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Reversible Primitive Permutations (RPP) are recursively defined functions designed to model Reversible Computation. We illustrate a proof, fully developed with the proof-assistant Lean, certifying that: "RPP can encode every Primitive…
This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…
Designing expressive typography that visually conveys a word's meaning while maintaining readability is a complex task, known as semantic typography. It involves selecting an idea, choosing an appropriate font, and balancing creativity with…
The progress of Large Language Models (LLMs) like ChatGPT raises the question of how they can be integrated into education. One hope is that they can support mathematics learning, including word-problem solving. Since LLMs can handle…
Transformer has demonstrated its great power to learn contextual word representations for multiple languages in a single model. To process multilingual sentences in the model, a learnable vector is usually assigned to each language, which…
We study the computational complexity of reachability, coverability and inclusion for extensions of context-free commutative grammars with integer counters and reset operations on them. Those grammars can alternatively be viewed as an…
Continual learning aims to update a model so that it can sequentially learn new tasks without forgetting previously acquired knowledge. Recent continual learning approaches often leverage the vision-language model CLIP for its…
We explain how to see finite combinatorics of preorders implicit in the {text} of basic topological definitions or arguments in (Bourbaki, General topology, Ch.I), and define a concise combinatorial notation such that complete definitions…
Visual-Language Alignment (VLA) has gained a lot of attention since CLIP's groundbreaking work. Although CLIP performs well, the typical direct latent feature alignment lacks clarity in its representation and similarity scores. On the other…
Pre-trained language models (PLMs) have made significant advances in natural language inference (NLI) tasks, however their sensitivity to textual perturbations and dependence on large datasets indicate an over-reliance on shallow…
Prompting techniques have significantly enhanced the capabilities of Large Language Models (LLMs) across various complex tasks, including reasoning, planning, and solving math word problems. However, most research has predominantly focused…
Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…
The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were formulated as computational tasks and the systematical study of their computational…
Large Language Models (LLMs) remain substantially less data-efficient than humans. Pre-pretraining (PPT) on synthetic languages has been proposed to close this gap, with prior work emphasizing highly expressive formal languages such as…
Recent advances in vision-language models (VLMs) have shown remarkable potential in bridging visual and textual modalities. In computational pathology, domain-specific VLMs, which are pre-trained on extensive histopathology image-text…
In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog that consists of the language LO enriched with the constant 1. We use constraints…
We introduce the $L_!^S$-calculus, a linear lambda-calculus extended with scalar multiplication and term addition, that acts as a proof language for intuitionistic linear logic (ILL). These algebraic operations enable the direct expression…
In this paper we provide for parsing with respect to grammars expressed in a general TFS-based formalism, a restriction of ALE. Our motivation being the design of an abstract (WAM-like) machine for the formalism, we consider parsing as a…
Vector-based word representations help countless Natural Language Processing (NLP) tasks capture the language's semantic and syntactic regularities. In this paper, we present the characteristics of existing word embedding approaches and…
Vector representations have become a central element in semantic language modelling, leading to mathematical overlaps with many fields including quantum theory. Compositionality is a core goal for such representations: given representations…