We rigorously study the joint evolution of training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in two canonical classification tasks for multi-class high-dimensional mixtures and either 1 or 2-layer neural networks, the SGD trajectory rapidly aligns with emerging low-rank outlier eigenspaces of the Hessian and gradient matrices. Moreover, in multi-layer settings this alignment occurs per layer, with the final layer's outlier eigenspace evolving over the course of training, and exhibiting rank deficiency when the SGD converges to sub-optimal classifiers. This establishes some of the rich predictions that have arisen from extensive numerical studies in the last decade about the spectra of Hessian and information matrices over the course of training in overparametrized networks.
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Cloth-changing person reidentification (ReID) is a newly emerging research topic that aims to retrieve pedestrians whose clothes are changed. Since the human appearance with different clothes exhibits large variations, it is very difficult for existing approaches to extract discriminative and robust feature representations. Current works mainly focus on body shape or contour sketches, but the human semantic information and the potential consistency of pedestrian features before and after changing clothes are not fully explored or are ignored. To solve these issues, in this work, a novel semantic-aware attention and visual shielding network for cloth-changing person ReID (abbreviated as SAVS) is proposed where the key idea is to shield clues related to the appearance of clothes and only focus on visual semantic information that is not sensitive to view/posture changes. Specifically, a visual semantic encoder is first employed to locate the human body and clothing regions based on human semantic segmentation information. Then, a human semantic attention module (HSA) is proposed to highlight the human semantic information and reweight the visual feature map. In addition, a visual clothes shielding module (VCS) is also designed to extract a more robust feature representation for the cloth-changing task by covering the clothing regions and focusing the model on the visual semantic information unrelated to the clothes. Most importantly, these two modules are jointly explored in an end-to-end unified framework. Extensive experiments demonstrate that the proposed method can significantly outperform state-of-the-art methods, and more robust features can be extracted for cloth-changing persons. Compared with FSAM (published in CVPR 2021), this method can achieve improvements of 32.7% (16.5%) and 14.9% (-) on the LTCC and PRCC datasets in terms of mAP (rank-1), respectively.
We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are only achieved by non-autonomous methods via open-loop damping (e.g., Nesterov's algorithm), we show that our system is the first one featuring a closed-loop damping while exhibiting a rate arbitrarily close to the optimal one. We do so by coupling the damping and the speed of convergence of the system via a well-chosen Lyapunov function. We then derive a practical first-order algorithm called LYDIA by discretizing our system, and present numerical experiments supporting our theoretical findings.
Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics during an epidemic. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to change in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and provide an estimate of the model state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the COVID-19 Italian pandemic. Our results show that the split implementation of PINNs outperforms the standard approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%).
Urban traffic congestion remains a pressing challenge in our rapidly expanding cities, despite the abundance of available data and the efforts of policymakers. By leveraging behavioral system theory and data-driven control, this paper exploits the DeePC algorithm in the context of urban traffic control performed via dynamic traffic lights. To validate our approach, we consider a high-fidelity case study using the state-of-the-art simulation software package Simulation of Urban MObility (SUMO). Preliminary results indicate that DeePC outperforms existing approaches across various key metrics, including travel time and CO$_2$ emissions, demonstrating its potential for effective traffic management
We introduce Resilient Multiple Choice Learning (rMCL), an extension of the MCL approach for conditional distribution estimation in regression settings where multiple targets may be sampled for each training input. Multiple Choice Learning is a simple framework to tackle multimodal density estimation, using the Winner-Takes-All (WTA) loss for a set of hypotheses. In regression settings, the existing MCL variants focus on merging the hypotheses, thereby eventually sacrificing the diversity of the predictions. In contrast, our method relies on a novel learned scoring scheme underpinned by a mathematical framework based on Voronoi tessellations of the output space, from which we can derive a probabilistic interpretation. After empirically validating rMCL with experiments on synthetic data, we further assess its merits on the sound source localization problem, demonstrating its practical usefulness and the relevance of its interpretation.
This work tackles the task of extractive text summarization in a limited labeled data scenario using a semi-supervised approach. Specifically, we propose a prompt-based pseudolabel selection strategy using GPT-4. We evaluate our method on three text summarization datasets: TweetSumm, WikiHow, and ArXiv/PubMed. Our experiments show that by using an LLM to evaluate and generate pseudolabels, we can improve the ROUGE-1 by 10-20\% on the different datasets, which is akin to enhancing pretrained models. We also show that such a method needs a smaller pool of unlabeled examples to perform better.
Tracking the fundamental frequency (f0) of a monophonic instrumental performance is effectively a solved problem with several solutions achieving 99% accuracy. However, the related task of automatic music transcription requires a further processing step to segment an f0 contour into discrete notes. This sub-task of note segmentation is necessary to enable a range of applications including musicological analysis and symbolic music generation. Building on CREPE, a state-of-the-art monophonic pitch tracking solution based on a simple neural network, we propose a simple and effective method for post-processing CREPE's output to achieve monophonic note segmentation. The proposed method demonstrates state-of-the-art results on two challenging datasets of monophonic instrumental music. Our approach also gives a 97% reduction in the total number of parameters used when compared with other deep learning based methods.
This work presents an abstract framework for the design, implementation, and analysis of the multiscale spectral generalized finite element method (MS-GFEM), a particular numerical multiscale method originally proposed in [I. Babuska and R. Lipton, Multiscale Model.\;\,Simul., 9 (2011), pp.~373--406]. MS-GFEM is a partition of unity method employing optimal local approximation spaces constructed from local spectral problems. We establish a general local approximation theory demonstrating exponential convergence with respect to local degrees of freedom under certain assumptions, with explicit dependence on key problem parameters. Our framework applies to a broad class of multiscale PDEs with $L^{\infty}$-coefficients in both continuous and discrete, finite element settings, including highly indefinite problems (convection-dominated diffusion, as well as the high-frequency Helmholtz, Maxwell and elastic wave equations with impedance boundary conditions), and higher-order problems. Notably, we prove a local convergence rate of $O(e^{-cn^{1/d}})$ for MS-GFEM for all these problems, improving upon the $O(e^{-cn^{1/(d+1)}})$ rate shown by Babuska and Lipton. Moreover, based on the abstract local approximation theory for MS-GFEM, we establish a unified framework for showing low-rank approximations to multiscale PDEs. This framework applies to the aforementioned problems, proving that the associated Green's functions admit an $O(|\log\epsilon|^{d})$-term separable approximation on well-separated domains with error $\epsilon>0$. Our analysis improves and generalizes the result in [M. Bebendorf and W. Hackbusch, Numerische Mathematik, 95 (2003), pp.~1-28] where an $O(|\log\epsilon|^{d+1})$-term separable approximation was proved for Poisson-type problems.
In the past few years, the emergence of pre-training models has brought uni-modal fields such as computer vision (CV) and natural language processing (NLP) to a new era. Substantial works have shown they are beneficial for downstream uni-modal tasks and avoid training a new model from scratch. So can such pre-trained models be applied to multi-modal tasks? Researchers have explored this problem and made significant progress. This paper surveys recent advances and new frontiers in vision-language pre-training (VLP), including image-text and video-text pre-training. To give readers a better overall grasp of VLP, we first review its recent advances from five aspects: feature extraction, model architecture, pre-training objectives, pre-training datasets, and downstream tasks. Then, we summarize the specific VLP models in detail. Finally, we discuss the new frontiers in VLP. To the best of our knowledge, this is the first survey on VLP. We hope that this survey can shed light on future research in the VLP field.
Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-viewcontrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, two extensions of HeCo are designed to generate harder negative samples with high quality, which further boosts the performance of HeCo. Extensive experiments conducted on a variety of real-world networks show the superior performance of the proposed methods over the state-of-the-arts.
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