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Circuit-Inspired High-Order Neural Networks with Unified Neural Dynamics Modeling for PDE Solving and Visual Perception
Announce Type: replace Abstract: Deep networks often rely on architectural heuristics to shape representation evolution, limiting their ability to model data governed by intrinsic dynamics. We present the Circuit-inspired High-Order Neural Network (CHONN), a modular framework that treats representation evolution as a latent potential process and increases its effective order through Kirchhoff-inspired cascade composition. A single Kirchhoff Neural Cell implements a stable first-order update,...
Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic
arXiv:2606.08985v1 Announce Type: new Abstract: While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles. We refine the explanation of this phenomenon in three directions. First, we formalize a...
The Need for Neural ISP in the Small-Pixel Era: How Shrinking Pixels Push Optics to the Limit and Neural Restoration Pushes Back
arXiv:2606.07675v1 Announce Type: Smartphone telephoto cameras are approaching a "telephoto physics wall": as pixel pitches shrink toward sub-0.5 micron, the optics remain limited by geometric aberrations, leading to diminishing returns on resolution. Traditional Image Signal Processors (ISPs) cannot eliminate these aberrations, because they operate through local, stage-wise processing with no explicit model of the underlying point spread function (PSF).
Neural decoding of speech using deep neural ensembles
Speech brain-computer interfaces (BCIs) can restore rapid communication to people with paralysis, but decoding errors still limit performance. In recent brain-to-text decoding competitions, deep ensemble methods, which combine predictions from multiple independently trained decoders, have delivered striking accuracy improvements and account for the largest gains over baseline approaches. However, these methods have not previously been tested in real-time, require substantial computational...
Theoretical Aspects of Lie Groupoid and Lie Algebroid Equivariant Convolutional Neural Networks
Announce Type: cross Abstract: We introduce Lie groupoid equivariant neural networks as a specialization of recently proposed topological category-equivariant neural networks to the differentiable setting. Lie groupoid equivariant neural networks are composed from Lie groupoid lifting convolutions and Lie groupoid convolution layers, and we show how for suitable Lie groupoids they are equivalent to certain Lie algebroid-equivariant neural networks. We additionally describe groupoid invariant...
Scientists mapped every neural connection in a fruit fly and found a surprise
Scientists mapped every neural connection in a fruit fly and found a surprise Scientists have completed the first full brain-to-body wiring map of a fruit fly, revealing that behavior may be driven more by local neural teamwork than by a central brain command center. - Date: - June 10, 2026 - Source: - Harvard Medical School - Summary: - A groundbreaking new connectome maps every neural connection in an adult fruit fly’s central nervous system, creating an unprecedented view of how the brain...
A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent L\'evy Jumps
Announce Type: new Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss. The protocol pairs each neural solve with at least one from-scratch independent reference, decomposes the Hamiltonian into drift, diffusion, compensator, and...
Neural birth time and somatosensory circuit assembly are linked by Robo3 regulation of dendrite morphology
Neural circuit wiring requires a remarkable level of precision, as thousands of neurons generate millions of synapses in distinct configurations. While neural circuits are known to be shaped by both neural birth timing and multiple classes of guidance molecules, the relationship between the two and how they coordinate circuit assembly has yet to be evaluated. Leveraging the well-defined stem cell lineages of the Drosophila embryonic nerve cord, we investigate how Roundabout (Robo) guidance...
Molecular basis of competence for neural induction in the chick embryo
Competence is the capacity of a cell or tissue to respond to a specific inducing signal from a neighbouring tissue, by changing its fate in a specific direction. Neural induction is the process by which the epiblast of the early embryo responds to signals from the organizer (the tip of the primitive streak in amniotes) by forming a neural plate. Here we study why three regions of the early chick embryo lack competence to respond to neural induction by a grafted organizer: the outer anterior...
Certified Neural Approximations of Nonlinear Dynamics
arXiv:2505.15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system. To address this fundamental challenge, we propose a novel, adaptive, and parallelizable verification method based...