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We present polygraphic programs, a subclass of Albert Burroni's polygraphs, as a computational model, showing how these objects can be seen as first-order functional programs. We prove that the model is Turing complete. We use polygraphic…
We consider the problem of combining machine learning models to perform higher-level cognitive tasks with clear specifications. We propose the novel problem of Visual Discrimination Puzzles (VDP) that requires finding interpretable…
Traditional code transformation structures, such as abstract syntax trees (ASTs), conteXtual flow graphs (XFGs), and more generally, compiler intermediate representations (IRs), may have limitations in extracting higher-order semantics from…
Symbolic reasoning and neural networks are often considered incompatible approaches. Connectionist models known as Vector Symbolic Architectures (VSAs) can potentially bridge this gap. However, classical VSAs and neural networks are still…
Recent transformer-based methods achieve notable gains in the Human-object Interaction Detection (HOID) task by leveraging the detection of DETR and the prior knowledge of Vision-Language Model (VLM). However, these methods suffer from…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
Neural-symbolic computing aims at integrating robust neural learning and sound symbolic reasoning into a single framework, so as to leverage the complementary strengths of both of these, seemingly unrelated (maybe even contradictory) AI…
Word-vector representations associate a high dimensional real-vector to every word from a corpus. Recently, neural-network based methods have been proposed for learning this representation from large corpora. This type of word-to-vector…
Learning first-order logic programs (LPs) from relational facts which yields intuitive insights into the data is a challenging topic in neuro-symbolic research. We introduce a novel differentiable inductive logic programming (ILP) model,…
Multiple Instance Learning (MIL) tasks impose a strict logical constraint: a bag is labeled positive if and only if at least one instance within it is positive. While this iff constraint aligns with many real-world applications, recent work…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Vision transformers have achieved leading performance on various visual tasks yet still suffer from high computational complexity. The situation deteriorates in dense prediction tasks like semantic segmentation, as high-resolution inputs…
Sequential programming and work-flow programming are two useful, but radically different, ways of describing computational processing. Of the two, it is sequential programming that we teach all programmers and support by programming…
Lucid programs are data-flow programs and can be visually represented as data flow graphs (DFGs) and composed visually. Forensic Lucid, a Lucid dialect, is a language to specify and reason about cyberforensic cases. It includes the encoding…
The problem of learning a minimal consistent model from a set of labeled sequences of symbols is addressed from a satisfiability modulo theories perspective. We present two encodings for deterministic finite automata and extend one of these…
We introduce a framework for learning continuous neural representations of formal specifications by distilling the geometry of their semantics into a latent space. Existing approaches rely either on symbolic kernels -- which preserve…
We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational…
Synthesizing large logic programs through symbolic Inductive Logic Programming (ILP) typically requires intermediate definitions. However, cluttering the hypothesis space with intensional predicates typically degrades performance. In…
The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…