Related papers: Generic and Isometric Embeddings in Reservoir Comp…
Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…
Given a class of embeddings into a contact or a symplectic manifold, we give a sufficient condition, that we call isocontact or isosymplectic realization, for this class to satisfy a general $h$-principle. The flexibility follows from the…
We define inductively isometric embeddings of $\mb{P}^n(\mb{R})$ and $\mb{P}^n(\mb{C})$ (with their canonical metrics conveniently scaled) into the standard unit sphere, which present the former as the restriction of the latter to the set…
A complete embedding is a symplectic embedding $\iota:Y\to M$ of a geometrically bounded symplectic manifold $Y$ into another geometrically bounded symplectic manifold $M$ of the same dimension. When $Y$ satisfies an additional finiteness…
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for…
A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir…
This paper introduces a novel approach to predicting periodic time series using reservoir computing. The model is tailored to deliver precise forecasts of rhythms, a crucial aspect for tasks such as generating musical rhythm. Leveraging…
Modern predictive modeling increasingly calls for a single learned dynamical substrate to operate across multiple regimes. From a dynamical-systems viewpoint, this capability decomposes into the storage of multiple attractors and the…
We present a general hardware framework for building networks that directly implement Reservoir Computing, a popular software method for implementing and training Recurrent Neural Networks and are particularly suited for temporal…
In this paper we study the embedding of Riemannian manifolds in low codimension. The well-known result of Nash and Kuiper says that any short embedding in codimension one can be uniformly approximated by $C^1$ isometric embeddings. This…
In this paper we prove a conjecture of Bryant, Griffiths, and Yang concerning the characteristic variety for the determined isometric embedding system. In particular, we show that the characteristic variety is not smooth for any dimension…
We demonstrate that transformers obtain impressive performance even when some of the layers are randomly initialized and never updated. Inspired by old and well-established ideas in machine learning, we explore a variety of non-linear…
Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…
A new machine learning scheme, termed versatile reservoir computing, is proposed for sustaining the dynamics of heterogeneous complex networks. We show that a single, small-scale reservoir computer trained on time series from a subset of…
Embeddings mapping high-dimensional discrete input to lower-dimensional continuous vector spaces have been widely adopted in machine learning applications as a way to capture domain semantics. Interviewing 13 embedding users across…
We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that…
The feasibility of reservoir computing based on dipole-coupled nanomagnets is demonstrated using micro-magnetic simulations. The reservoir consists of an 2x10 array of nanomagnets. The static-magnetization directions of the nanomagnets are…
Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…
There exist many examples of systems which have some symmetries, and which one may monitor with symmetry preserving controls. Since symmetries are preserved along the evolution, full controllability is not possible, and controllability has…