Related papers: An Elementary Proof of the Hook Content Formula
This paper proposes an iterative inference algorithm for multi-hop explanation regeneration, that retrieves relevant factual evidence in the form of text snippets, given a natural language question and its answer. Combining multiple sources…
The symplectic/orthogonal contents of partitions are related to the dimensions of irreducible representations of symplectic/orthogonal groups. In 2012, motivated by Nekrasov--Okounkov's hook-length formula and Stanley's hook-content…
This report defines (plain) Dag-like derivations in the purely implicational fragment of minimal logic $M_{\supset}$. Introduce the horizontal collapsing set of rules and the algorithm {\bf HC}. Explain why {\bf HC} can transform any…
In this work, we propose a fast content-based video querying system for large-scale video search. The proposed system is distinguished from similar works with two major contributions. First contribution is superiority of joint usage of…
Fine-tuning Large Language Models (LLMs) with reinforcement learning to produce an explicit Chain-of-Thought (CoT) before answering produces models that consistently raise overall performance on code, math, and general-knowledge benchmarks.…
After a brief introduction to Probability Bracket Notation (PBN) for discrete random variables in time-independent probability spaces, we apply both PBN and Dirac notation to investigate probabilistic modeling for information retrieval…
Hitting formulas have been studied in many different contexts at least since [Iwama,89]. A hitting formula is a set of Boolean clauses such that any two of them cannot be simultaneously falsified. [Peitl,Szeider,05] conjectured that hitting…
Distortion-based analysis has established itself as a fruitful framework for comparing voting mechanisms. m voters and n candidates are jointly embedded in an (unknown) metric space, and the voters submit rankings of candidates by…
In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…
We show that 't Hooft's representation of (2+1)-dimensional gravity in terms of flat polygonal tiles is closely related to a gauge-fixed version of the covariant Hamiltonian lattice theory. 't Hooft's gauge is remarkable in that it leads to…
Linear sequences of words are implicitly represented in our brains by hierarchical structures that organize the composition of words in sentences. Linguists formalize different frameworks to model this hierarchy; two of the most common…
End-to-end neural models have made significant progress in question answering, however recent studies show that these models implicitly assume that the answer and evidence appear close together in a single document. In this work, we propose…
LLMs demonstrate surface-level fluency in code generation but struggle with structured reasoning tasks requiring correctness and semantic alignment. While Chain-of-Thought (CoT) prompting enhances reasoning through intermediate steps, it…
In this paper, we study finitary 1-truncated higher inductive types (HITs) in homotopy type theory. We start by showing that all these types can be constructed from the groupoid quotient. We define an internal notion of signatures for HITs,…
Felty and Miller have described what they claim to be a faithful encoding of the dependently typed lambda calculus LF in the logic of hereditary Harrop formulas, a sublogic of an intuitionistic variant of Church's Simple Theory of Types.…
In this paper, we provide a short proof for the Hopf bifurcation theorem in the Gurtin-MacCamy's population dynamics model. Here we use the Crandall and Rabinowitz's approach, based on the implicit function theorem. Compared with previous…
We study a model of temporal voting where there is a fixed time horizon, and at each round the voters report their preferences over the available candidates and a single candidate is selected. Prior work has adapted popular notions of…
Factor score estimation in small sample sizes often encounters parameter bias and convergence failures when constructing hierarchical national/sub-national indices. This paper proposes a novel method for hierarchical factor analysis called…
We present an approach for performing the tallying work in the coercion-resistant JCJ voting protocol, introduced by Juels, Catalano, and Jakobsson, in linear time using fully homomorphic encryption (FHE). The suggested enhancement also…
Motivated by orthogonal dictionary learning problems, we propose a novel method for matrix factorization, where the data matrix $\mathbf{Y}$ is a product of a Householder matrix $\mathbf{H}$ and a binary matrix $\mathbf{X}$. First, we show…