Related papers: An Elementary Proof of the Hook Content Formula

We present hash embeddings, an efficient method for representing words in a continuous vector form. A hash embedding may be seen as an interpolation between a standard word embedding and a word embedding created using a random hash function…

We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with…

Limited Voting (LV) is an approval-based method for multi-winner elections where all ballots are required to have a same fixed size. While it appears to be used as voting method in corporate governance and has some political applications,…

Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…

Probabilistic inference offers a principled framework for understanding both behaviour and cortical computation. However, two basic and ubiquitous properties of cortical responses seem difficult to reconcile with probabilistic inference:…

Higher-order modal fixpoint logic (HFL) is a higher-order extension of the modal mu-calculus, and strictly more expressive than the modal mu-calculus. It has recently been shown that various program verification problems can naturally be…

The so called induction functors appear in several areas of Algebra in different forms. Interesting examples are the induction functors in the Theory of Affine Algebraic groups. In this note we investigate the so called Hopf pairings…

Hallucination in large language models (LLMs) during long-form generation remains difficult to address under existing reinforcement learning from human feedback (RLHF) frameworks, as their preference rewards often overlook the model's own…

Context: Navigating the knowledge of Stack Overflow (SO) remains challenging. To make the posts vivid to users, SO allows users to write and edit posts with Markdown or HTML so that users can leverage various formatting styles (e.g., bold,…

Recent advances in the study of voting classification algorithms have brought empirical and theoretical results clearly showing the discrimination power of ensemble classifiers. It has been previously argued that the search of this…

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…

Information retrieval systems retrieves relevant documents based on a query submitted by the user. The documents are initially indexed and the words in the documents are assigned weights using a weighting technique called TFIDF which is the…

Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem…

Reinforcement learning from human feedback (RLHF) implicitly aggregates heterogeneous human preferences into a single utility function, even though the underlying utilities of the participants are in practice diverse. Hence, RLHF can be…

Another bijective proof of Stanley's hook-content formula for the generating function for semistandard tableaux of a given shape is given that does not involve the involution principle of Garsia and Milne. It is the result of a merge of the…

This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of…

This paper provides a serious attempt towards constructing a switching-algebraic theory for weighted monotone voting systems, whether they are scalar-weighted or vector-weighted. The paper concentrates on the computation of a prominent…

We introduce HOIGPT, a token-based generative method that unifies 3D hand-object interactions (HOI) perception and generation, offering the first comprehensive solution for captioning and generating high-quality 3D HOI sequences from a…

Majority voting is considered an effective method to enhance chain-of-thought reasoning, as it selects the answer with the highest "self-consistency" among different reasoning paths (Wang et al., 2023). However, previous chain-of-thought…

We introduce a functional inductive framework to verify discrete-time dynamical systems against hyperproperties specified as Hyperlinear temporal logic formulae via a notion of HyperCertificates. Unlike linear temporal logic (LTL) formulae…