High-Order Neural Network
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Exploring Neural Network Surrogates for High-Order Mesh-Free Interpolants
arXiv:2503.23230v3 Announce Type: replace Abstract: Mesh-free numerical methods offer flexibility in the discretisation of complex geometries, showing significant potential for problems where mesh-based methods struggle. Although high-order approximations can be obtained through consistency-correction linear systems, such approaches remain prohibitively expensive for Lagrangian formulations, which commonly exhibit low-order convergence. Here we investigate the use of machine learning (ML) to...
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,...
Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs
arXiv:2603.29237v2 Announce Type: replace Abstract: Enforcing prescribed global integral constraints in mesh-free neural PDE solvers is challenging in high-dimensional domains. Existing projection methods for spatial integrals are often tied to fixed grids or uniform quadrature, which can conflict with randomly sampled physics-informed neural networks (PINNs) and scale poorly with dimension. High-order differential operators also increase reverse-mode automatic differentiation memory costs.
HyperPatch: Sequential Knowledge Editing Under n-ary Structural Drift
Announce Type: new Abstract: Large Language Models (LLMs) rely on Knowledge Editing (KE) to maintain temporal validity, yet real-world knowledge is inherently n-ary. We demonstrate that in non-stationary environments, sequential updates to complex relations induce N-ary Structural Drift, a phenomenon where the binary reification of n-ary events into triples fractures relational atomicity. This precipitates Structure-Conditioned Knowledge Transfer Failure, a systematic mis-grounding of the...
TransportBench: A Comprehensive Benchmark for Non-Equilibrium Flow Transport
Announce Type: new Abstract: Scientific machine learning models, as versatile tools for numerical simulation and analysis, are increasingly transforming the landscape of fluid mechanics research. However, existing datasets and benchmarks are primarily limited to continuum fluids and provide limited support for non-equilibrium transport phenomena. To address this gap, we present TransportBench, a high-fidelity dataset and standardized benchmark for non-equilibrium flow transport, designed to...
What can a neuron compute
Cortical pyramidal neurons possess elaborate dendritic trees with diverse nonlinear membrane conductances and thousands of plastic synapses, suggesting substantial computational capabilities at the single-cell level. Yet, what can a neuron compute remains an open question, largely due to the lack of a systematic framework to quantify its computational capabilities. We introduce TwinProp, a digital-twin-based backpropagation algorithm that enables gradient-based optimization of synaptic...