Related papers: Support-Conditioned Flow Matching Is Kernel Smooth…

Normative and task-driven theories offer powerful top-down explanations for biological systems, yet the goals of quantitatively arbitrating between competing theories, and utilizing them as inductive biases to improve data-driven fits of…

When concept shifts and sample scarcity are present in the target domain of interest, nonparametric regression learners often struggle to generalize effectively. The technique of transfer learning remedies these issues by leveraging data or…

Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the…

Many existing two-phase kernel-based hypothesis transfer learning algorithms employ the same kernel regularization across phases and rely on the known smoothness of functions to obtain optimality. Therefore, they fail to adapt to the…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Convolutional Neural Networks (CNNs) have shown impressive performance in computer vision tasks such as image classification, detection, and segmentation. Moreover, recent work in Generative Adversarial Networks (GANs) has highlighted the…

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

This paper addresses a cross-modal learning framework, where the objective is to enhance the performance of supervised learning in the primary modality using an unlabeled, unpaired secondary modality. Taking a probabilistic approach for…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Many sparse attention mechanisms such as Neighborhood Attention have typically failed to consistently deliver speedup over the self attention baseline. This is largely due to the level of complexity in attention infrastructure, and the…

Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…

Adjoint-based data assimilation for turbulent Navier-Stokes flows is fundamentally limited by the behavior of the adjoint dynamics: in backward time, adjoint fields exhibit exponential growth and become increasingly dominated by small-scale…

This paper is on the construction of structure-preserving, online-efficient reduced models for the barotropic Euler equations with a friction term on networks. The nonlinear flow problem finds broad application in the context of gas…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

Associated kernels have been introduced to improve the classical continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. This work deals with the effects of combined…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Causal Optimal Transport (COT) results from imposing a temporal causality constraint on classic optimal transport problems, which naturally generates a new concept of distances between distributions on path spaces. The first application of…

This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

Since its introduction in 2017, the Transformer has become one of the most widely adopted architectures in modern deep learning. Despite extensive efforts to improve positional encoding, attention mechanisms, and feed-forward networks, the…