Related papers: Query-to-Communication Lifting Using Low-Discrepan…
This work introduces liftings and their associated Young measures as new tools to study the asymptotic behaviour of sequences of pairs $(u_j,Du_j)j$ for $(u_j)_j \in \mathrm{BV}(\Omega;\mathbb{R}^m)$ under weak* convergence. These tools are…
Relational Continuous Models (RCMs) represent joint probability densities over attributes of objects, when the attributes have continuous domains. With relational representations, they can model joint probability distributions over large…
Despite the apparent similarity between shared randomness and shared entanglement in the context of Communication Complexity, our understanding of the latter is not as good as of the former. In particular, there is no known "entanglement…
We make two observations regarding a recent tight example for a composition theorem for randomized query complexity: (1) it implies general randomized query-to-communication lifting is not always true if one allows relations, (2) it is in a…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
Let $f: \{0,1\}^n \to \{0, 1\}$ be a boolean function, and let $f_\land (x, y) = f(x \land y)$ denote the AND-function of $f$, where $x \land y$ denotes bit-wise AND. We study the deterministic communication complexity of $f_\land$ and show…
We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, \zeta > 0$ and any $k\geq1$, we…
The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…
One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
We introduce the lifted Generalized Belief Propagation (GBP) message passing algorithm, for the computation of sum-product queries in Probabilistic Relational Models (e.g. Markov logic network). The algorithm forms a compact region graph…
Integrating knowledge graphs (KGs) to enhance the reasoning capabilities of large language models (LLMs) is an emerging research challenge in claim verification. While KGs provide structured, semantically rich representations well-suited…
We prove a general translation theorem for converting one-way communication lower bounds over a product distribution to dynamic cell-probe lower bounds. Specifically, we consider a class of problems considered in [Pat10] where: 1. $S_1,…
One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially…
In this paper, we show a direct product theorm in the model of two-party bounded-round public-coin randomized communication complexity. For a relation f subset of X times Y times Z (X,Y,Z are finite sets), let R^{(t), pub}_e (f) denote the…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…
A strong direct product theorem states that, in order to solve k instances of a problem, if we provide less than k times the resource required to compute one instance, then the probability of overall success is exponentially small in k. In…
We establish two results regarding the query complexity of bounded-error randomized algorithms. * Bounded-error separation theorem. There exists a total function $f : \{0,1\}^n \to \{0,1\}$ whose $\epsilon$-error randomized query complexity…
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…