Related papers: Note: On the memory kernel and the reduced system …
In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…
We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…
We investigate tensor-train approaches to the solution of the time-dependent Schr\"{o}dinger equation for chain-like quantum systems with on-site and nearest-neighbor interactions only. Using efficient low-rank tensor train representations,…
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…
Experiments performed on quantum systems often measure multitime correlation functions. When quantum systems are weakly coupled to their environment, the time evolution of such correlation functions can be reduced to that of the reduced…
Recently, classical kernel methods have been extended by the introduction of suitable tensor kernels so to promote sparsity in the solution of the underlying regression problem. Indeed, they solve an lp-norm regularization problem, with…
We are proposing an extension of the recursive neural network that makes use of a variant of the long short-term memory architecture. The extension allows information low in parse trees to be stored in a memory register (the `memory cell')…
The definition of memory in operational approaches to quantum non-Markovianity depends on the statistical properties of different sets of outcomes related to successive measurement processes performed over the system of interest. Using…
The method proposed by Inomata and his collaborators allows us to transform a damped Caldiroli-Kanai oscillator with time-dependent frequency to one with constant frequency and no friction by redefining the time variable, obtained by…
Metrics specifying distances between data points can be learned in a discriminative manner or from generative models. In this paper, we show how to unify generative and discriminative learning of metrics via a kernel learning framework.…
Diffusion is an ubiquitous phenomenon. It is a widespread belief that as long as the area under a current autocorrelation function converges in time, the corresponding spatiotemporal density dynamics should be diffusive. This may be viewed…
While Landauer's Principle sets a lower bound for the work required for a computation, that work is recoverable for efficient computations. However, practical physical computers, such as modern digital computers or biochemical systems, are…
The choice of transition kernel critically influences the performance of the Markov chain Monte Carlo method. Despite the importance of kernel choice, guiding principles for optimal kernels have not been established. Here, we propose a…
Microwave-to-optical quantum transducers will enable coherent interconnection between distant superconducting quantum devices. Ongoing explorations with several platforms have shown promising results at single-photon levels. However, in all…
The paper examines the problem of accessing a vector memory from a single neuron in a Hebbian neural network. It begins with the review of the author's earlier method, which is different from the Hopfield model in that it recruits…
We investigate how to train kernel approximation methods that generalize well under a memory budget. Building on recent theoretical work, we define a measure of kernel approximation error which we find to be more predictive of the empirical…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
It has been shown recently (Phys. Rev. Lett. 106, 090504 (2011)) that entangled light with Einstein-Podolsky-Rosen (EPR) correlations retrieves information from digital memory better than any classical light. In identifying this, a model of…
Temporal correlations are fundamental in quantum physics, yet their computation is often challenging. The regression theorem (or hypothesis) serves as a key tool in this context, offering a seemingly straightforward approach. However, it…
In this paper we introduce a generalization of the Nakayama functor for finite-dimensional algebras. This is obtained by abstracting its interaction with the forgetful functor to vector spaces. In particular, we characterize the Nakayama…