Related papers: Grammars over the Lambek Calculus with Permutation…
We investigate the relationship between finite terms in lambda-letrec, the lambda calculus with letrec, and the infinite lambda terms they express. As there are easy examples of lambda-terms that, intuitively, are not unfoldings of terms in…
Large language models (LLMs) can explain grammatical rules, yet they often fail to apply those rules when judging sentence acceptability. We present "grammar prompting", an explain-then-process paradigm: a large LLM first produces a concise…
In this paper we present two approaches to Lindenmayer systems: the rule-based (or generative) approach, which focuses on L-systems as Thue rewriting systems and a constraint-based (or model-theoretic) approach, in which rules are abandoned…
Bi-directional LSTMs are a powerful tool for text representation. On the other hand, they have been shown to suffer various limitations due to their sequential nature. We investigate an alternative LSTM structure for encoding text, which…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
In recent years, pre-trained large language models (LLMs) have demonstrated remarkable efficiency in achieving an inference-time few-shot learning capability known as in-context learning. However, existing literature has highlighted the…
We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill's calculi, and focus on their fragments…
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting.…
Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a…
We show that large language models (LLMs) are remarkably good at working with interpretable models that decompose complex outcomes into univariate graph-represented components. By adopting a hierarchical approach to reasoning, LLMs can…
Context-free session types provide a typing discipline for recursive structured communication protocols on bidirectional channels. They overcome the restriction of regular session type systems to tail recursive protocols. This extension…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
This paper presents NgramMarkov, a variant of the Markov constraints. It is dedicated to text generation in constraint programming (CP). It involves a set of n-grams (i.e., sequence of n words) associated with probabilities given by a large…
Despite the widespread use of statistical prior models in various fields, such models for neural network gradients have long been overlooked. The inherent challenge stems from their high-dimensional structures and complex interdependencies,…
We investigate the structure of Large Language Model (LLM) embedding spaces using mathematical concepts, particularly linear algebra and the Hamiltonian formalism, drawing inspiration from analogies with quantum mechanical systems.…
Systems now exist which are able to compile unification grammars into language models that can be included in a speech recognizer, but it is so far unclear whether non-trivial linguistically principled grammars can be used for this purpose.…
We investigate the phenomenon that "every monad is a linear state monad". We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value…
Large language models (LLMs) are powerful tools that, in a number of settings, overlap with the results of human pattern recognition and reasoning. Retrieval-augmented generation (RAG) further allows LLMs to produce tailored output…
Constraint Programming (CP) and Machine Learning (ML) face challenges in text generation due to CP's struggle with implementing "meaning'' and ML's difficulty with structural constraints. This paper proposes a solution by combining both…
Two formalisms, both based on context-free grammars, have recently been proposed as a basis for a non-uniform random generation of combinatorial objects. The former, introduced by Denise et al, associates weights with letters, while the…