arXiv subjects

Giuseppe Di Fatta

Publications and source records attributed to Giuseppe Di Fatta.

10 recordsLinked to original sources

arXiv2026

System-Wide Termination in Distributed Betweenness Centrality Computation

Computing betweenness centrality on large networks is inherently expensive, as it requires aggregating shortest-path dependencies across all pairs of vertices and becomes increasingly difficult to scale as network size grows. Scalable distributed algorithms can facilitate such computations, particularly when centralised processing is not feasible, and message exchanges must be carefully controlled, for example, in bandwidth-limited or very large-scale networks. However, existing distributed betweenness centrality implementations do not integrate a lightweight, system-wide termination detector. As a consequence, this can lead to extra messaging after local convergence or, if misconfigured, premature stops. In this work, a lightweight, system-wide global termination detection algorithm for this task is presented. The proposed method enables vertices to decide locally when the overall system has converged. The method is evaluated against a local stopping strategy in which vertices terminate individually once their own estimates stabilise. To compare these two approaches, namely global termination detection and local stopping, a custom Python simulator is implemented, and both approaches are tested on synthetic (Erdos-Renyi and geometric) and real (Email and Road) network topologies. Our results show that system-wide termination detection lets vertices stop safely after detecting global convergence, as indicated by zero final error in the evaluated networks, rather than stopping independently based only on local convergence. The local stopping approach, on the other hand, results in premature termination and some errors on heterogeneous networks. This work emphasises the need for coordinated halting in distributed centrality computation.

cs.DC↗

arXiv2026

Operator-Theoretic Generalization Bounds for Multitask Deep Learning

We develop operator-theoretic generalization bounds for deep multi-output function classes by representing network layers as Koopman composition operators on vector-valued reproducing kernel Hilbert spaces. In vector-valued Sobolev RKHSs, we derive Rademacher complexity bounds for invertible and width-expanding injective architectures. The estimates separate the output-coupling contribution, represented by the trace of the task matrix, from the layerwise operator norms, Sobolev symbol ratios, determinant factors, and restriction constants generated by the linear maps. We then analyze a distinct one-dimensional Brownian/Cameron--Martin regime. Using the exact anchored derivative-norm characterization of the vector-valued Brownian RKHS, we obtain layerwise bounds for domain-preserving scalar linear maps and anchored diffeomorphic activations; the corresponding factors scale as $|W_l|^{1/2}$ and $\|σ_l'\|_\infty^{1/2}$, respectively, and do not involve Sobolev smoothness exponents. Because the Sobolev and Brownian results concern different hypothesis spaces, neither is asserted to dominate the other uniformly. We additionally formulate shared operator learning across tasks, prove a finite-rank representer theorem, derive the exact finite-dimensional problem for squared loss, and establish a target-transfer bound when the learned operator is obtained independently of the target sample. Synthetic and MNIST studies examine stabilized Sobolev-inspired and Brownian-inspired complexity proxies; these empirical proxies are not evaluations of the proved bounds for rank-deficient architectures.

cs.LG↗

arXiv2026

Brownian Kernel Ladders

We introduce Brownian kernel ladders (BKLs), a recursive hierarchy of integral reproducing kernel Hilbert spaces built from linear functionals by repeatedly integrating Brownian pullback kernels indexed by functions from the preceding layer. The nonnegative 1-homogeneity of the Brownian kernel yields a kernel-preserving canonical spherical normalization and propagates square-root regularity through the hierarchy. Allowing all canonical ladder measures to vary produces a full adaptive BKL envelope with an infimal complexity. For this envelope, we prove depth-dependent Hölder and pointwise estimates, quasi-Banach structure, nestedness, and, under a geometric trace condition, strict growth with ballwise separation. We also establish existence of regularized empirical-risk minimizers for continuous losses uniformly bounded below, with almost-everywhere uniqueness of population predictions under strict convexity and pointwise uniqueness under full support. For statistical estimation, we study one realized ladder and finite dictionaries fixed independently of the estimation sample. For a dictionary of $M$ ladders, the Gaussian complexity of the union of radius-$r$ top-layer RKHS balls has $n^{-1/2}$ dependence, no explicit ambient-dimension factor, and model-selection factor $1+\sqrt{2\ln M}$. Corresponding high-probability oracle and excess-risk bounds follow; polynomial-size dictionaries retain a near-parametric rate. The theory separates adaptive representational richness from the statistical cost of ladder selection.

cs.LG↗

arXiv2026

On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning

The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobolev space as an expanded hypothesis space. This enhanced bound remains valid even in single output settings, outperforming existing Koopman based bounds. The resulting framework maintains key advantages such as flexibility and independence from network width, offering a more precise theoretical understanding of multitask deep learning in the context of kernel methods.

cs.LG↗

arXiv2026

Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learning

This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework. Our key development lies in strategically combining a Koopman based approach with existing techniques, achieving tighter generalization guarantees compared to traditional norm-based bounds. To mitigate computational challenges associated with Koopman-based methods, we introduce sketching techniques applicable to vector valued neural networks. These techniques yield excess risk bounds under generic Lipschitz losses, providing performance guarantees for applications including robust and multiple quantile regression. Furthermore, we propose a novel deep learning framework, deep vector-valued reproducing kernel Hilbert spaces (vvRKHS), leveraging Perron Frobenius (PF) operators to enhance deep kernel methods. We derive a new Rademacher generalization bound for this framework, explicitly addressing underfitting and overfitting through kernel refinement strategies. This work offers novel insights into the generalization properties of multitask learning with deep learning architectures, an area that has been relatively unexplored until recent developments.

cs.LG↗

arXiv2026

High-quality data augmentation for code comment classification

Code comments serve a crucial role in software development for documenting functionality, clarifying design choices, and assisting with issue tracking. They capture developers' insights about the surrounding source code, serving as an essential resource for both human comprehension and automated analysis. Nevertheless, since comments are in natural language, they present challenges for machine-based code understanding. To address this, recent studies have applied natural language processing (NLP) and deep learning techniques to classify comments according to developers' intentions. However, existing datasets for this task suffer from size limitations and class imbalance, as they rely on manual annotations and may not accurately represent the distribution of comments in real-world codebases. To overcome this issue, we introduce new synthetic oversampling and augmentation techniques based on high-quality data generation to enhance the NLBSE'26 challenge datasets. Our Synthetic Quality Oversampling Technique and Augmentation Technique (Q-SYNTH) yield promising results, improving the base classifier by $2.56\%$.

cs.SE↗

arXiv2025

Blockchain Epidemic Consensus for Large-Scale Networks

Blockchain is a distributed ledger technology that has applications in many domains such as cryptocurrency, smart contracts, supply chain management, and many others. Distributed consensus is a fundamental component of blockchain systems that enables secure, precise, and tamper-proof verification of data without relying on central authorities. Existing consensus protocols, nevertheless, suffer from drawbacks, some of which are related to scalability, resource consumption, and fault tolerance. We introduce Blockchain Epidemic Consensus Protocol (BECP), a novel fully decentralised consensus protocol for blockchain networks at a large scale. BECP follows epidemic communication principles, without fixed roles like validators or leaders, and achieves probabilistic convergence, efficient message dissemination, and tolerance to message delays. We provide an extensive experimental comparison of BECP against classic protocols like PAXOS, RAFT, and PBFT, and newer epidemic-based protocols like Avalanche and Snowman. The findings indicate that BECP provides desirable gains in throughput, consensus latency, and substantial message-passing efficiency compared to existing epidemic-based approaches, validating its usability as an effective and scalable approach for next-generation blockchain systems.

cs.DC↗

arXiv2025

Fully Decentralised Consensus for Extreme-scale Blockchain

Blockchain is a decentralised, immutable ledger technology that has been widely adopted in many sectors for various applications such as cryptocurrencies, smart contracts and supply chain management. Distributed consensus is a fundamental component of blockchain, which is required to ensure trust, security, and integrity of the data stored and the transactions processed in the blockchain. Various consensus algorithms have been developed, each affected from certain issues such as node failures, high resource consumption, collusion, etc. This work introduces a fully decentralised consensus protocol, Blockchain Epidemic Consensus Protocol (BECP), suitable for very large and extreme-scale blockchain systems. The proposed approach leverages the benefits of epidemic protocols, such as no reliance on a fixed set of validators or leaders, probabilistic guarantees of convergence, efficient use of network resources, and tolerance to node and network failures. A comparative experimental analysis has been carried out with traditional protocols including PAXOS, RAFT, and Practical Byzantine Fault Tolerance (PBFT), as well as a relatively more recent protocol such as Avalanche, which is specifically designed for very large-scale systems. The results illustrate how BECP outperforms them in terms of throughput, scalability and consensus latency. BECP achieves an average of 1.196 times higher throughput in terms of consensus on items and 4.775 times better average consensus latency. Furthermore, BECP significantly reduces the number of messages compared to Avalanche. These results demonstrate the effectiveness and efficiency of fully decentralised consensus for blockchain technology based on epidemic protocols.

cs.DC↗

arXiv2025

Gradient Similarity Surgery in Multi-Task Deep Learning

The multi-task learning ($MTL$) paradigm aims to simultaneously learn multiple tasks within a single model capturing higher-level, more general hidden patterns that are shared by the tasks. In deep learning, a significant challenge in the backpropagation training process is the design of advanced optimisers to improve the convergence speed and stability of the gradient descent learning rule. In particular, in multi-task deep learning ($MTDL$) the multitude of tasks may generate potentially conflicting gradients that would hinder the concurrent convergence of the diverse loss functions. This challenge arises when the gradients of the task objectives have either different magnitudes or opposite directions, causing one or a few to dominate or to interfere with each other, thus degrading the training process. Gradient surgery methods address the problem explicitly dealing with conflicting gradients by adjusting the overall gradient trajectory. This work introduces a novel gradient surgery method, the Similarity-Aware Momentum Gradient Surgery (SAM-GS), which provides an effective and scalable approach based on a gradient magnitude similarity measure to guide the optimisation process. The SAM-GS surgery adopts gradient equalisation and modulation of the first-order momentum. A series of experimental tests have shown the effectiveness of SAM-GS on synthetic problems and $MTL$ benchmarks. Gradient magnitude similarity plays a crucial role in regularising gradient aggregation in $MTDL$ for the optimisation of the learning process.

cs.LG↗

arXiv2025

Optimizing Deep Learning Models to Address Class Imbalance in Code Comment Classification

Developers rely on code comments to document their work, track issues, and understand the source code. As such, comments provide valuable insights into developers' understanding of their code and describe their various intentions in writing the surrounding code. Recent research leverages natural language processing and deep learning to classify comments based on developers' intentions. However, such labelled data are often imbalanced, causing learning models to perform poorly. This work investigates the use of different weighting strategies of the loss function to mitigate the scarcity of certain classes in the dataset. In particular, various RoBERTa-based transformer models are fine-tuned by means of a hyperparameter search to identify their optimal parameter configurations. Additionally, we fine-tuned the transformers with different weighting strategies for the loss function to address class imbalances. Our approach outperforms the STACC baseline by 8.9 per cent on the NLBSE'25 Tool Competition dataset in terms of the average F1$_c$ score, and exceeding the baseline approach in 17 out of 19 cases with a gain ranging from -5.0 to 38.2. The source code is publicly available at https://github.com/moritzmock/NLBSE2025.

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