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.

Existing FER methods typically report overall accuracy on highly imbalanced test sets but exhibit low performance in terms of the mean accuracy across all expression classes.

We further provide a comparison of results on the original FERPlus dataset, as displayed in Table 3.

For datasets with low/medium number of categories we used CIFAR-10 and CIFAR-100 (Krizhevsky et al., In the finetuning experiments we used the STL-10 dataset (Coates et al., 2011) For datasets with an high number of categories we used the tiny-ImageNet and SlimageNet (Antoniou et al., We use off-the-shelf Pytorch implementations of ResNets as described in the original paper (He et al., 2016). All the methods could fit on a single one of those GPUs. This baseline consists of standard supervised training. It represents an upper bound. When evaluated for the number of augmentations (Appendix B.6) the same strategy adopted in our method (Appendix A.3) has been used to Clustering has been performed at the beginning of each epoch by using the k-means algorithm available in Scikit-learn.

Face recognition (FR) systems are often prone to demographic biases, partially due to the entanglement of demographic-specific information with identity-relevant features in facial embeddings. This bias is extremely critical in large multicultural cities, especially where biometrics play a major role in smart city infrastructure. The entanglement can cause demographic attributes to overshadow identity cues in the embedding space, resulting in disparities in verification performance across different demographic groups. To address this issue, we propose a novel strategy, Unified Text-Image Embedding (UTIE), which aims to induce demographic ambiguity in face embeddings by enriching them with information related to other demographic groups. This encourages face embeddings to emphasize identity-relevant features and thus promotes fairer verification performance across groups. UTIE leverages the zero-shot capabilities and cross-modal semantic alignment of Vision-Language Models (VLMs). Given that VLMs are naturally trained to align visual and textual representations, we enrich the facial embeddings of each demographic group with text-derived demographic features extracted from other demographic groups. This encourages a more neutral representation in terms of demographic attributes. We evaluate UTIE using three VLMs, CLIP, OpenCLIP, and SigLIP, on two widely used benchmarks, RFW and BFW, designed to assess bias in FR. Experimental results show that UTIE consistently reduces bias metrics while maintaining, or even improving in several cases, the face verification accuracy.

Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands.

We further provide a comparison of results on the original FERPlus dataset, as displayed in Table 3.

Existing FER methods typically report overall accuracy on highly imbalanced test sets but exhibit low performance in terms of the mean accuracy across all expression classes.