arXiv subjects

Hajime Yoshino

Publications and source records attributed to Hajime Yoshino.

At least 19 recordsLinked to original sources

arXiv2026

Graphical model for factorization and completion of relatively high rank tensors by sparse sampling

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful in cases where a substantial amount of data is missing, as in completion of relatively high rank matrices for recommendation systems heavily used in social network services. In order to obtain theoretical insights on the setup, we consider statistical inference of the tensor factorization in a high dimensional limit, which we call as dense limit, where the graphs are large and dense but not fully connected. We build message-passing algorithms and test them in a Bayes optimal teacher-student setting in some specific cases. We also develop a replica theory to examine the performance of statistical inference in the dense limit based on a cumulant expansion. The latter approach allows one to avoid blind usage of Gaussian ansatz which fails in some fully connected systems.

stat.ML↗

arXiv2025

Replicated liquid theory in $1+\infty$ dimensions

We develop a replicated liquid theory for structural glasses which exhibit spatial variation of physical quantities along one axis, say $z$-axis. The theory becomes exact with infinite transverse dimension $d-1 \to \infty$. It provides an exact free-energy functional with space-dependent glass order parameter $Δ_{ab}(z)$. As a first application of the scheme, we study diverging lengths associated with dynamic/static glass transitions of hardspheres with/without confining cavity. The exponents agree with those obtained in previous studies on related mean-field models. Moreover, it predicts a non-trivial spatial profile of the glass order parameter $Δ_{ab}(z)$ within the cavity which exhibits a scaling feature approaching the dynamical glass transition.

cond-mat.soft↗

arXiv2025

Liquid and solid layers in a thermal deep learning machine

Based on deep neural networks (DNNs), deep learning has been successfully applied to many problems, but its mechanism is still not well understood -- especially the reason why over-parametrized DNNs can generalize. A recent statistical mechanics theory on supervised learning by a prototypical multi-layer perceptron (MLP) on some artificial learning scenarios predicts that adjustable parameters of over-parametrized MLPs become strongly constrained by the training data close to the input/output boundaries, while the parameters in the center remain largely free, giving rise to a solid-liquid-solid structure. Here we establish this picture, through numerical experiments on benchmark real-world data using a thermal deep learning machine that explores the phase space of the synaptic weights and neurons. The supervised training is implemented by a GPU-accelerated molecular dynamics algorithm, which operates at very low temperatures, and the trained machine exhibits good generalization ability in the test. Global and layer-specific dynamics, with complex non-equilibrium aging behavior, are characterized by time-dependent auto-correlation and replica-correlation functions. Our analyses reveal that the design space of the parameters in the liquid and solid layers are respectively structureless and hierarchical. Our main results are summarized by a data storage ratio -- network depth phase diagram with liquid and solid phases. The proposed thermal machine, which is a physical model with a well-defined Hamiltonian, that reduces to MLP in the zero-temperature limit, can serve as a starting point for physically interpretable deep learning.

cond-mat.dis-nn↗

arXiv2023

Uniform hyperbolicity of a class of scattering maps

In recent years fractal Weyl laws and related quantum eigenfunction hypothesis have been studied in a plethora of numerical model systems, called quantum maps. In some models studied there one can easily prove uniform hyperbolicity. Yet, a numerically sound method for computing quantum resonance states, did not exist. To address this challenge, we recently introduced a new class of quantum maps. For these quantum maps, we showed that, quantum resonance states can numerically be computed using theoretically grounded methods such as complex scaling or weak absorbing potentials. However, proving uniform hyperbolicty for this class of quantum maps was not straight forward. Going beyond that work this article generalizes the class of scattering maps and provides mathematical proofs for their uniform hyperbolicity. In particular, we show that the suggested class of two-dimensional symplectic scattering maps satisfies the topological horseshoe condition and uniform hyperbolicity. In order to prove these properties, we follow the procedure developed in the paper by Devaney and Nitecki. Specifically, uniform hyperbolicity is shown by identifying a proper region in which the non-wandering set satisfies a sufficient condition to have the so-called sector bundle or cone field. Since no quantum map is known where both a proof of uniform hyperbolicity and a methodologically sound method for numerically computing quantum resonance states exist simultaneously, the present result should be valuable to further test fractal Weyl laws and related topics such as chaotic eigenfunction hypothesis.

nlin.CD↗

arXiv2023

Spatially heterogeneous learning by a deep student machine

Deep neural networks (DNN) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNN, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons with $c$ inputs by a statistical mechanics approach called the teacher-student setting. We consider an ensemble of student machines that exactly reproduce $M$ sets of $N$ dimensional input/output relations provided by a teacher machine. We show that the problem becomes exactly solvable in what we call as 'dense limit': $N \gg c \gg 1$ and $M \gg 1$ with fixed $α=M/c$ using the replica method developed in (H. Yoshino, (2020)). We also study the model numerically performing simple greedy MC simulations. Simulations reveal that learning by the DNN is quite heterogeneous in the network space: configurations of the teacher and the student machines are more correlated within the layers closer to the input/output boundaries while the central region remains much less correlated due to the over-parametrization in qualitative agreement with the theoretical prediction. We evaluate the generalization-error of the DNN with various depth $L$ both theoretically and numerically. Remarkably both the theory and simulation suggest generalization-ability of the student machines, which are only weakly correlated with the teacher in the center, does not vanish even in the deep limit $L \gg 1$ where the system becomes heavily over-parametrized. We also consider the impact of effective dimension $D(\leq N)$ of data by incorporating the hidden manifold model (S. Goldt et. al., (2020)) into our model. The theory implies that the loop corrections to the dense limit become enhanced by either decreasing the width $N$ or decreasing the effective dimension $D$ of the data. Simulation suggests both lead to significant improvements in generalization-ability.

cond-mat.dis-nn↗

arXiv2023

A review on shear jamming

Jamming is a ubiquitous phenomenon that appears in many soft matter systems, including granular materials, foams, colloidal suspensions, emulsions, polymers, and cells -- when jamming occurs, the system undergoes a transition from flow-like to solid-like states. Conventionally, the jamming transition occurs when the system reaches a threshold jamming density under isotropic compression, but recent studies reveal that jamming can also be induced by shear. Shear jamming has attracted much interest in the context of non-equilibrium phase transitions, mechanics and rheology of amorphous materials. Here we review the phenomenology of shear jamming and its related physics. We first describe basic observations obtained in experiments and simulations, and results from theories. Shear jamming is then demonstrated as a "bridge" that connects the rheology of athermal soft spheres and thermal hard spheres. Based on a generalized jamming phase diagram, a universal description is provided for shear jamming in frictionless and frictional systems. We further review the isostaticity and criticality of the shear jamming transition, and the elasticity of shear jammed solids. The broader relevance of shear jamming is discussed, including its relation to other phenomena such as shear hardening, dilatancy, fragility, and discrete shear thickening.

cond-mat.soft↗

arXiv2023

Replica theory for disorder-free spin-lattice glass transition on a tree-like simplex network

A class of pyrochlore oxides, $A_2$Mo$_2$O$_7$ ($A =$ Ho, Y, Dy, Tb) with magnetic ions on corner-sharing tetrahedra is known to exhibit spin-glass transitions without appreciable amount of quenched disorder. Recently a disorder-free theoretical model for such a system has been proposed which takes into account not only spins but also lattice distortions as dynamical variables [K. Mitsumoto, C. Hotta and H. Yoshino, Phys. Rev. Lett. 124, 087201 (2020)]. In the present paper we develop and analyze an exactly solvable disorder-free mean-field model which is a higher-dimensional counterpart of the model. We find the system exhibit complex free-energy landscape accompanying replica symmetry breaking through the spin-lattice coupling.

cond-mat.dis-nn↗

arXiv2022

Supercooled Jahn-Teller Ice

When the spins on the frustrated pyrochlore lattice obey the celebrated 2-$in$-2-$out$ ice rule, they stay in a correlated disordered phase and break the third law of thermodynamics. Similarly, if the atomic ions on the pyrochlore lattice move in and outward of the tetrahedra, they may obey a constraint resembling the ice rule. We discover that a model for pyrochlore molybdates $A_2$Mo$_2$O$_7$ ($A=$Y, Dy, Tb) exhibits a "supercooled ice" state of the displacement degrees of freedom of Mo$^{4+}$ ions, when we take account of the Jahn-Teller (JT) effect. The JT effect occurs when the lattice distortions reduce the symmetry of the local crystal field, resulting in the orbital-energy-splitting that causes the local energy gain. Unlike the standard JT effect that leads to periodic long range ordering, the displacements of Mo$^{4+}$ ions are disordered following the ice-like rule. We microscopically derive a model that describes this situation by having the 2nd and 3rd neighbor interactions between in-out lattice displacements comparably as strong as the nearest neighbor interactions of standard ice. There, the well-known nearly flat energy landscape of the ice state is altered to a metastable highly quasi-degenerate ice-like liquid state coexisting with a crystalline-like ground state. Our Monte Carlo simulations show that this liquid remains remarkably stable down to low temperatures by avoiding the putative first order transition. The relaxation in the supercooled JT ice state exhibits glassy dynamics with a plateau structure. They fit the feature of a "good glassformer" very often found in molecular liquids, but that has never been observed in material solids. The high glass-forming ability of the interacting lattice degrees of freedom will play a key role in the spin-glass transition of the material.

cond-mat.str-el↗

arXiv2022

Computer simulations of the Gardner transition in structural glasses

The exact mean-field theory for the simplest glass-forming system - the dense assembly of hard spheres in the large dimensional limit - predicts the existence of a Gardner phase. This transition is characterized by full replica symmetry breaking that implies two fascinating physical consequences: (i) a hierarchical free-energy landscape, and (ii) marginal stability. Here we discuss recent results of numerical simulations to examine these mean-field predictions in physical dimensions.

cond-mat.dis-nn↗

arXiv2021

Scarring in classical chaotic dynamics with noise

We report the numerical observation of scarring, that is enhancement of probability density around unstable periodic orbits of a chaotic system, in the eigenfunctions of the classical Perron-Frobenius operator of noisy Anosov ("cat") maps, as well as in the noisy Bunimovich stadium. A parallel is drawn between classical and quantum scars, based on the unitarity or non-unitarity of the respective propagators. For uniformly hyperbolic systems such as the cat map, we provide a mechanistic explanation for the classical phase-space localization detected, based on the distribution of finite-time Lyapunov exponents, and the interplay of noise with deterministic dynamics. Classical scarring can be measured by studying autocorrelation functions and their power spectra.

nlin.CD↗

arXiv2021

A jamming plane of sphere packings

The concept of jamming has attracted great research interest due to its broad relevance in soft matter such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to the sphere packing problem and optimization problems. Here we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with a help of an efficient swap algorithm to prepare initial equilibrium configurations. The jamming-plane can be divided into reversible-jamming and irreversible-jamming regimes, based on the reversibility of the route from the initial configuration to jamming. Our results suggest that the irreversible-jamming behavior reflects an escape from the meta-stable glass basin to which the initial configuration belongs to, or the absence of such basins. All jammed states, either compression or shear jammed, are isostatic, and exhibit jamming criticality of the same universality class. However, the anisotropy of contact networks non-trivially depends on the jamming density and strain. Among all state points on the jamming-plane, the jamming-point is a unique one with the minimum jamming density and the maximum randomness. For lattice packings, the jamming-plane shrinks into a single shear jamming-line that is independent of initial configurations. Our study paves the way for solving the long-standing random close packing problem, and provides a more complete framework to understand jamming.

cond-mat.soft↗

arXiv2021

Multiple glass transitions and higher order replica symmetry breaking of binary mixtures

We extend the replica liquid theory in order to describe the multiple glass transitions of binary mixtures with large size disparities, by taking into account the two-step replica symmetry breaking (2RSB). We determine the glass phase diagram of the mixture of large and small particles in the large-dimension limit where the mean-field theory becomes exact. When the size ratio of particles is beyond a critical value, the theory predicts three distinct glass phases; (i) the 1RSB double glass where both components vitrify simultaneously, (ii) the 1RSB single glass where only large particles are frozen while small particles remain mobile, and (iii) a new glass phase called the 2RSB double glass where both components vitrify simultaneously but with an energy landscape topography distinct from the 1RSB double glass.

cond-mat.soft↗

arXiv2021

Eigenfunctions of the Perron-Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps

The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine the validity of the so-called Ulam method, a numerical scheme believed to provide eigenvalues and eigenfunctions of the Perron-Frobenius operator, both for linear and nonlinear maps on the torus. For the nonlinear case, the second-largest eigenvalues and the associated eigenfunctions of the Perron-Frobenius operator are investigated by calculating the Fokker-Planck operator with sufficiently small diffusivity. On the basis of numerical schemes thus established, we find that eigenfunctions for the subleading eigenvalues exhibit spatially inhomogeneous patterns, especially showing localization around the region where unstable manifolds are sparsely running. Finally, such spatial patterns of the eigenfunction are shown to be very close to the distribution of the maximal finite-time Lyapunov exponents.

nlin.CD↗

arXiv2020

From complex to simple : hierarchical free-energy landscape renormalized in deep neural networks

We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the synaptic weights and neurons in the hidden layers in a simple feed-forward perceptron network for two scenarios: a setting with random inputs/outputs and a teacher-student setting. By increasing the strength of constraints,~i.e. increasing the number of training data, successive 2nd order glass transition (random inputs/outputs) or 2nd order crystalline transition (teacher-student setting) take place layer-by-layer starting next to the inputs/outputs boundaries going deeper into the bulk with the thickness of the solid phase growing logarithmically with the data size. This implies the typical storage capacity of the network grows exponentially fast with the depth. In a deep enough network, the central part remains in the liquid phase. We argue that in systems of finite width N, the weak bias field can remain in the center and plays the role of a symmetry-breaking field that connects the opposite sides of the system. The successive glass transitions bring about a hierarchical free-energy landscape with ultrametricity, which evolves in space: it is most complex close to the boundaries but becomes renormalized into progressively simpler ones in deeper layers. These observations provide clues to understand why deep neural networks operate efficiently. Finally, we present some numerical simulations of learning which reveal spatially heterogeneous glassy dynamics truncated by a finite width $N$ effect.

cond-mat.dis-nn↗

arXiv2020

Spin-orbital glass transition in a model of a frustrated pyrochlore magnet without quenched disorder

We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y2Mo2O7, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical randomness to each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielectric non-linear susceptibilities, resolving the long-standing puzzle on the origin of the disorder-free spin glass.

cond-mat.dis-nn↗

arXiv2018

A stability-reversibility map unifies elasticity, plasticity, yielding and jamming in hard sphere glasses

Amorphous solids, such as glasses, have complex responses to deformations, with significant consequences in material design and applications. In this respect two intertwined aspects are important: stability and reversibility. It is crucial to understand on the one hand how a glass may become unstable due to increased plasticity under shear deformations; on the other hand, to what extent the response is reversible, meaning how much a system is able to recover the original configuration once the perturbation is released. Here we focus on assemblies of hard spheres as the simplest model of amorphous solids such as colloidal glasses and granular matter. We prepare glass states quenched from equilibrium supercooled liquid states, which are obtained by using the swap Monte Carlo algorithm and correspond to a wide range of structural relaxation time scales. We exhaustively map out their stability and reversibility under volume and shear strains, using extensive numerical simulations. The region on the volume-shear strain phase diagram where the original glass state remains solid is bounded by the shear-yielding and the shear-jamming lines which meet at a yielding-jamming crossover point. This solid phase can be further divided into two sub-phases: the stable glass phase where the system deforms purely elastically and is totally reversible, and the marginal glass phase where it experiences stochastic plastic deformations at mesoscopic scales and is partially irreversible. The details of the stability-reversibility map depend strongly on the quality of annealing of the glass. This study provides a unified framework for understanding elasticity, plasticity, yielding and jamming in amorphous solids.

cond-mat.soft↗

arXiv2018

Translational and orientational glass transitions in the large-dimensional limit : a generalized replicated liquid theory and an application to patchy colloids

We developed a generalized replicated liquid theory for glassy phases of non-spherical uniaxial molecules and colloids, which becomes exact in the large dimensional limit $d\to\infty$. We then applied the scheme to patchy colloids with sticky patches at their heads and tails. The system exhibits rich phase behaviors involving the translational and orientational degrees of freedom. We found a novel glass-glass transition between glasses with large/small orientational fluctuations.

cond-mat.soft↗

arXiv2018

Disorder-free spin glass transitions and jamming in exactly solvable mean-field models

We construct and analyze a family of $M$-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity $c=αM$ and becomes exactly solvable in the limit of large number of components $M \to \infty$. We consider generic $p$-body interactions between the vectorial Ising/continuous spins with linear/non-linear potentials. The existence of self-generated randomness is demonstrated by showing that the random energy model is recovered from a $M$-component ferromagnetic $p$-spin Ising model in $M \to \infty$ and $p \to \infty$ limit. In our systems the quenched disorder, if present, and the self-generated disorder act additively. Our theory provides a unified mean-field theoretical framework for glass transitions of rotational degree of freedoms such as orientation of molecules in glass forming liquids, color angles in continuous coloring of graphs and vector spins of geometrically frustrated magnets. The rotational glass transitions accompany various types of replica symmetry breaking. In the case of repulsive hardcore interactions in the spin space, continuous the criticality of the jamming or SAT/UNSTAT transition becomes the same as that of hardspheres.

cond-mat.stat-mech↗