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Computational differential privacy (CDP) is a natural relaxation of the standard notion of (statistical) differential privacy (SDP) proposed by Beimel, Nissim, and Omri (CRYPTO 2008) and Mironov, Pandey, Reingold, and Vadhan (CRYPTO 2009). In contrast to SDP, CDP only requires privacy guarantees to hold against computationally-bounded adversaries rather than computationally-unbounded statistical adversaries. Despite the question being raised explicitly in several works (e.g., Bun, Chen, and Vadhan, TCC 2016), it has remained tantalizingly open whether there is any task achievable with the CDP notion but not the SDP notion. Even a candidate such task is unknown. Indeed, it is even unclear what the truth could be! In this work, we give the first construction of a task achievable with the CDP notion but not the SDP notion. More specifically, under strong but plausible cryptographic assumptions, we construct a task for which there exists an $\varepsilon$-CDP mechanism with $\varepsilon = O(1)$ achieving $1-o(1)$ utility, but any $(\varepsilon, \delta)$-SDP mechanism, including computationally unbounded ones, that achieves a constant utility must use either a super-constant $\varepsilon$ or a non-negligible $\delta$. To prove this, we introduce a new approach for showing that a mechanism satisfies CDP: first we show that a mechanism is "private" against a certain class of decision tree adversaries, and then we use cryptographic constructions to "lift" this into privacy against computational adversaries. We believe this approach could be useful to devise further tasks separating CDP from SDP.

The paper considers the SUPPORTED model of distributed computing introduced by Schmid and Suomela [HotSDN'13], generalizing the LOCAL and CONGEST models. In this framework, multiple instances of the same problem, differing from each other by the subnetwork to which they apply, recur over time, and need to be solved efficiently online. To do that, one may rely on an initial preprocessing phase for computing some useful information. This preprocessing phase makes it possible, in some cases, to overcome locality-based time lower bounds. A first contribution of the current paper is expanding the spectrum of problem types to which the SUPPORTED model applies. In addition to subnetwork-defined recurrent problems, we introduce also recurrent problems of two additional types: (i) instances defined by partial client sets, and (ii) instances defined by partially fixed outputs. Our second contribution is illustrating the versatility of the SUPPORTED framework by examining recurrent variants of three classical graph problems. The first problem is Minimum Client Dominating Set (CDS), a recurrent version of the classical dominating set problem with each recurrent instance requiring us to dominate a partial client set. We provide a constant time approximation scheme for CDS on trees and planar graphs. The second problem is Color Completion (CC), a recurrent version of the coloring problem in which each recurrent instance comes with a partially fixed coloring (of some of the vertices) that must be completed. We study the minimum number of new colors and the minimum total number of colors necessary for completing this task. The third problem we study is a recurrent version of Locally Checkable Labellings (LCL) on paths of length $n$. We show that such problems have complexities that are either $\Theta(1)$ or $\Theta(n)$, extending the results of Foerster et al. [INFOCOM'19].

Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator applications has thus far been data-driven, which neglects the intrinsic preservation of fundamental physical laws in data. In this paper, we introduce a novel integral neural operator architecture, to learn physical models with fundamental conservation laws automatically guaranteed. In particular, by replacing the frame-dependent position information with its invariant counterpart in the kernel space, the proposed neural operator is by design translation- and rotation-invariant, and consequently abides by the conservation laws of linear and angular momentums. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental datasets, and show that, by automatically satisfying these essential physical laws, our learned neural operator is not only generalizable in handling translated and rotated datasets, but also achieves state-of-the-art accuracy and efficiency as compared to baseline neural operator models.

Recent advances of data-driven machine learning have revolutionized fields like computer vision, reinforcement learning, and many scientific and engineering domains. In many real-world and scientific problems, systems that generate data are governed by physical laws. Recent work shows that it provides potential benefits for machine learning models by incorporating the physical prior and collected data, which makes the intersection of machine learning and physics become a prevailing paradigm. In this survey, we present this learning paradigm called Physics-Informed Machine Learning (PIML) which is to build a model that leverages empirical data and available physical prior knowledge to improve performance on a set of tasks that involve a physical mechanism. We systematically review the recent development of physics-informed machine learning from three perspectives of machine learning tasks, representation of physical prior, and methods for incorporating physical prior. We also propose several important open research problems based on the current trends in the field. We argue that encoding different forms of physical prior into model architectures, optimizers, inference algorithms, and significant domain-specific applications like inverse engineering design and robotic control is far from fully being explored in the field of physics-informed machine learning. We believe that this study will encourage researchers in the machine learning community to actively participate in the interdisciplinary research of physics-informed machine learning.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

The era of big data provides researchers with convenient access to copious data. However, people often have little knowledge about it. The increasing prevalence of big data is challenging the traditional methods of learning causality because they are developed for the cases with limited amount of data and solid prior causal knowledge. This survey aims to close the gap between big data and learning causality with a comprehensive and structured review of traditional and frontier methods and a discussion about some open problems of learning causality. We begin with preliminaries of learning causality. Then we categorize and revisit methods of learning causality for the typical problems and data types. After that, we discuss the connections between learning causality and machine learning. At the end, some open problems are presented to show the great potential of learning causality with data.