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.

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.

Discriminator-Guided Adaptive Diffusion for Source-Free Test-Time Adaptation under Image Corruptions

In this work, we study Source-Free Unsupervised Domain Adaptation under corruption-induced domain shifts, where performance degradation is caused by natural image corruptions that go beyond additive noise, including blur, weather effects, and digital artifacts. We propose a diffusion-based, input-level adaptation framework that operates entirely at test time and keeps all source-trained models frozen, explicitly targeting robustness to corrupted target inputs. Our method leverages a source-trained diffusion model as a generative prior and introduces a discriminator-guided adaptive diffusion strategy that dynamically controls the amount of perturbation applied to each test sample. Rather than relying on a fixed diffusion depth, the discriminator determines, on a per-image basis, when sufficient forward diffusion has been applied to suppress corruption-specific artifacts, with each corruption type effectively defining a distinct target domain. This adaptive stopping mechanism applies only the necessary amount of noise to remove domainspecific corruption while preserving class-discriminative structure. The reverse diffusion process then reconstructs a source-aligned image, optionally stabilized through structural guidance, which is classified using a frozen source-trained classifier. We evaluate the proposed approach across a broad spectrum of corruption-induced target domains, covering 15 diverse corruption types, and demonstrate more balanced robustness with competitive or improved performance across non-noise corruptions. Additional analyses reveal how the adaptive diffusion schedule responds to different corruption characteristics, highlighting the practicality, generality, and robustness of the proposed framework. The code is publicly available at https://github.com/fmolivato/dgadiffusion/.

HAC: Parameter-Efficient Hyperbolic Adaptation of CLIP for Zero-Shot VQA

Recent advances in representation learning have shown that hyperbolic geometry can offer a more expressive alternative to the Euclidean embeddings used in CLIP models, capturing hierarchical structures and leading to better-organized representations. However, current hyperbolic CLIP variants are trained entirely from scratch, which is computationally expensive and resource-intensive. In this work, we propose HAC (Hyperbolic Adaptation of CLIP), a parameter-efficient framework that enables pretrained CLIP models to transition into hyperbolic space via lightweight fine-tuning. We apply HAC to Visual Question Answering (VQA), where models must interpret visual elements and align them with textual queries. Notably, HAC's training is performed on a dataset with no overlap with any VQA benchmark, resulting in a strict zero-shot evaluation paradigm that underscores HAC's task-agnostic adaptability. We evaluate HAC across a diverse suite of VQA benchmarks spanning General, Reasoning, and OCR categories. Both HAC-S (small) and HAC-B (medium) consistently surpass Euclidean baselines and prior hyperbolic approaches, with HAC-B delivering up to a +1.9 point average improvement over CLIP-B on reasoning-intensive tasks. Our code is available at https://github.com/fdibiton/HAC

Lifelong Imitation Learning with Multimodal Latent Replay and Incremental Adjustment

We introduce a lifelong imitation learning framework that enables continual policy refinement across sequential tasks under realistic memory and data constraints. Our approach departs from conventional experience replay by operating entirely in a multimodal latent space, where compact representations of visual, linguistic, and robot's state information are stored and reused to support future learning. To further stabilize adaptation, we introduce an incremental feature adjustment mechanism that regularizes the evolution of task embeddings through an angular margin constraint, preserving inter-task distinctiveness. Our method establishes a new state of the art in the LIBERO benchmarks, achieving 10-17 point gains in AUC and up to 65% less forgetting compared to previous leading methods. Ablation studies confirm the effectiveness of each component, showing consistent gains over alternative strategies. The code is available at: https://github.com/yfqi/lifelong_mlr_ifa.

MADPOT: Medical Anomaly Detection with CLIP Adaptation and Partial Optimal Transport

Medical anomaly detection (AD) is challenging due to diverse imaging modalities, anatomical variations, and limited labeled data. We propose a novel approach combining visual adapters and prompt learning with Partial Optimal Transport (POT) and contrastive learning (CL) to improve CLIP's adaptability to medical images, particularly for AD. Unlike standard prompt learning, which often yields a single representation, our method employs multiple prompts aligned with local features via POT to capture subtle abnormalities. CL further enforces intra-class cohesion and inter-class separation. Our method achieves state-of-the-art results in few-shot, zero-shot, and cross-dataset scenarios without synthetic data or memory banks. The code is available at https://github.com/mahshid1998/MADPOT.

Diffusing DeBias: a Recipe for Turning a Bug into a Feature

Deep learning model effectiveness in classification tasks is often challenged by the quality and quantity of training data which, whenever containing strong spurious correlations between specific attributes and target labels, can result in unrecoverable biases in model predictions. Tackling these biases is crucial in improving model generalization and trust, especially in real-world scenarios. This paper presents Diffusing DeBias (DDB), a novel approach acting as a plug-in for common methods in model debiasing while exploiting the inherent bias-learning tendency of diffusion models. Our approach leverages conditional diffusion models to generate synthetic bias-aligned images, used to train a bias amplifier model, to be further employed as an auxiliary method in different unsupervised debiasing approaches. Our proposed method, which also tackles the common issue of training set memorization typical of this type of tech- niques, beats current state-of-the-art in multiple benchmark datasets by significant margins, demonstrating its potential as a versatile and effective tool for tackling dataset bias in deep learning applications.

A Mutual Information Perspective on Multiple Latent Variable Generative Models for Positive View Generation

In image generation, Multiple Latent Variable Generative Models (MLVGMs) employ multiple latent variables to gradually shape the final images, from global characteristics to finer and local details (e.g., StyleGAN, NVAE), emerging as powerful tools for diverse applications. Yet their generative dynamics and latent variable utilization remain only empirically observed. In this work, we propose a novel framework to systematically quantify the impact of each latent variable in MLVGMs, using Mutual Information (MI) as a guiding metric. Our analysis reveals underutilized variables and can guide the use of MLVGMs in downstream applications. With this foundation, we introduce a method for generating synthetic data for Self-Supervised Contrastive Representation Learning (SSCRL). By leveraging the hierarchical and disentangled variables of MLVGMs, and guided by the previous analysis, we apply tailored latent perturbations to produce diverse views for SSCRL, without relying on real data altogether. Additionally, we introduce a Continuous Sampling (CS) strategy, where the generator dynamically creates new samples during SSCRL training, greatly increasing data variability. Our comprehensive experiments demonstrate the effectiveness of these contributions, showing that MLVGMs' generated views compete on par with or even surpass views generated from real data. This work establishes a principled approach to understanding and exploiting MLVGMs, advancing both generative modeling and self-supervised learning.

Pre-trained Multiple Latent Variable Generative Models are good defenders against Adversarial Attacks

Attackers can deliberately perturb classifiers' input with subtle noise, altering final predictions. Among proposed countermeasures, adversarial purification employs generative networks to preprocess input images, filtering out adversarial noise. In this study, we propose specific generators, defined Multiple Latent Variable Generative Models (MLVGMs), for adversarial purification. These models possess multiple latent variables that naturally disentangle coarse from fine features. Taking advantage of these properties, we autoencode images to maintain class-relevant information, while discarding and re-sampling any detail, including adversarial noise. The procedure is completely training-free, exploring the generalization abilities of pre-trained MLVGMs on the adversarial purification downstream task. Despite the lack of large models, trained on billions of samples, we show that smaller MLVGMs are already competitive with traditional methods, and can be used as foundation models. Official code released at https://github.com/SerezD/gen_adversarial.

Upper-Body Pose-based Gaze Estimation for Privacy-Preserving 3D Gaze Target Detection

Gaze Target Detection (GTD), i.e., determining where a person is looking within a scene from an external viewpoint, is a challenging task, particularly in 3D space. Existing approaches heavily rely on analyzing the person's appearance, primarily focusing on their face to predict the gaze target. This paper presents a novel approach to tackle this problem by utilizing the person's upper-body pose and available depth maps to extract a 3D gaze direction and employing a multi-stage or an end-to-end pipeline to predict the gazed target. When predicted accurately, the human body pose can provide valuable information about the head pose, which is a good approximation of the gaze direction, as well as the position of the arms and hands, which are linked to the activity the person is performing and the objects they are likely focusing on. Consequently, in addition to performing gaze estimation in 3D, we are also able to perform GTD simultaneously. We demonstrate state-of-the-art results on the most comprehensive publicly accessible 3D gaze target detection dataset without requiring images of the person's face, thus promoting privacy preservation in various application contexts. The code is available at https://github.com/intelligolabs/privacy-gtd-3D.