Related papers: Generating function for Naturalized Series: The ca…
In this paper, we first describe how to find the generating function for the sum of the areas under generalized Dyck paths (with an arbitrary set of steps) using Motzkin paths as a motivating example. We then focus on Motzkin and Dyck…
Recently, concatenating multiple keyphrases as a target sequence has been proposed as a new learning paradigm for keyphrase generation. Existing studies concatenate target keyphrases in different orders but no study has examined the effects…
Response generation for task-oriented dialogues implicitly optimizes two objectives at the same time: task completion and language quality. Conditioned response generation serves as an effective approach to separately and better optimize…
Lexicographic composition is a natural way to build an aggregate choice function from component choice functions. As the name suggests, the components are ordered and choose sequentially. The sets that subsequent components select from are…
Sentence ordering is a general and critical task for natural language generation applications. Previous works have focused on improving its performance in an external, downstream task, such as multi-document summarization. Given its…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
In this paper we find the generating function for the number of vertices which have $k$ elements in their subtree and use this generating function to calculate the probability that a vertex has a size $k$ subtree. We also show how this same…
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
Lists of equivalence classes of words under rotation or rotation plus reversal (i.e., necklaces and bracelets) have many uses, and efficient algorithms for generating these lists exist. In combinatorial group theory elements of a group are…
We introspect black-box sentence embeddings by conditionally generating from them with the objective to retrieve the underlying discrete sentence. We perceive of this as a new unsupervised probing task and show that it correlates well with…
In this paper, we consider combining the ideas of forbidden random context grammars as well as of ordered grammars with cooperating distributed grammar systems (CDGS). We focus on investigating their generative capacities. Both ideas can be…
We show that, for generative classifiers, conditional independence corresponds to linear constraints for the induced discrimination functions. Discrimination functions of undirected Markov network classifiers can thus be characterized by…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
Natural language is compositional; the meaning of a sentence is a function of the meaning of its parts. This property allows humans to create and interpret novel sentences, generalizing robustly outside their prior experience. Neural…
In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…
This work describes the task of metaphoric paraphrase generation, in which we are given a literal sentence and are charged with generating a metaphoric paraphrase. We propose two different models for this task: a lexical replacement…