Related papers: How glassy are neural networks?
For over half a century, statistical mechanics of spin glasses played as a paradigm to model and interpret disparate phenomena, ranging from quantitative biology to computer science. However, despite the extensive body of research in this…
Spin glass systems as lattices of disordered magnets with random interactions have important implications within the theory of magnetization and applications to a wide-range of hard combinatorial optimization problems. Nevertheless, despite…
Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers.…
We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original…
Associative memory, a form of content-addressable memory, facilitates information storage and retrieval in many biological and physical systems. In statistical mechanics models, associative memory at equilibrium is represented through…
In the study of disordered models like spin glasses the key object of interest is the rugged energy hypersurface defined in configuration space. The statistical mechanics calculation of the Gibbs-Boltzmann Partition Function gives the…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
Extensive experimental and numerical studies of the non-equilibrium dynamics of spin glasses subjected to temperature or bond perturbations have been performed to investigate chaos and memory effects in selected spin glass systems.…
The statistical mechanics of a two-state Ising spin-glass model with finite random connectivity, in which each site is connected to a finite number of other sites, is extended in this work within the replica technique to study the phase…
We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a "cage" is Gaussian, which is not…
The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…
Glasses possess complex energy landscapes and exhibit non-equilibrium aging dynamics. Here, we propose a generalized trap model for activated aging based on a key static property of the energy landscape: the distribution of energy barriers.…
Memory-augmented spiking neural networks (SNNs) promise energy-efficient neuromorphic computing, yet their generalization across sensory modalities remains unexplored. We present the first comprehensive cross-modal ablation study of memory…
We present results from molecular dynamics simulations exploring the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes. In particular, we discuss the transition from the low-density…
We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…
An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic…
Hessian captures important properties of the deep neural network loss landscape. Previous works have observed low rank structure in the Hessians of neural networks. In this paper, we propose a decoupling conjecture that decomposes the…
The site-random Ising spin glass model is investigated. We find a rigorous symmetry for the SG correlation and the free energy, which provides some restrictions in the phase diagram. Using the defect energies calculated by the numerical…
A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean <J_ij> = Jo. Incorporation of a quadrupolar interaction term…