Graphs data is crucial for many applications, and much of it exists in the relations described in textual format. As a result, being able to accurately recall and encode a graph described in earlier text is a basic yet pivotal ability that LLMs need to demonstrate if they are to perform reasoning tasks that involve graph-structured information. Human performance at graph recall has been studied by cognitive scientists for decades, and has been found to often exhibit certain structural patterns of bias that align with human handling of social relationships. To date, however, we know little about how LLMs behave in analogous graph recall tasks: do their recalled graphs also exhibit certain biased patterns, and if so, how do they compare with humans and affect other graph reasoning tasks? In this work, we perform the first systematical study of graph recall by LLMs, investigating the accuracy and biased microstructures (local structural patterns) in their recall. We find that LLMs not only underperform often in graph recall, but also tend to favor more triangles and alternating 2-paths. Moreover, we find that more advanced LLMs have a striking dependence on the domain that a real-world graph comes from -- by yielding the best recall accuracy when the graph is narrated in a language style consistent with its original domain.

The identification and classification of transitions in topological and microstructural regimes in pattern-forming processes are critical for understanding and fabricating microstructurally precise novel materials in many application domains. Unfortunately, relevant microstructure transitions may depend on process parameters in subtle and complex ways that are not captured by the classic theory of phase transition. While supervised machine learning methods may be useful for identifying transition regimes, they need labels which require prior knowledge of order parameters or relevant structures describing these transitions. Motivated by the universality principle for dynamical systems, we instead use a self-supervised approach to solve the inverse problem of predicting process parameters from observed microstructures using neural networks. This approach does not require predefined, labeled data about the different classes of microstructural patterns or about the target task of predicting microstructure transitions. We show that the difficulty of performing the inverse-problem prediction task is related to the goal of discovering microstructure regimes, because qualitative changes in microstructural patterns correspond to changes in uncertainty predictions for our self-supervised problem. We demonstrate the value of our approach by automatically discovering transitions in microstructural regimes in two distinct pattern-forming processes: the spinodal decomposition of a two-phase mixture and the formation of concentration modulations of binary alloys during physical vapor deposition of thin films. This approach opens a promising path forward for discovering and understanding unseen or hard-to-discern transition regimes, and ultimately for controlling complex pattern-forming processes.