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We address the need for expanding the presence of the Lisp family of programming languages in bioinformatics and computational biology research. Languages of this family, like Common Lisp, Scheme, or Clojure, facilitate the creation of…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
Motivated by the surge of large language models, there has been a push to formally characterize the symbolic abilities intrinsic to the transformer architecture. A programming language, called RASP, has been proposed, which can be directly…
Following the general theoretical framework of VSA (Vector Symbolic Architecture), a cognitive model with the use of sparse binary hypervectors is proposed. In addition, learning algorithms are introduced to bootstrap the model from…
Designing an explainable model becomes crucial now for Natural Language Processing(NLP) since most of the state-of-the-art machine learning models provide a limited explanation for the prediction. In the spectrum of an explainable model,…
Large language models (LLMs) often encode word-form variation (e.g., walk vs. walked) as linear directions in the embedding space. However, standard tokenization algorithms treat such variants as distinct words with different vocabulary…
Many calculi exist for modelling various features of object-oriented languages. Many of them are based on $\lambda$-calculus and focus either on statically typed class-based languages or dynamic prototype-based languages. We formalize…
In this paper, we review existing points-to Separation Logics for dynamic memory reasoning and we find that different usages of heap separation tend to be an obstacle. Hence, two total and strict spatial heap operations are proposed upon…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
It is always well believed that parsing an image into constituent visual patterns would be helpful for understanding and representing an image. Nevertheless, there has not been evidence in support of the idea on describing an image with a…
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer…
Predicting high-dimensional or extreme multilabels, such as in medical coding, requires both accuracy and interpretability. Existing works often rely on local interpretability methods, failing to provide comprehensive explanations of the…
Large language models (LLMs) have revolutionized NLP by solving downstream tasks with little to no labeled data. Despite their versatile abilities, the larger question of their ability to reason remains ill-understood. This paper addresses…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When…
Sign language recognition could significantly improve the user experience for d/Deaf people with the general consumer technology, such as IoT devices or videoconferencing. However, current sign language recognition architectures are usually…
Using tensor categories, we present new constructions of several of the exceptional simple Lie superalgebras with integer Cartan matrix in characteristic $p = 3$ and $p = 5$ from the complete classification of modular Lie superalgebras with…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
Clause sets saturated by hierarchic ordered resolution do not offer a model representation that can be effectively queried, in general. They only offer the guarantee of the existence of a model. We present an effective symbolic model…
Let L be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic p>3. We prove in this paper that if all tori of maximal dimansion in the semisimple p-envelope of L are standard, the L is up to…
Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…