Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0207356

Statistical mechanics of lossy data compression using a non-monotonic perceptron

T. Hosaka·Y. Kabashima·H. Nishimori
View original source ↗Read source document ↗Export metadata ↓

Abstract

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural networks, we utilize a perceptron of which the transfer function is appropriately designed in order to compress and decode the messages. Employing the replica method, we analytically show that our scheme can achieve the optimal performance known in the framework of lossy compression in most cases when the code length becomes infinity. The validity of the obtained results is numerically confirmed.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

T. Hosaka, Y. Kabashima, H. Nishimori. 2002-10-10. Statistical mechanics of lossy data compression using a non-monotonic perceptron. https://doi.org/10.1103/physreve.66.066126

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Feedback percolation on complex networks

Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified framework that dynamically couples the microscopic activation probability to the macroscopic size of the giant component. We show that this simple feedback mechanism produces a rich variety of behaviors both analytically and numerically. Depending on the feedback functions, the system exhibits explosive discontinuous jumps, hybrid transitions, limit-cycle oscillations, and routes to chaos, absent in classical percolation. Our findings establish that macroscopic feedback provides a unifying physical mechanism for phenomena ranging from self-regulating oscillations to systemic infrastructure collapse.

cond-mat.stat-mech↗
arXiv2026

$\mathbb{Z}_2$ gauge and exact solution of the $\pm J$ Edwards-Anderson model in a transverse field

Using the Majorana representation of spin-1/2 operators, we study the $\pm J$ Edwards--Anderson model in a transverse field at $T=0$. We show that, in this representation, the quantity describing the coupling between neighboring spins commutes with the Hamiltonian and, unlike in the Kitaev model, is not subject to any Gauss law. The resulting $\mathbb{Z}_2$ gauge freedom allows the disorder in the signs of the exchange integrals to be eliminated by an exact gauge transformation, so that the spectrum of the system coincides with that of the model with uniform couplings. The resulting theory is quadratic in the Majorana fields. Computing the local Green's functions, we find that the Edwards--Anderson order parameter vanishes for $Δ>J\sqrt{Z}$ and equals $1/4$ for $Δ<J\sqrt{Z}$, which signals a second-order transition from a paramagnetic phase to a spin-glass ground state that is degenerate over spin configurations and replica symmetric at $T=0$.

cond-mat.stat-mech↗
arXiv2026

Thermalization of coarse-grained variables in the Toda lattice: a numerical study

We present here a numerical study of the Toda lattice Hamiltonian dynamics showing how, despite model integrability, it is possible to find many macroscopic observables which display standard equilibrium behavior. In particular, we study numerically the energy time correlation of certain coarse-grained variables, showing that it decays with either exponential or stretched exponential behaviour, thus indicating good thermalization properties. The spirit of our observation is complementary to that of standard Fermi-Pasta-Ulam-Tsingou-like numerical experiments, in which the breaking of integrability is regarded as the key ingredient for relaxation to thermal equilibrium. The present communication corroborates, on the contrary, the view that integrability is not an obstacle to thermalization, provided that a sufficiently weak definition of the latter is accepted. In the Toda lattice we have introduced several kinds of coarse-grained variables, constructed with the purpose to maintain a thermodynamic relevance also for large system sizes, which all show good thermalization properties.

cond-mat.stat-mech↗