Emotion as a Distribution: Joint Valence-Arousal Probability Learning for Speaker-Independent Multimodal Emotion Recognition

Human emotion is graded and frequently mixed, yet most multimodal recognizers collapse it onto a single hard label. We argue the recognizer should instead expose a distribution over affective space. Our text+speech system, alongside its categorical decision, emits a 9×9 probability matrix over the Valence-Arousal plane, trained with a two-dimensional Gaussian soft target under a Kullback-Leibler/cross-entropy objective, aimed at counseling support. Evaluation is strict: speaker-independent 5-fold leave-one-session-out IEMOCAP with rotating-session inner validation, headline metrics only on the held-out session. Within one fixed encoder-fusion-head pipeline we compare Transformer and state-space (Mamba-1/2/3) backbones at matched depth and width, at two operating points (T≈550, T≈2750). The featured dual-head system reaches 73.0% ± 0.3 unweighted accuracy over three seeds (separate rerun: 72.1%), exceeding the Transformer fusion baseline by 3.0 UA points (95% session-bootstrap CI [1.0,4.7]; significant under paired t-test and session-level bootstrap), with no latency or memory advantage at these lengths; swapping the ~1M trainable front-end for frozen WavLM-Large features (learnable layer weights) lifts the same architecture to 76.6% ± 1.3. Pre-specified controls scope the claims honestly: simpler valence-arousal auxiliaries reproduce the classification lift within noise, and a dedicated regression head tracks the continuous ratings slightly better, so the head's specific value is the normalized affect distribution itself. That distribution recovers the circumplex: its center of mass tracks valence and arousal (CCC 0.66/0.66; predominantly between-class structure, weaker within-class tracking), and its entropy is weakly but consistently linked to categorical rater ambiguity, not dimensional spread.