Emotion recognition is essential across numerous fields, including medical applications and brain-computer interface (BCI). Emotional responses include behavioral reactions, such as tone of voice and body movement, and changes in physiological signals, such as the electroencephalogram (EEG). The latter are involuntary, thus they provide a reliable input for identifying emotions, in contrast to the former which individuals can consciously control. These signals reveal true emotional states without intentional alteration, thus increasing the accuracy of emotion recognition models. However, multimodal deep learning methods from physiological signals have not been significantly investigated. In this paper, we introduce PHemoNet, a fully hypercomplex network for multimodal emotion recognition from physiological signals. In detail, the architecture comprises modality-specific encoders and a fusion module. Both encoders and fusion modules are defined in the hypercomplex domain through parameterized hypercomplex multiplications (PHMs) that can capture latent relations between the different dimensions of each modality and between the modalities themselves. The proposed method outperforms current state-of-the-art models on the MAHNOB-HCI dataset in classifying valence and arousal using electroencephalograms (EEGs) and peripheral physiological signals. The code for this work is available at https://github.com/ispamm/MHyEEG.

Emotion recognition is relevant in various domains, ranging from healthcare to human-computer interaction. Physiological signals, being beyond voluntary control, offer reliable information for this purpose, unlike speech and facial expressions which can be controlled at will. They reflect genuine emotional responses, devoid of conscious manipulation, thereby enhancing the credibility of emotion recognition systems. Nonetheless, multimodal emotion recognition with deep learning models remains a relatively unexplored field. In this paper, we introduce a fully hypercomplex network with a hierarchical learning structure to fully capture correlations. Specifically, at the encoder level, the model learns intra-modal relations among the different channels of each input signal. Then, a hypercomplex fusion module learns inter-modal relations among the embeddings of the different modalities. The main novelty is in exploiting intra-modal relations by endowing the encoders with parameterized hypercomplex convolutions (PHCs) that thanks to hypercomplex algebra can capture inter-channel interactions within single modalities. Instead, the fusion module comprises parameterized hypercomplex multiplications (PHMs) that can model inter-modal correlations. The proposed architecture surpasses state-of-the-art models on the MAHNOB-HCI dataset for emotion recognition, specifically in classifying valence and arousal from electroencephalograms (EEGs) and peripheral physiological signals. The code of this study is available at https://github.com/ispamm/MHyEEG.

Hypercomplex algebras have recently been gaining prominence in the field of deep learning owing to the advantages of their division algebras over real vector spaces and their superior results when dealing with multidimensional signals in real-world 3D and 4D paradigms. This paper provides a foundational framework that serves as a roadmap for understanding why hypercomplex deep learning methods are so successful and how their potential can be exploited. Such a theoretical framework is described in terms of inductive bias, i.e., a collection of assumptions, properties, and constraints that are built into training algorithms to guide their learning process toward more efficient and accurate solutions. We show that it is possible to derive specific inductive biases in the hypercomplex domains, which extend complex numbers to encompass diverse numbers and data structures. These biases prove effective in managing the distinctive properties of these domains, as well as the complex structures of multidimensional and multimodal signals. This novel perspective for hypercomplex deep learning promises to both demystify this class of methods and clarify their potential, under a unifying framework, and in this way promotes hypercomplex models as viable alternatives to traditional real-valued deep learning for multidimensional signal processing.

Image-to-image translation (I2I) aims at transferring the content representation from an input domain to an output one, bouncing along different target domains. Recent I2I generative models, which gain outstanding results in this task, comprise a set of diverse deep networks each with tens of million parameters. Moreover, images are usually three-dimensional being composed of RGB channels and common neural models do not take dimensions correlation into account, losing beneficial information. In this paper, we propose to leverage hypercomplex algebra properties to define lightweight I2I generative models capable of preserving pre-existing relations among image dimensions, thus exploiting additional input information. On manifold I2I benchmarks, we show how the proposed Quaternion StarGANv2 and parameterized hypercomplex StarGANv2 (PHStarGANv2) reduce parameters and storage memory amount while ensuring high domain translation performance and good image quality as measured by FID and LPIPS scores. Full code is available at: https://github.com/ispamm/HI2I.

Hypercomplex neural networks have proved to reduce the overall number of parameters while ensuring valuable performances by leveraging the properties of Clifford algebras. Recently, hypercomplex linear layers have been further improved by involving efficient parameterized Kronecker products. In this paper, we define the parameterization of hypercomplex convolutional layers to develop lightweight and efficient large-scale convolutional models. Our method grasps the convolution rules and the filters organization directly from data without requiring a rigidly predefined domain structure to follow. The proposed approach is flexible to operate in any user-defined or tuned domain, from 1D to nD regardless of whether the algebra rules are preset. Such a malleability allows processing multidimensional inputs in their natural domain without annexing further dimensions, as done, instead, in quaternion neural networks for 3D inputs like color images. As a result, the proposed method operates with 1/n free parameters as regards its analog in the real domain. We demonstrate the versatility of this approach to multiple domains of application by performing experiments on various image datasets as well as audio datasets in which our method outperforms real and quaternionvalued counterparts. Recent state-of-the-art convolutional models achieved astonishing results in various fields of application by large-scaling the overall parameters amount (Karras et al., 2020; d'Ascoli et al., 2021; Dosovitskiy et al., 2021). Simultaneously, quaternion neural networks (QNNs) demonstrated to significantly reduce the number of parameters while still gaining comparable performances (Parcollet et al., 2019c; Grassucci et al., 2021a; Tay et al., 2019).