Busemann energy-based attention for emotion analysis in Poincaré discs
Traditional sentiment analysis treats emotions as discrete categories, failing to capture their semantic hierarchy and inherent ambiguity. This work proposes EmBolic, the first end-to-end trainable fully hyperbolic sentiment analysis architecture that integrates hyperbolic geometry with Busemann energy. Operating within the Poincaré disk model, EmBolic employs a Busemann energy–driven attention mechanism to map input text to query points in hyperbolic space and automatically generates boundary key points to represent emotional directions. The model can infer the curvature of the continuous emotion space, achieving high accuracy and strong generalization even with low-dimensional embeddings. Experimental results demonstrate that EmBolic significantly outperforms conventional classification paradigms, validating the efficacy and advantages of hyperbolic representations for fine-grained sentiment analysis.