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We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in $\mathbb{R}^{d(n)}$, whose $\nu$-th moments exist for ${\nu > 2}$, and provide tight bounds on the error of approximating both statistics by a quadratic form of Gaussians. In the case ${\nu=3}$, the error of approximation is $\Theta(n^{-1/12})$. The proof adapts a result of Huang, Austern and Orbanz [12] to U- and V-statistics. The lower bound for U-statistics is a simple example of the concept of variance domination used in [12].

Speech foundation models, trained on vast datasets, have opened unique opportunities in addressing challenging low-resource speech understanding, such as child speech. In this work, we explore the capabilities of speech foundation models on child-adult speaker diarization. We show that exemplary foundation models can achieve 39.5% and 62.3% relative reductions in Diarization Error Rate and Speaker Confusion Rate, respectively, compared to previous speaker diarization methods. In addition, we benchmark and evaluate the speaker diarization results of the speech foundation models with varying the input audio window size, speaker demographics, and training data ratio. Our results highlight promising pathways for understanding and adopting speech foundation models to facilitate child speech understanding., Comment: Interspeech 2024

We establish an invariance principle for polynomial functions of $n$ independent high-dimensional random vectors, and also show that the obtained rates are nearly optimal. Both the dimension of the vectors and the degree of the polynomial are permitted to grow with $n$. Specifically, we obtain a finite sample upper bound for the error of approximation by a polynomial of Gaussians, measured in Kolmogorov distance, and extend it to functions that are approximately polynomial in a mean squared error sense. We give a corresponding lower bound that shows the invariance principle holds up to polynomial degree $o(\log n)$. The proof is constructive and adapts an asymmetrisation argument due to V. V. Senatov. As applications, we obtain a higher-order delta method with possibly non-Gaussian limits, and generalise a number of known results on high-dimensional and infinite-order U-statistics, and on fluctuations of subgraph counts.

Precise arbitrary trajectory tracking for quadrotors is challenging due to unknown nonlinear dynamics, trajectory infeasibility, and actuation limits. To tackle these challenges, we present Deep Adaptive Trajectory Tracking (DATT), a learning-based approach that can precisely track arbitrary, potentially infeasible trajectories in the presence of large disturbances in the real world. DATT builds on a novel feedforward-feedback-adaptive control structure trained in simulation using reinforcement learning. When deployed on real hardware, DATT is augmented with a disturbance estimator using L1 adaptive control in closed-loop, without any fine-tuning. DATT significantly outperforms competitive adaptive nonlinear and model predictive controllers for both feasible smooth and infeasible trajectories in unsteady wind fields, including challenging scenarios where baselines completely fail. Moreover, DATT can efficiently run online with an inference time less than 3.2 ms, less than 1/4 of the adaptive nonlinear model predictive control baseline

A major challenge in robotics is to design robust policies which enable complex and agile behaviors in the real world. On one end of the spectrum, we have model-free reinforcement learning (MFRL), which is incredibly flexible and general but often results in brittle policies. In contrast, model predictive control (MPC) continually re-plans at each time step to remain robust to perturbations and model inaccuracies. However, despite its real-world successes, MPC often under-performs the optimal strategy. This is due to model quality, myopic behavior from short planning horizons, and approximations due to computational constraints. And even with a perfect model and enough compute, MPC can get stuck in bad local optima, depending heavily on the quality of the optimization algorithm. To this end, we propose Deep Model Predictive Optimization (DMPO), which learns the inner-loop of an MPC optimization algorithm directly via experience, specifically tailored to the needs of the control problem. We evaluate DMPO on a real quadrotor agile trajectory tracking task, on which it improves performance over a baseline MPC algorithm for a given computational budget. It can outperform the best MPC algorithm by up to 27% with fewer samples and an end-to-end policy trained with MFRL by 19%. Moreover, because DMPO requires fewer samples, it can also achieve these benefits with 4.3X less memory. When we subject the quadrotor to turbulent wind fields with an attached drag plate, DMPO can adapt zero-shot while still outperforming all baselines. Additional results can be found at https://tinyurl.com/mr2ywmnw., Comment: Main paper is 6 pages with 4 figures and 1 table. Code available at: https://github.com/jisacks/dmpo

Interactions involving children span a wide range of important domains from learning to clinical diagnostic and therapeutic contexts. Automated analyses of such interactions are motivated by the need to seek accurate insights and offer scale and robustness across diverse and wide-ranging conditions. Identifying the speech segments belonging to the child is a critical step in such modeling. Conventional child-adult speaker classification typically relies on audio modeling approaches, overlooking visual signals that convey speech articulation information, such as lip motion. Building on the foundation of an audio-only child-adult speaker classification pipeline, we propose incorporating visual cues through active speaker detection and visual processing models. Our framework involves video pre-processing, utterance-level child-adult speaker detection, and late fusion of modality-specific predictions. We demonstrate from extensive experiments that a visually aided classification pipeline enhances the accuracy and robustness of the classification. We show relative improvements of 2.38% and 3.97% in F1 macro score when one face and two faces are visible, respectively., Comment: In review for ICASSP 2024, 5 pages

The architecture of a deep neural network is defined explicitly in terms of the number of layers, the width of each layer and the general network topology. Existing optimisation frameworks neglect this information in favour of implicit architectural information (e.g. second-order methods) or architecture-agnostic distance functions (e.g. mirror descent). Meanwhile, the most popular optimiser in practice, Adam, is based on heuristics. This paper builds a new framework for deriving optimisation algorithms that explicitly leverage neural architecture. The theory extends mirror descent to non-convex composite objective functions: the idea is to transform a Bregman divergence to account for the non-linear structure of neural architecture. Working through the details for deep fully-connected networks yields automatic gradient descent: a first-order optimiser without any hyperparameters. Automatic gradient descent trains both fully-connected and convolutional networks out-of-the-box and at ImageNet scale. A PyTorch implementation is available at https://github.com/jxbz/agd and also in Appendix B. Overall, the paper supplies a rigorous theoretical foundation for a next-generation of architecture-dependent optimisers that work automatically and without hyperparameters.

In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify existing conditions as well as present new conditions that are sufficient to guarantee convergence. The first half of the paper focuses on the case where a Minty solution exists (also known as Minty condition), which is a common assumption in the recent developments for non-monotone VI. The second half explores alternative sufficient conditions that are different from the existing ones such as monotonicity or Minty condition, using an algorithm-based approach. Through examples and convergence analysis, we show that these conditions are capable of characterizing different classes of VI problems where the algorithms are guaranteed to converge., Comment: 29 pages

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the non-degenerate Gaussian limit to the degenerate limit, regardless of its degeneracy and depending only on a moment ratio. A surprising consequence is that a non-degenerate U-statistic in high dimensions can have a non-Gaussian limit with a larger variance and asymmetric distribution. Our bounds are valid for any finite $n$ and $d$, independent of individual eigenvalues of the underlying function, and dimension-independent under a mild assumption. As an application, we apply our theory to two popular kernel-based distribution tests, MMD and KSD, whose high-dimensional performance has been challenging to study. In a simple empirical setting, our results correctly predict how the test power at a fixed threshold scales with $d$ and the bandwidth., Comment: COLT camera-ready version

In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum monotone VI, where the operator consists of the sum of finitely many monotone VI mappings and the sum of finitely many monotone gradient mappings. We study the gradient complexities of the proposed algorithms under the settings when the sum of VI mappings is either strongly monotone or merely monotone. Furthermore, we consider the case when each of the VI mapping and gradient mapping is only accessible via noisy stochastic estimators and establish the sample gradient complexity. We demonstrate the application of the proposed algorithms for solving finite-sum convex optimization with finite-sum inequality constraints and develop a zeroth-order approach when only noisy and biased samples of objective/constraint function values are available., Comment: 45 pages, 4 figures

In this paper, we propose a general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient method (ARE). The first step of ARE solves a VI subproblem with an approximation operator satisfying a $p^{th}$-order Lipschitz bound with respect to the original mapping, further coupled with the gradient of a $(p+1)^{th}$-order regularization. The optimal global convergence is guaranteed by including an additional extra-gradient step, while a $p^{th}$-order superlinear local convergence is shown to hold if the VI is strongly monotone. The proposed ARE is inclusive and general, in the sense that a variety of solution methods can be formulated within this framework as different manifestations of approximations, and their iteration complexities would follow through in a unified fashion. The ARE framework relates to the first-order methods, while opening up possibilities to developing higher-order methods specifically for structured problems that guarantee the optimal iteration complexity bounds., Comment: 29 pages, 3 figures

Exposure to ideas in domains outside a scientist's own may benefit her in reformulating existing research problems in novel ways and discovering new application domains for existing solution ideas. While improved performance in scholarly search engines can help scientists efficiently identify relevant advances in domains they may already be familiar with, it may fall short of helping them explore diverse ideas \textit{outside} such domains. In this paper we explore the design of systems aimed at augmenting the end-user ability in cross-domain exploration with flexible query specification. To this end, we develop an exploratory search system in which end-users can select a portion of text core to their interest from a paper abstract and retrieve papers that have a high similarity to the user-selected core aspect but differ in terms of domains. Furthermore, end-users can `zoom in' to specific domain clusters to retrieve more papers from them and understand nuanced differences within the clusters. Our case studies with scientists uncover opportunities and design implications for systems aimed at facilitating cross-domain exploration and inspiration., Comment: NLP+HCI Workshop at NAACL 2022

We provide results that exactly quantify how data augmentation affects the variance and limiting distribution of estimates, and analyze several specific models in detail. The results confirm some observations made in machine learning practice, but also lead to unexpected findings: Data augmentation may increase rather than decrease the uncertainty of estimates, such as the empirical prediction risk. It can act as a regularizer, but fails to do so in certain high-dimensional problems, and it may shift the double-descent peak of an empirical risk. Overall, the analysis shows that several properties data augmentation has been attributed with are not either true or false, but rather depend on a combination of factors -- notably the data distribution, the properties of the estimator, and the interplay of sample size, number of augmentations, and dimension. Our main theoretical tool is a limit theorem for functions of randomly transformed, high-dimensional random vectors. The proof draws on work in probability on noise stability of functions of many variables., Comment: Changed title and added an analysis on the effect of augmentations on the double-descent risk curve of a high-dimensional ridgeless estimator

Current state-of-the-art model-based reinforcement learning algorithms use trajectory sampling methods, such as the Cross-Entropy Method (CEM), for planning in continuous control settings. These zeroth-order optimizers require sampling a large number of trajectory rollouts to select an optimal action, which scales poorly for large prediction horizons or high dimensional action spaces. First-order methods that use the gradients of the rewards with respect to the actions as an update can mitigate this issue, but suffer from local optima due to the non-convex optimization landscape. To overcome these issues and achieve the best of both worlds, we propose a novel planner, Cross-Entropy Method with Gradient Descent (CEM-GD), that combines first-order methods with CEM. At the beginning of execution, CEM-GD uses CEM to sample a significant amount of trajectory rollouts to explore the optimization landscape and avoid poor local minima. It then uses the top trajectories as initialization for gradient descent and applies gradient updates to each of these trajectories to find the optimal action sequence. At each subsequent time step, however, CEM-GD samples much fewer trajectories from CEM before applying gradient updates. We show that as the dimensionality of the planning problem increases, CEM-GD maintains desirable performance with a constant small number of samples by using the gradient information, while avoiding local optima using initially well-sampled trajectories. Furthermore, CEM-GD achieves better performance than CEM on a variety of continuous control benchmarks in MuJoCo with 100x fewer samples per time step, resulting in around 25% less computation time and 10% less memory usage. The implementation of CEM-GD is available at $\href{https://github.com/KevinHuang8/CEM-GD}{\text{https://github.com/KevinHuang8/CEM-GD}}$.

A music piece is both comprehended hierarchically, from sonic events to melodies, and sequentially, in the form of repetition and variation. Music from different cultures establish different aesthetics by having different style conventions on these two aspects. We propose a framework that could be used to quantitatively compare music from different cultures by looking at these two aspects. The framework is based on an Music Information Dynamics model, a Variable Markov Oracle (VMO), and is extended with a variational representation learning of audio. A variational autoencoder (VAE) is trained to map audio fragments into a latent representation. The latent representation is fed into a VMO. The VMO then learns a clustering of the latent representation via a threshold that maximizes the information rate of the quantized latent representation sequence. This threshold effectively controls the sensibility of the predictive step to acoustic changes, which determines the framework's ability to track repetitions on longer time scales. This approach allows characterization of the overall information contents of a musical signal at each level of acoustic sensibility. Our findings under this framework show that sensibility to subtle acoustic changes is higher for East-Asian musical traditions, while the Western works exhibit longer motivic structures at higher thresholds of differences in the latent space. This suggests that a profile of information contents, analyzed as a function of the level of acoustic detail can serve as a possible cultural characteristic.

In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the stochastic extra-momentum solution scheme. The first one is a general scheme based on updating the iterative sequence and an auxiliary extra-point sequence. In the case of deterministic VI model, this approach includes several state-of-the-art first-order methods as its special cases. The second scheme combines two momentum-based directions: the so-called heavy-ball direction and the optimism direction, where only one projection per iteration is required in its updating process. We show that, if the variance of the stochastic oracle is appropriately controlled, then both schemes can be made to achieve optimal iteration complexity of $\mathcal{O}\left(\kappa\ln\left(\frac{1}{\epsilon}\right)\right)$ to reach an $\epsilon$-solution for a strongly monotone VI problem with condition number $\kappa$. We show that these methods can be readily incorporated in a zeroth-order approach to solve stochastic minimax saddle-point problems, where only noisy and biased samples of the objective can be obtained, with a total sample complexity of $\mathcal{O}\left(\frac{\kappa^2}{\epsilon}\ln\left(\frac{1}{\epsilon}\right)\right)$, Comment: 36 pages, 4 figures

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave-function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic, and still unsolved, example is the transition of the heavy fermion compound URu$_2$Si$_2$ (URS) into the so-called hidden-order (HO) phase when the temperature drops below $T_0 = 17.5$K. Here we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a non-rigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO-to-AFM phase transition., Comment: 23 pages, 14 figures, 1 ancillary movie

The date of the first performance of a play of Shakespeare's time must usually be guessed with reference to multiple indirect external sources, or to some aspect of the content or style of the play. Identifying these dates is important to literary history and to accounts of developing authorial styles, such as Shakespeare's. In this study, we took a set of Shakespeare-era plays (181 plays from the period 1585--1610), added the best-guess dates for them from a standard reference work as metadata, and calculated a set of probabilities of individual words in these samples. We applied 11 regression methods to predict the dates of the plays at an 80/20 training/test split. We withdrew one play at a time, used the best-guess date metadata with the probabilities and weightings to infer its date, and thus built a model of date-probabilities interaction. We introduced a memetic algorithm-based Continued Fraction Regression (CFR) which delivered models using a small number of variables, leading to an interpretable model and reduced dimensionality. An in-depth analysis of the most commonly occurring 20 words in the CFR models in 100 independent runs helps explain the trends in linguistic and stylistic terms. The analysis with the subset of words revealed an interesting correlation of signature words with the Shakespeare-era play's genre., Comment: Submitted to Expert Systems with Applications

In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to guarantee the optimal iteration complexity bound of $\mathcal{O}\left(\kappa\ln(1/\epsilon)\right)$ to reach an $\epsilon$-solution, where $\kappa$ is the condition number. This framework provides the flexibility for algorithm designers to train -- among different parameter combinations -- the one that best suits the structure of the problem class at hand. The proposed framework includes the following iterative points and directions as its constituents: the extra-gradient, the optimistic gradient descent ascent (OGDA) direction (aka "optimism"), the "heavy-ball" direction, and Nesterov's extrapolation points. As a result, all the afore-mentioned methods become the special cases under the general scheme of extra points. We also specialize this approach to strongly convex minimization, and show that a similar extra-point approach achieves the optimal iteration complexity bound of $\mathcal{O}(\sqrt{\kappa}\ln(1/\epsilon))$ for this class of problems., Comment: 31 pages, 4 figures

A pair-density-wave (PDW) is a novel superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization group (DMRG) study of an effective $t$-$J$-$V$ model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four- and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the $K$ and $K^\prime$ points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge $c\approx 1$ are consistent with an unusual realization of a Luther-Emery liquid., Comment: 9 pages, 9 figures

Having a comprehensive, high-quality dataset of road sign annotation is critical to the success of AI-based Road Sign Recognition (RSR) systems. In practice, annotators often face difficulties in learning road sign systems of different countries; hence, the tasks are often time-consuming and produce poor results. We propose a novel approach using knowledge graphs and a machine learning algorithm - variational prototyping-encoder (VPE) - to assist human annotators in classifying road signs effectively. Annotators can query the Road Sign Knowledge Graph using visual attributes and receive closest matching candidates suggested by the VPE model. The VPE model uses the candidates from the knowledge graph and a real sign image patch as inputs. We show that our knowledge graph approach can reduce sign search space by 98.9%. Furthermore, with VPE, our system can propose the correct single candidate for 75% of signs in the tested datasets, eliminating the human search effort entirely in those cases., Comment: 12 pages, 5 figures

In the field of Artificial Intelligence (AI) and Machine Learning (ML), the approximation of unknown target functions $y=f(\mathbf{x})$ using limited instances $S={(\mathbf{x^{(i)}},y^{(i)})}$, where $\mathbf{x^{(i)}} \in D$ and $D$ represents the domain of interest, is a common objective. We refer to $S$ as the training set and aim to identify a low-complexity mathematical model that can effectively approximate this target function for new instances $\mathbf{x}$. Consequently, the model's generalization ability is evaluated on a separate set $T=\{\mathbf{x^{(j)}}\} \subset D$, where $T \neq S$, frequently with $T \cap S = \emptyset$, to assess its performance beyond the training set. However, certain applications require accurate approximation not only within the original domain $D$ but also in an extended domain $D'$ that encompasses $D$. This becomes particularly relevant in scenarios involving the design of new structures, where minimizing errors in approximations is crucial. For example, when developing new materials through data-driven approaches, the AI/ML system can provide valuable insights to guide the design process by serving as a surrogate function. Consequently, the learned model can be employed to facilitate the design of new laboratory experiments. In this paper, we propose a method for multivariate regression based on iterative fitting of a continued fraction, incorporating additive spline models. We compare the performance of our method with established techniques, including AdaBoost, Kernel Ridge, Linear Regression, Lasso Lars, Linear Support Vector Regression, Multi-Layer Perceptrons, Random Forests, Stochastic Gradient Descent, and XGBoost. To evaluate these methods, we focus on an important problem in the field: predicting the critical temperature of superconductors based on physical-chemical characteristics., Comment: Submitted to Algorithms ( ISSN: 1999-4893 )