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The deep learning models used for speaker verification rely heavily on large amounts of data and correct labeling. However, noisy (incorrect) labels often occur, which degrades the performance of the system. In this paper, we propose a novel two-stage learning method to filter out noisy labels from speaker datasets. Since a DNN will first fit data with clean labels, we first train the model with all data for several epochs. Then, based on this model, the model predictions are compared with the labels using our proposed the OR-Gate with top-k mechanism to select the data with clean labels and the selected data is used to train the model. This process is iterated until the training is completed. We have demonstrated the effectiveness of this method in filtering noisy labels through extensive experiments and have achieved excellent performance on the VoxCeleb (1 and 2) with different added noise rates.

Mobility systems often suffer from a high price of anarchy due to the uncontrolled behavior of selfish users. This may result in societal costs that are significantly higher compared to what could be achieved by a centralized system-optimal controller. Monetary tolling schemes can effectively align the behavior of selfish users with the system-optimum. Yet, they inevitably discriminate the population in terms of income. Artificial currencies were recently presented as an effective alternative that can achieve the same performance, whilst guaranteeing fairness among the population. However, those studies were based on behavioral models that may differ from practical implementations. This paper presents a data-driven approach to automatically adapt artificial-currency tolls within repetitive-game settings. We first consider a parallel-arc setting whereby users commute on a daily basis from an individual origin to an individual destination, choosing a route in exchange of an artificial-currency price or reward, while accounting for the impact of the choices of the other users on travel discomfort. Second, we devise a model-based reinforcement learning controller that autonomously learns the optimal pricing policy by interacting with the proposed framework considering the closeness of the observed aggregate flows to a desired system-optimal distribution as a reward function. Our numerical results show that the proposed data-driven pricing scheme can effectively align the users' flows with the system optimum, significantly reducing the societal costs with respect to the uncontrolled flows (by about 15% and 25% depending on the scenario), and respond to environmental changes in a robust and efficient manner.

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this classic problem in the fully dynamic setting, where elements can be both inserted and removed. Our main result is a randomized algorithm that maintains an efficient data structure with a poly-logarithmic amortized update time and yields a $(1/2-\epsilon)$-approximate solution. We complement our theoretical analysis with an empirical study of the performance of our algorithm.

Goal-oriented error estimation provides the ability to approximate the discretization error in a chosen functional quantity of interest. Adaptive mesh methods provide the ability to control this discretization error to obtain accurate quantity of interest approximations while still remaining computationally feasible. Traditional discrete goal-oriented error estimates incur linearization errors in their derivation. In this paper, we investigate the role of linearization errors in adaptive goal-oriented error simulations. In particular, we develop a novel two-level goal-oriented error estimate that is free of linearization errors. Additionally, we highlight how linearization errors can facilitate the verification of the adjoint solution used in goal-oriented error estimation. We then verify the newly proposed error estimate by applying it to a model nonlinear problem for several quantities of interest and further highlight its asymptotic effectiveness as mesh sizes are reduced. In an adaptive mesh context, we then compare the newly proposed estimate to a more traditional two-level goal-oriented error estimate. We highlight that accounting for linearization errors in the error estimate can improve its effectiveness in certain situations and demonstrate that localizing linearization errors can lead to more optimal adapted meshes.

The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal fluid velocity. However, numerical simulations can violate these constraints, leading to nonphysical results or even simulation failure. Designing genuinely physical-constraint-preserving (PCP) schemes is very difficult, as the primitive variables cannot be explicitly reformulated using conservative variables due to relativistic effects. In this paper, we propose three efficient Newton--Raphson (NR) methods for robustly recovering primitive variables from conservative variables. Importantly, we rigorously prove that these NR methods are always convergent and PCP, meaning they preserve the physical constraints throughout the NR iterations. The discovery of these robust NR methods and their PCP convergence analyses are highly nontrivial and technical. As an application, we apply the proposed NR methods to design PCP finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the RHD equations. Our PCP HWENO schemes incorporate high-order HWENO reconstruction, a PCP limiter, and strong-stability-preserving time discretization. We rigorously prove the PCP property of the fully discrete schemes using convex decomposition techniques. Moreover, we suggest the characteristic decomposition with rescaled eigenvectors and scale-invariant nonlinear weights to enhance the performance of the HWENO schemes in simulating large-scale RHD problems. Several demanding numerical tests are conducted to demonstrate the robustness, accuracy, and high resolution of the proposed PCP HWENO schemes and to validate the efficiency of our NR methods.

The mechanisms by which certain training interventions, such as increasing learning rates and applying batch normalization, improve the generalization of deep networks remains a mystery. Prior works have speculated that "flatter" solutions generalize better than "sharper" solutions to unseen data, motivating several metrics for measuring flatness (particularly $\lambda_{max}$, the largest eigenvalue of the Hessian of the loss); and algorithms, such as Sharpness-Aware Minimization (SAM) [1], that directly optimize for flatness. Other works question the link between $\lambda_{max}$ and generalization. In this paper, we present findings that call $\lambda_{max}$'s influence on generalization further into question. We show that: (1) while larger learning rates reduce $\lambda_{max}$ for all batch sizes, generalization benefits sometimes vanish at larger batch sizes; (2) by scaling batch size and learning rate simultaneously, we can change $\lambda_{max}$ without affecting generalization; (3) while SAM produces smaller $\lambda_{max}$ for all batch sizes, generalization benefits (also) vanish with larger batch sizes; (4) for dropout, excessively high dropout probabilities can degrade generalization, even as they promote smaller $\lambda_{max}$; and (5) while batch-normalization does not consistently produce smaller $\lambda_{max}$, it nevertheless confers generalization benefits. While our experiments affirm the generalization benefits of large learning rates and SAM for minibatch SGD, the GD-SGD discrepancy demonstrates limits to $\lambda_{max}$'s ability to explain generalization in neural networks.

Spiking neural networks have gained significant attention due to their brain-like information processing capabilities. The use of surrogate gradients has made it possible to train spiking neural networks with backpropagation, leading to impressive performance in various tasks. However, spiking neural networks trained with backpropagation typically approximate actual labels using the average output, often necessitating a larger simulation timestep to enhance the network's performance. This delay constraint poses a challenge to the further advancement of SNNs. Current training algorithms tend to overlook the differences in output distribution at various timesteps. Particularly for neuromorphic datasets, inputs at different timesteps can cause inconsistencies in output distribution, leading to a significant deviation from the optimal direction when combining optimization directions from different moments. To tackle this issue, we have designed a method to enhance the temporal consistency of outputs at different timesteps. We have conducted experiments on static datasets such as CIFAR10, CIFAR100, and ImageNet. The results demonstrate that our algorithm can achieve comparable performance to other optimal SNN algorithms. Notably, our algorithm has achieved state-of-the-art performance on neuromorphic datasets DVS-CIFAR10 and N-Caltech101, and can achieve superior performance in the test phase with timestep T=1.

Dataset Distillation is the task of synthesizing small datasets from large ones while still retaining comparable predictive accuracy to the original uncompressed dataset. Despite significant empirical progress in recent years, there is little understanding of the theoretical limitations/guarantees of dataset distillation, specifically, what excess risk is achieved by distillation compared to the original dataset, and how large are distilled datasets? In this work, we take a theoretical view on kernel ridge regression (KRR) based methods of dataset distillation such as Kernel Inducing Points. By transforming ridge regression in random Fourier features (RFF) space, we provide the first proof of the existence of small (size) distilled datasets and their corresponding excess risk for shift-invariant kernels. We prove that a small set of instances exists in the original input space such that its solution in the RFF space coincides with the solution of the original data. We further show that a KRR solution can be generated using this distilled set of instances which gives an approximation towards the KRR solution optimized on the full input data. The size of this set is linear in the dimension of the RFF space of the input set or alternatively near linear in the number of effective degrees of freedom, which is a function of the kernel, number of datapoints, and the regularization parameter $\lambda$. The error bound of this distilled set is also a function of $\lambda$. We verify our bounds analytically and empirically.

Many recent loss functions in deep metric learning are expressed with logarithmic and exponential forms, and they involve margin and scale as essential hyper-parameters. Since each data class has an intrinsic characteristic, several previous works have tried to learn embedding space close to the real distribution by introducing adaptive margins. However, there was no work on adaptive scales at all. We argue that both margin and scale should be adaptively adjustable during the training. In this paper, we propose a method called Adaptive Margin and Scale (AdaMS), where hyper-parameters of margin and scale are replaced with learnable parameters of adaptive margins and adaptive scales for each class. Our method is evaluated on Wall Street Journal dataset, and we achieve outperforming results for word discrimination tasks.

Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also intrigues great interests in the time series community. Among multiple advantages of transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review transformer schemes for time series modeling by highlighting their strengths as well as limitations through a new taxonomy to summarize existing time series transformers in two perspectives. From the perspective of network modifications, we summarize the adaptations of module level and architecture level of the time series transformers. From the perspective of applications, we categorize time series transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.