Related papers: Strong Convergence on Weakly Logarithmic Combinato…

The aim of this paper is to extend the aggregation convergence results given in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle and Fermin 2008) to doubly stochastic linear and nonlinear processes with weakly dependent innovations.…

A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibration-like properties that collectively induce and intrinsically structure the large collection of lemmata used in the proofs of…

In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…

The (extensional) theory of arrays is widely used to model systems. Hence, efficient decision procedures are needed to model check such systems. Current decision procedures for the theory of arrays saturate the read-over-write and…

We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations,…

Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…

We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that…

Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

The conditional distribution of the next outcome given the infinite past of a stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…

Ensembling Large Language Models (LLMs) has gained attention as a promising approach to surpass the performance of individual models by leveraging their complementary strengths. In particular, aggregating models' next-token probability…

We introduce a compositional framework for convex analysis based on the notion of convex bifunction of Rockafellar. This framework is well-suited to graphical reasoning, and exhibits rich dualities such as the Legendre-Fenchel transform,…

We propose a randomized algorithm to compute the log-partition function of weakly interacting fermions with polynomial runtime in both the system size and precision. Although weakly interacting fermionic systems are considered tractable for…

In tasks like semantic parsing, instruction following, and question answering, standard deep networks fail to generalize compositionally from small datasets. Many existing approaches overcome this limitation with model architectures that…

This paper gives a generic form of the diamond lemma, which includes support for additive and topological structures of the base set, and which does not require any further structure (e.g. an associative multiplication operation) to be…