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Jacopo Quizi

Publications and source records attributed to Jacopo Quizi.

5 recordsLinked to original sources

ERIS: Enhancing Privacy and Scalability in Federated Learning via Federated Shard Aggregation

Scaling Federated Learning (FL) to billion-parameter models forces a challenging trade-off between privacy, scalability, and model utility. Existing solutions often tackle these challenges in isolation, sacrificing accuracy, relying on costly cryptographic tools, or introducing communication and optimization inefficiencies that affect convergence. We introduce ERIS, an FL framework centered on Federated Shard Aggregation (FSA), a novel mechanism that partitions each client update into non-overlapping shards whose aggregation is distributed across multiple client-side aggregators. FSA removes the central aggregation bottleneck, limits the information visible to any single observer, and preserves the centralized FL update after reassembly. ERIS can further readily integrate Distributed Shifted Compression (DSC) to reduce transmitted payloads and exposed coordinates. We prove that ERIS preserves convergence under standard assumptions and bounds mutual information leakage by the observable fraction of each update, decreasing with the number of client-side aggregators, and with the compression level when DSC is enabled. Experiments across image and text tasks, including large language models, show that ERIS achieves FedAvg-level utility while substantially reducing communication bottlenecks and improving robustness to membership inference and reconstruction attacks, without relying on heavy cryptography or utility-degrading perturbations.

cs.LG

Samplet limits and multiwavelets

Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension 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, if choosing polynomials as primitives, the resulting samplet basis converges to signed measures with broken polynomial densities in the infinite data limit. 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.

math.NA

Bespoke multiresolution analysis of graph signals

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.

eess.SP

Observation-specific explanations through scattered data approximation

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.

stat.ML

The dimension weighted fast multipole method for scattered data approximation

The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we derive very efficient degenerate kernel approximations which we then use in a dimension weighted fast multipole method. This dimension weighted fast multipole method enables to deal with many more dimensions than the standard black-box fast multipole method based on interpolation. A thorough analysis of the method is provided including rigorous error estimates. The accuracy and the cost of the approach are validated by extensive numerical results. As a relevant application, we apply the approach to a shape uncertainty quantification problem.

math.NA