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Analysis of signals with oscillatory modes with crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this problem is lifting the 2-dimensional time-frequency representation to a 3-dimensional representation, called time-frequency-chirp rate (TFC) representation, by adding one extra chirp rate parameter so that crossover frequencies are disentangles in higher dimension. The chirplet transform is an algorithm for this lifting idea. However, in practice we found that it has a stronger "blurring" effect in the chirp rate axis, which limits its application in real world data. Moreover, to our knowledge, we have limited mathematical understanding of the chirplet transform in the literature. Motivated by real world data challenges, in this paper, we propose the synchrosqueezed chirplet transform (SCT) that gives a concentrated TFC representation that the contrast is enhanced so that one can distinguish different modes even with crossover instantaneous frequencies. We also analyze chirplet transform and provide theoretical guarantee of SCT.

Demonstrating quantum advantage requires experimental implementation of a computational task that is hard to achieve using state-of-the-art classical systems. One approach is to perform sampling from a probability distribution associated with a class of highly entangled many-body wavefunctions. It has been suggested that this approach can be certified with the Linear Cross-Entropy Benchmark (XEB). We critically examine this notion. First, in a "benign" setting where an honest implementation of noisy quantum circuits is assumed, we characterize the conditions under which the XEB approximates the fidelity. Second, in an "adversarial" setting where all possible classical algorithms are considered for comparison, we show that achieving relatively high XEB values does not imply faithful simulation of quantum dynamics. We present an efficient classical algorithm that, with 1 GPU within 2s, yields high XEB values, namely 2-12% of those obtained in experiments. By identifying and exploiting several vulnerabilities of the XEB, we achieve high XEB values without full simulation of quantum circuits. Remarkably, our algorithm features better scaling with the system size than noisy quantum devices for commonly studied random circuit ensembles. To quantitatively explain the success of our algorithm and the limitations of the XEB, we use a theoretical framework in which the average XEB and fidelity are mapped to statistical models. We illustrate the relation between the XEB and the fidelity for quantum circuits in various architectures, with different gate choices, and in the presence of noise. Our results show that XEB's utility as a proxy for fidelity hinges on several conditions, which must be checked in the benign setting but cannot be assumed in the adversarial setting. Thus, the XEB alone has limited utility as a benchmark for quantum advantage. We discuss ways to overcome these limitations.

In signal processing, several applications involve the recovery of a function given noisy modulo samples. The setting considered in this paper is that the samples corrupted by an additive Gaussian noise are wrapped due to the modulo operation. Typical examples of this problem arise in phase unwrapping problems or in the context of self-reset analog to digital converters. We consider a fixed design setting where the modulo samples are given on a regular grid. Then, a three stage recovery strategy is proposed to recover the ground truth signal up to a global integer shift. The first stage denoises the modulo samples by using local polynomial estimators. In the second stage, an unwrapping algorithm is applied to the denoised modulo samples on the grid. Finally, a spline based quasi-interpolant operator is used to yield an estimate of the ground truth function up to a global integer shift. For a function in H\"older class, uniform error rates are given for recovery performance with high probability. This extends recent results obtained by Fanuel and Tyagi for Lipschitz smooth functions wherein $k$NN regression was used in the denoising step.

We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by infinitely divisible kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite matrices that are obtained by evaluating the kernel over pairs of samples. The new measure shares similar properties to Jensen-Shannon divergence. Convergence of the proposed estimators follows from concentration results based on the difference between the ordered spectrum of the Gram matrices and the integral operators associated with the population quantities. The proposed measure of divergence avoids the estimation of the probability distribution underlying the data. Numerical experiments involving comparing distributions and applications to sampling unbalanced data for classification show that the proposed divergence can achieve state of the art results.

Time series modeling has attracted extensive research efforts; however, achieving both reliable efficiency and interpretability from a unified model still remains a challenging problem. Among the literature, shapelets offer interpretable and explanatory insights in the classification tasks, while most existing works ignore the differing representative power at different time slices, as well as (more importantly) the evolution pattern of shapelets. In this paper, we propose to extract time-aware shapelets by designing a two-level timing factor. Moreover, we define and construct the shapelet evolution graph, which captures how shapelets evolve over time and can be incorporated into the time series embeddings by graph embedding algorithms. To validate whether the representations obtained in this way can be applied effectively in various scenarios, we conduct experiments based on three public time series datasets, and two real-world datasets from different domains. Experimental results clearly show the improvements achieved by our approach compared with 17 state-of-the-art baselines.

Search in social networks such as Facebook poses different challenges than in classical web search: besides the query text, it is important to take into account the searcher's context to provide relevant results. Their social graph is an integral part of this context and is a unique aspect of Facebook search. While embedding-based retrieval (EBR) has been applied in eb search engines for years, Facebook search was still mainly based on a Boolean matching model. In this paper, we discuss the techniques for applying EBR to a Facebook Search system. We introduce the unified embedding framework developed to model semantic embeddings for personalized search, and the system to serve embedding-based retrieval in a typical search system based on an inverted index. We discuss various tricks and experiences on end-to-end optimization of the whole system, including ANN parameter tuning and full-stack optimization. Finally, we present our progress on two selected advanced topics about modeling. We evaluated EBR on verticals for Facebook Search with significant metrics gains observed in online A/B experiments. We believe this paper will provide useful insights and experiences to help people on developing embedding-based retrieval systems in search engines.

Tacotron-based text-to-speech (TTS) systems directly synthesize speech from text input. Such frameworks typically consist of a feature prediction network that maps character sequences to frequency-domain acoustic features, followed by a waveform reconstruction algorithm or a neural vocoder that generates the time-domain waveform from acoustic features. As the loss function is usually calculated only for frequency-domain acoustic features, that doesn't directly control the quality of the generated time-domain waveform. To address this problem, we propose a new training scheme for Tacotron-based TTS, referred to as WaveTTS, that has 2 loss functions: 1) time-domain loss, denoted as the waveform loss, that measures the distortion between the natural and generated waveform; and 2) frequency-domain loss, that measures the Mel-scale acoustic feature loss between the natural and generated acoustic features. WaveTTS ensures both the quality of the acoustic features and the resulting speech waveform. To our best knowledge, this is the first implementation of Tacotron with joint time-frequency domain loss. Experimental results show that the proposed framework outperforms the baselines and achieves high-quality synthesized speech.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

In this paper we address the problem of learning robust cross-domain representations for sketch-based image retrieval (SBIR). While most SBIR approaches focus on extracting low- and mid-level descriptors for direct feature matching, recent works have shown the benefit of learning coupled feature representations to describe data from two related sources. However, cross-domain representation learning methods are typically cast into non-convex minimization problems that are difficult to optimize, leading to unsatisfactory performance. Inspired by self-paced learning, a learning methodology designed to overcome convergence issues related to local optima by exploiting the samples in a meaningful order (i.e. easy to hard), we introduce the cross-paced partial curriculum learning (CPPCL) framework. Compared with existing self-paced learning methods which only consider a single modality and cannot deal with prior knowledge, CPPCL is specifically designed to assess the learning pace by jointly handling data from dual sources and modality-specific prior information provided in the form of partial curricula. Additionally, thanks to the learned dictionaries, we demonstrate that the proposed CPPCL embeds robust coupled representations for SBIR. Our approach is extensively evaluated on four publicly available datasets (i.e. CUFS, Flickr15K, QueenMary SBIR and TU-Berlin Extension datasets), showing superior performance over competing SBIR methods.

Content based video retrieval is an approach for facilitating the searching and browsing of large image collections over World Wide Web. In this approach, video analysis is conducted on low level visual properties extracted from video frame. We believed that in order to create an effective video retrieval system, visual perception must be taken into account. We conjectured that a technique which employs multiple features for indexing and retrieval would be more effective in the discrimination and search tasks of videos. In order to validate this claim, content based indexing and retrieval systems were implemented using color histogram, various texture features and other approaches. Videos were stored in Oracle 9i Database and a user study measured correctness of response.