cond-mat.stat-mech

arXiv:2501.06916v1 Announce Type: new Abstract: This study proposes an approach for removing mislabeled instances from contaminated training datasets by combining surrogate model-based black-box optimization (BBO) with postprocessing and quantum annealing. Mislabeled training instances, a common issue in real-world datasets, often degrade model generalization, necessitating robust and efficient noise-removal strategies. The proposed method evaluates filtered training subsets based on validation loss, iteratively refines loss estimates through surrogate model-based BBO with postprocessing, and leverages quantum annealing to efficiently sample diverse training subsets with low validation error. Experiments on a noisy majority bit task demonstrate the method's ability to prioritize the removal of high-risk mislabeled instances. Integrating D-Wave's clique sampler running on a physical quantum annealer achieves faster optimization and higher-quality training subsets compared to OpenJij's simulated quantum annealing sampler or Neal's simulated annealing sampler, offering a scalable framework for enhancing dataset quality. This work highlights the effectiveness of the proposed method for supervised learning tasks, with future directions including its application to unsupervised learning, real-world datasets, and large-scale implementations.

arXiv:2410.02711v3 Announce Type: replace Abstract: We propose an algorithm, termed the Non-Equilibrium Transport Sampler (NETS), to sample from unnormalized probability distributions. NETS can be viewed as a variant of annealed importance sampling (AIS) based on Jarzynski's equality, in which the stochastic differential equation used to perform the non-equilibrium sampling is augmented with an additional learned drift term that lowers the impact of the unbiasing weights used in AIS. We show that this drift is the minimizer of a variety of objective functions, which can all be estimated in an unbiased fashion without backpropagating through solutions of the stochastic differential equations governing the sampling. We also prove that some these objectives control the Kullback-Leibler divergence of the estimated distribution from its target. NETS is shown to be unbiased and, in addition, has a tunable diffusion coefficient which can be adjusted post-training to maximize the effective sample size. We demonstrate the efficacy of the method on standard benchmarks, high-dimensional Gaussian mixture distributions, and a model from statistical lattice field theory, for which it surpasses the performances of related work and existing baselines.

arXiv:2311.11200v2 Announce Type: replace-cross Abstract: Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution, which often follows a power-law distribution, where the probability mass function is proportional to $x^{-\alpha}$, with $\alpha$ typically ranging between $2 < \alpha < 3$. In this paper, we introduce Bayesian inference methods to obtain more accurate estimates than those obtained using traditional methods, which often yield biased estimates, and precise credible intervals. Through a simulation study, we demonstrate that our approach provides nearly unbiased estimates for the scaling parameter, enhancing the reliability of inferences. We also evaluate new goodness-of-fit tests to improve the effectiveness of the Kolmogorov-Smirnov test, commonly used for this purpose. Our findings show that the Watson test offers superior power while maintaining a controlled type I error rate, enabling us to better determine whether data adheres to a power-law distribution. Finally, we propose a piecewise extension of this model to provide greater flexibility, evaluating the estimation and its goodness-of-fit features as well. In the complex networks field, this extension allows us to model the full degree distribution, instead of just focusing on the tail, as is commonly done. We demonstrate the utility of these novel methods through applications to two real-world datasets, showcasing their practical relevance and potential to advance the analysis of power-law behavior.

arXiv:2409.06537v2 Announce Type: replace-cross Abstract: When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total number of possible states, and yet the characterization of the set of typical states -- the typical set -- alone is sufficient to describe the macroscopic behavior of a given system. Consequently, the concept of typicality, and the associated Asymptotic Equipartition Property allow for a drastic reduction of the degrees of freedom needed for system's statistical description. The mathematical rationale for such a simplification in the description is due to the phenomenon of concentration of measure. The later emerges for equilibrium configurations thanks to very strict constraints on the underlying dynamics, such as weekly interacting and (almost) independent system constituents. The question naturally arises as to whether the concentration of measure and related typicality considerations can be extended and applied to more general complex systems, and if so, what mathematical structure can be expected in the ensuing generalized thermodynamics. In this paper we illustrate the relevance of the concept of typicality in the toy model context of the "thermalized" coin and show how this leads naturally to Shannon entropy. We also show an intriguing connection: The characterization of typical sets in terms of Renyi and Tsallis entropies naturally leads to the free energy and partition function, respectively, and makes their relationship explicit. Finally, we propose potential ways to generalize the concept of typicality to systems where the standard microscopic assumptions do not hold.

arXiv:2501.07193v1 Announce Type: cross Abstract: The lack of cooperation can easily result in inequality among members of a society, which provides an increasing gap between individual incomes. To tackle this issue, we introduce an incentive mechanism based on individual strategies and incomes, wherein a portion of the income from defectors is allocated to reward low-income cooperators, aiming to enhance cooperation by improving the equitable distribution of wealth across the entire population. Moreover, previous research has typically employed network structures or game mechanisms characterized by homogeneity. In this study, we present a network framework that more accurately reflects real-world conditions, where agents are engaged in multiple games, including prisoner's dilemma games in the top-layer and public good games in the down-layer networks. Within this framework, we introduce the concept of ``external coupling'' which connects agents across different networks as acquaintances, thereby facilitating access to shared datasets. Our results indicate that the combined positive effects of external coupling and incentive mechanism lead to optimal cooperation rates and lower Gini coefficients, demonstrating a negative correlation between cooperation and inequality. From a micro-level perspective, this phenomenon primarily arises from the regular network, whereas suboptimal outcomes are observed within the scale-free network. These observations help to give a deeper insight into the interplay between cooperation and wealth disparity in evolutionary games in large populations.

arXiv:2501.03628v1 Announce Type: cross Abstract: This paper demonstrates real-time short-term traffic flow prediction through distributed fiber-optic sensing (DFOS) and data assimilation with a stochastic cell-automata-based traffic model. Traffic congestion on expressways is a severe issue. To alleviate its negative impacts, it is necessary to optimize traffic flow prior to becoming serious congestion. For this purpose, real-time short-term traffic flow prediction is promising. However, conventional traffic monitoring apparatus used in prediction methods faces a technical issue due to the sparsity in traffic flow data. To overcome the issue for realizing real-time traffic prediction, this paper employs DFOS, which enables to obtain spatially continuous and real-time traffic flow data along the road without dead zones. Using mean velocities derived from DFOS data as a feature extraction, this paper proposes a real-time data assimilation method for the short-term prediction. As the theoretical model, the stochastic Nishinari-Fukui-Schadschneider model is adopted. Future traffic flow is simulated with the optimal values of model parameters estimated from observed mean velocities and the initial condition estimated as the latest microscopic traffic state. This concept is validated using two congestion scenarios obtained in Japanese expressways. The results show that the mean absolute error of the predicted mean velocities is 10-15 km/h in the prediction horizon of 30 minutes. Furthermore, the prediction error in congestion length and travel time decreases by 40-84% depending on congestion scenarios when compared with conventional methods with traffic counters. This paper concludes that real-time data assimilation using DFOS enables an accurate short-term traffic prediction.

arXiv:2412.18624v2 Announce Type: replace-cross Abstract: Explanation of grokking (delayed generalization) in learning is given by modeling grokking by the stochastic gradient Langevin dynamics (Brownian motion) and applying the ideas of thermodynamics.

arXiv:2412.18290v1 Announce Type: cross Abstract: Quantum reservoir computing (QRC) has emerged as a promising paradigm for harnessing near-term quantum devices to tackle temporal machine learning tasks. Yet identifying the mechanisms that underlie enhanced performance remains challenging, particularly in many-body open systems where nonlinear interactions and dissipation intertwine in complex ways. Here, we investigate a minimal model of a driven-dissipative quantum reservoir described by two coupled Kerr-nonlinear oscillators, an experimentally realizable platform that features controllable coupling, intrinsic nonlinearity, and tunable photon loss. Using Partial Information Decomposition (PID), we examine how different dynamical regimes encode input drive signals in terms of redundancy (information shared by each oscillator) and synergy (information accessible only through their joint observation). Our key results show that, near a critical point marking a dynamical bifurcation, the system transitions from predominantly redundant to synergistic encoding. We further demonstrate that synergy amplifies short-term responsiveness, thereby enhancing immediate memory retention, whereas strong dissipation leads to more redundant encoding that supports long-term memory retention. These findings elucidate how the interplay of instability and dissipation shapes information processing in small quantum systems, providing a fine-grained, information-theoretic perspective for analyzing and designing QRC platforms.

arXiv:2412.17183v1 Announce Type: cross Abstract: We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.

arXiv:2404.02216v2 Announce Type: replace-cross Abstract: What happens when an infinite number of players play a quantum game? In this tutorial, we will answer this question by looking at the emergence of cooperation, in the presence of noise, in a one-shot quantum Prisoner's dilemma (QuPD). We will use the numerical Agent-based model (ABM), and compare it with the analytical Nash equilibrium mapping (NEM) technique. To measure cooperation, we consider five indicators, i.e., game magnetization, entanglement susceptibility, correlation, player's payoff average and payoff capacity, respectively. In quantum social dilemmas, entanglement plays a non-trivial role in determining the behaviour of the quantum players (or, \textit{qubits}) in the thermodynamic limit, and for QuPD, we consider the existence of bipartite entanglement between neighbouring quantum players. For the five indicators in question, we observe \textit{first}-order phase transitions at two entanglement values, and these phase transition points depend on the payoffs associated with the QuPD game. We numerically analyze and study the properties of both the \textit{Quantum} and the \textit{Defect} phases of the QuPD via the five indicators. The results of this tutorial demonstrate that both ABM and NEM, in conjunction with the chosen five indicators, provide insightful information on cooperative behaviour in an infinite-player one-shot quantum Prisoner's dilemma.