arXiv subjects

Filippo Maria Bianchi

Publications and source records attributed to Filippo Maria Bianchi.

At least 19 recordsLinked to original sources

arXiv2026

Data-driven Prediction of Satellite-observed Avalanche Activity from Snowpack Simulations

Avalanche forecasting requires knowledge of snowpack conditions and recent avalanche activity, but field observations are sparse across large mountain regions. We explore whether SNOWPACK simulations can predict avalanche activity mapped by synthetic aperture radar (SAR). We compiled five winters of Sentinel-1 avalanche detections across Norway and parts of Sweden, alongside SNOWPACK simulations forced by numerical weather predictions on a 20 x 20 km grid at different elevations and predefined slope angles. A transformer used five days of SNOWPACK outputs to predict the following day's SAR-detected Avalanche Activity Index (SAR-AAI). This index weights larger debris more heavily, spreads detections across possible occurrence dates and normalises by modelled runout area. The model was trained on four winters and evaluated on one validation winter. Regional mean predicted and reference SAR-AAI correlated at r = 0.803 after averaging over complete six-day periods. The model followed broad changes in time and space but produced smoother predictions and underestimated the strongest activity. Agreement at the 20 km cell scale was weaker (r = 0.549) after the same averaging. These results come from a single training run without evaluation on an untouched winter. Satellite observations also contain missed and false detections and uncertain timing. The results therefore do not establish operational forecast skill, but suggest that regional SNOWPACK simulations contain information about broad variations in satellite-observed avalanche activity.

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arXiv2026

Weakly Supervised Polar Low Segmentation in Sentinel-1 SAR Imagery

Polar lows are intense maritime cyclones that form rapidly at high latitudes. Deep learning can detect them in Synthetic Aperture Radar (SAR) imagery, but pixel-level segmentation remains an open challenge. No pixel-level masks are available for training, and a polar low's extent is inherently subjective, with diffuse boundaries that even experts delineate inconsistently. We propose Constrained Region Erasing with Soft Targets (CREST), a Weakly Supervised Semantic Segmentation (WSSS) framework that generates masks solely from image-level labels. Our approach builds on Adversarial Erasing (AER), which iteratively mines discriminative regions, erases them, and retrains a classifier to reveal complementary cues that become pseudo-labels for segmentation. However, standard AER also collects irrelevant background features, degrading pseudo-label quality. CREST addresses this with (i) a Constrained Ordinal Region Expansion (CORE) module that encodes the spatial-connectedness prior of polar lows, constraining region expansion from a high-confidence seed, and (ii) a Dynamic Bootstrapping (DB) loss that treats the mining order as a proxy for label reliability, attenuating supervision from noisier, later-mined regions. On Sentinel-1 SAR data, CREST follows the cyclone structure more closely than standard AER, and returns a multi-class rather than binary mask whose classes indicate the reliability assigned to each region. We further evaluate on BUS-UCLM breast ultrasound and PASCAL VOC person data, whose targets satisfy the same connectedness prior but come with the dense masks the SAR data lacks. On both datasets, CREST performs better than the equivalent AER pipeline under identical settings.

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arXiv2026

Hierarchical Pooling for Sheaf Neural Networks

Sheaf Neural Networks (SNNs) generalize Graph Neural Networks (GNNs) by replacing scalar node signals with stalk-valued signals and by using restriction maps to measure compatibility across edges. Unlike standard graph diffusion, which encourages neighboring node features to become similar, sheaf diffusion promotes consistency through the restriction maps and can therefore model more general relationships between neighboring nodes. However, existing sheaf neural architectures mainly operate at a fixed graph resolution and do not provide a principled pooling mechanism for building hierarchical representations. In this paper, we introduce Hierarchical Sheaf Pool (HiSP), a sheaf-aware pooling framework based on local spectral coarsening. Given a partition of the graph, HiSP constructs each coarse stalk by projecting fine stalk-valued features onto the low-frequency eigenmodes of the cluster-internal sheaf Laplacian. These local modes define a cochain-level prolongation map, which allows the fine sheaf energy to be represented on the coarse space through a Galerkin operator. We further analyze the approximation induced by coarsening by separating truncation loss, due to discarded local modes, from realization loss, due to representing the projected operator as a coarse sheaf. Finally, we implement HiSP as a GNN pooling layer compatible with SNNs and provide a PyG implementation supporting batching, lifted sheaf Laplacians, and hierarchical architectures.

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arXiv2026

A Generalized Tikhonov Layer for Interpretable-by-design Graph Neural Networks

We propose the Tikhonov layer, a graph neural network layer that is interpretable by design: once trained, its learned parameters directly reveal which node features and which aspects of the graph topology were leveraged for prediction. In practice, the layer's propagation matrix takes the closed-form $R = (p(L)+Q)^{-1} Q$, where $L$ is the normalized graph Laplacian, $Q = diag(q_1,...,q_n)$ a learnable diagonal matrix of positive node-importance scores, and $p(\cdot)$ a learnable polynomial. For any input feature $x$, the layer output $Rx$ is the exact minimizer of a generalized graph Tikhonov problem that trades off node-level data fidelity against a topology-driven regularization penalty. The learned pair $\{\{q_i\},p\}$ constitutes a built-in explanation: large $q_i$ indicates that node $i$'s own features drive the prediction, while small $q_i$ signals reliance on the local graph topology; the shape of $p$ reveals whether homophily, heterophily, or a band-pass response is exploited. Expressivity is preserved by routing complexity through a dedicated, arbitrarily deep Q-network that produces the importance scores, while the Tikhonov layer itself remains transparent. We prove that distinct node-importance matrices yield distinct propagation operators, structurally coupling the explanation to the computation. Additionally, the Tikhonov layer provides, in a single layer, a global receptive field, mitigating both oversmoothing and oversquashing. Experiments on standard graph classification benchmarks confirm that the model matches (and sometimes outperforms) opaque baselines while producing interpretable and faithful explanations.

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arXiv2026

Torch Geometric Pool: the PyTorch library for pooling in Graph Neural Networks

Torch Geometric Pool (tgp) is a pooling library built on top of PyTorch Geometric. Graph pooling methods differ in how they assign nodes to supernodes, how they handle batches, what they return after pooling, and whether they expose auxiliary losses. These differences make it hard to compare methods or reuse the same model code across them. tgp addresses this problem with a common software interface based on the Select-Reduce-Connect-Lift (SRCL) decomposition. The library provides 20 hierarchical poolers, standardized output objects, standalone readout modules, support for dense poolers in batched and unbatched mode, and workflows for caching and pre-coarsening. It is released under the MIT license on GitHub and PyPI, with comprehensive documentation, tutorials, and examples.

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arXiv2026

Interpreting Temporal Graph Neural Networks with Koopman Theory

Spatiotemporal graph neural networks (STGNNs) have shown promising results in many domains, from forecasting to epidemiology. However, understanding the dynamics learned by these models and explaining their behaviour is significantly more difficult than for models that deal with static data. Inspired by Koopman theory, which allows a simple description of intricate, nonlinear dynamical systems, we introduce new explainability approaches for temporal graphs. Specifically, we present two methods to interpret the STGNN's decision process and identify the most relevant spatial and temporal patterns in the input for the task at hand. The first relies on dynamic mode decomposition (DMD), a Koopman-inspired dimensionality reduction method. The second relies on sparse identification of nonlinear dynamics (SINDy), a popular method for discovering governing equations of dynamical systems, which we use for the first time as a general tool for explainability. On semi-synthetic dissemination datasets, our methods correctly identify interpretable features such as the times at which infections occur and the infected nodes. We also validate the methods qualitatively on a real-world human motion dataset, where the explanations highlight the body parts most relevant for action recognition.

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arXiv2026

BN-Pool: Bayesian Nonparametric Pooling for Graphs

We introduce BN-Pool, the first clustering-based pooling method for Graph Neural Networks that adaptively determines the number of supernodes in a coarsened graph. BN-Pool leverages a generative model based on a Bayesian nonparametric framework for partitioning graph nodes into an unbounded number of clusters. During training, the node-to-cluster assignments are learned by combining the supervised loss of the downstream task with an unsupervised auxiliary term, which encourages the reconstruction of the original graph topology while penalizing unnecessary proliferation of clusters. By automatically discovering the optimal coarsening level for each graph, BN-Pool preserves the performance of soft-clustering pooling methods while avoiding their typical redundancy by learning compact pooled graphs. The code is available at https://github.com/NGMLGroup/Bayesian-Nonparametric-Graph-Pooling.

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arXiv2026

ResCP: Reservoir Conformal Prediction for Time Series Forecasting

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal Prediction (ResCP), a novel training-free conformal prediction method for time series. Our approach leverages the efficiency and representation learning capabilities of reservoir computing to dynamically reweight conformity scores. In particular, we compute similarity scores among reservoir states and use them to adaptively reweight the observed residuals at each step. With this approach, ResCP enables us to account for local temporal dynamics when modeling the error distribution without compromising computational scalability. We prove that, under reasonable assumptions, ResCP achieves asymptotic conditional coverage, and we empirically demonstrate its effectiveness across diverse forecasting tasks.

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arXiv2026

Promptable Foundation Models for SAR Remote Sensing: Adapting the Segment Anything Model for Snow Avalanche Segmentation

Remote sensing solutions for avalanche segmentation and mapping are key to supporting risk forecasting and mitigation in mountain regions. Synthetic Aperture Radar (SAR) imagery from Sentinel-1 can be effectively used for this task, but training an effective detection model requires gathering a large dataset with high-quality annotations from domain experts, which is prohibitively time-consuming. In this work, we aim to facilitate and accelerate the annotation of SAR images for avalanche mapping. We build on the Segment Anything Model (SAM), a segmentation foundation model trained on natural images, and tailor it to Sentinel-1 SAR data. Adapting SAM to our use-case requires addressing several domain-specific challenges: (i) domain mismatch, since SAM was not trained on satellite/SAR imagery; (ii) input adaptation, because SAR products typically provide more than three channels, while SAM is constrained to RGB images; (iii) robustness to imprecise prompts that can affect target identification and degrade the segmentation quality, an issue exacerbated in small, low-contrast avalanches; and (iv) training efficiency, since standard fine-tuning is computationally demanding for SAM. We tackle these challenges through a combination of adapters to mitigate the domain gap, multiple encoders to handle multi-channel SAR inputs, prompt-engineering strategies to improve avalanche localization accuracy, and a training algorithm that limits the training time of the encoder, which is recognized as the major bottleneck. We integrate the resulting model into an annotation tool and show experimentally that it speeds up the annotation of SAR images.

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arXiv2025

Relational Conformal Prediction for Correlated Time Series

We address the problem of uncertainty quantification in time series forecasting by exploiting observations at correlated sequences. Relational deep learning methods leveraging graph representations are among the most effective tools for obtaining point estimates from spatiotemporal data and correlated time series. However, the problem of exploiting relational structures to estimate the uncertainty of such predictions has been largely overlooked in the same context. To this end, we propose a novel distribution-free approach based on the conformal prediction framework and quantile regression. Despite the recent applications of conformal prediction to sequential data, existing methods operate independently on each target time series and do not account for relationships among them when constructing the prediction interval. We fill this void by introducing a novel conformal prediction method based on graph deep learning operators. Our approach, named Conformal Relational Prediction (CoRel), does not require the relational structure (graph) to be known a priori and can be applied on top of any pre-trained predictor. Additionally, CoRel includes an adaptive component to handle non-exchangeable data and changes in the input time series. Our approach provides accurate coverage and achieves state-of-the-art uncertainty quantification in relevant benchmarks.

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arXiv2025

Monitoring snow avalanches from SAR data with deep learning

Snow avalanches present significant risks to human life and infrastructure, particularly in mountainous regions, making effective monitoring crucial. Traditional monitoring methods, such as field observations, are limited by accessibility, weather conditions, and cost. Satellite-borne Synthetic Aperture Radar (SAR) data has become an important tool for large-scale avalanche detection, as it can capture data in all weather conditions and across remote areas. However, traditional processing methods struggle with the complexity and variability of avalanches. This chapter reviews the application of deep learning for detecting and segmenting snow avalanches from SAR data. Early efforts focused on the binary classification of SAR images, while recent advances have enabled pixel-level segmentation, providing greater accuracy and spatial resolution. A case study using Sentinel-1 SAR data demonstrates the effectiveness of deep learning models for avalanche segmentation, achieving superior results over traditional methods. We also present an extension of this work, testing recent state-of-the-art segmentation architectures on an expanded dataset of over 4,500 annotated SAR images. The best-performing model among those tested was applied for large-scale avalanche detection across the whole of Norway, revealing important spatial and temporal patterns over several winter seasons.

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arXiv2025

MaxCutPool: differentiable feature-aware Maxcut for pooling in graph neural networks

We propose a novel approach to compute the MAXCUT in attributed graphs, i.e., graphs with features associated with nodes and edges. Our approach works well on any kind of graph topology and can find solutions that jointly optimize the MAXCUT along with other objectives. Based on the obtained MAXCUT partition, we implement a hierarchical graph pooling layer for Graph Neural Networks, which is sparse, trainable end-to-end, and particularly suitable for downstream tasks on heterophilic graphs.

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arXiv2024

Graph-based Forecasting with Missing Data through Spatiotemporal Downsampling

Given a set of synchronous time series, each associated with a sensor-point in space and characterized by inter-series relationships, the problem of spatiotemporal forecasting consists of predicting future observations for each point. Spatiotemporal graph neural networks achieve striking results by representing the relationships across time series as a graph. Nonetheless, most existing methods rely on the often unrealistic assumption that inputs are always available and fail to capture hidden spatiotemporal dynamics when part of the data is missing. In this work, we tackle this problem through hierarchical spatiotemporal downsampling. The input time series are progressively coarsened over time and space, obtaining a pool of representations that capture heterogeneous temporal and spatial dynamics. Conditioned on observations and missing data patterns, such representations are combined by an interpretable attention mechanism to generate the forecasts. Our approach outperforms state-of-the-art methods on synthetic and real-world benchmarks under different missing data distributions, particularly in the presence of contiguous blocks of missing values.

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arXiv2024

Hierarchical Representation Learning in Graph Neural Networks with Node Decimation Pooling

In graph neural networks (GNNs), pooling operators compute local summaries of input graphs to capture their global properties, and they are fundamental for building deep GNNs that learn hierarchical representations. In this work, we propose the Node Decimation Pooling (NDP), a pooling operator for GNNs that generates coarser graphs while preserving the overall graph topology. During training, the GNN learns new node representations and fits them to a pyramid of coarsened graphs, which is computed offline in a pre-processing stage. NDP consists of three steps. First, a node decimation procedure selects the nodes belonging to one side of the partition identified by a spectral algorithm that approximates the \maxcut{} solution. Afterwards, the selected nodes are connected with Kron reduction to form the coarsened graph. Finally, since the resulting graph is very dense, we apply a sparsification procedure that prunes the adjacency matrix of the coarsened graph to reduce the computational cost in the GNN. Notably, we show that it is possible to remove many edges without significantly altering the graph structure. Experimental results show that NDP is more efficient compared to state-of-the-art graph pooling operators while reaching, at the same time, competitive performance on a significant variety of graph classification tasks.

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arXiv2023

The expressive power of pooling in Graph Neural Networks

In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances in the design of pooling operators, there is not a principled criterion to compare them. In this work, we derive sufficient conditions for a pooling operator to fully preserve the expressive power of the MP layers before it. These conditions serve as a universal and theoretically grounded criterion for choosing among existing pooling operators or designing new ones. Based on our theoretical findings, we analyze several existing pooling operators and identify those that fail to satisfy the expressiveness conditions. Finally, we introduce an experimental setup to verify empirically the expressive power of a GNN equipped with pooling layers, in terms of its capability to perform a graph isomorphism test.

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arXiv2023

Probabilistic load forecasting with Reservoir Computing

Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios, decision-makers need both precise and reliable forecasts of, for example, power loads. For this reason, point forecasts are not enough hence it is necessary to adopt methods that provide an uncertainty quantification. This work focuses on reservoir computing as the core time series forecasting method, due to its computational efficiency and effectiveness in predicting time series. While the RC literature mostly focused on point forecasting, this work explores the compatibility of some popular uncertainty quantification methods with the reservoir setting. Both Bayesian and deterministic approaches to uncertainty assessment are evaluated and compared in terms of their prediction accuracy, computational resource efficiency and reliability of the estimated uncertainty, based on a set of carefully chosen performance metrics.

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arXiv2023

Total Variation Graph Neural Networks

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the $\ell_1$ distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

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arXiv2023

Combining Stochastic Explainers and Subgraph Neural Networks can Increase Expressivity and Interpretability

Subgraph-enhanced graph neural networks (SGNN) can increase the expressive power of the standard message-passing framework. This model family represents each graph as a collection of subgraphs, generally extracted by random sampling or with hand-crafted heuristics. Our key observation is that by selecting "meaningful" subgraphs, besides improving the expressivity of a GNN, it is also possible to obtain interpretable results. For this purpose, we introduce a novel framework that jointly predicts the class of the graph and a set of explanatory sparse subgraphs, which can be analyzed to understand the decision process of the classifier. We compare the performance of our framework against standard subgraph extraction policies, like random node/edge deletion strategies. The subgraphs produced by our framework allow to achieve comparable performance in terms of accuracy, with the additional benefit of providing explanations.

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