arXiv research

New metrics improve scRNA-seq perturbation modeling by reducing mode collapse.

Novel tensor perturbation bounds for orthogonal iteration methods.

Study on mode stability of gravitational instantons of type D.

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated R…

We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $η$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set o…

New method defines GCM spheres in Kerr perturbations, proving their stability.

This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.

New framework assesses graph-learning datasets for better evaluation.

Study examines deformations of Kerr-(A)dS near horizon geometry.

Improved KSD test for better detection of differences in distributions.

The paper provides robustness guarantees for mode estimation in bandits.

A method to explain disease transformation using biomarker covariance matrices.

In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general $3$-manifold $M$ is finite. We conjectured (and proved for the case of $2$-loops) that, after adding counterterms of the expecte…

Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…

Intervention loss stabilizes GAN training and reduces mode collapse.

Paper introduces FoMoH for optimization without backpropagation.

Twistor space constructions and actions are given for full Yang-Mills and conformal gravity using almost complex structures that are not, in general, integrable. These are used as the basis of a derivation of the twistor-string generating functionals for tree level perturbative scattering amplitudes of Yang-Mills and c…

PerturBench benchmarks ML models for cellular perturbation analysis.

We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …

The paper introduces a diagnostic method to detect grokking transitions in models before test accuracy improves.

Introduces PCG for better counterfactual explanations in vision models.

We quantify forgetting in post-training models, distinguishing mass and drift.

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponenti…

New measures quantify diversity of latent representations using metric space magnitude.

Quantum Kerr learning shows enhancements in convergence and generalization for kernel-based methods.

Periodic surfaces have a limited number of bending modes, equal to their membrane modes.

LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.

We prove boundedness and polynomial decay statements for solutions to the spin $\pm1$ Teukolsky-type equation projected to the $\ell=1$ spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor…

Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.

Motivated by advantages of current-mode design, this brief contribution explores the implementation of weight matrices in neuromemristive systems via current-mode memristor crossbar circuits. After deriving theoretical results for the range and distribution of weights in the current-mode design, it is shown that any we…

Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend verification algorithms to be able to certify richer properties of neural netwo…

Identifies root causes of outliers in unknown cyclic graphs.

The paper tackles sampling from Gibbs measures with constrained support, providing a sampling guarantee.

This paper explores tradeoffs between invariance and sensitivity in adversarial examples.

For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…

Characterizes neutral deformation modes of minimal surfaces.

Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.

This paper tackles adaptive control of unknown Markov jump systems with sample complexity and regret bounds.

This paper concludes the series begun in [M. Dafermos and I. Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: the cases |a| << M or axisymmetry, arXiv:1010.5132], providing the complete proof of definitive boundedness and decay results for the scalar wave equation on Kerr backgroun…

Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.

This paper analyzes GANs using Fourier modes to stabilize training.

Analyzes learning dynamics of RNNs under locality constraints.

Geodesics connect model modes in neural network loss landscapes.

A new, efficient $k$-modes algorithm improves clustering of categorical data.

Multimodal clustering is an unsupervised technique for mining interesting patterns in $n$-adic binary relations or $n$-mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n…

EDLP samples flat modes in discrete spaces using entropy.

Proposes a Gaussian process for Koopman mode decomposition.

We give a complete framework for the Gupta-Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta-Bleuler representations satisfy the t…