Related papers: Hey Pentti, We Did It!: A Fully Vector-Symbolic Li…
Using Frequency-domain Holographic Reduced Representations (FHRRs), we extend a Vector-Symbolic Architecture (VSA) encoding of Lisp 1.5 with primitives for arithmetic operations using Residue Hyperdimensional Computing (RHC). Encoding a…
We propose a novel architecture for integrating large language models (LLMs) with a persistent, interactive Lisp environment. This setup enables LLMs to define, invoke, and evolve their own tools through programmatic interaction with a live…
Library learning is the process of building a library of common functionalities from a given set of programs. Typically, this process is applied in the context of aiding program synthesis: concise functions can help the synthesizer produce…
This article introduces hinted dictionaries for expressing efficient ordered sets and maps functionally. As opposed to the traditional ordered dictionaries with logarithmic operations, hinted dictionaries can achieve better performance by…
Functional programming languages are particularly well-suited for building automated reasoning systems, since (among other reasons) a logical term is well modeled by an inductive type, traversing a term can be implemented generically as a…
Designing programming languages that enable intuitive and safe manipulation of data structures is a critical research challenge. Conventional destructive memory operations using pointers are complex and prone to errors. Existing type…
Though end-to-end neural approaches have recently been dominating NLP tasks in both performance and ease-of-use, they lack interpretability and robustness. We propose Binder, a training-free neural-symbolic framework that maps the task…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
In this paper, we present techniques used to implement our portable vectorized library of C standard mathematical functions written entirely in C language. In order to make the library portable while maintaining good performance, intrinsic…
Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
As a supplement to my talk at the workshop, this extended abstract motivates and summarizes my work with co-authors on problems in two separate areas: first, in the lambda-calculus with letrec, a universal model of computation, and second,…
In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…
Vector-space models, from word embeddings to neural network parsers, have many advantages for NLP. But how to generalise from fixed-length word vectors to a vector space for arbitrary linguistic structures is still unclear. In this paper we…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
Human vision is able to capture the part-whole hierarchical information from the entire scene. This paper presents the Visual Parser (ViP) that explicitly constructs such a hierarchy with transformers. ViP divides visual representations…
We present a typed computer language, Doug, in which all typed programs may be proved to halt in polynomial time, encoded in a vector-symbolic architecture (VSA). Doug is just an encoding of the light linear functional programming language…
This paper proposes {\pi}, a formal semantic framework for compiler construction together with program validation. {\pi} is comprised by {\pi} Lib, a set of programming languages constructs inspired by Peter Mosses' Component-Based…
Semantic text representation is a fundamental task in the field of natural language processing. Existing text embedding (e.g., SimCSE and LLM2Vec) have demonstrated excellent performance, but the values of each dimension are difficult to…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…