arXiv research

GamePad uses machine learning to help prove theorems in Coq proof assistant.

Machine learning automates proof generation in Coq proof assistant.

The paper improves dropout's utility by reducing interactions in deep neural networks.

A long-standing conjecture of Farrell and Zdravkovska and independently S.~T.~Yau states that every almost flat manifold is the boundary of a compact manifold. This paper gives a simple proof of this conjecture when the holonomy group is cyclic or quaternionic. The proof is based on the interaction between flat bundles…

A study on the communication complexity of estimating correlations between variables.

Spaces of polynomials are shown to be Euclidean balls.

A new learning method for prosthetic arms without explicit rewards.

Interactive game approach extracts action graphs from specialized text.

Surveying interactions between foliations and contact structures in 3D.

Classical clients can verify quantum learning tasks efficiently.

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fract…

We survey some recent topics on singularities, with a focus on their connection to the minimal model program. This includes the construction and properties of dual complexes, the proof of the ACC conjecture for log canonical thresholds and the recent progress on the `local stability theory' of an arbitrary Kawamata log…

Mathematical framework for cooperative communication explains belief transmission.

Paper develops PAC verification for hypothesis classes and statistical algorithms.

Study connects spectral geometry with Coulomb interactions in perforated manifolds.

Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.

Proposes ICE-based metric for better understanding interactions in black-box models.

AI virtual doctor predicts diabetes from non-invasive data.

Paper resolves open problems on sample complexity in binary hypothesis testing.

In this paper we obtain an existence theorem for normal geodesics joining two given submanifolds in a globally hyperbolic stationary spacetime. The proof is based on both variational and geometric arguments involving the causal structure of the spacetime, the completeness of suitable Finsler metrics associated to it an…

This paper analyzes in details the Batalin-Vilkovisky quantization procedure for BF theories on n-dimensional manifolds and describes a suitable superformalism to deal with the master equation and the search of observables. In particular, generalized Wilson loops for BF theories with additional polynomial B-interaction…

We translate into the double forms formalism the basic identities of Greub and Greub-Vanstone that were obtained in the mixed exterior algebra. In particular, we introduce a second product in the space of double forms, namely the composition product, which provides this space with a second associative algebra structure…

Centralized exchanges influence staking behavior and decentralization in Proof of Stake blockchain ecosystems.

Graphs improve theorem proving in higher-order logic.

Improved sampling from complex distributions with reduced bias.

We use Floer's exact triangle to study the u-map (cup product with the 4-dimensional class) in the Floer cohomology groups of admissible SO(3) bundles over closed, oriented 3-manifolds. In the case of non-trivial bundles we show that (u^2-64)^n = 0 for some positive integer n. For homology 3-spheres Y the same holds fo…

Formalizes vNM utility theorem using Lean 4, proving existence and uniqueness.

DeepDrummer generates drum loops with human preferences via active learning.

Improved regret bound for adversarial bandit convex optimisation.

Relational Graph Neural Networks improve fraud detection in Super-Apps.

Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-equilibrium statistical mechanics model in Euclidean space consisting of the stochastic gradient flow of a given (possibly singular) quasi-convex N-particle interaction energy. We show that a deterministic "macroscopic" evolution…

We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic. Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines induces meromorphic data, which we use to recover the conformal str…

Infants are experts at playing, with an amazing ability to generate novel structured behaviors in unstructured environments that lack clear extrinsic reward signals. We seek to replicate some of these abilities with a neural network that implements curiosity-driven intrinsic motivation. Using a simple but ecologically …

New proof shows a link problem is hard without complex links.

New proof of minimal vector fields on spheres using calibrations.

Symmetric functions learn better with strategic initial conditions.

Upper bound found for systolic geometry on manifolds with positive scalar curvature.

Deep neural networks tackle high-dimensional nonparametric interaction models.

New proof improves differential privacy guarantees for adaptive data analysis.

LeanDojo removes barriers to theorem proving with open-source tools and data.

We consider systems of diffusion processes ("particles") interacting through their ranks (also referred to as "rank-based models" in the mathematical finance literature). We show that, as the number of particles becomes large, the process of fluctuations of the empirical cumulative distribution functions converges to t…

IFM improves recommender systems by learning flexible feature interactions.

Proves the relative h-principle for SL(3,R)^2 3-forms on 6-manifolds.

Surrogate-based analysis of interactions via local effect smooths

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian particle system, in which …

A robot assists a human in a bandit task to learn and improve performance.

We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C. Radin, J. Stat. Phys. 22, 281-287, 1980), which concerns a system of $N$ identical at…

Formal methods verify continuous auctions at exchanges.