Neural networks parameterize finite-rank generators for ODEs on the orthogonal Lie group, allowing optimization of orthonormal bases in function space with a universality result that rank-2 generators suffice for density.
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From data to functa: Your data point is a function and you can treat it like one.arXiv preprint arXiv:2201.12204
11 Pith papers cite this work. Polarity classification is still indexing.
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Optimal INR freeze depth matches highest weight stable rank layer; SAEs reveal SIREN atoms are localized while FFMLP atoms trace cohort contours with causal impact on PSNR.
NOVA represents world states as INR weights for decoder-free rendering, compactness, and unsupervised disentanglement of background, foreground, and motion in video world models.
DynaDiff uses weight-graph diffusion with a functional consistency loss and dynamics-informed prompting to generate adapted predictors, reporting 10.78% average accuracy gains over baselines while amortizing adaptation cost offline.
FOT-CFM generates turbulent fields in function space with superior high-order statistics and energy spectra on Navier-Stokes, Kolmogorov flow, and Hasegawa-Wakatani equations compared to baselines.
Shap-E encodes 3D assets into implicit function parameters then uses a conditional diffusion model to generate new ones from text, enabling fast multi-representation 3D asset creation.
A two-stage method trains NeRF latents then a diffusion prior to sample posteriors for 3D reconstruction from varied observations including single-view, multi-view, noisy, sparse pixels, and sparse depth.
Physics-informed constraints on implicit neural representations yield more accurate and stable predictions of stirred-tank flows than purely data-driven models when training data is scarce, with diminishing returns at larger dataset sizes.
A conditional diffusion model trained on partitioned incomplete samples for physical dynamics achieves asymptotic convergence to the true generative process under mild conditions and outperforms baselines in imputation.
A synthesis of diffusion-based simulation-based inference methods that address model misspecification, irregular observations, and missing data in scientific applications.
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Learning Orthonormal Bases for Function Spaces
Neural networks parameterize finite-rank generators for ODEs on the orthogonal Lie group, allowing optimization of orthonormal bases in function space with a universality result that rank-2 generators suffice for density.
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What Cohort INRs Encode and Where to Freeze Them
Optimal INR freeze depth matches highest weight stable rank layer; SAEs reveal SIREN atoms are localized while FFMLP atoms trace cohort contours with causal impact on PSNR.
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Render, Don't Decode: Weight-Space World Models with Latent Structural Disentanglement
NOVA represents world states as INR weights for decoder-free rendering, compactness, and unsupervised disentanglement of background, foreground, and motion in video world models.
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Generative Adaptation of Dynamics to Environmental Shifts via Weight-space Diffusion
DynaDiff uses weight-graph diffusion with a functional consistency loss and dynamics-informed prompting to generate adapted predictors, reporting 10.78% average accuracy gains over baselines while amortizing adaptation cost offline.
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Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space
FOT-CFM generates turbulent fields in function space with superior high-order statistics and energy spectra on Navier-Stokes, Kolmogorov flow, and Hasegawa-Wakatani equations compared to baselines.
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Shap-E: Generating Conditional 3D Implicit Functions
Shap-E encodes 3D assets into implicit function parameters then uses a conditional diffusion model to generate new ones from text, enabling fast multi-representation 3D asset creation.
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Predicting 3D structure by latent posterior sampling
A two-stage method trains NeRF latents then a diffusion prior to sample posteriors for 3D reconstruction from varied observations including single-view, multi-view, noisy, sparse pixels, and sparse depth.
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Accelerated and data-efficient flow prediction in stirred tanks via physics-informed learning
Physics-informed constraints on implicit neural representations yield more accurate and stable predictions of stirred-tank flows than purely data-driven models when training data is scarce, with diminishing returns at larger dataset sizes.
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Incomplete Data, Complete Dynamics: A Diffusion Approach
A conditional diffusion model trained on partitioned incomplete samples for physical dynamics achieves asymptotic convergence to the true generative process under mild conditions and outperforms baselines in imputation.
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A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios
A synthesis of diffusion-based simulation-based inference methods that address model misspecification, irregular observations, and missing data in scientific applications.
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