Knowledge distillation (KD) is a powerful strategy for training deep neural networks (DNNs). Although it was originally proposed to train a more compact ``student'' model from a large ``teacher'' model, many recent efforts have focused on adapting it to promote generalization of the model itself, such as online KD and self KD. % as an effective way Here, we propose an accessible and compatible strategy named Spaced KD to improve the effectiveness of both online KD and self KD, in which the student model distills knowledge from a teacher model trained with a space interval ahead. This strategy is inspired by a prominent theory named \emph{spacing effect} in biological learning and memory, positing that appropriate intervals between learning trials can significantly enhance learning performance. With both theoretical and empirical analyses, we demonstrate that the benefits of the proposed Spaced KD stem from convergence to a flatter loss landscape during stochastic gradient descent (SGD). We perform extensive experiments to validate the effectiveness of Spaced KD in improving the learning performance of DNNs (e.g., the performance gain is up to 2.31\% and 3.34\% on Tiny-ImageNet over online KD and self KD, respectively).

The functional characterization of different neuronal types has been a longstanding and crucial challenge. With the advent of physical quantum computers, it has become possible to apply quantum machine learning algorithms to translate theoretical research into practical solutions. Previous studies have shown the advantages of quantum algorithms on artificially generated datasets, and initial experiments with small binary classification problems have yielded comparable outcomes to classical algorithms. However, it is essential to investigate the potential quantum advantage using realworld data. To the best of our knowledge, this study is the first to propose the utilization of quantum systems to classify neuron morphologies, thereby enhancing our understanding of the performance of automatic multiclass neuron classification using quantum kernel methods. We examined the influence of feature engineering on classification accuracy and found that quantum kernel methods achieved similar performance to classical methods, with certain advantages observed in various configurations. Furthermore, the advances in quantum computing systems have allowed a progress in the study of quantum ML algorithms, especially with kernel methods. The number of features determined the number of qubits, and a quantum circuit used to implement the feature map was of a depth that was a linear or polylogarithmic function of the dataset's size. Thus far, the studies that have been conducted to support the advantages of a quantum feature map have carefully selected synthetic datasets or applied it to small binary classification problems. Despite the fact that research on cortical circuits has been conducted for over a century, determining how many classes of cortical neurons exist remains an ongoing and uncompleted task. Moreover, the continuous development of techniques and the availability of an increasing number of phenotype datasets have not led to the maintenance of a unique classification system that is easy to update and can consider the different defining features of neurons specific to a given type. Despite the inherent complexity and challenges that neuroscientists must deal with while addressing neuronal classification, numerous reasons exist for interest in this topic.

Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify forecasting and representational uncertainty, simultaneously alleviating the challenge of computing the distribution of trajectories from a GP-based dynamical system and enabling a new probabilistic treatment of learning Koopman operator representations. Using a trajectory-based equivariance -- which we refer to as \textit{Koopman equivariance} -- we obtain a GP model with enhanced generalization capabilities. To allow for large-scale regression, we equip our framework with variational inference based on suitable inducing points. Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.

In data mining, when binary prediction rules are used to predict a binary outcome, many performance measures are used in a vast array of literature for the purposes of evaluation and comparison. Some examples include classification accuracy, precision, recall, F measures, and Jaccard index. Typically, these performance measures are only approximately estimated from a finite dataset, which may lead to findings that are not statistically significant. In order to properly quantify such statistical uncertainty, it is important to provide confidence intervals associated with these estimated performance measures. We consider statistical inference about general performance measures used in data mining, with both individual and joint confidence intervals. These confidence intervals are based on asymptotic normal approximations and can be computed fast, without needs to do bootstrap resampling. We study the finite sample coverage probabilities for these confidence intervals and also propose a `blurring correction' on the variance to improve the finite sample performance. This 'blurring correction' generalizes the plus-four method from binomial proportion to general performance measures used in data mining. Our framework allows multiple performance measures of multiple classification rules to be inferred simultaneously for comparisons.

Federated ensemble distillation addresses client heterogeneity by generating pseudo-labels for an unlabeled server dataset based on client predictions and training the server model using the pseudo-labeled dataset. The unlabeled server dataset can either be pre-existing or generated through a data-free approach. The effectiveness of this approach critically depends on the method of assigning weights to client predictions when creating pseudo-labels, especially in highly heterogeneous settings. Inspired by theoretical results from GANs, we propose a provably near-optimal weighting method that leverages client discriminators trained with a server-distributed generator and local datasets. Our experiments on various image classification tasks demonstrate that the proposed method significantly outperforms baselines. Furthermore, we show that the additional communication cost, client-side privacy leakage, and client-side computational overhead introduced by our method are negligible, both in scenarios with and without a pre-existing server dataset.

Given the ubiquity of streaming data, online algorithms have been widely used for parameter estimation, with second-order methods particularly standing out for their efficiency and robustness. In this paper, we study an online sketched Newton method that leverages a randomized sketching technique to perform an approximate Newton step in each iteration, thereby eliminating the computational bottleneck of second-order methods. While existing studies have established the asymptotic normality of sketched Newton methods, a consistent estimator of the limiting covariance matrix remains an open problem. We propose a fully online covariance matrix estimator that is constructed entirely from the Newton iterates and requires no matrix factorization. Compared to covariance estimators for first-order online methods, our estimator for second-order methods is batch-free. We establish the consistency and convergence rate of our estimator, and coupled with asymptotic normality results, we can then perform online statistical inference for the model parameters based on sketched Newton methods. We also discuss the extension of our estimator to constrained problems, and demonstrate its superior performance on regression problems as well as benchmark problems in the CUTEst set.

Conformal prediction methods create prediction bands with distribution-free guarantees but do not explicitly capture epistemic uncertainty, which can lead to overconfident predictions in data-sparse regions. Although recent conformal scores have been developed to address this limitation, they are typically designed for specific tasks, such as regression or quantile regression. Moreover, they rely on particular modeling choices for epistemic uncertainty, restricting their applicability. We introduce $\texttt{EPICSCORE}$, a model-agnostic approach that enhances any conformal score by explicitly integrating epistemic uncertainty. Leveraging Bayesian techniques such as Gaussian Processes, Monte Carlo Dropout, or Bayesian Additive Regression Trees, $\texttt{EPICSCORE}$ adaptively expands predictive intervals in regions with limited data while maintaining compact intervals where data is abundant. As with any conformal method, it preserves finite-sample marginal coverage. Additionally, it also achieves asymptotic conditional coverage. Experiments demonstrate its good performance compared to existing methods. Designed for compatibility with any Bayesian model, but equipped with distribution-free guarantees, $\texttt{EPICSCORE}$ provides a general-purpose framework for uncertainty quantification in prediction problems.

For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\sim10^9$ points in high-dimensions ($d\geq100$). All current practical methods for this problem have runtimes at least $\Omega(k^2)$. We find that initialization routines are not a bottleneck for this case. Instead, it is critical to improve the speed of Lloyd's local-search algorithm, particularly the step that reassigns points to their closest center. Attempting to improve this step naturally leads us to leverage approximate nearest-neighbor search methods, although this alone is not enough to be practical. Instead, we propose a family of problems we call "Seeded Approximate Nearest-Neighbor Search", for which we propose "Seeded Search-Graph" methods as a solution.

We investigate the fundamental limits of transformer-based foundation models, extending our analysis to include Visual Autoregressive (VAR) transformers. VAR represents a big step toward generating images using a novel, scalable, coarse-to-fine ``next-scale prediction'' framework. These models set a new quality bar, outperforming all previous methods, including Diffusion Transformers, while having state-of-the-art performance for image synthesis tasks. Our primary contributions establish that, for single-head VAR transformers with a single self-attention layer and single interpolation layer, the VAR Transformer is universal. From the statistical perspective, we prove that such simple VAR transformers are universal approximators for any image-to-image Lipschitz functions. Furthermore, we demonstrate that flow-based autoregressive transformers inherit similar approximation capabilities. Our results provide important design principles for effective and computationally efficient VAR Transformer strategies that can be used to extend their utility to more sophisticated VAR models in image generation and other related areas.

Electroencephalogram (EEG) provides a non-invasive, highly accessible, and cost-effective solution for Alzheimer's Disease (AD) detection. However, existing methods, whether based on manual feature extraction or deep learning, face two major challenges: the lack of large-scale datasets for robust feature learning and evaluation, and poor detection performance due to inter-subject variations. To address these challenges, we curate an EEG-AD corpus containing 813 subjects, which forms the world's largest EEG-AD dataset to the best of our knowledge. Using this unique dataset, we propose LEAD, the first large foundation model for EEG-based AD detection. Our method encompasses an entire pipeline, from data selection and preprocessing to self-supervised contrastive pretraining, fine-tuning, and key setups such as subject-independent evaluation and majority voting for subject-level detection. We pre-train the model on 11 EEG datasets and unified fine-tune it on 5 AD datasets. Our self-supervised pre-training design includes sample-level and subject-level contrasting to extract useful general EEG features. Fine-tuning is performed on 5 channel-aligned datasets together. The backbone encoder incorporates temporal and channel embeddings to capture features across both temporal and spatial dimensions. Our method demonstrates outstanding AD detection performance, achieving up to a 9.86% increase in F1 score at the sample-level and up to a 9.31% at the subject-level compared to state-of-the-art methods. The results of our model strongly confirm the effectiveness of contrastive pre-training and channel-aligned unified fine-tuning for addressing inter-subject variation. The source code is at https://github.com/DL4mHealth/LEAD.