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Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood, their convergence for nonconvex functions stands on weak mathematical foundations. Most existing studies on the nonconvex convergence of SGD show the complexity results based on either the minimum of the expected gradient norm or the functional sub-optimality gap (for functions with extra structural property) by searching the entire range of iterates. Hence the last iterations of SGDs do not necessarily maintain the same complexity guarantee. This paper shows that an $\epsilon$-stationary point exists in the final iterates of SGDs, given a large enough total iteration budget, $T$, not just anywhere in the entire range of iterates -- a much stronger result than the existing one. Additionally, our analyses allow us to measure the density of the $\epsilon$-stationary points in the final iterates of SGD, and we recover the classical $O(\frac{1}{\sqrt{T}})$ asymptotic rate under various existing assumptions on the objective function and the bounds on the stochastic gradient. As a result of our analyses, we addressed certain myths and legends related to the nonconvex convergence of SGD and posed some thought-provoking questions that could set new directions for research.

In this short communication, we describe the recent debate on whether the hazard function should be used for causal inference in time-to-event studies and consider three different potential outcomes frameworks (by Rubin, Robins, and Pearl, respectively) as well as use the single-world intervention graph to show mathematically that the hazard function has causal interpretations under all three frameworks. In addition, we argue that the hazard ratio over time can provide a useful interpretation in practical settings.

Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like complex joint friction lack clear first-principles models and are usually ignored by physics simulators. Further, numerically-stiff contact dynamics can make common model-building approaches struggle. We propose a method to simultaneously learn contact and continuous dynamics of a novel, possibly multi-link object by observing its motion through contact-rich trajectories. We formulate a system identification process with a loss that infers unmeasured contact forces, penalizing their violation of physical constraints and laws of motion given current model parameters. Our loss is unlike prediction-based losses used in differentiable simulation. Using a new dataset of real articulated object trajectories and an existing cube toss dataset, our method outperforms differentiable simulation and end-to-end alternatives with more data efficiency. See our project page for code, datasets, and media: //sites.google.com/view/continuous-contact-nets/home

Explainable recommender systems (RS) have traditionally followed a one-size-fits-all approach, delivering the same explanation level of detail to each user, without considering their individual needs and goals. Further, explanations in RS have so far been presented mostly in a static and non-interactive manner. To fill these research gaps, we aim in this paper to adopt a user-centered, interactive explanation model that provides explanations with different levels of detail and empowers users to interact with, control, and personalize the explanations based on their needs and preferences. We followed a user-centered approach to design interactive explanations with three levels of detail (basic, intermediate, and advanced) and implemented them in the transparent Recommendation and Interest Modeling Application (RIMA). We conducted a qualitative user study (N=14) to investigate the impact of providing interactive explanations with varying level of details on the users' perception of the explainable RS. Our study showed qualitative evidence that fostering interaction and giving users control in deciding which explanation they would like to see can meet the demands of users with different needs, preferences, and goals, and consequently can have positive effects on different crucial aspects in explainable recommendation, including transparency, trust, satisfaction, and user experience.

We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting optimal constant factors in the leading terms in a number of different models. In the randomized model, 1) we give a general technique to convert public-coin protocols to private-coin protocols by incurring a small multiplicative error, at a small additive cost. This is an improvement over Newman's theorem [Inf. Proc. Let.'91] in the dependence on the error parameter. 2) Using this we obtain a $(\log(n/\epsilon^2)+4)$-cost private-coin communication protocol that computes the $n$-bit Equality function, to error $\epsilon$. This improves upon the $\log(n/\epsilon^3)+O(1)$ upper bound implied by Newman's theorem, and matches the best known lower bound, which follows from Alon [Comb. Prob. Comput.'09], up to an additive $\log\log(1/\epsilon)+O(1)$. In the quantum model, 1) we exhibit a one-way protocol of cost $\log(n/\epsilon)+4$, that uses only pure states and computes the $n$-bit Equality function to error $\epsilon$. This bound was implicitly already shown by Nayak [PhD thesis'99]. 2) We show that any $\epsilon$-error one-way protocol for $n$-bit Equality that uses only pure states communicates at least $\log(n/\epsilon)-\log\log(1/\epsilon)-O(1)$ qubits. 3) We exhibit a one-way protocol of cost $\log(\sqrt{n}/\epsilon)+3$, that uses mixed states and computes the $n$-bit Equality function to error $\epsilon$. This is also tight up to an additive $\log\log(1/\epsilon)+O(1)$, which follows from Alon's result. 4) We study the number of EPR pairs required to be shared in an entanglement-assisted one-way protocol. Our upper bounds also yield upper bounds on the approximate rank and related measures of the Identity matrix.

Previous studies have relied on existing question-answering benchmarks to evaluate the knowledge stored in large language models (LLMs). However, this approach has limitations regarding factual knowledge coverage, as it mostly focuses on generic domains which may overlap with the pretraining data. This paper proposes a framework to systematically assess the factual knowledge of LLMs by leveraging knowledge graphs (KGs). Our framework automatically generates a set of questions and expected answers from the facts stored in a given KG, and then evaluates the accuracy of LLMs in answering these questions. We systematically evaluate the state-of-the-art LLMs with KGs in generic and specific domains. The experiment shows that ChatGPT is consistently the top performer across all domains. We also find that LLMs performance depends on the instruction finetuning, domain and question complexity and is prone to adversarial context.

The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized models. Overparameterized models are excessively complex with respect to the size of the training dataset, which results in them perfectly fitting (i.e., interpolating) the training data, which is usually noisy. Such interpolation of noisy data is traditionally associated with detrimental overfitting, and yet a wide range of interpolating models -- from simple linear models to deep neural networks -- have recently been observed to generalize extremely well on fresh test data. Indeed, the recently discovered double descent phenomenon has revealed that highly overparameterized models often improve over the best underparameterized model in test performance. Understanding learning in this overparameterized regime requires new theory and foundational empirical studies, even for the simplest case of the linear model. The underpinnings of this understanding have been laid in very recent analyses of overparameterized linear regression and related statistical learning tasks, which resulted in precise analytic characterizations of double descent. This paper provides a succinct overview of this emerging theory of overparameterized ML (henceforth abbreviated as TOPML) that explains these recent findings through a statistical signal processing perspective. We emphasize the unique aspects that define the TOPML research area as a subfield of modern ML theory and outline interesting open questions that remain.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.