Related papers: Entropy Collapse: A Universal Failure Mode of Inte…
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…
In this paper, we introduce the notion of recurrence entropy in the context of nonlinear control systems. A set is said to be ($\tau$-)recurrent if every trajectory that starts in the set returns to it (within at most $\tau$ units of time).…
The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is…
We study inference in models where a transformation of parameters exhibits first-order degeneracy -- that is, its gradient is zero or close to zero, making the standard delta method invalid. A leading example is causal mediation analysis,…
We show explicitly the entropy reduction from a detailed fluctuation theorem for the general stochastic system driven by nonequilibrium process under feedback control. The effect of interaction of the feedback controller with the system is…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
Feedback in compound quantum systems is effected by using the output from one sub-system (``the system'') to control the evolution of a second sub-system (``the ancilla'') which is reversibly coupled to the system. In the limit where the…
We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of…
We investigate the dynamical stability and phase transition behavior in a holographic superfluid model incorporating higher-order self-interaction terms $\lambda |\psi|^4$, $\tau|\psi|^6$, and a non-minimal coupling…
Measurement-induced phase transition (MIPT) describes the nonanalytical change of the entanglement entropy resulting from the interplay between measurement and unitary evolution. In this paper, we investigate the relaxation critical…
Entanglement plays a key role in quantum physics, but how much information it can extract from many-body systems is still an open question, particularly regarding quantum criticalities and emergent symmetries. In this work, we…
Recent advances in reinforcement learning from human feedback (RLHF) and preference optimization have substantially improved the usability, coherence, and safety of large language models. However, recurring behaviors such as performative…
A one dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a…
Widespread deployment of societal-scale machine learning systems necessitates a thorough understanding of the resulting long-term effects these systems have on their environment, including loss of trustworthiness, bias amplification, and…
We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a…
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…
In systems undergoing second order phase transitions, the temperature integral of the specific heat over temperature from zero to the critical temperature is the same in both the normal and ordered phases. This entropy balance relates the…
It is generally believed that in spatial dimension d > 1 the leading contribution to the entanglement entropy S = - tr rho_A log rho_A scales as the area of the boundary of subsystem A. The coefficient of this "area law" is non-universal.…
Neural Collapse (NC) presents an elegant geometric structure that enables individual activations (features), class means and classifier (weights) vectors to reach \textit{optimal} inter-class separability during the terminal phase of…