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Visual reasoning tasks such as visual question answering (VQA) require an interplay of visual perception with reasoning about the question semantics grounded in perception. However, recent advances in this area are still primarily driven by…

Hyperbolic space naturally encodes hierarchical structures such as phylogenies (binary trees), where inward-bending geodesics reflect paths through least common ancestors, and the exponential growth of neighborhoods mirrors the…

A number of scientists suggested that human visual perception may emerge from image statistics, shaping efficient neural representations in early vision. In this work, a bio-inspired architecture that can accommodate several known facts in…

Reconstructing the cortex from longitudinal magnetic resonance imaging (MRI) is indispensable for analyzing morphological alterations in the human brain. Despite the recent advancement of cortical surface reconstruction with deep learning,…

Surface analysis of the cortex is ubiquitous in human neuroimaging with MRI, e.g., for cortical registration, parcellation, or thickness estimation. The convoluted cortical geometry requires isotropic scans (e.g., 1mm MPRAGEs) and good…

In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into…

Recent studies have shown how spiking networks can learn complex functionality through error-correcting plasticity, but the resulting structures and dynamics remain poorly studied. To elucidate how these models may link to observed dynamics…

We introduce a new class of discrete conformal structures on surfaces with boundary, which have nice interpolations in 3-dimensional hyperbolic geometry. Then we prove the global rigidity of the new discrete conformal structures using…

The human cerebral cortex has many bumps and grooves called gyri and sulci. Even though there is a high inter-individual consistency for the main cortical folds, this is not the case when we examine the exact shapes and details of the…

The human visual system contains a hierarchical sequence of modules that take part in visual perception at superordinate, basic, and subordinate categorization levels. During the last decades, various computational models have been proposed…

Data representation in non-Euclidean spaces has proven effective for capturing hierarchical and complex relationships in real-world datasets. Hyperbolic spaces, in particular, provide efficient embeddings for hierarchical structures. This…

We study existence, uniqueness, and distributional aspects of generalized solutions to the Cauchy problem for first-order symmetric (or Hermitian) hyperbolic systems of partial differential equations with Colombeau generalized functions as…

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…

In a joint paper, Jean Petitot together with the authors of the present paper described the functional geometry of the visual cortex as the symplectization of a contact form to describe the family of cells sensitive to position, orientation…

We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…

A compact analytic model is proposed to describe the combined orientation preference (OP) and ocular dominance (OD) features of simple cells and their layout in the primary visual cortex (V1). This model consists of three parts: (i) an…

In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our…

Convolutional neural networks (CNN) have made significant advances in hyperspectral image (HSI) classification. However, standard convolutional kernel neglects the intrinsic connections between data points, resulting in poor region…

In cognitive science and AI, a longstanding question is whether machines learn representations that align with those of the human mind. While current models show promise, it remains an open question whether this alignment is superficial or…

While some convolutional neural networks (CNNs) have achieved great success in object recognition, they struggle to identify objects in images corrupted with different types of common noise patterns. Recently, it was shown that simulating…