Speech Emotion Recognition (SER) plays a crucial role in advancing human-computer interaction and speech processing capabilities. We introduce a novel deep-learning architecture designed specifically for the functional data model known as the multiple-index functional model. Our key innovation lies in integrating adaptive basis layers and an automated data transformation search within the deep learning framework. Simulations for this new model show good performances. This allows us to extract features tailored for chunk-level SER, based on Mel Frequency Cepstral Coefficients (MFCCs). We demonstrate the effectiveness of our approach on the benchmark IEMOCAP database, achieving good performance compared to existing methods.