Related papers: What does it mean for a system to compute?
This is the first of a series of papers in which we study deep computations (ultracomputations) and deep iterates, formalizing the ideas of "asymptotic limit" of computations and compositional iterates, respectively. In this first paper of…
By dynamic planning, we refer to the ability of the human brain to infer and impose motor trajectories related to cognitive decisions. A recent paradigm, active inference, brings fundamental insights into the adaptation of biological…
Approaching limitations of digital computing technologies have spurred research in neuromorphic and other unconventional approaches to computing. Here we argue that if we want to systematically engineer computing systems that are based on…
Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on…
Analysing how neural networks represent data features in their activations can help interpret how they perform tasks. Hence, a long line of work has focused on mathematically characterising the geometry of such "neural representations." In…
We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which ``particles'' embedded in…
Is it possible to generally construct a dynamical system to simulate a black system without recovering the equations of motion of the latter? Here we show that this goal can be approached by a learning machine. Trained by a set of…
As put forward by neuroscientists, the mechanisms of consciousness can be elucidated by revealing correlations between neural dynamics and specific conscious percepts. Recently, I have elaborated on the mathematical formulation for a system…
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks and neuromorphic computing. Further important examples are cellular automata and differential analyzers.…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…
This paper discusses the meaning and scope of biological hypercomputation (BH). The framework here is computational, and from the outset it should be clear that life is not a standard Turing Machine. Living systems hypercompute, but the…
The increase of existing computational capabilities has made simulation emerge as a third discipline of Science, lying midway between experimental and purely theoretical branches [1, 2]. Simulation enables the evaluation of quantities which…
To learn how cognition is implemented in the brain, we must build computational models that can perform cognitive tasks, and test such models with brain and behavioral experiments. Cognitive science has developed computational models of…
This text presents the research field of natural/unconventional computing as it appears in the book COMPUTING NATURE. The articles discussed consist a selection of works from the Symposium on Natural Computing at AISB-IACAP (British Society…
The study of system complexity primarily has two objectives: to explore underlying patterns and to develop theoretical explanations. Pattern exploration seeks to clarify the mechanisms behind the emergence of system complexity, while…
While the engineering of operating systems is well understood, their formal structure and properties are not. The latter needs a clear definition of the purpose of an OS and an identification of the core. In this paper I offer definitions…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
A computational revolution unleashed the power of artificial neural networks. At the heart of that revolution is automatic differentiation, which calculates the derivative of a performance measure relative to a large number of parameters.…