Related papers: Hey Pentti, We Did It!: A Fully Vector-Symbolic Li…
We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce three-dimensional scalar and vector expressions…
This paper attempts a more formal approach to the legibility of text based programming languages, presenting, with proof, minimum possible ways of representing structure in text interleaved with information. This presumes that a minimalist…
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…
This paper introduces the Harmonic Token Projection (HTP), a reversible and deterministic framework for generating text embeddings without training, vocabularies, or stochastic parameters. Unlike neural embeddings that rely on statistical…
Programmatic weak supervision methodologies facilitate the expedited labeling of extensive datasets through the use of label functions (LFs) that encapsulate heuristic data sources. Nonetheless, the creation of precise LFs necessitates…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…
Data structures that realize a dictionary are characterized by three basic instructions: (1) Insert (a new entry <key,value>). (2) Search by a key, returning the associated value. (3) Delete an entry. Known realizations are hashing schemes…
Symbolic holes are one of the fundamental building blocks of solver-aided and interactive programming. Unknown values can be soundly integrated into programs, and automated tools such as SAT solvers can be used to prove properties of…
We introduce a new formalisation of languages, called keyboards. We consider a set of elementary operations (writing/erasing a letter, going to the right or to the left,...) and we define a keyboard as a set of finite sequences of such…
The library of practical abstractions (LIBPA) provides efficient implementations of conceptually simple abstractions, in the C programming language. We believe that the best library code is conceptually simple so that it will be easily…
Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that…
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We…
Contrastive Language-Image Pre-Training (CLIP) is a popular method for learning multimodal latent spaces with well-organized semantics. Despite its wide range of applications, CLIP's latent space is known to fail at handling complex…
Enabling robotic agents to perform complex long-horizon tasks has been a long-standing goal in robotics and artificial intelligence (AI). Despite the potential shown by large language models (LLMs), their planning capabilities remain…
String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a…
This article reviews recent progress in the development of the computing framework vector symbolic architectures (VSA) (also known as hyperdimensional computing). This framework is well suited for implementation in stochastic, emerging…
We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms…
We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The…
We give an analysis and generalizations of some long-established constructive completeness results in terms of categorical logic and pre-sheaf and sheaf semantics. The purpose is in no small part conceptual and organizational: from a few…