Face Recognition (FR) tasks have made significant progress with the advent of Deep Neural Networks, particularly through margin-based triplet losses that embed facial images into high-dimensional feature spaces. During training, these contrastive losses focus exclusively on identity information as labels. However, we observe a multiscale geometric structure emerging in the embedding space, influenced by interpretable facial (e.g., hair color) and image attributes (e.g., contrast). We propose a geometric approach to describe the dependence or invariance of FR models to these attributes and introduce a physics-inspired alignment metric. We evaluate the proposed metric on controlled, simplified models and widely used FR models fine-tuned with synthetic data for targeted attribute augmentation. Our findings reveal that the models exhibit varying degrees of invariance across different attributes, providing insight into their strengths and weaknesses and enabling deeper interpretability. Code available here: https://github.com/mantonios107/attrs-fr-embs.

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency, and lack flexibility. This paper introduces a novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology, paving the way towards topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.

Studying the interplay between the geometry of the loss landscape and the optimization trajectories of simple neural networks is a fundamental step for understanding their behavior in more complex settings. This paper reveals the presence of topological obstruction in the loss landscape of shallow ReLU neural networks trained using gradient flow. We discuss how the homogeneous nature of the ReLU activation function constrains the training trajectories to lie on a product of quadric hypersurfaces whose shape depends on the particular initialization of the network's parameters. When the neural network's output is a single scalar, we prove that these quadrics can have multiple connected components, limiting the set of reachable parameters during training. We analytically compute the number of these components and discuss the possibility of mapping one to the other through neuron rescaling and permutation. In this simple setting, we find that the non-connectedness results in a topological obstruction, which, depending on the initialization, can make the global optimum unreachable. We validate this result with numerical experiments.

Industrial vehicles equipped with CAN bus devices transmit large volumes of IoT signals. The analysis of CAN bus data can be helpful to monitor the current vehicles’ workload, namely the vehicle duty levels, in an automated fashion. Despite the use of machine learning techniques to automatically detect vehicle duty levels is particularly appealing, existing approaches are challenged by the high cost of human data annotation and by the high heterogeneity of the analyzed vehicles types and models. In this paper, we present a self-supervised approach to automatically detect vehicles’ duty levels based on contrastive learning. The multivariate CAN Bus signals are first divided into fixed-sized segments and then embedded into a vector space shared by all vehicles of the same model by leveraging a constrastive approach with a mixup augmentation strategy. The key idea is to embed similar segments in close proximity by self-learning a model-specific clustering, which allows automatic duty level assignment with minimal human supervision. We validate the proposed approach in a real industrial use case, analyzing CAN Bus data acquired from test heavy-duty vehicles. Data were provided by a multinational Internet-of-Things company specialized in telematics solution. The experiments show clustering performance superior to state-of-the-art models and as well as an higher ability to differentiate between Moving and Working duty levels.

In their original setting, both spectral sequences and persistent homology are algebraic topology tools defined from filtrations of objects (e.g. topological spaces or simplicial complexes) indexed over the set \Z of integer numbers. Recently, generalizations of both concepts have been proposed which originate from a different choice of the set of indices of the filtration, producing the new notions of multipersistence and spectral system. In this paper, we show that these notions are related, generalizing results valid in the case of filtrations over \Z. By using this relation and some previous programs for computing spectral systems, we have developed a new module for the Kenzo system computing multipersistence. We also present a new invariant providing information on multifiltrations and applications of our algorithms to spaces of infinite type.