Related papers: Conformal models for hypercolumns in the primary v…
The cerebral cortex performs higher-order brain functions and is thus implicated in a range of cognitive disorders. Current analysis of cortical variation is typically performed by fitting surface mesh models to inner and outer cortical…
Hyperbolic geometry, a Riemannian manifold endowed with constant sectional negative curvature, has been considered an alternative embedding space in many learning scenarios, \eg, natural language processing, graph learning, \etc, as a…
This paper gives an in-depth theoretical analysis of the direction and speed selectivity properties of idealized models of the spatio-temporal receptive fields of simple cells and complex cells, based on the generalized Gaussian derivative…
In this paper we developed a hierarchical network model, called Hierarchical Prediction Network (HPNet), to understand how spatiotemporal memories might be learned and encoded in the recurrent circuits in the visual cortical hierarchy for…
We show that the space of first-order deformations of an orthogonal (resp. symplectic) sheaf over a smooth projective scheme is the first hypercohomology space of a complex which is naturally constructed out of the orthogonal (resp.…
All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set…
We consider a coset construction of minimal models. We define it rigorously and prove that it gives superconformal minimal models. This construction allows to build all primary fields of superconformal models and to calculate their…
This paper presents results of combining (i) theoretical analysis regarding connections between the orientation selectivity and the elongation of receptive fields for the affine Gaussian derivative model with (ii) biological measurements of…
We present a computational model for the semantic interpretation of symmetry in naturalistic scenes. Key features include a human-centred representation, and a declarative, explainable interpretation model supporting deep semantic…
In this paper, we introduce the discrete conformal structures on surfaces with boundary in an axiomatic approach, which ensures that the Poincar\'{e} dual of an ideally triangulated surface with boundary has a good geometric structure.Then…
The primary visual cortex processes a large amount of visual information, however, due to its large receptive fields, when multiple stimuli fall within one receptive field, there are computational problems. To solve this problem, the visual…
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds…
Deep convolutional neural networks are powerful tools for learning visual representations from images. However, designing efficient deep architectures to analyse volumetric medical images remains challenging. This work investigates…
Visual perception, the brain's construction of a stable world from sensory data, faces several long-standing, fundamental challenges. While often studied separately, these problems have resisted a single, unifying computational framework.…
The mechanisms involved in transforming early visual signals to curvature representations in V4 are unknown. We propose a hierarchical model that reveals V1/V2 encodings that are essential components for this transformation to the reported…
In this thesis we study two-dimensional conformal field theories with Virasoro algebra symmetry, following the conformal bootstrap approach. Under the assumption that degenerate fields exist, we provide an extension of the analytic…
We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in…
We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of…
A linear neural network is proposed for mamalian vision system in which backward connections from the primary visual cortex (V1) to the lateral geniculate nucleus play a key role. The backward connections control the flow of information…
The primate visual system has an exquisite ability to discriminate partially occluded shapes. Recent electrophysiological recordings suggest that response dynamics in intermediate visual cortical area V4, shaped by feedback from prefrontal…