arXiv research

Geometric framework for signed multivariate tail-dependence compatibility at various thresholds.

New graphs show hierarchical hyperbolic properties, extending previous work.

We provide a new approach to training neural models to exhibit transparency in a well-defined, functional manner. Our approach naturally operates over structured data and tailors the predictor, functionally, towards a chosen family of (local) witnesses. The estimation problem is setup as a co-operative game between an …

Proximal Mediation Analysis with Hidden Recanting Witnesses

Mathematicians decode geometric properties from eigenvalues over 112 years.

A new method detects hidden driving forces in systems with multiple observables.

USD algorithm transports distributions with or without mass conservation.

A new witness two-sample test improves data efficiency and power.

Loxodromic elements are pseudo-Anosov on specific graphs.

AutoML simplifies two-sample tests for detecting distribution shifts.

This paper extends geometric study of neural networks to non-differentiable layers and random walks.

Link's sphere number equals its bridge number.

Proposes a method to learn representations of higher-dimensional simplicial complexes.

Unified geometric principles unify neural network architectures.

Equivariant cohomology simplifies symplectic manifold integrals with group actions.

In this paper we show that certain generalizations of the $C^r$-Whitney topology, which include the Hölder-Whitney and Sobolev-Whitney topologies on smooth manifolds, satisfy the Baire property, to wit, the countable intersection of open and dense sets is dense.

New lower bounds for sampling from log-concave distributions in higher dimensions.

Early last century witnessed both the complete classification of 2-dimensional manifolds and a proof that classification of 4-dimensional manifolds is undecidable, setting up 3-dimensional manifolds as a central battleground of topology to this day. A rather important subset of the 3-manifolds has turned out to be the …

A new method for analyzing adaptive experiments using kernel treatment effects.

Example shows dense subgroup of SL5(Z) not finitely presented.

A new test detects differences between two distributions without flow.

This note shows how to transform high-probability to in-expectation guarantees in machine learning.

We study the sample complexity of model-based reinforcement learning (henceforth RL) in general contextual decision processes that require strategic exploration to find a near-optimal policy. We design new algorithms for RL with a generic model class and analyze their statistical properties. Our algorithms have sample …

Unified approach for multicalibration in weakly supervised learning.

This work robustifies Wasserstein distance estimation with MoM estimators for outlier-polluted data.

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems involving cohomology groups by converting them into problems about homology groups…

The paper examines the sampling dynamics of diffusion models using ODEs.

We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number theory on sets of integers with no three-term arithmetic progressions. We also carr…

We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to $η$-generalized Bayesian, MDL, and empirical risk minimization estimators. …

New methods estimate causal effects through mediators, handling confounding without strict assumptions.

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimizat…

Proposes DR-ME test for interpretable distributional treatment effects.

In machine learning, we are given a dataset of the form $\{(\mathbf{x}_j,y_j)\}_{j=1}^M$, drawn as i.i.d. samples from an unknown probability distribution $μ$; the marginal distribution for the $\mathbf{x}_j$'s being $μ^*$. We propose that rather than using a positive kernel such as the Gaussian for estimation of these…

We study a continuous-time version of the intermediation model of Grossman and Miller (1988). To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market …

This article constructs the moduli stack of torsionfree $G$-jet-structures in homotopy type theory with one monadic modality. This yields a construction of this moduli stack for any $\infty$-topos equipped with any stable factorization systems. In the intended applications of this theory, the factorization systems are …

Foundation for learning in changing conditions.

Given a closed simply connected manifold $M$ of dimension $2n\ge6$, we compare the ring of characteristic classes of smooth oriented bundles with fibre $M$ to the analogous ring resulting from replacing $M$ by the connected sum $M\sharpΣ$ with an exotic sphere $Σ$. We show that, after inverting the order of $Σ$ in the …

A new rotation invariant method for 3D medical imaging classification.

Proposes GFMMD for comparing signals on graphs.

Sharp comparison for sub-Gaussian random variables in convex order.

New bounds for non-convex estimators without Bernstein condition.

It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed to solve Boolean satisfiability (SAT), it remains a mystery of GNN-based solvers for more complex predicate logic formulae. In this work,…

Oleg Viro studied in arXiv:math/0204290 two interpretations of the (multivariable) Alexander polynomial as a quantum link invariant: either by considering the quasi triangular Hopf algebra associated to $U_q sl(2)$ at fourth roots of unity, or by considering the super Hopf algebra $U_q gl(1|1)$. In this paper, we show …

Survey on AI math foundations, focusing on neural networks.

Saliency methods can aid understanding of deep neural networks. Recent years have witnessed many improvements to saliency methods, as well as new ways for evaluating them. In this paper, we 1) present a novel region-based attribution method, XRAI, that builds upon integrated gradients (Sundararajan et al. 2017), 2) int…

We propose a new NFT price index to track the digital art market.

ShapeVis visualizes high-dimensional data efficiently.

The study shows that several properties are not profinite invariants.