A Geometric Perspective on Composable Emotion Steering in Text-to-Speech Models

While prior work has explored emotion control in hybrid text-to-speech systems, the geometric properties of these modules, and their implications for steerability, remain poorly understood. We present the first comparative study of speech language model (SLM) and conditional flow-matching (CFM) modules as activation steering sites for mixed-emotion speech synthesis. We first characterize emotion representations using linear probing and local intrinsic dimensionality (LID), and then evaluate single-site and joint steering for mixed-emotion synthesis. Our results show that SLM offers a clean, low-dimensional emotion-specific subspace with strong speaker--emotion disentanglement, while CFM exhibits poor cross-speaker generalization due to speaker--emotion entanglement.Joint steering increases emotion intensity but degrades proportional control and speech quality on in-distribution data. These findings provide practical guidance for multi-site activation steering in hybrid TTS systems and highlight the importance of representation geometry in controllable speech generation.