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Understanding the reasons for the success of deep neural networks trained using stochastic gradient-based methods is a key open problem for the nascent theory of deep learning. The types of data where these networks are most successful, such as images or sequences of speech, are characterized by intricate correlations. Yet, most theoretical work on neural networks does not explicitly model training data or assumes that elements of each data sample are drawn independently from some factorized probability distribution. These approaches are, thus, by construction blind to the correlation structure of real-world datasets and their impact on learning in neural networks. Here, we introduce a generative model for structured datasets that we call the hidden manifold model. The idea is to construct high-dimensional inputs that lie on a lower-dimensional manifold, with labels that depend only on their position within this manifold, akin to a single-layer decoder or generator in a generative adversarial network. We demonstrate that learning of the hidden manifold model is amenable to an analytical treatment by proving a “Gaussian equivalence property” (GEP), and we use the GEP to show how the dynamics of two-layer neural networks trained using one-pass stochastic gradient descent is captured by a set of integro-differential equations that track the performance of the network at all times. This approach permits us to analyze in detail how a neural network learns functions of increasing complexity during training, how its performance depends on its size, and how it is impacted by parameters such as the learning rate or the dimension of the hidden manifold.

As a schematic model of the complexity economic agents are confronted with, we introduce the ``SK-game'', a discrete time binary choice model inspired from mean-field spin-glasses. We show that even in a completely static environment, agents are unable to learn collectively-optimal strategies. This is either because the learning process gets trapped in a sub-optimal fixed point, or because learning never converges and leads to a never ending evolution of agents intentions. Contrarily to the hope that learning might save the standard ``rational expectation'' framework in economics, we argue that complex situations are generically unlearnable and agents must do with satisficing solutions, as argued long ago by Herbert Simon (Simon 1955). Only a centralized, omniscient agent endowed with enormous computing power could qualify to determine the optimal strategy of all agents. Using a mix of analytical arguments and numerical simulations, we find that (i) long memory of past rewards is beneficial to learning whereas over-reaction to recent past is detrimental and leads to cycles or chaos; (ii) increased competition destabilizes fixed points and leads first to chaos and, in the high competition limit, to quasi-cycles; (iii) some amount of randomness in the learning process, perhaps paradoxically, allows the system to reach better collective decisions; (iv) non-stationary, ``aging'' behaviour spontaneously emerge in a large swath of parameter space of our complex but static world. On the positive side, we find that the learning process allows cooperative systems to coordinate around satisficing solutions with rather high (but markedly sub-optimal) average reward. However, hyper-sensitivity to the game parameters makes it impossible to predict ex ante who will be better or worse off in our stylized economy.

We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics simulations to analyze the equilibrium relaxation dynamics of model supercooled liquids over a time window covering 10 orders of magnitude for temperatures down to the experimental glass transition temperatureTg. The analysis of several time correlation functions coupled to spatiotemporal resolution of particle motion allow us to elucidate the nature of the equilibrium dynamics in deeply supercooled liquids. We find that structural relaxation starts at early times in rare localized regions characterized by a waiting-time distribution that develops a power law nearTg. At longer times, relaxation events accumulate with increasing probability in these regions asTgis approached. This accumulation leads to a power-law growth of the linear extension of relaxed domains with time with a large, temperature-dependent dynamic exponent. Past the average relaxation time, unrelaxed domains slowly shrink with time due to relaxation events happening at their boundaries. Our results provide a complete microscopic description of the particle motion responsible for key experimental signatures of glassy dynamics, from the shape and temperature evolution of relaxation spectra to the core features of dynamic heterogeneity. They also provide a microscopic basis to understand the emergence of dynamic facilitation in deeply supercooled liquids and allow us to critically reassess theoretical descriptions of the glass transition.

We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behaviors found in amorphous materials does not necessarily result from the diversity of particle interactions or microscopic dynamics but is instead unified by carefully considering the role of the initial stability of the system.

Tissue, cell, and nucleus morphology change during tumor progression. In 2D confluent cell cultures, different tissue states, such as fluid (unjammed) and solid (jammed), are correlated with cell shapes. These results do not have to apply a priori to three dimensions. Cancer cell motility requires and corresponds to a fluidization of the tumor tissue on the bulk level. Here, we investigate bulk tissue fluidity in 3D and determine how it correlates with cell and nucleus shape. In patient samples of mamma and cervix carcinoma, we find areas where cells can move or are immobile. We compare 3D cell spheroids composed of cells from a cancerous and a noncancerous cell line. Through bulk mechanical spheroid-fusion experiments and single live-cell tracking, we show that the cancerous sample is fluidized by active cells moving through the tissue. The healthy, epithelial sample with immobile cells behaves more solidlike. 3D segmentations of the samples show that the degree of tissue fluidity correlates with elongated cell and nucleus shapes. This correlation links cell shapes to cell motility and bulk mechanical behavior. We find two active states of matter in solid tumors: an amorphous glasslike state with characteristics of 3D cell jamming and a disordered fluid state. Individual cell and nucleus shape may serve as a marker for metastatic potential to foster personalized cancer treatment.

Unusual features of the vibrational density of states D ( ω ) of glasses allow one to rationalize their peculiar low-temperature properties. Simulational studies of D ( ω ) have been restricted to studying poorly annealed glasses that may not be relevant to experiments. Here we report on D ( ω ) of zero-temperature glasses with kinetic stabilities ranging from poorly annealed to ultrastable glasses. For all preparations, the low-frequency part of D ( ω ) splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behavior ( D ex ( ω ) ~  ω 2 ) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes obey D loc ( ω ) ~  ω 4 , irrespective of the stability. The prefactor of this quartic law decreases with increasing stability, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glasses’ stability and their soft vibrational modes The nature of the vibrational modes of amorphous solids is of fundamental interest, but assessing them is challenging due to very long equilibrium times involved. Wang et al. numerically model the localized low-frequency vibrational modes in glasses and show the sensitivity of their populations to glass stability.

Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye’s theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye’s theory (i.e., a boson peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time- and lengthscales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.

Traffic forecasting has attracted widespread attention recently. In reality, traffic data usually contains missing values due to sensor or communication errors. The Spatio-temporal feature in traffic data brings more challenges for processing such missing values, for which the classic techniques (e.g., data imputations) are limited: (1) in temporal axis, the values can be randomly or consecutively missing; (2) in spatial axis, the missing values can happen on one single sensor or on multiple sensors simultaneously. Recent models powered by Graph Neural Networks achieved satisfying performance on traffic forecasting tasks. However, few of them are applicable to such a complex missing-value context. To this end, we propose GCN-M, a Graph Convolutional Network model with the ability to handle the complex missing values in the Spatio-temporal context. Particularly, we jointly model the missing value processing and traffic forecasting tasks, considering both local Spatio-temporal features and global historical patterns in an attention-based memory network. We propose as well a dynamic graph learning module based on the learned local-global features. The experimental results on real-life datasets show the reliability of our proposed method.

Excitons with binding energies of a few hundreds of meV control the optical properties of transition metal dichalcogenide monolayers. Knowledge of the fine structure of these excitons is therefore essential to understand the optoelectronic properties of these 2D materials. Here we measure the exciton fine structure of MoS 2 and MoSe 2 monolayers encapsulated in boron nitride by magneto-photoluminescence spectroscopy in magnetic fields up to 30 T. The experiments performed in transverse magnetic field reveal a brightening of the spin-forbidden dark excitons in MoS 2 monolayer: we find that the dark excitons appear at 14 meV below the bright ones. Measurements performed in tilted magnetic field provide a conceivable description of the neutral exciton fine structure. The experimental results are in agreement with a model taking into account the effect of the exchange interaction on both the bright and dark exciton states as well as the interaction with the magnetic field. Excitons control the optical properties of transition metal dichalcogenide monolayers. Here, the authors measure the exciton fine structure of MoS 2 and MoSe 2 monolayers encapsulated in hBN in magnetic fields up to 30 T, and observe a brightening of the spin-forbidden dark excitons in MoS 2 .