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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 generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However,…

Over the last decade, a variety of new neurophysiological experiments have led to new insights as to how, when and where retinal processing takes place, and the nature of the retinal representation encoding sent to the cortex for further…

We propose a learned image-guided rendering technique that combines the benefits of image-based rendering and GAN-based image synthesis. The goal of our method is to generate photo-realistic re-renderings of reconstructed objects for…

Neural reflectance models are capable of reproducing the spatially-varying appearance of many real-world materials at different scales. Unfortunately, existing techniques such as NeuMIP have difficulties handling materials with strong…

Linear-Nonlinear-Poisson (LNP) models are a popular and powerful tool for describing encoding (stimulus-response) transformations by single sensory as well as motor neurons. Recently, there has been rising interest in the second- and…

Human similarity judgments are inconsistent with Euclidean, Hamming, Mahalanobis, and the majority of measures used in the extensive literatures on similarity and dissimilarity. From intrinsic properties of brain circuitry, we derive…

Conventional image inpainting techniques typically process entire images, which often leads to computational inefficiency and susceptibility to information redundancy, particularly in occluded or cluttered scenes. Inspired by cortical…

Hallucinations in LLMs--especially in multimodal settings--undermine reliability. We present a rigorous information-geometric framework, grounded in diffusion dynamics, to quantify hallucinations in MLLMs where model outputs are embedded…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

Understanding how the brain encodes stimuli has been a fundamental problem in computational neuroscience. Insights into this problem have led to the design and development of artificial neural networks that learn representations by…

Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…

Basic phenomenology of human color vision has been widely taken as an inspiration to devise explicit color correction algorithms. The behavior of these models in terms of significative image features (such as contrast and dispersion) can be…

Thanks to novel, powerful brain activity recording techniques, we can create data-driven models from thousands of recording channels and large portions of the cortex, which can improve our understanding of brain-states neuromodulation and…

The inductive biases of graph representation learning algorithms are often encoded in the background geometry of their embedding space. In this paper, we show that general directed graphs can be effectively represented by an embedding model…

The reliable and accurate numerical approximation of the $p$-Laplacian is particularly challenging in the extreme regimes $p \to 1^{+}$ and $p \gg 1$, where the operator becomes either highly singular or strongly degenerate, often causing…

We introduce a sub-Riemannian analogue of the Bence-Merriman-Osher diffusion driven algorithm and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups. The proof follows the…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

The interaction between wavelet-like sensors in Divisive Normalization is classically described through Gaussian kernels that decay with spatial distance, angular distance and frequency distance. However, simultaneous explanation of (a)…