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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Approximation by superpositions of a sigmoidal function.Mathematics of Control, Signals and Systems, 2(4):303–314
13 Pith papers cite this work. Polarity classification is still indexing.
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A shared mixed-activation network of width 2dN+d+2 yields layer-wise L^p approximation rates bounded by the modulus of continuity at geometric scale N^{-ℓ}, reducing to (2d+1)N^{-ℓ} for 1-Lipschitz targets.
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.
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.
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.
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.
citing papers explorer
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Preisach Attention: A Hysteretic Model of Sequential Memory
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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Geometric Layer-wise Approximation Rates for Deep Networks
A shared mixed-activation network of width 2dN+d+2 yields layer-wise L^p approximation rates bounded by the modulus of continuity at geometric scale N^{-ℓ}, reducing to (2d+1)N^{-ℓ} for 1-Lipschitz targets.
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Time-Frequency Analysis for Neural Networks
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.
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LTBs-KAN: Linear-Time B-splines Kolmogorov-Arnold Networks
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.
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Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusion
Finite Gaussian-mixture ReLU reverse kernels in conditional diffusion models are dense in conditional KL divergence under exact terminal matching.
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Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs
A spatiotemporally decoupled physics-informed Stone-Weierstrass neural operator for stable long-time prediction of time-dependent parametric PDEs.
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Scaling Laws and Tradeoffs in Recurrent Networks of Expressive Neurons
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.
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Neural operators for solving nonlinear inverse problems
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.
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Bayesian Reasoning for Physics Informed Neural Networks
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
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Machine-Learning-Enhanced Non-Invasive Testing for MASLD Fibrosis: Shallow-Deep Neural Networks Versus FIB-4, Tabular Foundation Models, and Large Language Models
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.
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Position: Agentic AI System Is a Foreseeable Pathway to AGI
Agentic AI systems with DAG topologies are claimed to deliver exponentially superior generalization and sample efficiency compared to monolithic scaling for achieving AGI.
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Self-Organising Memristive Networks as Physical Learning Systems
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.
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Lecture Notes on Statistical Physics and Neural Networks
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.