Jacopo Quizi

Dario Fenoglio, Pasquale Polverino, Jacopo Quizi et al.

Scaling federated learning (FL) to billion-parameter models introduces critical trade-offs between communication efficiency, model accuracy, and privacy guarantees. Existing solutions often tackle these challenges in isolation, sacrificing accuracy or relying on costly cryptographic tools. We propose ERIS, a serverless FL framework that balances privacy and accuracy while eliminating the server bottleneck and distributing the communication load. ERIS combines a model partitioning strategy, distributing aggregation across multiple client-side aggregators, with a distributed shifted gradient compression mechanism. We theoretically prove that ERIS (i) converges at the same rate as FedAvg under standard assumptions, and (ii) bounds mutual information leakage inversely with the number of aggregators, enabling strong privacy guarantees with no accuracy degradation. Experiments across image and text tasks, including large language models, confirm that ERIS achieves FedAvg-level accuracy while substantially reducing communication cost and improving robustness to membership inference and reconstruction attacks, without relying on heavy cryptography or noise injection.

Gianluca Giacchi, Michael Multerer, Jacopo Quizi

Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension and such that they exhibit vanishing moments with respect to any prescribed set of primitives. We consider the samplet construction in a probabilistic framework and show that, when choosing polynomials as primitives, the resulting samplet basis converges in the infinite data limit to signed measures with broken polynomial densities. These densities amount to multiwavelets with respect to a hierarchical partition of the region containing the data sites. As a byproduct, we therefore obtain a construction of general multiwavelets that allows for a flexible prescription of vanishing moments going beyond tensor product constructions. For congruent partitions we particularly recover classical multiwavelets with scale- and partition- independent filter coefficients. The theoretical findings are complemented by numerical experiments that illustrate the convergence results in case of random as well as low-discrepancy data sites.

Giacomo Elefante, Gianluca Giacchi, Michael Multerer et al.

We present a novel framework for discrete multiresolution analysis of graph signals. The main analytical tool is the samplet transform, originally defined in the Euclidean framework as a discrete wavelet-like construction, tailored to the analysis of scattered data. The first contribution of this work is defining samplets on graphs. To this end, we subdivide the graph into a fixed number of patches, embed each patch into a Euclidean space, where we construct samplets, and eventually pull the construction back to the graph. This ensures orthogonality, locality, and the vanishing moments property with respect to properly defined polynomial spaces on graphs. Compared to classical Haar wavelets, this framework broadens the class of graph signals that can efficiently be compressed and analyzed. Along this line, we provide a definition of a class of signals that can be compressed using our construction. We support our findings with different examples of signals defined on graphs whose vertices lie on smooth manifolds. For efficient numerical implementation, we combine heavy edge clustering, to partition the graph into meaningful patches, with landmark \texttt{Isomap}, which provides low-dimensional embeddings for each patch. Our results demonstrate the method's robustness, scalability, and ability to yield sparse representations with controllable approximation error, significantly outperforming traditional Haar wavelet approaches in terms of compression efficiency and multiresolution fidelity.

Valentina Ghidini, Michael Multerer, Jacopo Quizi et al.

This work introduces the definition of observation-specific explanations to assign a score to each data point proportional to its importance in the definition of the prediction process. Such explanations involve the identification of the most influential observations for the black-box model of interest. The proposed method involves estimating these explanations by constructing a surrogate model through scattered data approximation utilizing the orthogonal matching pursuit algorithm. The proposed approach is validated on both simulated and real-world datasets.