A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper shows robust generative learning with minimal assumptions on target distributions.
Reduced sample complexity for group-invariant distributions.
Generative algorithms learn high-dimensional data efficiently and generate new samples.
New method tightens Lipschitz bounds for CNNs efficiently.
Study Lipschitz regularity for manifold-constrained ROF model on curved surfaces.
The paper proves Lipschitz regularity of graph Laplacian eigenvectors on random data clouds.
The paper uses neural networks to learn system dynamics from data with Lipschitz regularization.
Neural operators learn to solve LQ MFGs efficiently in infinite dimensions.
We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for o…
Generative adversarial networks (GANs) are one of the most popular approaches when it comes to training generative models, among which variants of Wasserstein GANs are considered superior to the standard GAN formulation in terms of learning stability and sample quality. However, Wasserstein GANs require the critic to b…
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
We augment adversarial training (AT) with worst case adversarial training (WCAT) which improves adversarial robustness by 11% over the current state-of-the-art result in the norm on CIFAR-10. We obtain verifiable average case and worst case robustness guarantees, based on the expected and maximum values of the…
Bi-Lipschitz flows approximate a wide range of distributions.
We provide a characterization of r-regular sets in terms of the Lipschitz regularity of normal vector fields to the boundary.
The paper proves new comparison theorems for sub-Laplacian in foliations with minimal leaves.
In this work we study input gradient regularization of deep neural networks, and demonstrate that such regularization leads to generalization proofs and improved adversarial robustness. The proof of generalization does not overcome the curse of dimensionality, but it is independent of the number of layers in the networ…
Deep neural networks are considered to be state of the art models in many offline machine learning tasks. However, their performance and generalization abilities in online learning tasks are much less understood. Therefore, we focus on online learning and tackle the challenging problem where the underlying process is s…
Enhances SSL with mixup and Lipschitz regularization.
We investigate robustness of deep feed-forward neural networks when input data are subject to random uncertainties. More specifically, we consider regularization of the network by its Lipschitz constant and emphasize its role. We highlight the fact that this regularization is not only a way to control the magnitude of …
Adaptive LR improves neural network Lipschitz regularity without slowing convergence.
Study on free boundary problems in RCD spaces, proving existence and regularity.
Consistent partial identification of causal effects proved for neural models.
We extend the Newlander-Nirenberg theorem to manifolds with almost complex structures that have somewhat less than Lipschitz regularity. We also discuss the regularity of local holomorphic coordinates in the integrable case, with particular attention to Lipschitz almost complex structures.
Lipschitz regularity proved for harmonic map heat flows into CAT(0) spaces.
Proves regularity for quasilinear elliptic equations in metric spaces.
Local Lipschitz continuity of sub-elliptic harmonic maps into CAT(0) spaces proved.
In this paper, we prove the Lipschitz regularity of continuous harmonic maps from an finite dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conjecture of F. H. Lin in \cite{lin97}. The proof extends the argument of Huang-Wang \cite {hua-w10}.
Hyperbolic space outperforms Euclidean in learning hierarchical data.
Adversarial perturbations fool deepfake detectors with high accuracy.
Unified analysis of removal-based feature attributions robustness.
Researchers find second-order estimates for -Laplacian in RCD spaces.
LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.
Generative models improve for multiscale scientific data with new noise and interpolation techniques.
In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally Hölder continuous. In [39], F. H. Lin proposed a challenge problem: Can the Hölder continuity …
This paper explores how the generalization of substitute classifiers affects the success of black-box adversarial attacks.
Bi-Lipschitz proof for 2-varifolds near critical Allard condition.
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In th…
We determine regularity results for energy minimizing maps from an -dimensional Riemannian polyhedral complex into a CAT(1) space. Provided that the metric on is Lipschitz regular, we prove Hölder regularity with Hölder constant and exponent dependent on the total energy of the map and the metric on the doma…
Recent studies on the adversarial vulnerability of neural networks have shown that models trained to be more robust to adversarial attacks exhibit more interpretable saliency maps than their non-robust counterparts. We aim to quantify this behavior by considering the alignment between input image and saliency map. We h…
Proves Hawking's theorem for less smooth spacetime metrics.
In this paper, we aim to understand the generalization properties of generative adversarial networks (GANs) from a new perspective of privacy protection. Theoretically, we prove that a differentially private learning algorithm used for training the GAN does not overfit to a certain degree, i.e., the generalization gap …
We consider deep feedforward neural networks with rectified linear units from a signal processing perspective. In this view, such representations mark the transition from using a single (data-driven) linear representation to utilizing a large collection of affine linear representations tailored to particular regions of…
In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some properties similar to the Bregman or skew Jensen divergence. We show these g-diverge…
Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In this paper, we show that the symmetric Bregman divergence can be …
Recent studies on the adversarial vulnerability of neural networks have shown that models trained with the objective of minimizing an upper bound on the worst-case loss over all possible adversarial perturbations improve robustness against adversarial attacks. Beside exploiting adversarial training framework, we show t…
Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high confidence. This raises concerns that such classifiers are vulnerable to attacks and ca…
Study explores relationship between Hölder and FDPD divergences.
Unified representation of density-power-based divergences simplifies estimation to M-estimation.