Searcharxiv⌕ Search

arXiv subjects

Alberto Cattaneo

Publications and source records attributed to Alberto Cattaneo.

13 recordsLinked to original sources
arXiv2026

JetSCI: A Hybrid JAX-PETSc Framework for Scalable Differentiable Simulation

The rapid rise of scientific machine learning (SciML) has expanded the role of differentiable modeling, surrogate modeling, and data-driven constitutive laws in large-scale simulation. The JAX framework provides an attractive environment for these workflows through automatically differentiable programs, vectorization, GPU acceleration, and while enabling seamless learning of surrogate models. However, large-scale simulation still relies on mature HPC infrastructure. Libraries, such as PETSc, provide scalable MPI-based parallelism, robust linear and nonlinear solvers, and advanced preconditioning capabilities that remain difficult to reproduce in JAX-only workflows. We present JetSCI, a hybrid JAX-PETSc framework that unifies these complementary strengths. JetSCI uses JAX for GPU-parallel differentiable discretizations and PETSc for robust, scalable solution of the resulting systems on distributed-memory architectures, exposing multilevel parallelism through GPU acceleration within nodes and MPI parallelism across nodes. For finite element discretizations of heterogeneous micromechanics problems, JetSCI outperforms JAX-only implementations in efficiency and accuracy.

cs.MS↗
arXiv2026

UltRAG: a Universal Simple Scalable Recipe for Knowledge Graph RAG

Large language models (LLMs) frequently generate confident yet factually incorrect content when used for language generation (a phenomenon often known as hallucination). Retrieval augmented generation (RAG) tries to reduce factual errors by identifying information in a knowledge corpus and putting it in the context window of the model. While this approach is well-established for document-structured data, it is non-trivial to adapt it for Knowledge Graphs (KGs), especially for queries that require multi-node/multi-hop reasoning on graphs. We introduce ULTRAG, a general framework for retrieving information from Knowledge Graphs that shifts away from classical RAG. By endowing LLMs with off-the-shelf neural query executing modules, we highlight how readily available language models can achieve state-of-the-art results on Knowledge Graph Question Answering (KGQA) tasks without any retraining of the LLM or executor involved. In our experiments, ULTRAG achieves better performance when compared to state-of-the-art KG-RAG solutions, and it enables language models to interface with Wikidata-scale graphs (116M entities, 1.6B relations) at comparable or lower costs.

cs.IR↗
arXiv2025

Ground-Truth Subgraphs for Better Training and Evaluation of Knowledge Graph Augmented LLMs

Retrieval of information from graph-structured knowledge bases represents a promising direction for improving the factuality of LLMs. While various solutions have been proposed, a comparison of methods is difficult due to the lack of challenging QA datasets with ground-truth targets for graph retrieval. We present SynthKGQA, an LLM-powered framework for generating high-quality Knowledge Graph Question Answering datasets from any Knowledge Graph, providing the full set of ground-truth facts in the KG to reason over questions. We show how, in addition to enabling more informative benchmarking of KG retrievers, the data produced with SynthKGQA also allows us to train better models.We apply SynthKGQA to Wikidata to generate GTSQA, a new dataset designed to test zero-shot generalization abilities of KG retrievers with respect to unseen graph structures and relation types, and benchmark popular solutions for KG-augmented LLMs on it.

cs.LG↗
arXiv2025

Rootfinding and Optimization Techniques for Solving Nonlinear Systems of Equations Arising from Cohesive Zone Models

While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a rich body of work spanning back to at least the first century, providing the opportunity for advancement in the field of computational discrete damage modeling. In this paper, we explore the performance of established methods when applied to problems involving cohesive zone models to identify promising methods for further improvement in this specialized application. We first use a simple 1D example problem with low degrees of freedom (DoF) to compare nonlinear solution methods, thereby allowing for both straightforward and intuitive visualization of the residual space and reasoning about the cause for each method's performance. We then explore the impact of higher DoF discretizations of the same problem on the performance of the solution methods. Finally, we discuss techniques to improve performance or to overcome limitations of the various methods.

math.NA↗
arXiv2024

Approximate Top-$k$ for Increased Parallelism

We present an evaluation of bucketed approximate top-$k$ algorithms. Computing top-$k$ exactly suffers from limited parallelism, because the $k$ largest values must be aggregated along the vector, thus is not well suited to computation on highly-parallel machine learning accelerators. By relaxing the requirement that the top-$k$ is exact, bucketed algorithms can dramatically increase the parallelism available by independently computing many smaller top-$k$ operations. We explore the design choices of this class of algorithms using both theoretical analysis and empirical evaluation on downstream tasks. Our motivating examples are sparsity algorithms for language models, which often use top-$k$ to select the most important parameters or activations. We also release a fast bucketed top-$k$ implementation for PyTorch.

cs.LG↗
arXiv2024

The Role of Graph Topology in the Performance of Biomedical Knowledge Graph Completion Models

Knowledge Graph Completion has been increasingly adopted as a useful method for helping address several tasks in biomedical research, such as drug repurposing or drug-target identification. To that end, a variety of datasets and Knowledge Graph Embedding models have been proposed over the years. However, little is known about the properties that render a dataset, and associated modelling choices, useful for a given task. Moreover, even though theoretical properties of Knowledge Graph Embedding models are well understood, their practical utility in this field remains controversial. In this work, we conduct a comprehensive investigation into the topological properties of publicly available biomedical Knowledge Graphs and establish links to the accuracy observed in real-world tasks. By releasing all model predictions and a new suite of analysis tools we invite the community to build upon our work and continue improving the understanding of these crucial applications.

cs.LG↗
arXiv2022

BESS: Balanced Entity Sampling and Sharing for Large-Scale Knowledge Graph Completion

We present the award-winning submission to the WikiKG90Mv2 track of OGB-LSC@NeurIPS 2022. The task is link-prediction on the large-scale knowledge graph WikiKG90Mv2, consisting of 90M+ nodes and 600M+ edges. Our solution uses a diverse ensemble of $85$ Knowledge Graph Embedding models combining five different scoring functions (TransE, TransH, RotatE, DistMult, ComplEx) and two different loss functions (log-sigmoid, sampled softmax cross-entropy). Each individual model is trained in parallel on a Graphcore Bow Pod$_{16}$ using BESS (Balanced Entity Sampling and Sharing), a new distribution framework for KGE training and inference based on balanced collective communications between workers. Our final model achieves a validation MRR of 0.2922 and a test-challenge MRR of 0.2562, winning the first place in the competition. The code is publicly available at: https://github.com/graphcore/distributed-kge-poplar/tree/2022-ogb-submission.

cs.LG↗
arXiv2021

On the Chow ring of certain Lehn-Lehn-Sorger-van Straten eightfolds

We consider a $10$-dimensional family of Lehn-Lehn-Sorger-van Straten hyperkähler eightfolds which have a non-symplectic automorphism of order $3$. Using the theory of finite-dimensional motives, we show that the action of this automorphism on the Chow group of $0$-cycles is as predicted by the Bloch-Beilinson conjectures. We prove a similar statement for the anti-symplectic involution on varieties in this family. This has interesting consequences for the intersection product in the Chow ring of these varieties.

math.AG↗
arXiv2020

On birational transformations of Hilbert schemes of points on K3 surfaces

We classify the group of birational automorphisms of Hilbert schemes of points on algebraic K3 surfaces of Picard rank one. We study whether these automorphisms are symplectic or non-symplectic and if there exists a hyperk\"ahler birational model on which they become biregular. We also present new geometrical constructions of these automorphisms.

math.AG↗
arXiv2019

Non-symplectic involutions on manifolds of $K3^{[n]}$-type

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and anti-invariant lattice for the action of the involution on cohomology, and explicitly describe the lattices in the cases where the invariant has small rank. We also give a modular description of all $d$-dimensional families of manifolds of $K3^{[n]}$-type with a non-symplectic involution for $d\geq 19$ and $n\leq 5$, and provide examples arising as moduli spaces of twisted sheaves on a $K3$ surface.

math.AG↗
arXiv2018

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of $n$ points on a generic projective K3 surface $S$, for any $n \geq 2$. We show that the automorphism group of $S^{[n]}$ is either trivial or generated by a non-symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any $n \geq 2$, there exist infinite values for the degree of $S$ such that $S^{[n]}$ admits a non-natural involution. This provides a generalization of results by Boissière--Cattaneo--Nieper-Wisskirchen--Sarti for $n=2$.

math.AG↗
arXiv2018

Non-symplectic automorphisms of odd prime order on manifolds of $K3^{[n]}$-type

We classify non-symplectic automorphisms of odd prime order on irreducible holomorphic symplectic manifolds which are deformations of Hilbert schemes of any number n of points on K3 surfaces, extending results already known for n=2. In order to do so, we study the properties of the invariant lattice of the automorphism (and its orthogonal complement) inside the second cohomology lattice of the manifold. We also explain how to construct automorphisms with fixed action on cohomology: in the cases n=3,4 the examples provided allow to realize all admissible actions in our classification. For n=4, we present a construction of non-symplectic automorphisms on the Lehn-Lehn-Sorger-van Straten eightfold, which come from automorphisms of the underlying cubic fourfold.

math.AG↗