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We establish a universal framework for concentration inequalities based on invariance under diffeomorphism groups. Given a probability measure $\mu$ on a space $E$ and a diffeomorphism $\psi: E \to F$, concentration properties transfer…
Capsule networks (CapsNets) were introduced to address convolutional neural networks limitations, learning object-centric representations that are more robust, pose-aware, and interpretable. They organize neurons into groups called…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…
Despite remarkable progress in computer vision, modern recognition systems remain fundamentally limited by their dependence on rich, redundant visual inputs. In contrast, humans can effortlessly understand sparse, minimal representations…
It is a fundamental behavior that different individuals see the world in a largely similar manner. This is an essential basis for humans' ability to cooperate and communicate. However, what are the neuronal properties that underlie these…
Selfridge, along with Sutherland and Marr provided some of the earliest proposals for how to program computers to recognize shapes. Their emphasis on filtering for contour features, especially the orientation of boundary segments, was…
Higher-order networks, naturally described as hypergraphs, are essential for modeling real-world systems involving interactions among three or more entities. Stochastic block models offer a principled framework for characterizing mesoscale…
The hippocampal system contains neural populations that encode an animal's position and velocity as it navigates through space. Here, we show that such populations can embed two codes within their spike trains: a firing rate code (R)…
This paper proposes a data-driven motion-planning framework for nonlinear systems that constructs a sequence of overlapping invariant polytopes. Around each randomly sampled waypoint, the algorithm identifies a convex admissible region and…
We propose a differential geometric model of hypercolumns in the primary visual cortex V1 that combines features of the symplectic model of the primary visual cortex by A. Sarti, G. Citti and J. Petitot and of the spherical model of…
Uncertainty quantification complements model predictions by characterizing their reliability, which is essential for high-stakes decision making such as medical image segmentation. However, most existing methods reduce uncertainty to a…
Predictive coding is an influential theory of cortical function which posits that the principal computation the brain performs, which underlies both perception and learning, is the minimization of prediction errors. While motivated by…
Predictive coding (PC) is an influential theory in computational neuroscience, which argues that the cortex forms unsupervised world models by implementing a hierarchical process of prediction error minimization. PC networks (PCNs) are…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal…
Networks of neurons in the brain encode preferred patterns of neural activity via their synaptic connections. Despite receiving considerable attention, the precise relationship between network connectivity and encoded patterns is still…
Left-right axis specification establishes embryonic laterality through asymmetric signaling cascades originating at the cellular scale. We previously reported the presence of a directionality bias in confined pairs of endothelial (and…
The skeleton conception of elementary particles is considered in the paper. Conventional particle dynamics is formulated in an unaccomplished form, which is adequate only in the continuous space-time geometry. The conventional differential…
Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt…
This paper focuses on the complex relationship between Heisenberg's Uncertainty Principle and the nodal structure of wave functions in a variety of quantum systems including the quantum harmonic oscillator, the particle in a 1D box , and…