Related papers: What can we learn from universal Turing machines?
This work summarizes part of current knowledge on High-level Cognitive process and its relation with biological hardware. Thus, it is possible to identify some paradoxes which could impact the development of future technologies and…
The structure of covariant instruments is studied and a general structure theorem is derived. A detailed characterization is given to covariant instruments in the case of an irreducible representation of a locally compact group.
A learning machine, like all machines, is an open system driven far from thermal equilibrium by access to a low entropy source of free energy. We discuss the connection between machines that learn, with low probability of error, and the…
Transparent machine learning is introduced as an alternative form of machine learning, where both the model and the learning system are represented in source code form. The goal of this project is to enable direct human understanding of…
In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
Large language models are capable of in-context learning, the ability to perform new tasks at test time using a handful of input-output examples, without parameter updates. We develop a universal approximation theory to elucidate how…
Reaction systems are a formal model that has been introduced to investigate the interactive behaviors of biochemical reactions. Based on the formal framework of reaction systems, we propose new computing models called reaction automata that…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
We propose Token Turing Machines (TTM), a sequential, autoregressive Transformer model with memory for real-world sequential visual understanding. Our model is inspired by the seminal Neural Turing Machine, and has an external memory…
How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern…
We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to…
As the frontiers of biology become increasingly interdisciplinary, the physics education community has engaged in ongoing efforts to make physics classes more relevant to life sciences majors. These efforts are complicated by the many…
This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret…
Time-series data exists in every corner of real-world systems and services, ranging from satellites in the sky to wearable devices on human bodies. Learning representations by extracting and inferring valuable information from these time…
This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models. The journey begins with the result that there is a single…
Humans can learn a variety of concepts and skills incrementally over the course of their lives while exhibiting many desirable properties, such as continual learning without forgetting, forward transfer and backward transfer of knowledge,…