Related papers: Two-dimensional Dyck words
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
Recent progress on image captioning has made it possible to generate novel sentences describing images in natural language, but compressing an image into a single sentence can describe visual content in only coarse detail. While one new…
We present a new Deep Dictionary Learning and Coding Network (DDLCN) for image recognition tasks with limited data. The proposed DDLCN has most of the standard deep learning layers (e.g., input/output, pooling, fully connected, etc.), but…
Self-supervised word embedding algorithms such as word2vec provide a minimal setting for studying representation learning in language modeling. We examine the quartic Taylor approximation of the word2vec loss around the origin, and we show…
We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category.…
Given a real number $\lambda > 1$, we say that $d|n$ is a $\lambda$-middle divisor of $n$ if $$ \sqrt{\frac{n}{\lambda}} < d \leq \sqrt{\lambda n}. $$ We will prove that there are integers having an arbitrarily large number of…
Data-Free Quantization (DFQ) offers a practical solution for model compression without requiring access to real data, making it particularly attractive in privacy-sensitive scenarios. While DFQ has shown promise for unimodal models, its…
We study combinatorial properties of a rational Dyck path by decomposing it into a tuple of Dyck paths. The combinatorial models such as $b$-Stirling permutations, $(b+1)$-ary trees, parenthesis presentations, and binary trees play central…
Semantic matching of natural language sentences or identifying the relationship between two sentences is a core research problem underlying many natural language tasks. Depending on whether training data is available, prior research has…
Deep neural networks (DNNs) have achieved substantial predictive performance in various speech processing tasks. Particularly, it has been shown that a monaural speech separation task can be successfully solved with a DNN-based method…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Change captioning aims to succinctly describe the semantic change between a pair of similar images, while being immune to distractors (illumination and viewpoint changes). Under these distractors, unchanged objects often appear pseudo…
Neural networks are often described as black boxes, reflecting the significant challenge of understanding their internal workings and interactions. We propose a different perspective that challenges the prevailing view: rather than being…
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
Recent studies have consistently given positive hints that morphology is helpful in enriching word embeddings. In this paper, we argue that Chinese word embeddings can be substantially enriched by the morphological information hidden in…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
Image paragraph captioning aims to describe a given image with a sequence of coherent sentences. Most existing methods model the coherence through the topic transition that dynamically infers a topic vector from preceding sentences.…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
Automatic abstractive text summarization is an important and challenging research topic of natural language processing. Among many widely used languages, the Chinese language has a special property that a Chinese character contains rich…