arXiv subjects

Yudong Chen

Publications and source records attributed to Yudong Chen.

At least 73 records · Page 4Linked to original sources

arXiv2023

Improved Feature Distillation via Projector Ensemble

In knowledge distillation, previous feature distillation methods mainly focus on the design of loss functions and the selection of the distilled layers, while the effect of the feature projector between the student and the teacher remains under-explored. In this paper, we first discuss a plausible mechanism of the projector with empirical evidence and then propose a new feature distillation method based on a projector ensemble for further performance improvement. We observe that the student network benefits from a projector even if the feature dimensions of the student and the teacher are the same. Training a student backbone without a projector can be considered as a multi-task learning process, namely achieving discriminative feature extraction for classification and feature matching between the student and the teacher for distillation at the same time. We hypothesize and empirically verify that without a projector, the student network tends to overfit the teacher's feature distributions despite having different architecture and weights initialization. This leads to degradation on the quality of the student's deep features that are eventually used in classification. Adding a projector, on the other hand, disentangles the two learning tasks and helps the student network to focus better on the main feature extraction task while still being able to utilize teacher features as a guidance through the projector. Motivated by the positive effect of the projector in feature distillation, we propose an ensemble of projectors to further improve the quality of student features. Experimental results on different datasets with a series of teacher-student pairs illustrate the effectiveness of the proposed method.

cs.CV↗

arXiv2022

Asymmetric Transfer Hashing with Adaptive Bipartite Graph Learning

Thanks to the efficient retrieval speed and low storage consumption, learning to hash has been widely used in visual retrieval tasks. However, existing hashing methods assume that the query and retrieval samples lie in homogeneous feature space within the same domain. As a result, they cannot be directly applied to heterogeneous cross-domain retrieval. In this paper, we propose a Generalized Image Transfer Retrieval (GITR) problem, which encounters two crucial bottlenecks: 1) the query and retrieval samples may come from different domains, leading to an inevitable {domain distribution gap}; 2) the features of the two domains may be heterogeneous or misaligned, bringing up an additional {feature gap}. To address the GITR problem, we propose an Asymmetric Transfer Hashing (ATH) framework with its unsupervised/semi-supervised/supervised realizations. Specifically, ATH characterizes the domain distribution gap by the discrepancy between two asymmetric hash functions, and minimizes the feature gap with the help of a novel adaptive bipartite graph constructed on cross-domain data. By jointly optimizing asymmetric hash functions and the bipartite graph, not only can knowledge transfer be achieved but information loss caused by feature alignment can also be avoided. Meanwhile, to alleviate negative transfer, the intrinsic geometrical structure of single-domain data is preserved by involving a domain affinity graph. Extensive experiments on both single-domain and cross-domain benchmarks under different GITR subtasks indicate the superiority of our ATH method in comparison with the state-of-the-art hashing methods.

cs.CV↗

arXiv2022

Algorithmic Regularization in Model-free Overparametrized Asymmetric Matrix Factorization

We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed matrix, where the global optima provably overfit. We show that vanilla gradient descent with small random initialization sequentially recovers the principal components of the observed matrix. Consequently, when equipped with proper early stopping, gradient descent produces the best low-rank approximation of the observed matrix without explicit regularization. We provide a sharp characterization of the relationship between the approximation error, iteration complexity, initialization size and stepsize. Our complexity bound is almost dimension-free and depends logarithmically on the approximation error, with significantly more lenient requirements on the stepsize and initialization compared to prior work. Our theoretical results provide accurate prediction for the behavior gradient descent, showing good agreement with numerical experiments.

cs.LG↗

arXiv2022

Reflectors to quantales

In this paper, we show that marked quantales have a reflection into quantales. To obtain the reflection we construct free quantales over marked quantales using appropriate lower sets. A marked quantale is a posemigroup in which certain admissible subsets are required to have joins, and multiplication distributes over these. Sometimes are the admissible subsets in question specified by means of a so-called selection function. A distinguishing feature of the study of marked quantales is that a small collection of axioms of an elementary nature allows one to do much that is traditional at the level of quantales. The axioms are sufficiently general to include as examples of marked quantales the classes of posemigroups, $σ$-quantales, prequantales and quantales. Furthermore, we discuss another reflection to quantales obtained by the injective hull of a posemigroup.

math.CT↗

arXiv2022

Extension of the bright high-harmonic photon energy range via nonadiabatic critical phase matching

Extending the photon energy range of bright high-harmonic generation to cover the entire soft X-ray region is important for many applications in science and technology. The concept of critical ionization fraction has been essential, because it dictates the maximum driving laser intensity that can be used while preserving bright harmonic emission. In this work, we reveal a second, nonadiabatic critical ionization fraction that substantially extends the maximum phase-matched high-harmonic photon energy, that arises due to strong reshaping of the intense driving laser field. We validate this understanding through a systematic comparison between experiment and theory, for a wide range of pulse durations and driving laser wavelengths. In particular, high harmonics driven by intense few-cycle pulses experience the most pronounced spectral reshaping, significantly extending the bright photon energy range. We also present an analytical model that predicts the spectral extension that can be achieved for different driving lasers. This reveals an increasing role of nonadiabatic critical phase matching when driven by few-cycle mid-infrared lasers. These findings are important for the development of high-brightness soft X-ray sources for applications in spectroscopy and imaging.

physics.optics↗

arXiv2021

Complete 2π Phase Control by Photonic Crystal Slabs

Photonic crystal slabs are the state of the art in studies for the light confinement, optical wave modulating and guiding, as well as nonlinear optical response. Previous studies have shown abundant real-world implementations of photonic crystals in planar optics, metamaterials, sensors, and lasers. Here, we report a novel full 2π phase control method in the reflected light beam over the interaction with a photonic crystal resonant mode, verified by the temporal coupled-mode analysis and S-parameter simulations. Enhanced by the asymmetric coupling with the output ports, the 2π phase shift can be achieved with the silicon photonics platforms such as Silicon-on-Silica and Silicon-on-Insulator heterostructures. Such photonic crystal phase control method provides a general guide in the design of phase-shift metamaterials, suggesting a wide range of applications in the field of sensing, spatial light modulation, and beam steering.

physics.optics↗

arXiv2021

Low-rank matrix recovery with non-quadratic loss: projected gradient method and regularity projection oracle

Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well conditioning over all low rank matrices. However, many interesting problems involve more general, non-quadratic losses, which do not satisfy such properties. For these problems, standard nonconvex approaches such as rank-constrained projected gradient descent (a.k.a. iterative hard thresholding) and Burer-Monteiro factorization could have poor empirical performance, and there is no satisfactory theory guaranteeing global and fast convergence for these algorithms. In this paper, we show that a critical component in provable low-rank recovery with non-quadratic loss is a regularity projection oracle. This oracle restricts iterates to low-rank matrices within an appropriate bounded set, over which the loss function is well behaved and satisfies a set of approximate RSC/RSM conditions. Accordingly, we analyze an (averaged) projected gradient method equipped with such an oracle, and prove that it converges globally and linearly. Our results apply to a wide range of non-quadratic low-rank estimation problems including one bit matrix sensing/completion, individualized rank aggregation, and more broadly generalized linear models with rank constraints.

stat.ML↗

arXiv2021

Exponential Bellman Equation and Improved Regret Bounds for Risk-Sensitive Reinforcement Learning

We study risk-sensitive reinforcement learning (RL) based on the entropic risk measure. Although existing works have established non-asymptotic regret guarantees for this problem, they leave open an exponential gap between the upper and lower bounds. We identify the deficiencies in existing algorithms and their analysis that result in such a gap. To remedy these deficiencies, we investigate a simple transformation of the risk-sensitive Bellman equations, which we call the exponential Bellman equation. The exponential Bellman equation inspires us to develop a novel analysis of Bellman backup procedures in risk-sensitive RL algorithms, and further motivates the design of a novel exploration mechanism. We show that these analytic and algorithmic innovations together lead to improved regret upper bounds over existing ones.

cs.LG↗

arXiv2021

Rank Overspecified Robust Matrix Recovery: Subgradient Method and Exact Recovery

We study the robust recovery of a low-rank matrix from sparsely and grossly corrupted Gaussian measurements, with no prior knowledge on the intrinsic rank. We consider the robust matrix factorization approach. We employ a robust $\ell_1$ loss function and deal with the challenge of the unknown rank by using an overspecified factored representation of the matrix variable. We then solve the associated nonconvex nonsmooth problem using a subgradient method with diminishing stepsizes. We show that under a regularity condition on the sensing matrices and corruption, which we call restricted direction preserving property (RDPP), even with rank overspecified, the subgradient method converges to the exact low-rank solution at a sublinear rate. Moreover, our result is more general in the sense that it automatically speeds up to a linear rate once the factor rank matches the unknown rank. On the other hand, we show that the RDPP condition holds under generic settings, such as Gaussian measurements under independent or adversarial sparse corruptions, where the result could be of independent interest. Both the exact recovery and the convergence rate of the proposed subgradient method are numerically verified in the overspecified regime. Moreover, our experiment further shows that our particular design of diminishing stepsize effectively prevents overfitting for robust recovery under overparameterized models, such as robust matrix sensing and learning robust deep image prior. This regularization effect is worth further investigation.

math.OC↗

arXiv2021

Hidden Integrality and Semi-random Robustness of SDP Relaxation for Sub-Gaussian Mixture Model

We consider the problem of estimating the discrete clustering structures under the Sub-Gaussian Mixture Model. Our main results establish a hidden integrality property of a semidefinite programming (SDP) relaxation for this problem: while the optimal solution to the SDP is not integer-valued in general, its estimation error can be upper bounded by that of an idealized integer program. The error of the integer program, and hence that of the SDP, are further shown to decay exponentially in the signal-to-noise ratio. In addition, we show that the SDP relaxation is robust under the semi-random setting in which an adversary can modify the data generated from the mixture model. In particular, we generalize the hidden integrality property to the semi-random model and thereby show that SDP achieves the optimal error bound in this setting. These results together highlight the "global-to-local" mechanism that drives the performance of the SDP relaxation. To the best of our knowledge, our result is the first exponentially decaying error bound for convex relaxations of mixture models. A corollary of our results shows that in certain regimes the SDP solutions are in fact integral and exact. More generally, our results establish sufficient conditions for the SDP to correctly recover the cluster memberships of $(1-δ)$ fraction of the points for any $δ\in(0,1)$. As a special case, we show that under the $d$-dimensional Stochastic Ball Model, SDP achieves non-trivial (sometimes exact) recovery when the center separation is as small as $\sqrt{1/d}$, which improves upon previous exact recovery results that require constant separation.

stat.ML↗

arXiv2021

Spatially homogeneous few-cycle compression of Yb lasers via all-solid-state free-space soliton management

The high power and variable repetition rate of Yb femtosecond lasers make them very attractive for ultrafast science. However, for capturing sub-200 fs dynamics, efficient, high-fidelity, and high-stability pulse compression techniques are essential. Spectral broadening using an all-solid-state free-space geometry is particularly attractive, as it is simple, robust, and low-cost. However, spatial and temporal losses caused by spatio-spectral inhomogeneities have been a major challenge to date, due to coupled space-time dynamics associated with unguided nonlinear propagation. In this work, we use all-solid-state free-space compressors to demonstrate compression of 170 fs pulses at a wavelength of 1030nm from a Yb:KGW laser to ~9.2 fs, with a highly spatially homogeneous mode. This is achieved by ensuring that the nonlinear beam propagation in periodic layered Kerr media occurs in soliton modes and confining the nonlinear phase through each material layer to less than 1.0 rad. A remarkable spatio-spectral homogeneity of ~0.87 can be realized, which yields a high efficiency of >50% for few-cycle compression. The universality of the method is demonstrated by implementing high-quality pulse compression under a wide range of laser conditions. The high spatiotemporal quality and the exceptional stability of the compressed pulses are further verified by high-harmonic generation. This work represents the highest efficiency and the best spatio-spectral quality ever achieved by an all-solid-state free-space pulse compressor for few-cycle-pulse generation.

physics.optics↗

arXiv2021

Deep Self-Adaptive Hashing for Image Retrieval

Hashing technology has been widely used in image retrieval due to its computational and storage efficiency. Recently, deep unsupervised hashing methods have attracted increasing attention due to the high cost of human annotations in the real world and the superiority of deep learning technology. However, most deep unsupervised hashing methods usually pre-compute a similarity matrix to model the pairwise relationship in the pre-trained feature space. Then this similarity matrix would be used to guide hash learning, in which most of the data pairs are treated equivalently. The above process is confronted with the following defects: 1) The pre-computed similarity matrix is inalterable and disconnected from the hash learning process, which cannot explore the underlying semantic information. 2) The informative data pairs may be buried by the large number of less-informative data pairs. To solve the aforementioned problems, we propose a Deep Self-Adaptive Hashing (DSAH) model to adaptively capture the semantic information with two special designs: Adaptive Neighbor Discovery (AND) and Pairwise Information Content (PIC). Firstly, we adopt the AND to initially construct a neighborhood-based similarity matrix, and then refine this initial similarity matrix with a novel update strategy to further investigate the semantic structure behind the learned representation. Secondly, we measure the priorities of data pairs with PIC and assign adaptive weights to them, which is relies on the assumption that more dissimilar data pairs contain more discriminative information for hash learning. Extensive experiments on several datasets demonstrate that the above two technologies facilitate the deep hashing model to achieve superior performance.

cs.CV↗

arXiv2021

Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond

Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of work on random features has grown rapidly, and hence it is desirable to have a comprehensive overview on this topic explaining the connections among various algorithms and theoretical results. In this survey, we systematically review the work on random features from the past ten years. First, the motivations, characteristics and contributions of representative random features based algorithms are summarized according to their sampling schemes, learning procedures, variance reduction properties and how they exploit training data. Second, we review theoretical results that center around the following key question: how many random features are needed to ensure a high approximation quality or no loss in the empirical/expected risks of the learned estimator. Third, we provide a comprehensive evaluation of popular random features based algorithms on several large-scale benchmark datasets and discuss their approximation quality and prediction performance for classification. Last, we discuss the relationship between random features and modern over-parameterized deep neural networks (DNNs), including the use of high dimensional random features in the analysis of DNNs as well as the gaps between current theoretical and empirical results. This survey may serve as a gentle introduction to this topic, and as a users' guide for practitioners interested in applying the representative algorithms and understanding theoretical results under various technical assumptions. We hope that this survey will facilitate discussion on the open problems in this topic, and more importantly, shed light on future research directions.

stat.ML↗

arXiv2021

Towards a Unified Quadrature Framework for Large-Scale Kernel Machines

In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels, are fully symmetric, we leverage deterministic fully symmetric interpolatory rules to efficiently compute quadrature nodes and associated weights for kernel approximation. The developed interpolatory rules are able to reduce the number of needed nodes while retaining a high approximation accuracy. Further, we randomize the above deterministic rules by the classical Monte-Carlo sampling and control variates techniques with two merits: 1) The proposed stochastic rules make the dimension of the feature mapping flexibly varying, such that we can control the discrepancy between the original and approximate kernels by tuning the dimnension. 2) Our stochastic rules have nice statistical properties of unbiasedness and variance reduction with fast convergence rate. In addition, we elucidate the relationship between our deterministic/stochastic interpolatory rules and current quadrature rules for kernel approximation, including the sparse grids quadrature and stochastic spherical-radial rules, thereby unifying these methods under our framework. Experimental results on several benchmark datasets show that our methods compare favorably with other representative kernel approximation based methods.

cs.LG↗

arXiv2021

A Survey on Curriculum Learning

Curriculum learning (CL) is a training strategy that trains a machine learning model from easier data to harder data, which imitates the meaningful learning order in human curricula. As an easy-to-use plug-in, the CL strategy has demonstrated its power in improving the generalization capacity and convergence rate of various models in a wide range of scenarios such as computer vision and natural language processing etc. In this survey article, we comprehensively review CL from various aspects including motivations, definitions, theories, and applications. We discuss works on curriculum learning within a general CL framework, elaborating on how to design a manually predefined curriculum or an automatic curriculum. In particular, we summarize existing CL designs based on the general framework of Difficulty Measurer+Training Scheduler and further categorize the methodologies for automatic CL into four groups, i.e., Self-paced Learning, Transfer Teacher, RL Teacher, and Other Automatic CL. We also analyze principles to select different CL designs that may benefit practical applications. Finally, we present our insights on the relationships connecting CL and other machine learning concepts including transfer learning, meta-learning, continual learning and active learning, etc., then point out challenges in CL as well as potential future research directions deserving further investigations.

cs.LG↗

arXiv2021

Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates

In large-scale distributed learning, security issues have become increasingly important. Particularly in a decentralized environment, some computing units may behave abnormally, or even exhibit Byzantine failures -- arbitrary and potentially adversarial behavior. In this paper, we develop distributed learning algorithms that are provably robust against such failures, with a focus on achieving optimal statistical performance. A main result of this work is a sharp analysis of two robust distributed gradient descent algorithms based on median and trimmed mean operations, respectively. We prove statistical error rates for three kinds of population loss functions: strongly convex, non-strongly convex, and smooth non-convex. In particular, these algorithms are shown to achieve order-optimal statistical error rates for strongly convex losses. To achieve better communication efficiency, we further propose a median-based distributed algorithm that is provably robust, and uses only one communication round. For strongly convex quadratic loss, we show that this algorithm achieves the same optimal error rate as the robust distributed gradient descent algorithms.

cs.LG↗

arXiv2021

MetaDelta: A Meta-Learning System for Few-shot Image Classification

Meta-learning aims at learning quickly on novel tasks with limited data by transferring generic experience learned from previous tasks. Naturally, few-shot learning has been one of the most popular applications for meta-learning. However, existing meta-learning algorithms rarely consider the time and resource efficiency or the generalization capacity for unknown datasets, which limits their applicability in real-world scenarios. In this paper, we propose MetaDelta, a novel practical meta-learning system for the few-shot image classification. MetaDelta consists of two core components: i) multiple meta-learners supervised by a central controller to ensure efficiency, and ii) a meta-ensemble module in charge of integrated inference and better generalization. In particular, each meta-learner in MetaDelta is composed of a unique pretrained encoder fine-tuned by batch training and parameter-free decoder used for prediction. MetaDelta ranks first in the final phase in the AAAI 2021 MetaDL Challenge\footnote{https://competitions.codalab.org/competitions/26638}, demonstrating the advantages of our proposed system. The codes are publicly available at https://github.com/Frozenmad/MetaDelta.

cs.CV↗

arXiv2020

High-dimensional, multiscale online changepoint detection

We introduce a new method for high-dimensional, online changepoint detection in settings where a $p$-variate Gaussian data stream may undergo a change in mean. The procedure works by performing likelihood ratio tests against simple alternatives of different scales in each coordinate, and then aggregating test statistics across scales and coordinates. The algorithm is online in the sense that both its storage requirements and worst-case computational complexity per new observation are independent of the number of previous observations; in practice, it may even be significantly faster than this. We prove that the patience, or average run length under the null, of our procedure is at least at the desired nominal level, and provide guarantees on its response delay under the alternative that depend on the sparsity of the vector of mean change. Simulations confirm the practical effectiveness of our proposal, which is implemented in the R package 'ocd', and we also demonstrate its utility on a seismology data set.

stat.ME↗