SPEAR-EELS: Physically Constrained Attention for Interpretable STEM Spectroscopy

Electron energy-loss spectroscopy (EELS) in scanning transmission electron microscopy provides rich information on chemical composition, bonding, and electronic structure at nanometer resolution [1,2]. However, quantitative interpretation of core-loss edges and fine structure remains sensitive to noise, background subtraction, energy drift, and correlations across neighboring energy channels. Machine learning approaches have recently been explored for spectrum–property inference, yet the interpretability of such models remains a challenge [3-5]. In particular, unconstrained attention mechanisms often produce fragmented or intensity-driven attribution patterns that do not align with the physically continuous structure of ionization edges and near-edge fine structure [6-8]. We introduce a structurally constrained attention framework for regression of EELS data that explicitly regularizes attention distributions during training to improve interpretability and stability. The model treats attention as a learnable explanatory object and imposes two complementary constraints: (i) a learnable concentration control that regulates how selectively the model emphasizes spectral regions, and (ii) a smoothness penalty that enforces coherence across neighboring energy-loss channels, consistent with the extended structure of core-loss edges and ELNES features. These constraints are embedded directly into the training objective rather than applied post hoc. The approach is evaluated on synthetic EELS-like spectra with known generative structure and is being applied to experimental core-loss datasets acquired in STEM spectrum-imaging mode. Preliminary results indicate that attention regularization promotes contiguous, edge-level attribution patterns while preserving predictive accuracy for quantities such as edge position and white-line metrics. Ongoing analysis examines attribution stability under controlled spectral perturbations that emulate experimental noise and energy drift. These findings suggest that structurally constrained attention provides a physically motivated inductive bias for interpretable, data-driven EELS analysis and may support future semi-autonomous spectroscopy workflows in electron microscopy. Conceptual illustration of structurally constrained attention applied to STEM–EELS spectra. The model enforces energy-coherent attention over core-loss edges to promote interpretable spectrum–property inference.