Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
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arXiv preprint arXiv:1901.06523 (2019)
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Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
PnP-Corrector decouples physics simulation from error correction via a plug-and-play agent, cutting error by 29% in 300-day global ocean-atmosphere forecasts.
Neural networks trained on crossing symmetry accurately reconstruct conformal correlators from minimal inputs due to alignment between their spectral bias and CFT smoothness.
Latent diffusability is quantified by decomposing the MMSE rate along diffusion trajectories into Fisher Information and Fisher Information Rate, with three geometric penalties (dimensional compression, tangential distortion, curvature injection) identified as sources of failure.
An approximate greedy router for hybrid PDE solvers that mimics optimal selection without true error access and shows faster, more stable error reduction on test equations.
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
WebSailor trains open-source web agents to match proprietary performance on complex information-seeking tasks by generating high-uncertainty scenarios and using a new RL method called DUPO.
SincKANs integrate Sinc interpolation into KAN activations and report better empirical results than alternatives on function approximation and PINN tasks.
Parity supervision improves exact KL fit and recovery of unseen high-value states in IQP Born machines beyond MSE training or max-entropy controls via parity-moment evidence transfer.
HRGrad resolves gradient conflicts in multi-task learning for asymptotic-preserving neural networks by encoding small parameters and using a gradient alignment metric, enabling stable training across all Knudsen numbers for BGK and linear transport equations.
Quantum computers may enable more natural manipulation of Fourier spectra in ML models via the Quantum Fourier Transform, potentially leading to resource-efficient spectral methods.
Beta Sampling uses spectral analysis to select critical denoising steps in diffusion models, outperforming uniform sampling on FID and IS metrics.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
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Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
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Learning on the Temporal Tangent Bundle for Physics-Informed Neural Networks
Parameterizing the temporal derivative in PINNs and reconstructing via Volterra integral yields 100-200x lower errors on advection, Burgers, and Klein-Gordon equations while proving equivalence to the original PDE.
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PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting
PnP-Corrector decouples physics simulation from error correction via a plug-and-play agent, cutting error by 29% in 300-day global ocean-atmosphere forecasts.
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Neural Networks Reveal a Universal Bias in Conformal Correlators
Neural networks trained on crossing symmetry accurately reconstruct conformal correlators from minimal inputs due to alignment between their spectral bias and CFT smoothness.
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Understanding Latent Diffusability via Fisher Geometry
Latent diffusability is quantified by decomposing the MMSE rate along diffusion trajectories into Fisher Information and Fisher Information Rate, with three geometric penalties (dimensional compression, tangential distortion, curvature injection) identified as sources of failure.
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A Greedy PDE Router for Blending Neural Operators and Classical Methods
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WebSailor: Navigating Super-human Reasoning for Web Agent
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Sinc Kolmogorov-Arnold Network and Its Applications on Physics-informed Neural Networks
SincKANs integrate Sinc interpolation into KAN activations and report better empirical results than alternatives on function approximation and PINN tasks.
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Parity Supervision as a Driver of Generalization in Quantum Generative Modeling
Parity supervision improves exact KL fit and recovery of unseen high-value states in IQP Born machines beyond MSE training or max-entropy controls via parity-moment evidence transfer.
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Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes
HRGrad resolves gradient conflicts in multi-task learning for asymptotic-preserving neural networks by encoding small parameters and using a gradient alignment metric, enabling stable training across all Knudsen numbers for BGK and linear transport equations.
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Spectral methods: crucial for machine learning, natural for quantum computers?
Quantum computers may enable more natural manipulation of Fourier spectra in ML models via the Quantum Fourier Transform, potentially leading to resource-efficient spectral methods.
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Beta Sampling is All You Need: Efficient Image Generation Strategy for Diffusion Models using Stepwise Spectral Analysis
Beta Sampling uses spectral analysis to select critical denoising steps in diffusion models, outperforming uniform sampling on FID and IS metrics.
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A Practitioner's Guide to Kolmogorov-Arnold Networks
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.