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Cigdem Beyan

Cigdem Beyan appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Computer Vision Machine Learning Artificial Intelligence Human-Computer Interaction

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preprint2026arXiv

AffineLens: Capturing the Continuous Piecewise Affine Functions of Neural Networks

Piecewise affine neural networks (PANNs) provide a principled geometric perspective on neural network expressivity by characterizing the input--output map as a continuous piecewise affine (CPA) function whose complexity is governed by the number, arrangement, and shapes of its affine regions. However, existing interpretability and expressivity analyses often rely on indirect proxies (e.g., activation statistics or theoretical upper bounds) and rarely offer practical, accurate tools for enumerating and visualizing the induced region partition under realistic architectures and bounded input domains. In this work, we present AffineLens, a unified framework for computing the hyperplane arrangements and polyhedral structures underlying PANNs. Given a calibrated (bounded) input polytope, AffineLens identifies the subset of neuron-induced hyperplanes that intersect the domain, enumerates the resulting affine sub-regions in a layer-wise manner, and returns provably non-empty maximal CPA regions together with interior representatives. The framework further provides visualizations of region partitioning and decision boundaries, enabling qualitative inspection alongside quantitative region counts. By exploiting the affine restriction property of CPA networks under fixed activation patterns, AffineLens supports a broad class of modern components, including batch normalization, pooling, residual connections, multilayer perceptrons, and convolutional layers. Finally, we use AffineLens to perform a systematic empirical study of architectural expressivity, comparing networks through region complexity metrics and revealing how design choices influence the geometry of learned functions.

preprint2026arXiv

Training-Time Batch Normalization Reshapes Local Partition Geometry in Piecewise-Affine Networks

Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We study training-time BN in continuous piecewise-affine (CPA) networks through the geometry of switching hyperplanes and the induced affine-region partition. Conditioned on a mini-batch, we show that BN defines for each neuron a reference hyperplane through the batch centroid, and that breakpoint-switching hyperplanes are parallel translates whose offsets are expressed in batch-standardized coordinates and are independent of the raw bias. This yields an exact criterion for when a switching hyperplane intersects a local $\ell_\infty$ window and motivates a local region-density functional based on exact affine-region counts. Under explicit sufficient conditions, we show that BN increases expected local partition refinement in ReLU and more general piecewise-affine networks, and that this mechanism transfers locally through depth inside parent affine regions where the upstream representation map is an affine embedding. These results provide a function-level geometric account of training-time BN as a batch-conditional recentering mechanism near the data.

preprint2022arXiv

Multimodal Across Domains Gaze Target Detection

This paper addresses the gaze target detection problem in single images captured from the third-person perspective. We present a multimodal deep architecture to infer where a person in a scene is looking. This spatial model is trained on the head images of the person-of- interest, scene and depth maps representing rich context information. Our model, unlike several prior art, do not require supervision of the gaze angles, do not rely on head orientation information and/or location of the eyes of person-of-interest. Extensive experiments demonstrate the stronger performance of our method on multiple benchmark datasets. We also investigated several variations of our method by altering joint-learning of multimodal data. Some variations outperform a few prior art as well. First time in this paper, we inspect domain adaption for gaze target detection, and we empower our multimodal network to effectively handle the domain gap across datasets. The code of the proposed method is available at https://github.com/francescotonini/multimodal-across-domains-gaze-target-detection.

preprint2022arXiv

Unsupervised Human Action Recognition with Skeletal Graph Laplacian and Self-Supervised Viewpoints Invariance

This paper presents a novel end-to-end method for the problem of skeleton-based unsupervised human action recognition. We propose a new architecture with a convolutional autoencoder that uses graph Laplacian regularization to model the skeletal geometry across the temporal dynamics of actions. Our approach is robust towards viewpoint variations by including a self-supervised gradient reverse layer that ensures generalization across camera views. The proposed method is validated on NTU-60 and NTU-120 large-scale datasets in which it outperforms all prior unsupervised skeleton-based approaches on the cross-subject, cross-view, and cross-setup protocols. Although unsupervised, our learnable representation allows our method even to surpass a few supervised skeleton-based action recognition methods. The code is available in: www.github.com/IIT-PAVIS/UHAR_Skeletal_Laplacian

preprint2020arXiv

Subspace Clustering for Action Recognition with Covariance Representations and Temporal Pruning

This paper tackles the problem of human action recognition, defined as classifying which action is displayed in a trimmed sequence, from skeletal data. Albeit state-of-the-art approaches designed for this application are all supervised, in this paper we pursue a more challenging direction: Solving the problem with unsupervised learning. To this end, we propose a novel subspace clustering method, which exploits covariance matrix to enhance the action's discriminability and a timestamp pruning approach that allow us to better handle the temporal dimension of the data. Through a broad experimental validation, we show that our computational pipeline surpasses existing unsupervised approaches but also can result in favorable performances as compared to supervised methods.

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