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When choosing between options, we must solve an important binding problem. The values of the options must be associated with information about the action needed to select them. We hypothesize that the brain solves this binding problem…

We propose Fiber Bundle Networks (FiberNet), a novel machine learning framework integrating differential geometry with machine learning. Unlike traditional deep neural networks relying on black-box function fitting, we reformulate…

There has been great progress in understanding of anatomical and functional microcircuitry of the primate cortex. However, the fundamental principles of cortical computation - the principles that allow the visual cortex to bind retinal…

Artificial intelligence has shown remarkable success in materials discovery and property prediction, particularly for crystalline and polymer systems where material properties and structures are dominated by discrete graph representations.…

This article presents a novel computational model to study the selective filtering of biological hydrogels due to the surface charge and size of diffusing particles. It is the first model that includes the random 3D fiber orientation and…

The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…

The current leading computer vision models are typically feed forward neural models, in which the output of one computational block is passed to the next one sequentially. This is in sharp contrast to the organization of the primate visual…

What visual information is encoded in individual brain regions, and how do distributed patterns combine to create their neural representations? Prior work has used generative models to replicate known category selectivity in isolated…

Real-time robotic systems require advanced perception, computation, and action capability. However, the main bottleneck in current autonomous systems is the trade-off between computational capability, energy efficiency and model…

The human visual system exhibits non-uniform spatial resolution across the visual field, which is characterized by the cortical magnification factor (CMF) that reflects its anatomical basis. However, current approaches for quantifying CMF…

Symbolic computer vision represents diagrams through explicit logical rules and structured representations, enabling interpretable understanding in machine vision. This requires fundamentally different learning paradigms from pixel-based…

In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value…

We consider Wilson-Cowan-type models for the mathematical description of orientation-dependent Poggendorff-like illusions. Our modelling improves two previously proposed cortical-inspired approaches embedding the sub-Riemannian heat kernel…

For a class of compactly supported windows we characterize the frame property for a Gabor system $\mts,$ for translation parameters $a$ belonging to a certain range depending on the support size. We show that the obstructions to the frame…

In this paper we construct frames of Gabor type for the space $L^2_{rad}(\R^d)$ of radial $L^2$-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a…

Invariant object recognition is one of the most fundamental cognitive tasks performed by the brain. In the neural state space, different objects with stimulus variabilities are represented as different manifolds. In this geometrical…

Learning 3D point sets with rotational invariance is an important and challenging problem in machine learning. Through rotational invariant architectures, 3D point cloud neural networks are relieved from requiring a canonical global pose…

Implicit neural representations (INRs) mark a fundamental shift in signal modeling, moving from discrete sampled data to continuous functional representations. By parameterizing signals as neural networks, INRs provide a unified framework…

The first diffraction order of a planar 1D grating has a plane wavefront for a plane wave incidence. We propose an algorithm to tailor the shape of this wavefront to the desired propagation mode. The algorithm works by segmenting the 1D…

Many scenes in real life can be abstracted to the sparse reward visual scenes, where it is difficult for an agent to tackle the task under the condition of only accepting images and sparse rewards. We propose to decompose this problem into…