Related papers: Two-dimensional Dyck words
We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS in $C^d\otimes C^d$ (symmetric qudits) can be…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
Learning high-quality dialogue representations is essential for solving a variety of dialogue-oriented tasks, especially considering that dialogue systems often suffer from data scarcity. In this paper, we introduce Dialogue Sentence…
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…
In previous work we gave a mathematical foundation, referred to as DisCoCat, for how words interact in a sentence in order to produce the meaning of that sentence. To do so, we exploited the perfect structural match of grammar and…
Compressing vision-language models for on-device deployment is increasingly important in clinical settings, but knowledge distillation (KD) degrades sharply when the teacher-student capacity gap spans an order of magnitude or more. We argue…
Word sense disambiguation primarily addresses the lexical ambiguity of common words based on a predefined sense inventory. Conversely, proper names are usually considered to denote an ad-hoc real-world referent. Once the reference is…
This paper describes an alternative method of generating fixed points of certain substitution systems. This method centres on taking infinite words consisting of one repeated letter per word. These infinite words are then interlaced to form…
As the foundation of current natural language processing methods, pre-trained language model has achieved excellent performance. However, the black-box structure of the deep neural network in pre-trained language models seriously limits the…
Separation logic is a concise method for specifying programs that manipulate dynamically allocated storage. Partially inspired by separation logic, Implicit Dynamic Frames has recently been proposed, aiming at first-order tool support. In…
Word embedding, a high-dimensional (HD) numerical representation of words generated by machine learning models, has been used for different natural language processing tasks, e.g., translation between two languages. Recently, there has been…
We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give…
How do humans learn language, and can the first language be learned at all? These fundamental questions are still hotly debated. In contemporary linguistics, there are two major schools of thought that give completely opposite answers.…
We revisit the duality between Kripke and algebraic semantics of intuitionistic and intuitionistic modal logic. We find that there is a certain mismatch between the two semantics, which means that not all algebraic models can be embedded…
A key solution to visual question answering (VQA) exists in how to fuse visual and language features extracted from an input image and question. We show that an attention mechanism that enables dense, bi-directional interactions between the…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
Even though most interfaces in the real world are discrete, no efficient way exists to train neural networks to make use of them, yet. We enhance an Interaction Network (a Reinforcement Learning architecture) with discrete interfaces and…
Recent advancements in unsupervised feature learning have developed powerful latent representations of words. However, it is still not clear what makes one representation better than another and how we can learn the ideal representation.…
Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The…
Distributed representations of words learned from text have proved to be successful in various natural language processing tasks in recent times. While some methods represent words as vectors computed from text using predictive model…