Related papers: Stochastic Thermodynamics of Associative Memory
Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the…
Quantum open systems evolve according to completely positive, trace preserving maps acting on the density operator, which can equivalently be unraveled in term of so-called quantum trajectories. These stochastic sequences of pure states…
Landauer's principle makes a strong connection between information theory and thermodynamics by stating that erasing a one-bit memory at temperature $T_0$ requires an average energy larger than $W_{LB}=k_BT_0 \ln2$, with $k_B$ Boltzmann's…
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper,…
Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…
Accurate characterization of the equilibrium distributions of complex molecular systems and their dependence on environmental factors such as temperature is essential for understanding thermodynamic properties and transition mechanisms.…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction…
Deep Neural Networks (DNNs) excel at many tasks, often rivaling or surpassing human performance. Yet their internal processes remain elusive, frequently described as "black boxes." While performance can be refined experimentally, achieving…
This tutorial investigates the convergence of statistical mechanics and learning theory, elucidating the potential enhancements in machine learning methodologies through the integration of foundational principles from physics. The tutorial…
The neural activity of the human brain is dominated by self-sustained activities. External sensory stimuli influence this autonomous activity but they do not drive the brain directly. Most standard artificial neural network models are…
Continuous improvement in silicon process technologies has made possible the integration of hundreds of cores on a single chip. However, power and heat have become dominant constraints in designing these massive multicore chips causing…
Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on…
The Hopfield associative memory model stores random patterns in synaptic couplings according to Hebb's rule and retrieves them through gradient descent on an energy function. This conventional setting, where neurons are assumed to have…
Natural memories are associative, declarative and distributed. Symbolic computing memories resemble natural memories in their declarative character, and information can be stored and recovered explicitly; however, they lack the associative…
We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular,…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
G\'acs' coarse-grained algorithmic entropy leverages universal computation to quantify the information content of any given physical state. Unlike the Boltzmann and Gibbs-Shannon entropies, it requires no prior commitment to macrovariables…