Related papers: Generating function for Naturalized Series: The ca…
We introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated. For the case of some algebras of Frobenius endomorphisms we describe this…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
This paper presents a machine learning approach to discourse planning in natural language generation. More specifically, we address the problem of learning the most natural ordering of facts in discourse plans for a specific domain. We…
Generative Artificial Intelligence (AI) has rapidly become a powerful tool, capable of generating various types of data, such as images and text. However, despite the significant advancement of generative AI, time series generative AI…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
Neural language model-based approaches to automated story generation suffer from two important limitations. First, language model-based story generators generally do not work toward a given goal or ending. Second, they often lose coherence…
Text classification is one of the most widely studied tasks in natural language processing. Motivated by the principle of compositionality, large multilayer neural network models have been employed for this task in an attempt to effectively…
Our goal in this work is to found a closed form for rational generat- ing functions, these generate a various families of polynomials and generalized polynomials, in order to get the general recursive formula satisfied by these polynomials.
We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and…
Morpho-syntactic lexicons provide information about the morphological and syntactic roles of words in a language. Such lexicons are not available for all languages and even when available, their coverage can be limited. We present a…
In this paper we define Ordered Generating System for finite non-abelian groups, which is a generalization of the basis theorem for finite abelian groups. We prove the following: If each composition factor of a group G has Ordered…
This note examines linear combinations of multi-indexed sequences and derives the multivariate generating function of such a linear combination in terms of the original sequence's m.g.f. Applications include finding distributions and…
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…
Conditional text generation has been a challenging task that is yet to see human-level performance from state-of-the-art models. In this work, we specifically focus on the Commongen benchmark, wherein the aim is to generate a plausible…
We give the generating function for the index of integer lattice points, relative to a finite order ideal. The index is an important concept in the theory of border bases, an alternative to Gr\"obner bases. Equivalently, we explicitly solve…
Distributed representations of words have been shown to capture lexical semantics, as demonstrated by their effectiveness in word similarity and analogical relation tasks. But, these tasks only evaluate lexical semantics indirectly. In this…
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit…
Word ordering is a constrained language generation task taking unordered words as input. Existing work uses linear models and neural networks for the task, yet pre-trained language models have not been studied in word ordering, let alone…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
There exist very lucid explanations of the combinatorial origins of rational and algebraic functions, in particular with respect to regular and context free languages. In the search to understand how to extend these natural correspondences,…