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In materials science, the relationship between microstructure and material properties underpins rational design and performance optimization. Still, due to the complexity, heterogeneity, and multiscale nature of microstructural data, it is difficult to recognize. Electron microscopy provides rich visual access to microstructures. Still, existing analysis approaches rely heavily on manual interpretation or supervised machine learning, both of which are limited by the scarcity of annotations and limited generalizability. This paper presents the hierarchical invariant microstructure representation (HIMR) framework as a purely theoretical contribution to self-supervised representation learning for analyzing the microstructure of electron microscopy images. Rather than proposing an algorithm or empirical pipeline, HIMR provides a conceptual framework for learning, structuring, and relating microstructural information to material properties without labeled data. This framework conceptualizes microstructures as hierarchically organized latent representations, where physically meaningful features emerge through invariance-driven self-supervision and scale-aware aggregation. By integrating principles from representation learning, self-supervised paradigms, and materials physics, HIMR addresses foundational challenges, including imaging variability, scale entanglement, and the disconnect between the learned properties and physically interpretable property reasoning. Central to the framework is the alignment of the learned representation manifolds with property spaces governed by physical laws, enabling interpretable and theoretically grounded microstructure–property reasoning. By articulating explicit theoretical commitments regarding hierarchy, invariance, interpretability, and epistemic restraint, this work advances a framework-level understanding of self-supervised learning in materials science. As a result, HIMR provides a durable conceptual foundation for autonomous, data-efficient, and physically grounded analysis in AI-driven materials discovery and engineering.

The field of materials science has witnessed a transformative shift with the advent of representation learning techniques, particularly for analyzing complex microstructures. This review synthesizes recent conceptual advances in representation learning, including deep neural networks, autoencoders, and vision transformers, applied to microstructure data for tasks such as property prediction, inverse design, and evolution modeling. We explore how these methods extract latent features from high-dimensional microstructure images, enabling efficient computation and discovery of structure-property relationships. However, interpretability remains a significant challenge, as black-box models often obscure the physical meaning of learned representations, hindering trust and scientific insight. We discuss strategies for enhancing interpretability, such as attention mechanisms, heat maps, and post-hoc explanations, drawing from recent studies in alloy microstructures and additive manufacturing. The review highlights the integration of domain knowledge to disentangle representations and address data scarcity issues. By examining case studies in metals, ceramics, and composites, we identify gaps in current approaches, including bias in learned features and limited generalizability across materials classes. Ultimately, this review aims to guide future research toward interpretable representation-learning frameworks that accelerate materials design and foster a deeper understanding of microstructural phenomena.

Compressed representations—such as handcrafted descriptors, autoencoder embeddings, and graph-neural-network latent spaces—have become indispensable in artificial-intelligence-driven materials science because they enable scalable property prediction from high-dimensional atomic configurations. Yet the very act of compression, while optimizing statistical correlation with target properties, systematically discards information whose scientific value lies outside mere predictive utility. This theoretical analysis applies information-theoretic principles from Shannon and Cover and Thomas to examine how dimensionality reduction in materials representations affects the retention of scientifically relevant content. Drawing on the concept of model entropy introduced by S. S., the paper introduces “model entropy” as a quantitative lens for assessing the information content preserved in any compressed materials representation. It articulates a core theoretical claim: compression optimized for predictive accuracy maximizes statistical information but can erode scientific information—mechanistic, causal, and counterfactual structures essential for understanding, explanation, and extrapolation. A typology of five distinct information-loss mechanisms is developed, each illustrated with representative materials-science scenarios. The analysis culminates in concrete implications for representation design and scientific inference, arguing that future materials AI must move beyond accuracy-centric evaluation toward explicit auditing and preservation of scientific information. By distinguishing statistical signal from epistemic content, this work offers a conceptual framework for building representations that serve both prediction and discovery without hidden epistemic costs.