The paper studies the approximation and statistical learning of nonlinear functionals defined on reproducing kernel Hilbert spaces (RKHSs) using neural networks. It is motivated by functional data such as time series and images.
A new arXiv preprint describes an approach that derives logical explanations for neural network classifications by analyzing neuron activations. The work situates itself within formal explainability, which aims to give provable guarantees about model behavior across regions of the input space. The abstract notes that existing formal techniques have limitations the proposed method seeks to address, though details of the approach are not included in the announcement.
A new arXiv preprint examines using neural networks to represent ground-state electron charge density in real space. The work is motivated by the Hohenberg-Kohn theorem, which holds that ground-state density encodes all ground-state information about a many-electron system. The authors also study how well such learned models generalize.
Researchers present a multi-head feed-forward neural network that jointly estimates conditional average treatment effects and the full distribution of those effects. The approach is framed as a generative learner for distributional causal effects, aimed at capturing heterogeneity beyond single-point estimates. It is a preprint posted to arXiv.
A new arXiv paper introduces SPICE, a technique that applies clustering to explain polysemantic features in neural networks, where individual neurons respond to multiple unrelated concepts. The approach aims to make functional interpretation of such neurons clearer for interpretability research. The abstract describes the work as a simple method for clustering-based explanation of these overlapping activations.
This arXiv preprint is the second installment in a series examining derivative-controlled networks that pair cubic polynomial layers with a lightweight forward-mode per-layer Jacobian penalty called DREG. The authors assess how well these ChainzRule-based models generalize under different data conditions, reporting competitive accuracy alongside stable gradients. No code, deployment, or product details are announced.
A revised arXiv preprint argues that neural combinatorial optimization has largely been limited to policies that work on a single candidate solution, whether by building one from scratch or refining it step by step. The authors propose shifting toward population-based architectures that evaluate and evolve multiple solutions together. The work appears in the cs.LG category as a replacement submission.
Researchers introduce lPINN, a reduced-order neural basis approach for both forward and inverse differential equation problems. In an offline phase, the method derives operator-compatible continuous neural basis functions from an ensemble, then solves equations in a lower-dimensional space. The work aims to combine physics-informed modeling with the efficiency of pretrained linearized representations.
A research paper examines how the scale of a network's initial weights influences which features individual ReLU neurons end up learning during training. The authors argue that this initialization-dependent effect, framed as a hidden gauge, helps explain why trained networks organize representations the way they do.
Researchers propose SechKAN, a variant of Kolmogorov-Arnold Networks that replaces the usual basis functions with hyperbolic secant functions. The paper argues this design keeps KAN's strengths in machine learning and scientific computing while offering a new direction for neural network architecture. It is a revised arXiv preprint, not yet a released product.
A revised arXiv preprint proposes a hybrid approach for predicting railway bogie responses, combining a time-delay neural network with physics-informed residual learning across simulations of differing fidelity. The method targets operating conditions that are impractical to test exhaustively, using agreement with representative measurements as validation evidence. It sits within ongoing work on surrogate modeling for engineering simulation.
A new arXiv preprint introduces SH-WRNN, a neural architecture that replaces conventional static fully connected weight matrices with a routing scheme based on implicit spherical harmonics weight fields. The authors frame the work as a challenge to the standard synapse-layer design that most deep learning models still rely on. The paper targets asymmetric edge intelligence settings, where compute and bandwidth are unevenly distributed across devices.
A revised arXiv paper proposes a symplectic neural network approach for learning non-separable Hamiltonians directly from noisy state observations. Hamiltonian Neural Networks embed physical priors by learning a system's energy function, which can improve generalization and reduce data needs compared with standard models. The work focuses on extending this to systems whose Hamiltonians cannot be split into kinetic and potential parts.
Researchers propose ACR-PINN, a physics-informed neural network framework that pairs layer-wise dynamic adaptation of coordinate representations with a method for resolving conflicts among gradients coming from heterogeneous physical constraints. The work frames architecture and optimization as a joint design problem, aiming to improve training when competing constraints pull the model in different directions.
A new arXiv paper presents a physics-constrained neural network that predicts rigorous coupled-wave analysis outputs directly as Jones matrices for lossless layered periodic structures. The approach builds on energy conservation to constrain the model, aiming to replace or accelerate conventional simulations that are computationally expensive. The work falls under machine learning for scientific computing and photonics design.
A revised arXiv preprint examines why neural network subgrid stress models perform well in a priori tests but deteriorate in a posteriori large eddy simulations. The authors propose approaches to reduce this discrepancy so that model evaluation better reflects real simulation behavior. The work sits in computational fluid dynamics research rather than commercial AI deployment.
This preprint analyzes the ℓ^p-Lipschitz constants of ReLU neural networks mapping from R^d to R when the weights are randomly initialized using a variant of the He scheme, covering p from 1 to infinity. The author derives estimates that are near-optimal, meaning the upper and lower bounds match up to constant factors. The work targets theoretical understanding of how depth and width affect the sensitivity of randomly initialized networks.
A revised arXiv paper argues that feature learning in neural networks is not fully captured by the prevailing view that networks converge on a single global low-dimensional representation. The authors point to neuron specialization inside multilayer perceptrons as an additional, separate mechanism through which features are acquired and organized. The work aims to broaden the theoretical picture of how networks structure what they learn.
A new arXiv paper proves two distinct lower bounds on how well shallow ReLU^k neural networks can approximate functions defined on the unit sphere. For any fixed choice of inner network parameters, the best L2 approximation error is bounded from below, with a second result addressing a related configuration-dependent setting. The work characterizes fundamental limits of shallow architectures with higher-order ReLU activations rather than proposing a new method.
An arXiv preprint studies teacher-student frameworks, where one neural network produces training data for another network that must learn to reproduce its behavior, a standard abstraction in learning theory. The authors find that the geometric structure of the teacher network plays a decisive role in determining whether and how well the student can learn the target function. The paper was posted as a new submission and cross-listed in the cs.AI and cs.LG categories.
New research indicates that while the edge-of-chaos initialization scheme keeps first-order input perturbations stable in very wide randomly initialized networks, higher-order input derivatives become unstable under the same setup. Because techniques such as physics-informed losses, score matching, and derivative regularization rely on those higher derivatives, the results expose a gap in how such networks should be initialized for derivative-based training. The analysis focuses on smooth fully connected networks with scalar inputs.
An arXiv preprint examines how singular learning theory and information geometry describe the same parameter spaces for machine learning models, but from different coordinate perspectives. The work focuses on the non-degeneracy assumptions behind information geometry, which overparameterised neural networks violate, and develops a geometric account of singular learning behaviour. The paper connects these frameworks to explain directions in parameter space that lose significance under model degeneracy.
A preprint cross-listed on arXiv's AI and machine-learning feeds investigates how networks store more concepts than they have dimensions via superposition, and how interference between stored features restricts how many can be recovered through linear read-out. By casting this recovery problem as a compressed sensing task, the authors establish conditions under which multiple simultaneously active features can be decoded with high probability.
A newly posted arXiv paper in cs.AI hypothesizes that the structure of phenomenal experience mirrors the first-order structure of physical interactions, mathematically captured by gradients or Jacobians. The authors develop this idea within an idealized world called Gradland, inhabited by neural networks. The work is a theoretical contribution to discussions of machine consciousness rather than an empirical study.
Researchers have introduced a neural-network-based parametric geometry representation designed for thin-shell structures. The method offers a differentiable surface description that can feed gradient-based shape optimisation workflows, where flexible geometric modelling is a key requirement. The paper is available on arXiv in the machine learning category as an updated version.
A new arXiv paper addresses how the same 3D solid can be described by multiple boundary representations (B-reps) in CAD systems, which creates ambiguity for machine learning models. The authors propose learning canonical inputs so that neural networks operate on the underlying solid rather than the particular file encoding. This aims to make predictions consistent regardless of how a model was originally constructed.
A new arXiv paper introduces CAT-GS, a training approach that combines calibrated gating with a "fusion surgery" technique for multimodal neural networks. The authors identify three linked failure modes in end-to-end multimodal training, including one modality dominating optimization and unstable dynamics. The method aims to balance learning across modalities and stabilize training.
Researchers present an inverse physics-informed neural network that estimates how the scrape-off layer's perpendicular heat conductivity varies with plasma density and temperature in stellarator devices. The approach embeds physical constraints into the learning process rather than relying solely on labeled data, allowing the conductivity function to be recovered from available measurements. This is an arXiv preprint on fusion plasma modeling and has not yet been peer reviewed.
The paper studies a neural semi-discrete scheme for solving high-dimensional first-order Hamilton-Jacobi-Bellman equations, assuming either known or learned dynamics. Monotonicity is achieved by combining centered differences with an artificial viscosity term that scales linearly with the mesh size. The authors evaluate the resulting monotone operator within a policy iteration framework.
A developer known as Makestreme used neural-network-based compression to shrink an MP3 file so its data fits across several QR codes printed on a single page. The codes can be scanned and decoded to play the track without any internet connection.