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We introduce a new second-order inertial optimization method for machine learning called INNA. It exploits the geometry of the loss function while only requiring stochastic approximations of the function values and the generalized…
It is well known that in a generally covariant gravitational theory the choice of spacetime scalars as coordinates yields phase-space observables (or "invariants"). However their relation to the symmetry group of diffeomorphism…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
We present a manifestly covariant formulation of the gradient descent method, ensuring consistency across arbitrary coordinate systems and general curved trainable spaces. The optimization dynamics is defined using a covariant force vector…
Quantum reservoir computing has emerged as a promising machine learning paradigm for processing temporal data on near-term quantum devices, as it allows for exploiting the large computational capacity of the qubits without suffering from…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
The stochastic differential equations for a model of dissipative particle dynamics, with both total energy and total momentum conservation at every time-step, are presented. The algorithm satisfies detailed balance as well as the…
We introduce an ambidextrous view of stochastic dynamical systems, comparing their forward-time and reverse-time representations and then integrating them into a single time-symmetric representation. The perspective is useful theoretically,…
We study a spatial-temporal structure of quantum fluctuations in the stress-energy tensor of zero-point modes for a scalar field in order to formulate a covariant model. The model describes an invariant vacuum contribution to the…
3+1-dimensional free inviscid fluid dynamics is shown to satisfy the criteria for exact integrability, i.e. having an infinite set of independent, conserved quantities in involution, with the Hamiltonian being one of them. With (density…
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…
We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a…
An abstract 2nd-order evolution equation or inclusion is discretised in time in such a way that the energy is conserved at least in qualified cases, typically in the cases when the governing energy is component-wise quadratic or…
Physical learning machines, be they classical or quantum, are necessarily dissipative systems. The rate of energy dissipation decreases as the learning error rate decreases linking thermodynamic efficiency and learning efficiency. In the…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general…
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
In noisy physical reservoirs, the classical information-processing capacity $C_{\mathrm{ip}}$ quantifies how well a linear readout can realize tasks measurable from the input history, yet $C_{\mathrm{ip}}$ can be far smaller than the…
Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…