Related papers: Zigzags in Turing machines
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
A new discontinuous model of computation called one-way jumping finite automata was defined by H. Chigahara et. al. This model was a restricted version of the model jumping finite automata. These automata read an input symbol-by-symbol and…
Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the…
Features in machine learning problems are often time-varying and may be related to outputs in an algebraic or dynamical manner. The dynamic nature of these machine learning problems renders current higher order accelerated gradient descent…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…
Multi-head attention enables transformer models to represent multiple attention patterns simultaneously. Empirically, head specialization emerges in distinct stages during training, while many heads remain redundant and learn similar…
Many scientific and combinatorial problems admit multiple correct solutions, not a single label. Standard supervised learning resolves this ambiguity by choosing one solution as the target, but this hidden selector can be arbitrary,…
We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict…
Transformers have recently revolutionized many domains in modern machine learning and one salient discovery is their remarkable in-context learning capability, where models can solve an unseen task by utilizing task-specific prompts without…
We consider the computational model of the Queue Automaton. An old result is that the deterministic queue automaton is equally expressive as the Turing machine. We introduced the Reactive Turing Machine, enhancing the Turing machine with a…
The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological data analysis. In this paper, we discuss three…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
It is well-known that one-tape Turing machines working in linear time are no more powerful than finite automata, namely they recognize exactly the class of regular languages. We prove that it is not decidable if a one-tape machine works in…
Robotic systems are ever more capable of automation and fulfilment of complex tasks, particularly with reliance on recent advances in intelligent systems, deep learning and artificial intelligence. However, as robots and humans come closer…
Explaining and reasoning about processes which underlie observed black-box phenomena enables the discovery of causal mechanisms, derivation of suitable abstract representations and the formulation of more robust predictions. We propose to…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
We define a class of groups based on parallel computations by pushdown automata. This class generalizes automatic groups. It includes the fundamental groups of all 3-manifolds which obey Thurston' s geometrization conjecture. It also…
Control theory of dynamical systems offers a powerful framework for tackling challenges in deep neural networks and other machine learning architectures. We show that concepts such as simultaneous and ensemble controllability offer new…
Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable.…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…