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In this paper we review the mathematical foundations of convolutional neural nets (CNNs) with the goals of: i) highlighting connections with techniques from statistics, signal processing, linear algebra, differential equations, and…
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar…
This paper is concerned with rule-based programs that go wrong. The unwanted behavior of rule applications is non-termination or failure of a computation. We propose a static program analysis of the non-termination problem for recursion in…
Dynamical systems in biology are complex, and one often does not have comprehensive knowledge about the interactions involved. Chemical reaction network (CRN) inference aims to identify, from observing species concentrations over time, the…
Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in…
Recent neural network architectures such as the basic recurrent neural network (RNN) and Gated Recurrent Unit (GRU) have gained prominence as end-to-end learning architectures for natural language processing tasks. But what is the…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
Representation based classification method (RBCM) remains one of the hottest topics in the community of pattern recognition, and the recently proposed non-negative representation based classification (NRC) achieved impressive recognition…
In recent years, CP-nets have emerged as a useful tool for supporting preference elicitation, reasoning, and representation. CP-nets capture and support reasoning with qualitative conditional preference statements, statements that are…
Computational cognitive modeling investigates human cognition by building detailed computational models for cognitive processes. Adaptive Control of Thought - Rational (ACT-R) is a rule-based cognitive architecture that offers a widely…
Are deep convolutional neural networks (CNNs) for image classification explainable by utility maximization with information acquisition costs? We demonstrate that deep CNNs behave equivalently (in terms of necessary and sufficient…
Natural language syntax yields an unbounded array of hierarchically structured expressions. We claim that these are used in the service of active inference in accord with the free-energy principle (FEP). While conceptual advances alongside…
Deep Neural Networks (DNNs) deliver impressive performance but their black-box nature limits deployment in high-stakes domains requiring transparency. We introduce Compositional Function Networks (CFNs), a novel framework that builds…
The interaction of phase-separating systems with chemical reactions is of great interest in various contexts, from biology to material science. In biology, phase separation is thought to be the driving force behind the formation of…
The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
The popularity of molecular computation has given rise to several models of abstraction, one of the more recent ones being Chemical Reaction Networks (CRNs). These are equivalent to other popular computational models, such as Vector…
The study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal…
This paired article aims to develop an automated and programmable biochemical fully connected neural network (BFCNN) with solid theoretical support. In Part I, a concrete design for BFCNN is presented, along with the validation of the…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…