Related papers: Intrinsic Smallness
We prove a Krieger like embedding theorem for asymptotically expansive systems with the small boundary property. We show that such a system $(X; T)$ embeds in the $K$-full shift with $h_{top}(T) < \log K $ and $\sharp Per_n(X; T) \leq…
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to…
In this survey we discuss work of Levin and V'yugin on collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. More precisely, Levin and V'yugin…
What does it mean to claim that a physical or natural system computes? One answer, endorsed here, is that computing is about programming a system to behave in different ways. This paper offers an account of what it means for a physical…
The immune system provides an ideal metaphor for anomaly detection in general and computer security in particular. Based on this idea, artificial immune systems have been used for a number of years for intrusion detection, unfortunately so…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
We give solutions to two of the questions in a paper by Brendle, Brooke-Taylor, Ng and Nies. Our examples derive from a 2014 construction by Khan and Miller as well as new direct constructions using martingales. At the same time, we…
Working within the framework of free actions of countable amenable groups on compact metrizable spaces, we show that the small boundary property is equivalent to a density version of almost finiteness, which we call almost finiteness in…
A computable structure A is x-computably categorical for some Turing degree x, if for every computable structure B isomorphic to A there is an isomorphism f:B -> A with f computable in x. A degree x is a degree of categoricity if there is a…
An upper quasi-density on $\bf H$ (the integers or the non-negative integers) is a real-valued subadditive function $\mu^\ast$ defined on the whole power set of $\mathbf H$ such that $\mu^\ast(X) \le \mu^\ast({\bf H}) = 1$ and $\mu^\ast(k…
The aim of dataset distillation is to encode the rich features of an original dataset into a tiny dataset. It is a promising approach to accelerate neural network training and related studies. Different approaches have been proposed to…
Representations pervade our daily experience, from letters representing sounds to bit strings encoding digital files. While such representations require externally defined decoders to convey meaning, conscious experience appears…
Understanding internal representations of neural models is a core interest of mechanistic interpretability. Due to its large dimensionality, the representation space can encode various aspects about inputs. To what extent are different…
We review and investigate the general theory of thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities…
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
We introduce the notion of universal memcomputing machines (UMMs): a class of brain-inspired general-purpose computing machines based on systems with memory, whereby processing and storing of information occur on the same physical location.…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
Most modern neural networks for classification fail to take into account the concept of the unknown. Trained neural networks are usually tested in an unrealistic scenario with only examples from a closed set of known classes. In an attempt…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…