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We prove impossibility results for adaptivity in non-smooth stochastic convex optimization. Given a set of problem parameters we wish to adapt to, we define a "price of adaptivity" (PoA) that, roughly speaking, measures the multiplicative increase in suboptimality due to uncertainty in these parameters. When the initial distance to the optimum is unknown but a gradient norm bound is known, we show that the PoA is at least logarithmic for expected suboptimality, and double-logarithmic for median suboptimality. When there is uncertainty in both distance and gradient norm, we show that the PoA must be polynomial in the level of uncertainty. Our lower bounds nearly match existing upper bounds, and establish that there is no parameter-free lunch.

Anomaly detection is a critical challenge across various research domains, aiming to identify instances that deviate from normal data distributions. This paper explores the application of Generative Adversarial Networks (GANs) in fraud detection, comparing their advantages with traditional methods. GANs, a type of Artificial Neural Network (ANN), have shown promise in modeling complex data distributions, making them effective tools for anomaly detection. The paper systematically describes the principles of GANs and their derivative models, emphasizing their application in fraud detection across different datasets. And by building a collection of adversarial verification graphs, we will effectively prevent fraud caused by bots or automated systems and ensure that the users in the transaction are real. The objective of the experiment is to design and implement a fake face verification code and fraud detection system based on Generative Adversarial network (GANs) algorithm to enhance the security of the transaction process.The study demonstrates the potential of GANs in enhancing transaction security through deep learning techniques.

Disentangled representation learning strives to extract the intrinsic factors within observed data. Factorizing these representations in an unsupervised manner is notably challenging and usually requires tailored loss functions or specific structural designs. In this paper, we introduce a new perspective and framework, demonstrating that diffusion models with cross-attention can serve as a powerful inductive bias to facilitate the learning of disentangled representations. We propose to encode an image to a set of concept tokens and treat them as the condition of the latent diffusion for image reconstruction, where cross-attention over the concept tokens is used to bridge the interaction between the encoder and diffusion. Without any additional regularization, this framework achieves superior disentanglement performance on the benchmark datasets, surpassing all previous methods with intricate designs. We have conducted comprehensive ablation studies and visualization analysis, shedding light on the functioning of this model. This is the first work to reveal the potent disentanglement capability of diffusion models with cross-attention, requiring no complex designs. We anticipate that our findings will inspire more investigation on exploring diffusion for disentangled representation learning towards more sophisticated data analysis and understanding.

We provide a quantitative assessment of welfare in the classical model of risk-sharing and exchange under uncertainty. We prove three kinds of results. First, that in an equilibrium allocation, the scope for improving individual welfare by a given margin (an $\varepsilon$-improvement) vanishes as the number of states increases. Second, that the scope for a change in aggregate resources that may be distributed to enhance individual welfare by a given margin also vanishes. Equivalently: in an inefficient allocation, for a given level of resource sub-optimality (as measured by the coefficient of resource under-utilization), the possibilities for enhancing welfare by perturbing aggregate resources decrease exponentially to zero with the number of states. Finally, we consider efficient risk-sharing in standard models of uncertainty aversion with multiple priors, and show that, in an inefficient allocation, certain sets of priors shrink with the size of the state space.

The purpose of this paper is to develop a practical strategy to accelerate Newton's method in the vicinity of singular points. We do this by developing an adaptive safeguarding scheme, which we call gamma-safeguarding, that one can apply to Anderson accelerated Newton's method when solving problems near singular points. The key features of adaptive gamma-safeguarding are that it converges locally for singular problems, and it can detect nonsingular problems, in which case the Newton-Anderson iterates are scaled towards a standard Newton step. This leads to faster local convergence compared to both Newton's method and Newton-Anderson without safeguarding, at no additional computational cost. We demonstrate three strategies one can use when implementing Newton-Anderson and gamma-safeguarded Newton-Anderson to solve parameter-dependent problems near singular points. For our benchmark problems, we take two parameter-dependent incompressible flow systems: flow in a channel and Rayleigh-Benard convection.

Understanding causality helps to structure interventions to achieve specific goals and enables predictions under interventions. With the growing importance of learning causal relationships, causal discovery tasks have transitioned from using traditional methods to infer potential causal structures from observational data to the field of pattern recognition involved in deep learning. The rapid accumulation of massive data promotes the emergence of causal search methods with brilliant scalability. Existing summaries of causal discovery methods mainly focus on traditional methods based on constraints, scores and FCMs, there is a lack of perfect sorting and elaboration for deep learning-based methods, also lacking some considers and exploration of causal discovery methods from the perspective of variable paradigms. Therefore, we divide the possible causal discovery tasks into three types according to the variable paradigm and give the definitions of the three tasks respectively, define and instantiate the relevant datasets for each task and the final causal model constructed at the same time, then reviews the main existing causal discovery methods for different tasks. Finally, we propose some roadmaps from different perspectives for the current research gaps in the field of causal discovery and point out future research directions.

Deep neural models in recent years have been successful in almost every field, including extremely complex problem statements. However, these models are huge in size, with millions (and even billions) of parameters, thus demanding more heavy computation power and failing to be deployed on edge devices. Besides, the performance boost is highly dependent on redundant labeled data. To achieve faster speeds and to handle the problems caused by the lack of data, knowledge distillation (KD) has been proposed to transfer information learned from one model to another. KD is often characterized by the so-called `Student-Teacher' (S-T) learning framework and has been broadly applied in model compression and knowledge transfer. This paper is about KD and S-T learning, which are being actively studied in recent years. First, we aim to provide explanations of what KD is and how/why it works. Then, we provide a comprehensive survey on the recent progress of KD methods together with S-T frameworks typically for vision tasks. In general, we consider some fundamental questions that have been driving this research area and thoroughly generalize the research progress and technical details. Additionally, we systematically analyze the research status of KD in vision applications. Finally, we discuss the potentials and open challenges of existing methods and prospect the future directions of KD and S-T learning.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

We examine the problem of question answering over knowledge graphs, focusing on simple questions that can be answered by the lookup of a single fact. Adopting a straightforward decomposition of the problem into entity detection, entity linking, relation prediction, and evidence combination, we explore simple yet strong baselines. On the popular SimpleQuestions dataset, we find that basic LSTMs and GRUs plus a few heuristics yield accuracies that approach the state of the art, and techniques that do not use neural networks also perform reasonably well. These results show that gains from sophisticated deep learning techniques proposed in the literature are quite modest and that some previous models exhibit unnecessary complexity.

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.