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Classical frameworks like Fisher Information approximate the cost of neural adaptation only in low-density regimes, failing to explain the explosive computational overhead incurred during deep structural reconfiguration. To address this, we…
The emergence of Deep Learning has marked a profound shift in machine learning, driven by numerous breakthroughs achieved in recent years. However, as Deep Learning becomes increasingly present in everyday tools and applications, there is a…
Irreversibility implies a preferred flow of time, yet special relativity denies the existence of a preferred clock. This tension has long obstructed the formulation of a relativistic master equation: standard Markovian approximations either…
We present a learning algorithm for discovering conservation laws given as sums of geometrically local observables in quantum dynamics. This includes conserved quantities that arise from local and global symmetries in closed and open…
As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the…
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
This paper begins with a dynamical model that was obtained by applying a machine learning technique (FJet) to time-series data; this dynamical model is then analyzed with Lie symmetry techniques to obtain constants of motion. This analysis…
Properties of the turbulent cascade of kinetic energy are studied using direct numerical simulations of three-dimensional hydrodynamic decaying turbulence with a moderate Reynolds number and the initial Mach number $M=1$. Compressible and…
Deep learning systems achieve remarkable empirical performance, yet the stability of the training process itself remains poorly understood. Training unfolds as a high-dimensional dynamical system in which small perturbations to…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries small perturbations can lead to large deviations over long times, while…
The notion of inertial reference frame is abandoned and I replaced it by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of cause and effect are modeled by the propagation of waves…
A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant and phenomenological model of dissipation) is known to be in odds with the detailed balance in the thermodynamic limit. We show that this is…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, has revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous…
We present an alternative field theoretical approach to the definition of conserved quantities, based directly on the field equations content of a Lagrangian theory (in the standard framework of the Calculus of Variations in jet bundles).…
In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies…