arXiv Machine Learning
Aug 10
Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
arXiv:2608. 06428v1 Announce Type: new Abstract: Deep Operator Networks (DeepONets; arXiv:1910.
Discretization and Statistical Consistency of Functional Flow Matching
arXiv:2608. 04531v1 Announce Type: new Abstract: Functional flow matching is posed on distributions of functions but implemented from finitely many coefficients or point values.
Related stories
arXiv Machine Learning
Jun 30
A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
arXiv Machine Learning
Jun 3
Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization
arXiv:2605. 15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends.
arXiv Machine Learning
Jun 30
Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
arXiv Machine Learning
Jun 5
Coreset-Induced Conditional Velocity Flow Matching
arXiv:2605. 12951v2 Announce Type: replace-cross Abstract: We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution.
arXiv Machine Learning
Jun 3
A Quantitative Approximation Framework for Flow Distillation in Diffusion Models
arXiv:2606. 03820v1 Announce Type: cross Abstract: We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps.
arXiv AI
Jul 7
PedestrianDiffusion: Multimodal Generative Denoising and Dense State Estimation for Inertial Navigation
arXiv:2607. 03349v1 Announce Type: cross Abstract: The accuracy of consumer-grade inertial navigation is bottlenecked by the stochastic noise of Micro-Electro-Mechanical Systems (MEMS).
arXiv Machine Learning
Jun 9
Self-Consistent Generative Paths via Admissible Random Variational Transport
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
arXiv Machine Learning
Jul 10
Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
arXiv:2607. 08757v1 Announce Type: cross Abstract: Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory.
arXiv Machine Learning
Aug 4
Computational and Statistical Guarantees of the \textit{c}-Rectified flow
arXiv:2608. 02487v1 Announce Type: cross Abstract: Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.
arXiv AI
Jun 10
A Theory on Flow Matching with Neural Networks
arXiv:2606. 10089v1 Announce Type: cross Abstract: In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields.
Hugging Face Trending Papers
3d ago
Operator-Theoretic Generalization Bounds for Multitask Deep Learning
We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces. In vector-valued Sobolev RKHSs, we derive Rademacher complexity bounds for invertible and width-expanding injective architectures.