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Bayesian Optimal Experimental Design (BOED) provides a rigorous framework for decision-making tasks in which data acquisition is often the critical bottleneck, especially in resource-constrained settings. Traditionally, BOED typically…

We establish that semidefinite programs (SDPs) over the unbounded positive semidefinite cone are mathematically equivalent to thermodynamic systems of independent bosonic modes: the eigenvalues of the optimization variable play the role of…

An Event-Related Potential (ERP)-based Brain-Computer Interface (BCI) Speller System assists people with disabilities to communicate by decoding electroencephalogram (EEG) signals. A P300-ERP embedded in EEG signals arises in response to a…

Accurate, fast, and reliable multiclass classification of electroencephalography (EEG) signals is a challenging task towards the development of motor imagery brain-computer interface (MI-BCI) systems. We propose enhancements to different…

Text embeddings are essential components in modern NLP pipelines. Although numerous embedding models have been proposed, no single model consistently dominates across domains and tasks. This variability motivates the use of ensemble…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

Symmetric Positive Definite (SPD) matrix learning methods have become popular in many image and video processing tasks, thanks to their ability to learn appropriate statistical representations while respecting Riemannian geometry of…

Weight tying, i.e. sharing parameters between input and output embedding matrices, is common practice in language model design, yet its impact on the learned embedding space remains poorly understood. In this paper, we show that tied…

Electroencephalography (EEG) recordings are analyzed using battery-powered wearable devices to monitor brain activities and neurological disorders. These applications require long and continuous processing to generate feasible results.…

We propose a new method for spatial power spectrum estimation in array processing that leverages the Riemannian geometry of Hermitian positive definite (HPD) matrices. We show that conventional approaches minimize variants of the Euclidean…

An important problem in machine learning theory is to understand the approximation and generalization properties of two-layer neural networks in high dimensions. To this end, researchers have introduced the Barron space…

We consider covariance estimation under Toeplitz structure. Numerous sophisticated optimization methods have been developed to maximize the Gaussian log-likelihood under Toeplitz constraints. In contrast, recent advances in deep learning…

Studies have shown that modern neural networks tend to be poorly calibrated due to over-confident predictions. Traditionally, post-processing methods have been used to calibrate the model after training. In recent years, various trainable…

Deep learning models have shown promise in EEG-based outcome prediction for comatose patients after cardiac arrest, but their reliability is often compromised by subtle forms of data leakage. In particular, when long EEG recordings are…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

Covariance matrices of noisy multichannel electroencephalogram time series data are hard to estimate due to high dimensionality. In brain-computer interfaces (BCI) based on event-related potentials and a linear discriminant analysis (LDA)…

Electroencephalography (EEG) foundation models have recently emerged as a promising paradigm for brain-computer interfaces (BCIs), aiming to learn transferable neural representations from large-scale heterogeneous recordings. Despite rapid…

We study the problem of recovering a globally consistent Euclidean embedding of data, given only a local distance graph and propose a method that optimally represents these distances. The method operates solely on a neighborhood graph…

Electroencephalogram (EEG) signal classification faces significant challenges due to data distribution shifts caused by heterogeneous electrode configurations, acquisition protocols, and hardware discrepancies across domains. This paper…

Electroencephalography (EEG) plays a crucial role in brain-computer interfaces (BCIs) and neurological diagnostics, but its real-world deployment faces challenges due to noise artifacts, missing data, and high annotation costs. We introduce…