arXiv research

Paper develops a splitting principle for RCD spaces, extending manifold properties.

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.

We prove a Lorentzian splitting theorem with weakened curvature conditions.

Study Loday algebroids, prove splitting theorem, and linearize problems.

Differential K-theory gets a $λ$-ring structure.

New Einstein manifolds split into symmetric and compact parts.

Optimizes data splitting for shorter conformal prediction intervals.

We embed KKT points in neural networks of different sizes.

Paper establishes a new formula for Atiyah-Patodi-Singer index using eta invariants.

It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from the families of Dirac operators over the two halves. This curvatur…

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splittin…

This paper looks at the splitting problem for globally hyperbolic spacetimes with timelike Ricci curvature bounded below containing a (spacelike, acausal, future causally complete) hypersurface with mean curvature bounded from above. For such spacetimes we show a splitting theorem under the assumption of either the exi…

New method escapes local optima in neural architecture optimization.

Improves decision tree performance by correcting split selection errors.

A new method speeds up sampling in diffusion models.

The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…

MCP extends conformal prediction to vector-valued score functions without data splitting.

A hybrid algorithm fuses significance-based splitting with honest sample-splitting for estimating heterogeneous treatment effects.

CAOS aggregates multiple one-shot predictors for efficient uncertainty quantification.

New method connects knot Floer homology with bordered Floer homology.

FedForest adapts RF for federated learning, improving performance and efficiency.

Generalizes data thinning for various distributions.

We develop techniques for computing the integer valued SU(3) Casson invariant. Our method involves resolving the singularities in the flat moduli space using a twisting perturbation and analyzing its effect on the topology of the perturbed flat moduli space. These techniques, together with Bott-Morse theory and the spl…

Quantized-TinyLLaVA reduces communication costs in split learning for multimodal models.

Compact Kähler spaces with zero first Chern class have special geometric properties.

We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an important task is to choose the regularization parameter $\lam$ appropriately, i.e.…

CSE-FSL reduces communication and storage costs in federated learning.

A new transformer model accelerates training with optimization techniques.

Survey on rigidity results for graphs with prescribed mean curvature.

Diffusion models' consistency across splits explained by random matrix theory.

Study of SO(3)-irreducible geometry in complex 5D and ternary Pauli exclusion principle.

Minimal Morse functions on Poincaré dodecahedral space are selected via spectral properties.

Proposes autoencoding with random forests using spectral graph theory.

Evolutions of the trading landscape lead to the capability to exchange the same financial instrument on different venues. Because of liquidity issues, the trading firms split large orders across several trading destinations to optimize their execution. To solve this problem we devised two stochastic recursive learning …

Using the relativistic Fermat's principle, we establish a bridge between stationary-complete manifolds which satisfy the observer-manifold condition and pre-Randers metrics, namely, Randers metrics without any restriction on the one-form. As a consequence, we give a description of the causal ladder of such spacetimes i…

Improved guarantees for misspecified kernelized bandit optimization.

The Transformer architecture is widely used in natural language processing. Despite its success, the design principle of the Transformer remains elusive. In this paper, we provide a novel perspective towards understanding the architecture: we show that the Transformer can be mathematically interpreted as a numerical Or…

We consider quantum invariants of 3-manifolds associated with arbitrary simple Lie algebras. Using the symmetry principle we show how to decompose the quantum invariant as the product of two invariants, one of them is the invariant corresponding to the projective group. We then show that the projective quantum invarian…

Given a pair of second order diffusion operators, one on the total space of a principle bundle $N$ and the other on the base space $M$, intertwined by the projection $π:N\to M$, if the operator ${\mathcal A}$ on the base manifold has constant rank, we define a semi-connection on the principal bundle which allows to spl…

We give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal G-action on a real tree is dual to the lift of a measured foliation. Analytic too…

A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for networks, the sparse exchangeable graphs, have been introduced to resolve some imp…

In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with bounded nonnegative sectional curvature of dimension greater than or equal to fo…

FREEtree improves tree-based methods for correlated longitudinal data.

Efficient methods accelerate diffusion model sampling.

SPlit optimizes dataset splitting for better model performance.

Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as spin glasses. Proximal algorithms form a class of methods that are broadly applica…

The paper extends keenness concept to bridge splittings and finds conditions for existence.

Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …