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Researcher profile

Angelica I. Aviles-Rivero

Angelica I. Aviles-Rivero contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningComputer Visioneess.IVmath.NAArtificial Intelligencemath.FA

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Published work

9 published item(s)

preprint2026arXiv

CATO: Charted Attention for Neural PDE Operators

Neural operators have emerged as powerful data-driven solvers for PDEs, offering substantial acceleration over classical numerical methods. However, existing transformer-based operators still face critical challenges when modeling PDEs on complex geometries: directly processing over massive mesh points is computationally expensive, while operating in raw discretization coordinates may obscure the intrinsic geometry where physical interactions are more naturally expressed. To address these limitations, we introduce the Charted Axial Transformer Operator (CATO), a geometry-adaptive and derivative-aware neural operator for PDEs on general geometries. Instead of applying attention directly in the physical coordinate system, CATO learns a continuous latent chart that maps mesh coordinates into a learned chart space, where chart-conditioned axial attention efficiently captures long-range dependencies with reduced computational cost. In addition, CATO introduces a derivative-aware physics loss for steady-state PDEs that jointly supervises solution values, mesh-consistent gradients, and an auxiliary flux-like field, improving physical fidelity and reducing oversmoothing. We further provide a theoretical approximation result showing that, under a favorable chart, charted axial attention can represent low-rank axial solution operators with controlled error, and that small chart perturbations induce bounded approximation degradation. CATO achieves the best performance across all evaluated datasets, yielding an average improvement of approximately 26.76\% over the strongest competing baselines while reducing the number of parameters by 81.98\%. These results highlight the effectiveness of learning geometry-adaptive charts and derivative-aware physical supervision for accurate and efficient PDE operator learning.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learning

Neural operators perform well on structured domains, yet their behaviour on irregular geometries remains poorly understood. We show that this limitation is not merely an encoding issue, but a depth-wise failure mode inherent to deep operator architectures. We formalise the Geometric Forgetting Hypothesis: due to the Markovian structure of operator layers and their reliance on global mixing mechanisms, neural operators progressively lose access to domain geometry as depth increases. Using layer-wise geometric probing, we demonstrate that both spectral and attention-based operators systematically lose geometric fidelity. We show that this geometric forgetting degrades accuracy, stability, and generalisation. To counteract it, we introduce a lightweight geometry memory injection mechanism that restores geometric constraints at intermediate depths with minimal architectural overhead. This simple intervention consistently mitigates forgetting and exposes a geometric shortcut instability in transformer-based operators, revealing that geometric retention is a structural requirement rather than a design choice.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs

Spectral neural operators achieve strong performance for PDE learning, but rely on fixed global bases that limit their ability to represent spatially heterogeneous and multiscale dynamics. We propose Adaptive Basis Learning (ABLE), a framework that learns data-dependent spectral representations instead of relying on predefined bases. ABLE constructs a spatially adaptive Parseval frame via a learned ancillary density, enabling the operator to act in a lifted spectral space while preserving invertibility and maintaining $O(N\log N)$ complexity through FFT-based implementation. This shifts the source of expressivity from spectral coefficients to the representation itself, allowing the model to capture localized structures and non-translation-invariant interactions more efficiently. ABLE integrates seamlessly into existing neural operator architectures as a drop-in replacement for spectral layers. Across a range of benchmarks ABLE improves accuracy over strong baselines, with the largest gains in regimes characterized by sharp gradients and multiscale behavior. Moreover, augmenting existing models (e.g., U-FNO, HPM) with ABLE further enhances their performance, demonstrating its role as a general and complementary spectral refinement. Our results highlight that the data-driven choice of representation, rather than operator complexity alone, is a key bottleneck in neural operator design. By learning the basis itself, ABLE provides a principled and efficient framework for improving spectral methods in PDE learning.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

LEGATO: Good Identity Unlearning Is Continuous

Machine unlearning has become a crucial role in enabling generative models trained on large datasets to remove sensitive, private, or copyright-protected data. However, existing machine unlearning methods face three challenges in learning to forget identity of generative models: 1) inefficient, where identity erasure requires fine-tuning all the model's parameters; 2) limited controllability, where forgetting intensity cannot be controlled and explainability is lacking; 3) catastrophic collapse, where the model's retention capability undergoes drastic degradation as forgetting progresses. Forgetting has typically been handled through discrete and unstable updates, often requiring full-model fine-tuning and leading to catastrophic collapse. In this work, we argue that identity forgetting should be modeled as a continuous trajectory, and introduce LEGATO - Learn to ForgEt Identity in GenerAtive Models via Trajectory-consistent Neural Ordinary Differential Equations. LEGATO augments pre-trained generators with fine-tunable lightweight Neural ODE adapters, enabling smooth, controllable forgetting while keeping the original model weights frozen. This formulation allows forgetting intensity to be precisely modulated via ODE step size, offering interpretability and robustness. To further ensure stability, we introduce trajectory consistency constraints that explicitly prevent catastrophic collapse during unlearning. Extensive experiments across in-domain and out-of-domain identity unlearning benchmarks show that LEGATO achieves state-of-the-art forgetting performance, avoids catastrophic collapse and reduces fine-tuned parameters.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Multi-Modal Hypergraph Diffusion Network with Dual Prior for Alzheimer Classification

The automatic early diagnosis of prodromal stages of Alzheimer's disease is of great relevance for patient treatment to improve quality of life. We address this problem as a multi-modal classification task. Multi-modal data provides richer and complementary information. However, existing techniques only consider either lower order relations between the data and single/multi-modal imaging data. In this work, we introduce a novel semi-supervised hypergraph learning framework for Alzheimer's disease diagnosis. Our framework allows for higher-order relations among multi-modal imaging and non-imaging data whilst requiring a tiny labelled set. Firstly, we introduce a dual embedding strategy for constructing a robust hypergraph that preserves the data semantics. We achieve this by enforcing perturbation invariance at the image and graph levels using a contrastive based mechanism. Secondly, we present a dynamically adjusted hypergraph diffusion model, via a semi-explicit flow, to improve the predictive uncertainty. We demonstrate, through our experiments, that our framework is able to outperform current techniques for Alzheimer's disease diagnosis.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

PC-SwinMorph: Patch Representation for Unsupervised Medical Image Registration and Segmentation

Medical image registration and segmentation are critical tasks for several clinical procedures. Manual realisation of those tasks is time-consuming and the quality is highly dependent on the level of expertise of the physician. To mitigate that laborious task, automatic tools have been developed where the majority of solutions are supervised techniques. However, in medical domain, the strong assumption of having a well-representative ground truth is far from being realistic. To overcome this challenge, unsupervised techniques have been investigated. However, they are still limited in performance and they fail to produce plausible results. In this work, we propose a novel unified unsupervised framework for image registration and segmentation that we called PC-SwinMorph. The core of our framework is two patch-based strategies, where we demonstrate that patch representation is key for performance gain. We first introduce a patch-based contrastive strategy that enforces locality conditions and richer feature representation. Secondly, we utilise a 3D window/shifted-window multi-head self-attention module as a patch stitching strategy to eliminate artifacts from the patch splitting. We demonstrate, through a set of numerical and visual results, that our technique outperforms current state-of-the-art unsupervised techniques.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Simultaneous Semantic and Instance Segmentation for Colon Nuclei Identification and Counting

We address the problem of automated nuclear segmentation, classification, and quantification from Haematoxylin and Eosin stained histology images, which is of great relevance for several downstream computational pathology applications. In this work, we present a solution framed as a simultaneous semantic and instance segmentation framework. Our solution is part of the Colon Nuclei Identification and Counting (CoNIC) Challenge. We first train a semantic and instance segmentation model separately. Our framework uses as backbone HoverNet and Cascade Mask-RCNN models. We then ensemble the results with a custom Non-Maximum Suppression embedding (NMS). In our framework, the semantic model computes a class prediction for the cells whilst the instance model provides a refined segmentation. We demonstrate, through our experimental results, that our model outperforms the provided baselines by a large margin.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Compressed Sensing Plus Motion (CS+M): A New Perspective for Improving Undersampled MR Image Reconstruction

We address the problem of reconstructing high quality images from undersampled MRI data. This is a challenging task due to the highly ill-posed nature of the problem. In particular, in dynamic MRI scans, the interaction between the target structure and the physical motion affects the acquired measurements leading to blurring artefacts and loss of fine details. In this work, we propose a framework for dynamic MRI reconstruction framed under a new multi-task optimisation model called Compressed Sensing Plus Motion (CS+M). Firstly, we propose a single optimisation problem that simultaneously computes the MRI reconstruction and the physical motion. Secondly, we show our model can be efficiently solved by breaking it up into two more computationally tractable problems. The potentials and generalisation capabilities of our approach are demonstrated in different clinical applications including cardiac cine, cardiac perfusion and brain perfusion imaging. We show, through numerical and graphical experiments, that the proposed scheme reduces blurring artefacts and preserves the target shape and fine details. We also report the highest quality reconstruction under highly undersampling rates in comparison to several state of the art techniques.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

GraphX$^{NET}-$ Chest X-Ray Classification Under Extreme Minimal Supervision

The task of classifying X-ray data is a problem of both theoretical and clinical interest. Whilst supervised deep learning methods rely upon huge amounts of labelled data, the critical problem of achieving a good classification accuracy when an extremely small amount of labelled data is available has yet to be tackled. In this work, we introduce a novel semi-supervised framework for X-ray classification which is based on a graph-based optimisation model. To the best of our knowledge, this is the first method that exploits graph-based semi-supervised learning for X-ray data classification. Furthermore, we introduce a new multi-class classification functional with carefully selected class priors which allows for a smooth solution that strengthens the synergy between the limited number of labels and the huge amount of unlabelled data. We demonstrate, through a set of numerical and visual experiments, that our method produces highly competitive results on the ChestX-ray14 data set whilst drastically reducing the need for annotated data.

0 citations0 reviewsNo code linkedOpen access