Related papers: Transcendental Encoding conjecture
Previous work indicates that large language models exhibit a significant "English bias", i.e. they often perform better when tasks are presented in English. Interestingly, we have observed that using certain other languages in reasoning…
The study of rational relations is fundamental to the study of formal languages and automata theory. A rational relation is conjugate if each pair of words in the relation is conjugate (or cyclic shifts of each other). The notion of…
The choice of sentence encoder architecture reflects assumptions about how a sentence's meaning is composed from its constituent words. We examine the contribution of these architectures by holding them randomly initialised and fixed,…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Representation learning is the foundation of natural language processing (NLP). This work presents new methods to employ visual information as assistant signals to general NLP tasks. For each sentence, we first retrieve a flexible number of…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…
Reasoning is key to many decision making processes. It requires consolidating a set of rule-like premises that are often associated with degrees of uncertainty and observations to draw conclusions. In this work, we address both the case…
Programming language processing (similar to natural language processing) is a hot research topic in the field of software engineering; it has also aroused growing interest in the artificial intelligence community. However, different from a…
Language models trained on billions of tokens have recently led to unprecedented results on many NLP tasks. This success raises the question of whether, in principle, a system can ever ``understand'' raw text without access to some form of…
We investigate the equational theory for Kleene algebra terms with variable complements and constant complements -- (language) complement where it applies only to variables or constants -- w.r.t. languages. While the equational theory…
We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages…
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary…
A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(\mu_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overline{\mu}$, the…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation…
Transformer has demonstrated its great power to learn contextual word representations for multiple languages in a single model. To process multilingual sentences in the model, a learnable vector is usually assigned to each language, which…