Riemannian neural networks have proven effective in solving a variety of machine learning tasks. The key to their success lies in the development of principled Riemannian analogs of fundamental building blocks in deep neural networks (DNNs). Among those, Riemannian batch normalization (BN) layers have shown to enhance training stability and improve accuracy. In this paper, we propose BN layers for neural networks on complex domains. The proposed layers have close connections with existing Riemannian BN layers. We derive essential components for practical implementations of BN layers on some complex domains which are less studied in previous works, e.g., the Siegel disk domain. We conduct experiments on radar clutter classification, node classification, and action recognition demonstrating the efficacy of our method.

Such message exchanging isparameter-free andselfadaptive, as it is dynamically controlled by the scaling factors that are determined by the training itself.

Drowsy driving is a growing cause of traffic accidents, prompting recent exploration of electroencephalography (EEG)-based drowsiness detection systems. However, the inherent variability of EEG signals due to psychological and physical factors necessitates a cumbersome calibration process. In particular, the inter-subject variability of EEG signals leads to a domain shift problem, which makes it challenging to generalize drowsiness detection models to unseen target subjects. To address these issues, we propose a novel driver drowsiness detection framework that leverages online test-time adaptation (TTA) methods to dynamically adjust to target subject distributions. Our proposed method updates the learnable parameters in batch normalization (BN) layers, while preserving pretrained normalization statistics, resulting in a modified configuration that ensures effective adaptation during test time. We incorporate a memory bank that dynamically manages streaming EEG segments, selecting samples based on their reliability determined by negative energy scores and persistence time. In addition, we introduce prototype learning to ensure robust predictions against distribution shifts over time. We validated our method on the sustained-attention driving dataset collected in a simulated environment, where drowsiness was estimated from delayed reaction times during monotonous lane-keeping tasks. Our experiments show that our method outperforms all baselines, achieving an average F1-score of 81.73\%, an improvement of 11.73\% over the best TTA baseline. This demonstrates that our proposed method significantly enhances the adaptability of EEG-based drowsiness detection systems in non-i.i.d. scenarios.

In recent advancements in Test Time Adaptation (TTA), most existing methodologies focus on updating normalization layers to adapt to the test domain. However, the reliance on normalization-based adaptation presents key challenges. First, normalization layers such as Batch Normalization (BN) are highly sensitive to small batch sizes, leading to unstable and inaccurate statistics. Moreover, normalization-based adaptation is inherently constrained by the structure of the pre-trained model, as it relies on training-time statistics that may not generalize well to unseen domains. These issues limit the effectiveness of normalization-based TTA approaches, especially under significant domain shift. In this paper, we introduce a novel paradigm based on the concept of a Buffer layer, which addresses the fundamental limitations of normalization layer updates. Unlike existing methods that modify the core parameters of the model, our approach preserves the integrity of the pre-trained backbone, inherently mitigating the risk of catastrophic forgetting during online adaptation. Through comprehensive experimentation, we demonstrate that our approach not only outperforms traditional methods in mitigating domain shift and enhancing model robustness, but also exhibits strong resilience to forgetting. Furthermore, our Buffer layer is modular and can be seamlessly integrated into nearly all existing TTA frameworks, resulting in consistent performance improvements across various architectures. These findings validate the effectiveness and versatility of the proposed solution in real-world domain adaptation scenarios. The code is available at https://github.com/hyeongyu-kim/Buffer_TTA.

A variety of works have been done towards deep multimodal fusion [37].