arXiv subjects

Pietro Liò

Publications and source records attributed to Pietro Liò.

At least 127 records · Page 7Linked to original sources

arXiv2024

Position: Topological Deep Learning is the New Frontier for Relational Learning

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

cs.LG↗

arXiv2024

Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networks

Sheaf Neural Networks (SNNs) naturally extend Graph Neural Networks (GNNs) by endowing a cellular sheaf over the graph, equipping nodes and edges with vector spaces and defining linear mappings between them. While the attached geometric structure has proven to be useful in analyzing heterophily and oversmoothing, so far the methods by which the sheaf is computed do not always guarantee a good performance in such settings. In this work, drawing inspiration from opinion dynamics concepts, we propose two novel sheaf learning approaches that (i) provide a more intuitive understanding of the involved structure maps, (ii) introduce a useful inductive bias for heterophily and oversmoothing, and (iii) infer the sheaf in a way that does not scale with the number of features, thus using fewer learnable parameters than existing methods. In our evaluation, we show the limitations of the real-world benchmarks used so far on SNNs, and design a new synthetic task -- leveraging the symmetries of n-dimensional ellipsoids -- that enables us to better assess the strengths and weaknesses of sheaf-based models. Our extensive experimentation on these novel datasets reveals valuable insights into the scenarios and contexts where SNNs in general -- and our proposed approaches in particular -- can be beneficial.

cs.LG↗

arXiv2024

TabMDA: Tabular Manifold Data Augmentation for Any Classifier using Transformers with In-context Subsetting

Tabular data is prevalent in many critical domains, yet it is often challenging to acquire in large quantities. This scarcity usually results in poor performance of machine learning models on such data. Data augmentation, a common strategy for performance improvement in vision and language tasks, typically underperforms for tabular data due to the lack of explicit symmetries in the input space. To overcome this challenge, we introduce TabMDA, a novel method for manifold data augmentation on tabular data. This method utilises a pre-trained in-context model, such as TabPFN, to map the data into an embedding space. TabMDA performs label-invariant transformations by encoding the data multiple times with varied contexts. This process explores the learned embedding space of the underlying in-context models, thereby enlarging the training dataset. TabMDA is a training-free method, making it applicable to any classifier. We evaluate TabMDA on five standard classifiers and observe significant performance improvements across various tabular datasets. Our results demonstrate that TabMDA provides an effective way to leverage information from pre-trained in-context models to enhance the performance of downstream classifiers. Code is available at https://github.com/AdrianBZG/TabMDA.

cs.LG↗

arXiv2024

E(n) Equivariant Message Passing Cellular Networks

This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1) enhancing their expressiveness by incorporating arbitrary cells, and 2) achieving this in a computationally efficient way with a decoupled EMPCNs technique. We demonstrate that EMPCNs achieve close to state-of-the-art performance on multiple tasks without the need for steerability, including many-body predictions and motion capture. Moreover, ablation studies confirm that decoupled EMPCNs exhibit stronger generalization capabilities than their non-topologically informed counterparts. These findings show that EMPCNs can be used as a scalable and expressive framework for higher-order message passing in geometric and topological graphs

cs.LG↗

arXiv2024

Metric Learning for Clifford Group Equivariant Neural Networks

Clifford Group Equivariant Neural Networks (CGENNs) leverage Clifford algebras and multivectors as an alternative approach to incorporating group equivariance to ensure symmetry constraints in neural representations. In principle, this formulation generalizes to orthogonal groups and preserves equivariance regardless of the metric signature. However, previous works have restricted internal network representations to Euclidean or Minkowski (pseudo-)metrics, handpicked depending on the problem at hand. In this work, we propose an alternative method that enables the metric to be learned in a data-driven fashion, allowing the CGENN network to learn more flexible representations. Specifically, we populate metric matrices fully, ensuring they are symmetric by construction, and leverage eigenvalue decomposition to integrate this additional learnable component into the original CGENN formulation in a principled manner. Additionally, we motivate our method using insights from category theory, which enables us to explain Clifford algebras as a categorical construction and guarantee the mathematical soundness of our approach. We validate our method in various tasks and showcase the advantages of learning more flexible latent metric representations. The code and data are available at https://github.com/rick-ali/Metric-Learning-for-CGENNs

cs.LG↗

arXiv2024

AB$\mathbb{C}$MB: Deep Delensing Assisted Likelihood-Free Inference from CMB Polarization Maps

The existence of a cosmic background of primordial gravitational waves (PGWB) is a robust prediction of inflationary cosmology, but it has so far evaded discovery. The most promising avenue of its detection is via measurements of Cosmic Microwave Background (CMB) $B$-polarization. However, this is not straightforward due to (a) the fact that CMB maps are distorted by gravitational lensing and (b) the high-dimensional nature of CMB data, which renders likelihood-based analysis methods computationally extremely expensive. In this paper, we introduce an efficient likelihood-free, end-to-end inference method to directly infer the posterior distribution of the tensor-to-scalar ratio $r$ from lensed maps of the Stokes $Q$ and $U$ polarization parameters. Our method employs a generative model to delense the maps and utilizes the Approximate Bayesian Computation (ABC) algorithm to sample $r$. We demonstrate that our method yields unbiased estimates of $r$ with well-calibrated uncertainty quantification.

astro-ph.CO↗

arXiv2024

Neural Bipartite Matching

Graph neural networks (GNNs) have found application for learning in the space of algorithms. However, the algorithms chosen by existing research (sorting, Breadth-First search, shortest path finding, etc.) usually align perfectly with a standard GNN architecture. This report describes how neural execution is applied to a complex algorithm, such as finding maximum bipartite matching by reducing it to a flow problem and using Ford-Fulkerson to find the maximum flow. This is achieved via neural execution based only on features generated from a single GNN. The evaluation shows strongly generalising results with the network achieving optimal matching almost 100% of the time.

cs.LG↗

arXiv2024

Explaining the Explainers in Graph Neural Networks: a Comparative Study

Following a fast initial breakthrough in graph based learning, Graph Neural Networks (GNNs) have reached a widespread application in many science and engineering fields, prompting the need for methods to understand their decision process. GNN explainers have started to emerge in recent years, with a multitude of methods both novel or adapted from other domains. To sort out this plethora of alternative approaches, several studies have benchmarked the performance of different explainers in terms of various explainability metrics. However, these earlier works make no attempts at providing insights into why different GNN architectures are more or less explainable, or which explainer should be preferred in a given setting. In this survey, we fill these gaps by devising a systematic experimental study, which tests ten explainers on eight representative architectures trained on six carefully designed graph and node classification datasets. With our results we provide key insights on the choice and applicability of GNN explainers, we isolate key components that make them usable and successful and provide recommendations on how to avoid common interpretation pitfalls. We conclude by highlighting open questions and directions of possible future research.

cs.LG↗

arXiv2024

Graph Representation Learning Strategies for Omics Data: A Case Study on Parkinson's Disease

Omics data analysis is crucial for studying complex diseases, but its high dimensionality and heterogeneity challenge classical statistical and machine learning methods. Graph neural networks have emerged as promising alternatives, yet the optimal strategies for their design and optimization in real-world biomedical challenges remain unclear. This study evaluates various graph representation learning models for case-control classification using high-throughput biological data from Parkinson's disease and control samples. We compare topologies derived from sample similarity networks and molecular interaction networks, including protein-protein and metabolite-metabolite interactions (PPI, MMI). Graph Convolutional Network (GCNs), Chebyshev spectral graph convolution (ChebyNet), and Graph Attention Network (GAT), are evaluated alongside advanced architectures like graph transformers, the graph U-net, and simpler models like multilayer perceptron (MLP). These models are systematically applied to transcriptomics and metabolomics data independently. Our comparative analysis highlights the benefits and limitations of various architectures in extracting patterns from omics data, paving the way for more accurate and interpretable models in biomedical research.

cs.LG↗

arXiv2024

FLUID-LLM: Learning Computational Fluid Dynamics with Spatiotemporal-aware Large Language Models

Learning computational fluid dynamics (CFD) traditionally relies on computationally intensive simulations of the Navier-Stokes equations. Recently, large language models (LLMs) have shown remarkable pattern recognition and reasoning abilities in natural language processing (NLP) and computer vision (CV). However, these models struggle with the complex geometries inherent in fluid dynamics. We introduce FLUID-LLM, a novel framework combining pre-trained LLMs with spatiotemporal-aware encoding to predict unsteady fluid dynamics. Our approach leverages the temporal autoregressive abilities of LLMs alongside spatial-aware layers, bridging the gap between previous CFD prediction methods. Evaluations on standard benchmarks reveal significant performance improvements across various fluid datasets. Our results demonstrate that FLUID-LLM effectively integrates spatiotemporal information into pre-trained LLMs, enhancing CFD task performance.

cs.LG↗

arXiv2024

Sheaf HyperNetworks for Personalized Federated Learning

Graph hypernetworks (GHNs), constructed by combining graph neural networks (GNNs) with hypernetworks (HNs), leverage relational data across various domains such as neural architecture search, molecular property prediction and federated learning. Despite GNNs and HNs being individually successful, we show that GHNs present problems compromising their performance, such as over-smoothing and heterophily. Moreover, we cannot apply GHNs directly to personalized federated learning (PFL) scenarios, where a priori client relation graph may be absent, private, or inaccessible. To mitigate these limitations in the context of PFL, we propose a novel class of HNs, sheaf hypernetworks (SHNs), which combine cellular sheaf theory with HNs to improve parameter sharing for PFL. We thoroughly evaluate SHNs across diverse PFL tasks, including multi-class classification, traffic and weather forecasting. Additionally, we provide a methodology for constructing client relation graphs in scenarios where such graphs are unavailable. We show that SHNs consistently outperform existing PFL solutions in complex non-IID scenarios. While the baselines' performance fluctuates depending on the task, SHNs show improvements of up to 2.7% in accuracy and 5.3% in lower mean squared error over the best-performing baseline.

cs.LG↗

arXiv2024

SQLformer: Deep Auto-Regressive Query Graph Generation for Text-to-SQL Translation

In recent years, the task of text-to-SQL translation, which converts natural language questions into executable SQL queries, has gained significant attention for its potential to democratize data access. Despite its promise, challenges such as adapting to unseen databases and aligning natural language with SQL syntax have hindered widespread adoption. To overcome these issues, we introduce SQLformer, a novel Transformer architecture specifically crafted to perform text-to-SQL translation tasks. Our model predicts SQL queries as abstract syntax trees (ASTs) in an autoregressive way, incorporating structural inductive bias in the encoder and decoder layers. This bias, guided by database table and column selection, aids the decoder in generating SQL query ASTs represented as graphs in a Breadth-First Search canonical order. Our experiments demonstrate that SQLformer achieves state-of-the-art performance across six prominent text-to-SQL benchmarks.

cs.CL↗

arXiv2024

Optimizing Polynomial Graph Filters: A Novel Adaptive Krylov Subspace Approach

Graph Neural Networks (GNNs), known as spectral graph filters, find a wide range of applications in web networks. To bypass eigendecomposition, polynomial graph filters are proposed to approximate graph filters by leveraging various polynomial bases for filter training. However, no existing studies have explored the diverse polynomial graph filters from a unified perspective for optimization. In this paper, we first unify polynomial graph filters, as well as the optimal filters of identical degrees into the Krylov subspace of the same order, thus providing equivalent expressive power theoretically. Next, we investigate the asymptotic convergence property of polynomials from the unified Krylov subspace perspective, revealing their limited adaptability in graphs with varying heterophily degrees. Inspired by those facts, we design a novel adaptive Krylov subspace approach to optimize polynomial bases with provable controllability over the graph spectrum so as to adapt various heterophily graphs. Subsequently, we propose AdaptKry, an optimized polynomial graph filter utilizing bases from the adaptive Krylov subspaces. Meanwhile, in light of the diverse spectral properties of complex graphs, we extend AdaptKry by leveraging multiple adaptive Krylov bases without incurring extra training costs. As a consequence, extended AdaptKry is able to capture the intricate characteristics of graphs and provide insights into their inherent complexity. We conduct extensive experiments across a series of real-world datasets. The experimental results demonstrate the superior filtering capability of AdaptKry, as well as the optimized efficacy of the adaptive Krylov basis.

cs.LG↗

arXiv2024

Artificial Intelligence-powered fossil shark tooth identification: Unleashing the potential of Convolutional Neural Networks

All fields of knowledge are being impacted by Artificial Intelligence. In particular, the Deep Learning paradigm enables the development of data analysis tools that support subject matter experts in a variety of sectors, from physics up to the recognition of ancient languages. Palaeontology is now observing this trend as well. This study explores the capability of Convolutional Neural Networks (CNNs), a particular class of Deep Learning algorithms specifically crafted for computer vision tasks, to classify images of isolated fossil shark teeth gathered from online datasets as well as from the authors$'$ experience on Peruvian Miocene and Italian Pliocene fossil assemblages. The shark taxa that are included in the final, composite dataset (which consists of more than one thousand images) are representative of both extinct and extant genera, namely, Carcharhinus, Carcharias, Carcharocles, Chlamydoselachus, Cosmopolitodus, Galeocerdo, Hemipristis, Notorynchus, Prionace and Squatina. We developed a CNN, named SharkNet-X, specifically tailored on our recognition task, reaching a 5-fold cross validated mean accuracy of 0.85 to identify images containing a single shark tooth. Furthermore, we elaborated a visualization of the features extracted from images using the last dense layer of the CNN, achieved through the application of the clustering technique t-SNE. In addition, in order to understand and explain the behaviour of the CNN while giving a paleontological point of view on the results, we introduced the explainability method SHAP. To the best of our knowledge, this is the first instance in which this method is applied to the field of palaeontology. The main goal of this work is to showcase how Deep Learning techniques can aid in identifying isolated fossil shark teeth, paving the way for developing new information tools for automating the recognition and classification of fossils.

cs.CV↗

arXiv2024

The Deep Equilibrium Algorithmic Reasoner

Recent work on neural algorithmic reasoning has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. Doing so, however, has always used a recurrent architecture, where each iteration of the GNN aligns with an algorithm's iteration. Since an algorithm's solution is often an equilibrium, we conjecture and empirically validate that one can train a network to solve algorithmic problems by directly finding the equilibrium. Note that this does not require matching each GNN iteration with a step of the algorithm.

cs.LG↗

arXiv2024

Language Model Knowledge Distillation for Efficient Question Answering in Spanish

Recent advances in the development of pre-trained Spanish language models has led to significant progress in many Natural Language Processing (NLP) tasks, such as question answering. However, the lack of efficient models imposes a barrier for the adoption of such models in resource-constrained environments. Therefore, smaller distilled models for the Spanish language could be proven to be highly scalable and facilitate their further adoption on a variety of tasks and scenarios. In this work, we take one step in this direction by developing SpanishTinyRoBERTa, a compressed language model based on RoBERTa for efficient question answering in Spanish. To achieve this, we employ knowledge distillation from a large model onto a lighter model that allows for a wider implementation, even in areas with limited computational resources, whilst attaining negligible performance sacrifice. Our experiments show that the dense distilled model can still preserve the performance of its larger counterpart, while significantly increasing inference speedup. This work serves as a starting point for further research and investigation of model compression efforts for Spanish language models across various NLP tasks.

cs.CL↗

arXiv2024

Sheaf4Rec: Sheaf Neural Networks for Graph-based Recommender Systems

Recent advancements in Graph Neural Networks (GNN) have facilitated their widespread adoption in various applications, including recommendation systems. GNNs have proven to be effective in addressing the challenges posed by recommendation systems by efficiently modeling graphs in which nodes represent users or items and edges denote preference relationships. However, current GNN techniques represent nodes by means of a single static vector, which may inadequately capture the intricate complexities of users and items. To overcome these limitations, we propose a solution integrating a cutting-edge model inspired by category theory: Sheaf4Rec. Unlike single vector representations, Sheaf Neural Networks and their corresponding Laplacians represent each node (and edge) using a vector space. Our approach takes advantage from this theory and results in a more comprehensive representation that can be effectively exploited during inference, providing a versatile method applicable to a wide range of graph-related tasks and demonstrating unparalleled performance. Our proposed model exhibits a noteworthy relative improvement of up to 8.53% on F1-Score@10 and an impressive increase of up to 11.29% on NDCG@10, outperforming existing state-of-the-art models such as Neural Graph Collaborative Filtering (NGCF), KGTORe and other recently developed GNN-based models. In addition to its superior predictive capabilities, Sheaf4Rec shows remarkable improvements in terms of efficiency: we observe substantial runtime improvements ranging from 2.5% up to 37% when compared to other GNN-based competitor models, indicating a more efficient way of handling information while achieving better performance. Code is available at https://github.com/antoniopurificato/Sheaf4Rec.

cs.IR↗

arXiv2024

A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

cs.LG↗