22 papers · ranked by Valyu relevance
Zvi Schreiber
We investigate possible approaches to what might be called an epi-constructionist approach to mathematics. While most constructive mathematics is concerned with constructive proofs, the agenda here is that the objects that we study, specifically the class of numbers that we study, should be an enumerable set of finite…
Aras Bacho, Holger Boche, Gitta Kutyniok
In this survey, we aim to explore the fundamental question of whether the next generation of artificial intelligence requires quantum computing. Artificial intelligence is increasingly playing a crucial role in many aspects of our daily lives and is central to the fourth industrial revolution. It is therefore…
Nima Dehghani, Gianluca Caterina
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective, the paper rigorously recontextualizes what constitutes physical computing devices…
K. L. Kirkpatrick
The theoretical foundation of neuroscience differs from that of artificial intelligence, and to bridge this gap with AI, we would need a new computing paradigm that describes both fields well. The gap came from mathematicians’ invention of computability theory, which was deliberately narrower than cognition and yet…
Vincent C. Müller
This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the 'maximality thesis'), it discusses proposals for digital…
Gustavo Deco, Yonatan Sanz Perl, Jakub Vohryzek, Andrea Luppi + 1 more
The perhaps most important unsolved problem in neuroscience is how the brain survives in a complex world by performing a rich repertoire of computation on a minimal energy budget. The brain is much better at adapting to the multiplicity of stimuli and outcomes than current generations of computers, artificial neural…
Matthew Fox
Building on work by Alfonseca et al. (2021), we study the conditions necessary for it to be logically possible to prove that an arbitrary artificially intelligent machine will exhibit certain behavior. To do this, we develop a formalism like—but mathematically distinct from—the theory of formal languages and their…
Yinsheng Zhang, Stanislav N. Gorb
Consciousness is liable to not be defined in scientific research, because it is an object of study in philosophy too, which actually hinders the integration of research on a large scale. The present study attempts to define consciousness with mathematical approaches by including the common meaning of consciousness…
Gabriel A. Melo, Marcos R. O. A. Máximo, Nei Y. Soma, Paulo A. L. Castro
'Paulo A. L. Castro'] The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice’s theorem, which is also equivalent to a reduction to Turing’s Halting…
Tiasa Mondol, Daniel G. Brown, Ercan Kuruoglu
We build an analysis based on the Algorithmic Information Theory of computational creativity and extend it to revisit computational aesthetics, thereby, improving on the existing efforts of its formulation. We discuss Kolmogorov complexity, models and randomness deficiency (which is a measure of how much a model falls…
Herbert Jaeger, Beatriz Noheda, Wilfred G. van der Wiel
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 engineer unconventional computing systems in a systematic way, we need guidance from a formal theory that is different from the classical…
Duško Pavlović
| Preface | | v | | --- | --- | --- | | What? | | vii | | 1 Drawing types and functions | | 3 | | 2 | Monoidal computers: computability as a structure | 23 | | 3 | Fixpoints | 39 | | 4 | What can be computed | 53 | | 5 | What cannot be computed | 71 | | 6 | Computing programs | 79 | | 7 Stateful computing | | 97 | | 8…
Alexander Ngu
This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of Dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero Time complexity…
Abrahim Ladha, Yiran Luo, Alan Tian
While the Church-Turing thesis asserts that effective calculability explicates to sets decidable by a Turing machine, the Cobham-Edmonds thesis asserts that feasible computation explicates to the complexity class $\mathsf{P}$, those decidable by a polynomial-time bounded Turing machine. The Church-Turing thesis has…
Boya Wang, Siyuan S. Wang, Cameron Chalk, Andrew D. Ellington + 1 more
DNA is an incredibly dense storage medium for digital data, but computing on the stored information is expensive and slow (rounds of sequencing, in silico computation, and DNA synthesis). Augmenting DNA storage with “in-memory” molecular computation, we use strand displacement reactions to algorithmically modify data…
Tristan Stérin, Abeer Eshra, Janet Adio, Constantine Glen Evans + 1 more
Like life, computers are out-of-equilibrium.^1,2^ Thermodynamically favoured error states are thwarted by energetically-costly processes such as kinetic proofreading of biological polymers, error-correcting codes in computer data storage, and redundancy in molecular programming. Decades of theoretical work shows that…
Authors not listed
Step-by-step thinking is essential in all domains of chemical sciences and engineering. While machine learning tools are broadly used, algorithms that automate reasoning are far less common. We elaborate on seven categories of human reasoning activities and connect each to applications in chemical science and…
Authors not listed
Data-driven strategies are reshaping computational materials design by accelerating the prediction of novel compounds with targeted functionalities. Beyond high-throughput screening, the integration of generative artificial intelligence enables exploration across vast chemical spaces comprising millions of known and…
Lewis Grozinger, Jesús Miró-Bueno, Ángel Goñi-Moreño
The programming of computations in living cells can be done by manipulating information flows within genetic networks. Typically, a single bit of information is encoded by a single gene’s steady state expression. Expression is discretized into high and low levels that correspond to 0 and 1 logic values, analogous to…
Ken Mogi
The computational significance of consciousness is an important and potentially more tractable research theme than the hard problem of consciousness, as one could look at the correlation of consciousness and computational capacities through, e.g., algorithmic or complexity analyses. In the literature, consciousness is…
Authors not listed
The era of exascale computing presents both exciting opportunities and unique challenges for quantum mechanical simulations. While the transition from petaflops to exascale computing has been marked by a steady increase in computational power, the shift towards heterogeneous architectures, particularly the dominant…
V. L. Kalmykov, L. V. Kalmykov
Mathematical black box models, which hide the structure and behavior of the subsystems, currently dominate science. Errors and paradoxes, such as the biodiversity paradox and the limiting similarity hypothesis, often arise from subjective interpretations of these hidden mechanisms. To address these problems, we have…