Related papers: An Internal Language for Categories Enriched over …
We present a complete reasoning principle for contextual equivalence in an untyped probabilistic language. The language includes continuous (real-valued) random variables, conditionals, and scoring. It also includes recursion, since the…
In natural language processing (NLP), the semantic similarity task requires large-scale, high-quality human-annotated labels for fine-tuning or evaluation. By contrast, in cases of music similarity, such labels are expensive to collect and…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
The quantum measurement problem is often presented as a conflict between unitary evolution and non-unitary collapse. Drawing on Wittgenstein's later philosophy of language and Bohr's principle of complementarity, we argue that this conflict…
A novel learnable dictionary encoding layer is proposed in this paper for end-to-end language identification. It is inline with the conventional GMM i-vector approach both theoretically and practically. We imitate the mechanism of…
The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
Classic grammars and regular expressions can be used for a variety of purposes, including parsing, intent detection, and matching. However, the comparisons are performed at a structural level, with constituent elements (words or characters)…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…
We consider the problems of language inclusion and language equivalence for Vector Addition Systems with States (VASS) with the acceptance condition defined by the set of accepting states (and more generally by some upward-closed…
We introduce categorical modularity, a novel low-resource intrinsic metric to evaluate word embedding quality. Categorical modularity is a graph modularity metric based on the $k$-nearest neighbor graph constructed with embedding vectors of…
This paper introduces a general method for the exploration of equivalence classes in the input space of Transformer models. The proposed approach is based on sound mathematical theory which describes the internal layers of a Transformer…
We investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction. This construction works well for…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
Objective and scalable measurement of teaching quality is a persistent challenge in education. While Large Language Models (LLMs) offer potential, general-purpose models have struggled to reliably apply complex, authentic classroom…
Over the past decade, analogies, in the form of word-level analogies, have played a significant role as an intrinsic measure of evaluating the quality of word embedding methods such as word2vec. Modern large language models (LLMs), however,…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…