning commonly assume uniform probability density. In this paper we focus on unsupervised learning for transferring visual information in a truly online setting by using a computational model that is inspired to the principle of least action in physics. The maximization of the mutual information is carried out by a temporal process which yields online estimation of the entropy terms. The model, which is based on second-order differential equations, maximizes the information transfer from the input to a discrete space of symbols related to the visual features of the input, whose computation is supported by hidden neurons.

We formulate the continual learning (CL) problem via dynamic programming and model the trade-off between catastrophic forgetting and generalization as a two-player sequential game. We show theoretically that a balance point between the two players exists for each task and that this point is stable (once the balance is achieved, the two players stay at the balance point). Next, we introduce balanced continual learning (BCL), which is designed to attain balance between generalization and forgetting and empirically demonstrate that BCL is comparable to or better than the state of the art.

We provide a detailed asymptotic study of gradient flow trajectories and their implicit optimization bias when minimizing the exponential loss over "diagonal linear networks". This is the simplest model displaying a transition between "kernel" and non-kernel ("rich" or "active") regimes. We show how the transition is controlled by the relationship between the initialization scale and how accurately we minimize the training loss. Our results indicate that some limit behavior of gradient descent only kick in at ridiculous training accuracies (well beyond 10 -100). Moreover, the implicit bias at reasonable initialization scales and training accuracies is more complex and not captured by these limits.

Unsupervised distribution alignment estimates a transformation that maps two or more source distributions to a shared aligned distribution given only samples from each distribution. This task has many applications including generative modeling, unsupervised domain adaptation, and socially aware learning. Most prior works use adversarial learning (i.e., min-max optimization), which can be challenging to optimize and evaluate. A few recent works explore non-adversarial flow-based (i.e., invertible) approaches, but they lack a unified perspective and are limited in efficiently aligning multiple distributions. Therefore, we propose to unify and generalize previous flow-based approaches under a single non-adversarial framework, which we prove is equivalent to minimizing an upper bound on the Jensen-Shannon Divergence (JSD).

To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, synthesis of multi-modular grid cells in deep recurrent neural networks remains absent. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: dynamical systems, coding theory, function optimization and supervised deep learning.

Federated learning is a learning paradigm to enable collaborative learning across different parties without revealing raw data. Notably, vertical federated learning (VFL), where parties share the same set of samples but only hold partial features, has a wide range of real-world applications. They design algorithms either assuming the data from different parties can be exactly linked or simply linking each record with its most similar neighboring record. These approaches may fail to capture the key features from other less similar records. Moreover, such improper linkage cannot be corrected by training since existing approaches provide no feedback on linkage during training. In this paper, we design a novel coupled training paradigm, FedSim, that integrates one-to-many linkage into the training process.