Reinforcement Learning for Microcanonical Graph Ensemble with Assortativity Constraints

How network structure determines function is a fundamental question, and it can be investigated by graph ensembles with precisely controlled structural properties. Canonical approaches, formulated as exponential random graph models (ERGMs), enforce constraints only in expectation, allowing individual realizations to fluctuate around the target. Conversely, microcanonical ensembles impose hard constraints exactly, but practical sampling methods beyond fixing the degree sequence have remained out of reach. Here we introduce the Deep Microcanonical Graph Generator (DMGG), a reinforcement learning (RL) framework that transforms any given graph through degree-preserving rewirings to exactly reach a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. Instead of relying on the entropically dominated Metropolis--Hastings dynamics of the ERGM, DMGG employs a policy-guided search that maximally alters the joint-degree matrix. This eliminates exhaustive parameter tuning and accelerates generation by at least an order of magnitude while preserving configurational diversity. As DMGG generalizes across various graph sizes, sparsities, and topologies, it provides exact null models that allow for the quantitative isolation of secondary observables, such as the clustering coefficient. These results establish RL as a practical and powerful paradigm for generating hard-constrained graphs, opening avenues to investigate structure-function relationships free from ensemble artifacts.

Watch your neighbors: Training statistically accurate chaotic systems with local phase space information

Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a good surrogate model for chaotic dynamics is. Prior work has largely focused either on reproducing the Jacobian of the underlying dynamics, which governs local expansion and contraction rates, or on training surrogate models that reproduce the ground-truth dynamics' long-term statistical behavior. In this work, we propose a new framework that aims to bridge these two paradigms by training surrogate dynamics models with accurate Jacobians and long-term statistical properties. Our method constructs a local covering of a chaotic attractor in phase space and analyzes the expansion and contraction of these coverings under the dynamics. The surrogate model is trained by minimizing the maximum mean discrepancy between the pushforward distributions of the coverings under the surrogate and ground-truth dynamics. Experiments show that our method significantly improves Jacobian accuracy while remaining competitive with state-of-the-art statistically accurate dynamics learning methods. Our code is fully available at https://anonymous.4open.science/r/neighborwatch.