PAL uses the classical Preisach hysteresis operator with learned thresholds and an extrema stack to model sequences, proving O(1)-depth Turing completeness via two-stack PDA simulation and incomparability with standard transformers on rate-independent vs. random-access functions.
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Karin Dahmen and James P
21 Pith papers cite this work. Polarity classification is still indexing.
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Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
Derives computable a posteriori error bounds for decoupled neural approximations of fully coupled FBSDEs that depend on terminal defect, pathwise residual, and control mismatch, backed by continuous-time stability estimates and numerical tests.
Generative models for cosmological field-level inference can reproduce posterior means and cross-correlations yet fail to capture correct uncertainty geometry when validated against HMC reference samples.
Models composed from bilinear factor, exponential link, Gamma prior, Gaussian likelihood, and equality node admit closed-form variational message passing under mean-field factorization.
LTBs-KAN delivers linear-time B-spline evaluation in KANs plus parameter reduction via product-of-sums factorization, with competitive results on MNIST, Fashion-MNIST, and CIFAR-10.
Finite Gaussian-mixture ReLU reverse kernels in conditional diffusion models are dense in conditional KL divergence under exact terminal matching.
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.
Proves total variation distance between finite neural network output laws and their order-(4m-1) Edgeworth approximations is O(n^{-m}) with matching lower bounds, under invertible covariance and polynomially bounded activations; extends to conditionally Gaussian sequences.
A spatiotemporally decoupled physics-informed Stone-Weierstrass neural operator for stable long-time prediction of time-dependent parametric PDEs.
Recurrent networks built from tunable expressive neurons reveal scaling laws with an optimal parameter split that shifts toward higher per-neuron complexity at larger scales.
Tikhonov regularization is analyzed using neural operators as learned surrogates for ill-posed nonlinear operator equations, with error balancing and approximation results extended to Sobolev and Lebesgue spaces.
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
PhySwarm combines a multi-phase advection-diffusion-reaction density model with an equivalent microscopic motion model and a neural-physics controller trained via RL-PINN to generate and control multi-stage emergent behaviors in robot swarms.
An interpretable three-model framework links multisensory tactile features to perceptual attributes and material classification, finding that thermal cues and combined interactions improve accuracy.
Presents a single functional form for neural scaling that unifies multiple scaling dimensions and claims higher extrapolation accuracy than prior forms across diverse tasks and architectures.
A 354-parameter shallow-deep neural network using age, AST, ALT, platelets and FIB-4 achieved external ROC-AUCs of 0.77 and 0.67 for advanced MASLD fibrosis, slightly above FIB-4's 0.75 and 0.60 on Malaysian and Indian cohorts.
Agentic AI systems with DAG topologies are claimed to deliver exponentially superior generalization and sample efficiency compared to monolithic scaling for achieving AGI.
Self-organising memristive networks exhibit collective nonlinear dynamics that can support physical learning with parallels to biological plasticity and potential for energy-efficient edge intelligence.
Lecture notes that treat statistical physics as probability theory and connect Ising models, spin glasses, and renormalization group ideas to Hopfield networks, restricted Boltzmann machines, and large language models.
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Optimal Non-Asymptotic Edgeworth Expansions for Multivariate Neural Network Outputs
Proves total variation distance between finite neural network output laws and their order-(4m-1) Edgeworth approximations is O(n^{-m}) with matching lower bounds, under invertible covariance and polynomially bounded activations; extends to conditionally Gaussian sequences.