无序伊辛系统有效模型推断中的共识
Consensus in Effective Model Inference for Disordered Ising Systems
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中文总结 AI 辅助
本文通过教师-学生框架研究无序伊辛系统，发现独立学习器推断的共识宽度在临界区最小，但错误设定偏差使最一致温度不同于最忠实温度。
中文摘要 AI 辅助
当独立学习器在同一无序系统的数据上训练时，有限且含噪的样本可能导致它们对底层物理的描述不同。我们通过共识（即独立训练模型之间的一致程度）来量化此类描述的可复现性。在二维随机键伊辛模型的教师-学生框架中，一组学生各自从单个淬火键实现中抽取的一组有限平衡构型中推断出一个均匀的有效耦合。将学生和实现中推断出的耦合聚合起来，得到共识分布，其宽度量化了学习器之间的一致程度。该分布的方差精确地分解为有限采样贡献（其下界由Fisher信息倒数给出）和淬火无序贡献。这两个方差之和在临界区域附近最小化，因此共识宽度在赝临界温度附近存在最小值，且该最小值随无序增强而变得尖锐。这两个最小值源于不同机制：采样项继承了Fisher信息的临界峰，而无序项在领头阶与温度无关，仅在无序强度的四阶上通过键无序的线性和三次响应之间的协方差获得其临界最小值。由于学生将均匀耦合拟合到异质晶格上，推断出的耦合还带有在无限数据极限下仍存在的错误设定偏差。该偏差将均方误差的最小值移至共识最小值之上，因此独立学习器最一致的温度并非其共同答案最忠实的温度。
英文摘要
When independent learners are trained on data from the same disordered system, finite and noisy samples can lead them to different descriptions of the underlying physics. We quantify the reproducibility of such descriptions through consensus, the degree of agreement among independently trained models. In a teacher-student framework on the two-dimensional random-bond Ising model, an ensemble of students each infers a single uniform effective coupling from a finite set of equilibrium configurations drawn from one quenched bond realization. Aggregating the inferred couplings across students and realizations yields the consensus distribution, whose width quantifies the agreement among learners. The variance of this distribution separates exactly into a finite-sampling contribution, bounded below by inverse of Fisher information, and a quenched-disorder contribution. Sum of these two variance is minimized near critical region, so the consensus width has a minimum near the pseudocritical temperature that sharpens with increasing disorder. The two minima arise from different mechanisms: the sampling term inherits the critical peak of the Fisher information, while the disorder term is temperature-independent at leading order and acquires its critical minimum only at fourth order in the disorder strength, through the covariance between the linear and cubic responses to the bond disorder. Because the students fit a uniform coupling to a heterogeneous lattice, the inferred coupling also carries a misspecification bias that survives in the infinite-data limit. This bias displaces the minimum of the mean-squared error above the consensus minimum, so the temperature at which independent learners agree most closely is not the temperature at which their shared answer is most faithful.
发表机构
- Gandhi Institute of Technology and Management (GITAM) University（甘地技术与管理大学）
机构由 AI 辅助整理，请以论文原文为准。
