Related papers: Foundations of Digital Circuits: Denotation, Opera…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
A comprehensive model of natural language processing in the brain must accommodate four components: representations, operations, structures and encoding. It further requires a principled account of how these components mechanistically, and…
We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order -- the extensional order -- and a bistable coherence, which captures…
Answering compositional questions requiring multi-step reasoning is challenging. We introduce an end-to-end differentiable model for interpreting questions about a knowledge graph (KG), which is inspired by formal approaches to semantics.…
*Automated circuit discovery* is a central tool in mechanistic interpretability for identifying the internal components of neural networks responsible for specific behaviors. While prior methods have made significant progress, they…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
Semantic parsing aims at mapping natural language utterances into structured meaning representations. In this work, we propose a structure-aware neural architecture which decomposes the semantic parsing process into two stages. Given an…
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 present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade off in terms of depth and space complexity. As a result we…
Several technological limitations of traditional silicon based computing are leading towards the paradigm shift, from silicon to carbon, in computational world. Among the unconventional modes of computing evolved in past several decades,…
Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…
The category Set_* of sets and partial functions is well-known to be traced monoidal, meaning that a partial function S+U -/-> T+U can be coherently transformed into a partial function S -/-> T. This transformation is generally described in…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
A widely used strategy to discover and understand language model mechanisms is circuit analysis. A circuit is a minimal subgraph of a model's computation graph that executes a specific task. We identify a gap in existing circuit discovery…
This monograph is a comprehensive study of the combinatorial structure of various operads of wiring diagrams and undirected wiring diagrams. Our first main objective is to prove a finite presentation theorem for each operad of wiring…
The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering, where non-determinism is a consequence of the fact that modelling is made in the presence of unknown and…
This document is an introduction to two related formalisms to define Boolean functions: binary decision diagrams, and Boolean circuits. It presents these formalisms and several of their variants studied in the setting of knowledge…
We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…