Towards Explaining Hypercomplex Neural Networks

Hypercomplex neural networks are gaining increasing interest in the deep learning community. The attention directed towards hypercomplex models originates from several aspects, spanning from purely theoretical and mathematical characteristics to the practical advantage of lightweight models over conventional networks, and their unique properties to capture both global and local relations. In particular, a branch of these architectures, parameterized hypercomplex neural networks (PHNNs), has also gained popularity due to their versatility across a multitude of application domains. Nonetheless, only few attempts have been made to explain or interpret their intricacies. In this paper, we propose inherently interpretable PHNNs and quaternion-like networks, thus without the need for any post-hoc method. To achieve this, we define a type of cosine-similarity transform within the parameterized hypercomplex domain. This PHB-cos transform induces weight alignment with relevant input features and allows to reduce the model into a single linear transform, rendering it directly interpretable. In this work, we start to draw insights into how this unique branch of neural models operates. We observe that hypercomplex networks exhibit a tendency to concentrate on the shape around the main object of interest, in addition to the shape of the object itself. We provide a thorough analysis, studying single neurons of different layers and comparing them against how real-valued networks learn. The code of the paper is available at https://github.com/ispamm/HxAI.

Generative AI Meets Semantic Communication: Evolution and Revolution of Communication Tasks

While deep generative models are showing exciting abilities in computer vision and natural language processing, their adoption in communication frameworks is still far underestimated. These methods are demonstrated to evolve solutions to classic communication problems such as denoising, restoration, or compression. Nevertheless, generative models can unveil their real potential in semantic communication frameworks, in which the receiver is not asked to recover the sequence of bits used to encode the transmitted (semantic) message, but only to regenerate content that is semantically consistent with the transmitted message. Disclosing generative models capabilities in semantic communication paves the way for a paradigm shift with respect to conventional communication systems, which has great potential to reduce the amount of data traffic and offers a revolutionary versatility to novel tasks and applications that were not even conceivable a few years ago. In this paper, we present a unified perspective of deep generative models in semantic communication and we unveil their revolutionary role in future communication frameworks, enabling emerging applications and tasks. Finally, we analyze the challenges and opportunities to face to develop generative models specifically tailored for communication systems.

Generalizing Medical Image Representations via Quaternion Wavelet Networks

Neural network generalizability is becoming a broad research field due to the increasing availability of datasets from different sources and for various tasks. This issue is even wider when processing medical data, where a lack of methodological standards causes large variations being provided by different imaging centers or acquired with various devices and cofactors. To overcome these limitations, we introduce a novel, generalizable, data- and task-agnostic framework able to extract salient features from medical images. The proposed quaternion wavelet network (QUAVE) can be easily integrated with any pre-existing medical image analysis or synthesis task, and it can be involved with real, quaternion, or hypercomplex-valued models, generalizing their adoption to single-channel data. QUAVE first extracts different sub-bands through the quaternion wavelet transform, resulting in both low-frequency/approximation bands and high-frequency/fine-grained features. Then, it weighs the most representative set of sub-bands to be involved as input to any other neural model for image processing, replacing standard data samples. We conduct an extensive experimental evaluation comprising different datasets, diverse image analysis, and synthesis tasks including reconstruction, segmentation, and modality translation. We also evaluate QUAVE in combination with both real and quaternion-valued models. Results demonstrate the effectiveness and the generalizability of the proposed framework that improves network performance while being flexible to be adopted in manifold scenarios.

Hypercomplex Multimodal Emotion Recognition from EEG and Peripheral Physiological Signals

Multimodal emotion recognition from physiological signals is receiving an increasing amount of attention due to the impossibility to control them at will unlike behavioral reactions, thus providing more reliable information. Existing deep learning-based methods still rely on extracted handcrafted features, not taking full advantage of the learning ability of neural networks, and often adopt a single-modality approach, while human emotions are inherently expressed in a multimodal way. In this paper, we propose a hypercomplex multimodal network equipped with a novel fusion module comprising parameterized hypercomplex multiplications. Indeed, by operating in a hypercomplex domain the operations follow algebraic rules which allow to model latent relations among learned feature dimensions for a more effective fusion step. We perform classification of valence and arousal from electroencephalogram (EEG) and peripheral physiological signals, employing the publicly available database MAHNOB-HCI surpassing a multimodal state-of-the-art network. The code of our work is freely available at https://github.com/ispamm/MHyEEG.

Attention-Map Augmentation for Hypercomplex Breast Cancer Classification

Breast cancer is the most widespread neoplasm among women and early detection of this disease is critical. Deep learning techniques have become of great interest to improve diagnostic performance. Nonetheless, discriminating between malignant and benign masses from whole mammograms remains challenging due to them being almost identical to an untrained eye and the region of interest (ROI) occupying a minuscule portion of the entire image. In this paper, we propose a framework, parameterized hypercomplex attention maps (PHAM), to overcome these problems. Specifically, we deploy an augmentation step based on computing attention maps. Then, the attention maps are used to condition the classification step by constructing a multi-dimensional input comprised of the original breast cancer image and the corresponding attention map. In this step, a parameterized hypercomplex neural network (PHNN) is employed to perform breast cancer classification. The framework offers two main advantages. First, attention maps provide critical information regarding the ROI and allow the neural model to concentrate on it. Second, the hypercomplex architecture has the ability to model local relations between input dimensions thanks to hypercomplex algebra rules, thus properly exploiting the information provided by the attention map. We demonstrate the efficacy of the proposed framework on both mammography images as well as histopathological ones, surpassing attention-based state-of-the-art networks and the real-valued counterpart of our method. The code of our work is available at https://github.com/elelo22/AttentionBCS.

Dual Quaternion Rotational and Translational Equivariance in 3D Rigid Motion Modelling

Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information. Previous works exploit quaternion algebra and their ability to model rotations in 3D space. However, these algebras do not properly encode translations, leading to sub-optimal performance in 3D learning tasks. To overcome these limitations, we employ a dual quaternion representation of rigid motions in the 3D space that jointly describes rotations and translations of point sets, processing each of the points as a single entity. Our approach is translation and rotation equivariant, so it does not suffer from shifts in the data and better learns object trajectories, as we validate in the experimental evaluations. Models endowed with this formulation outperform previous approaches in a human pose forecasting application, attesting to the effectiveness of the proposed dual quaternion formulation for rigid motions in 3D space.

PHYDI: Initializing Parameterized Hypercomplex Neural Networks as Identity Functions

Neural models based on hypercomplex algebra systems are growing and prolificating for a plethora of applications, ranging from computer vision to natural language processing. Hand in hand with their adoption, parameterized hypercomplex neural networks (PHNNs) are growing in size and no techniques have been adopted so far to control their convergence at a large scale. In this paper, we study PHNNs convergence and propose parameterized hypercomplex identity initialization (PHYDI), a method to improve their convergence at different scales, leading to more robust performance when the number of layers scales up, while also reaching the same performance with fewer iterations. We show the effectiveness of this approach in different benchmarks and with common PHNNs with ResNets- and Transformer-based architecture. The code is available at https://github.com/ispamm/PHYDI.

Diffusion models for audio semantic communication

Directly sending audio signals from a transmitter to a receiver across a noisy channel may absorb consistent bandwidth and be prone to errors when trying to recover the transmitted bits. On the contrary, the recent semantic communication approach proposes to send the semantics and then regenerate semantically consistent content at the receiver without exactly recovering the bitstream. In this paper, we propose a generative audio semantic communication framework that faces the communication problem as an inverse problem, therefore being robust to different corruptions. Our method transmits lower-dimensional representations of the audio signal and of the associated semantics to the receiver, which generates the corresponding signal with a particular focus on its meaning (i.e., the semantics) thanks to the conditional diffusion model at its core. During the generation process, the diffusion model restores the received information from multiple degradations at the same time including corruption noise and missing parts caused by the transmission over the noisy channel. We show that our framework outperforms competitors in a real-world scenario and with different channel conditions. Visit the project page to listen to samples and access the code: https://ispamm.github.io/diffusion-audio-semantic-communication/.

Enhancing Semantic Communication with Deep Generative Models -- An ICASSP Special Session Overview

Semantic communication is poised to play a pivotal role in shaping the landscape of future AI-driven communication systems. Its challenge of extracting semantic information from the original complex content and regenerating semantically consistent data at the receiver, possibly being robust to channel corruptions, can be addressed with deep generative models. This ICASSP special session overview paper discloses the semantic communication challenges from the machine learning perspective and unveils how deep generative models will significantly enhance semantic communication frameworks in dealing with real-world complex data, extracting and exploiting semantic information, and being robust to channel corruptions. Alongside establishing this emerging field, this paper charts novel research pathways for the next generative semantic communication frameworks.

Generative Semantic Communication: Diffusion Models Beyond Bit Recovery

Semantic communication is expected to be one of the cores of next-generation AI-based communications. One of the possibilities offered by semantic communication is the capability to regenerate, at the destination side, images or videos semantically equivalent to the transmitted ones, without necessarily recovering the transmitted sequence of bits. The current solutions still lack the ability to build complex scenes from the received partial information. Clearly, there is an unmet need to balance the effectiveness of generation methods and the complexity of the transmitted information, possibly taking into account the goal of communication. In this paper, we aim to bridge this gap by proposing a novel generative diffusion-guided framework for semantic communication that leverages the strong abilities of diffusion models in synthesizing multimedia content while preserving semantic features. We reduce bandwidth usage by sending highly-compressed semantic information only. Then, the diffusion model learns to synthesize semantic-consistent scenes through spatially-adaptive normalizations from such denoised semantic information. We prove, through an in-depth assessment of multiple scenarios, that our method outperforms existing solutions in generating high-quality images with preserved semantic information even in cases where the received content is significantly degraded. More specifically, our results show that objects, locations, and depths are still recognizable even in the presence of extremely noisy conditions of the communication channel. The code is available at https://github.com/ispamm/GESCO.