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Large Language Models (LLMs) changed the way we design and interact with software systems. Their ability to process and extract information from text has drastically improved productivity in a number of routine tasks. Developers that want to include these models in their software stack, however, face a dreadful challenge: debugging LLMs' inconsistent behavior across minor variations of the prompt. We therefore introduce two metrics for classification tasks, namely sensitivity and consistency, which are complementary to task performance. First, sensitivity measures changes of predictions across rephrasings of the prompt, and does not require access to ground truth labels. Instead, consistency measures how predictions vary across rephrasings for elements of the same class. We perform an empirical comparison of these metrics on text classification tasks, using them as guideline for understanding failure modes of the LLM. Our hope is that sensitivity and consistency will be helpful to guide prompt engineering and obtain LLMs that balance robustness with performance.

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message-passing architectures. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. This work introduces higher-rank irreducible Cartesian tensors as an alternative to spherical tensors, addressing the above limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical models.

Temporal Knowledge Graph (TKG) Forecasting aims at predicting links in Knowledge Graphs for future timesteps based on a history of Knowledge Graphs. To this day, standardized evaluation protocols and rigorous comparison across TKG models are available, but the importance of simple baselines is often neglected in the evaluation, which prevents researchers from discerning actual and fictitious progress. We propose to close this gap by designing an intuitive baseline for TKG Forecasting based on predicting recurring facts. Compared to most TKG models, it requires little hyperparameter tuning and no iterative training. Further, it can help to identify failure modes in existing approaches. The empirical findings are quite unexpected: compared to 11 methods on five datasets, our baseline ranks first or third in three of them, painting a radically different picture of the predictive quality of the state of the art., Comment: Accepted at IJCAI 2024

Long-range interactions are essential for the correct description of complex systems in many scientific fields. The price to pay for including them in the calculations, however, is a dramatic increase in the overall computational costs. Recently, deep graph networks have been employed as efficient, data-driven surrogate models for predicting properties of complex systems represented as graphs. These models rely on a local and iterative message passing strategy that should, in principle, capture long-range information without explicitly modeling the corresponding interactions. In practice, most deep graph networks cannot really model long-range dependencies due to the intrinsic limitations of (synchronous) message passing, namely oversmoothing, oversquashing, and underreaching. This work proposes a general framework that learns to mitigate these limitations: within a variational inference framework, we endow message passing architectures with the ability to freely adapt their depth and filter messages along the way. With theoretical and empirical arguments, we show that this simple strategy better captures long-range interactions, by surpassing the state of the art on five node and graph prediction datasets suited for this problem. Our approach consistently improves the performances of the baselines tested on these tasks. We complement the exposition with qualitative analyses and ablations to get a deeper understanding of the framework's inner workings.

Efficiently creating a concise but comprehensive data set for training machine-learned interatomic potentials (MLIPs) is an under-explored problem. Active learning (AL), which uses either biased or unbiased molecular dynamics (MD) simulations to generate candidate pools, aims to address this objective. Existing biased and unbiased MD simulations, however, are prone to miss either rare events or extrapolative regions -- areas of the configurational space where unreliable predictions are made. Simultaneously exploring both regions is necessary for developing uniformly accurate MLIPs. In this work, we demonstrate that MD simulations, when biased by the MLIP's energy uncertainty, effectively capture extrapolative regions and rare events without the need to know \textit{a priori} the system's transition temperatures and pressures. Exploiting automatic differentiation, we enhance bias-forces-driven MD simulations by introducing the concept of bias stress. We also employ calibrated ensemble-free uncertainties derived from sketched gradient features to yield MLIPs with similar or better accuracy than ensemble-based uncertainty methods at a lower computational cost. We use the proposed uncertainty-driven AL approach to develop MLIPs for two benchmark systems: alanine dipeptide and MIL-53(Al). Compared to MLIPs trained with conventional MD simulations, MLIPs trained with the proposed data-generation method more accurately represent the relevant configurational space for both atomic systems.

The performance of Hamiltonian Monte Carlo crucially depends on its parameters, in particular the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune these parameters based on a loss function which promotes the fast exploration of phase-space. For this, we make use of a fully-differentiable set-up and use backpropagation for optimization. An attention-like loss is defined which allows for the gradient driven learning of the distribution of integration steps. We also highlight the importance of jittering for a smooth loss-surface. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein common as a test-case for simulation methods. We find a good correspondence between our loss and the autocorrelation times, resulting in well-tuned parameters for Hamiltonian Monte Carlo.

In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with better node classification predictions of message-passing methods. More recently, however, researchers pointed out that such dichotomy is too simplistic as we can construct node classification tasks where graphs are completely heterophilic but the performances remain high. Most of these works have also proposed new quantitative metrics to understand when a graph structure is useful, which implicitly or explicitly assume the correlation between node features and target labels. Our work empirically investigates what happens when this strong assumption does not hold, by formalising two generative processes for node classification tasks that allow us to build and study ad-hoc problems. To quantitatively measure the influence of the node features on the target labels, we also use a metric we call Feature Informativeness. We construct six synthetic tasks and evaluate the performance of six models, including structure-agnostic ones. Our findings reveal that previously defined metrics are not adequate when we relax the above assumption. Our contribution to the workshop aims at presenting novel research findings that could help advance our understanding of the field.

We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian network mapping edge features into discrete states to be used by the original model. In doing so, we are also able to build richer graph representations even in the absence of edge features, which is confirmed by the performance improvements on standard graph classification benchmarks. Moreover, we successfully test our proposal in a graph regression scenario where edge features are of fundamental importance, and we show that the learned edge representation provides substantial performance improvements against the original model on three link prediction tasks. By keeping the computational complexity linear in the number of edges, the proposed model is amenable to large-scale graph processing., Comment: Releasing pre-print version to comply with TAILOR project requirements

We introduce Graph-Induced Sum-Product Networks (GSPNs), a new probabilistic framework for graph representation learning that can tractably answer probabilistic queries. Inspired by the computational trees induced by vertices in the context of message-passing neural networks, we build hierarchies of sum-product networks (SPNs) where the parameters of a parent SPN are learnable transformations of the a-posterior mixing probabilities of its children's sum units. Due to weight sharing and the tree-shaped computation graphs of GSPNs, we obtain the efficiency and efficacy of deep graph networks with the additional advantages of a probabilistic model. We show the model's competitiveness on scarce supervision scenarios, under missing data, and for graph classification in comparison to popular neural models. We complement the experiments with qualitative analyses on hyper-parameters and the model's ability to answer probabilistic queries., Comment: The 12th International Conference on Learning Representations (ICLR 2024)

The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an increasing interest in the adaptive processing of graphs, which led to the development of different neural network-based methodologies. In this thesis, we take a different route and develop a Bayesian Deep Learning framework for graph learning. The dissertation begins with a review of the principles over which most of the methods in the field are built, followed by a study on graph classification reproducibility issues. We then proceed to bridge the basic ideas of deep learning for graphs with the Bayesian world, by building our deep architectures in an incremental fashion. This framework allows us to consider graphs with discrete and continuous edge features, producing unsupervised embeddings rich enough to reach the state of the art on several classification tasks. Our approach is also amenable to a Bayesian nonparametric extension that automatizes the choice of almost all model's hyper-parameters. Two real-world applications demonstrate the efficacy of deep learning for graphs. The first concerns the prediction of information-theoretic quantities for molecular simulations with supervised neural models. After that, we exploit our Bayesian models to solve a malware-classification task while being robust to intra-procedural code obfuscation techniques. We conclude the dissertation with an attempt to blend the best of the neural and Bayesian worlds together. The resulting hybrid model is able to predict multimodal distributions conditioned on input graphs, with the consequent ability to model stochasticity and uncertainty better than most works. Overall, we aim to provide a Bayesian perspective into the articulated research field of deep learning for graphs., Comment: PhD Thesis

In this work, we study the phenomenon of catastrophic forgetting in the graph representation learning scenario. The primary objective of the analysis is to understand whether classical continual learning techniques for flat and sequential data have a tangible impact on performances when applied to graph data. To do so, we experiment with a structure-agnostic model and a deep graph network in a robust and controlled environment on three different datasets. The benchmark is complemented by an investigation on the effect of structure-preserving regularization techniques on catastrophic forgetting. We find that replay is the most effective strategy in so far, which also benefits the most from the use of regularization. Our findings suggest interesting future research at the intersection of the continual and graph representation learning fields. Finally, we provide researchers with a flexible software framework to reproduce our results and carry out further experiments., Comment: Accepted at the 2021 Web Conference Workshop on Graph Learning Benchmarks (GLB 2021). Code available at https://github.com/diningphil/continual_learning_for_graphs

We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph representation learning, we address a broader class of challenging conditional density estimation problems that rely on structured data. In this respect, we evaluate our method on a new benchmark application that leverages random graphs for stochastic epidemic simulations. We show a significant improvement in the likelihood of epidemic outcomes when taking into account both multimodality and structure. The empirical analysis is complemented by two real-world regression tasks showing the effectiveness of our approach in modeling the output prediction uncertainty. Graph Mixture Density Networks open appealing research opportunities in the study of structure-dependent phenomena that exhibit non-trivial conditional output distributions.

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless developments of computer architectures and algorithms. This explosion in the number and extent (in size and time) of MD trajectories induces the need of automated and transferable methods to rationalise the raw data and make quantitative sense out of them. Recently, an algorithmic approach was developed by some of us to identify the subset of a protein's atoms, or mapping, that enables the most informative description of it. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to the simplification. Albeit relatively straightforward, this calculation can be time consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. The method relies on deep graph networks, which provide extreme flexibility in the input format. We show that deep graph networks are accurate and remarkably efficient, with a speedup factor as large as $10^5$ with respect to the algorithmic computation of the mapping entropy. Applications of this method, which entails a great potential in the study of biomolecules when used to reconstruct its mapping entropy landscape, reach much farther than this, being the scheme easily transferable to the computation of arbitrary functions of a molecule's structure.

We propose a model to tackle classification tasks in the presence of very little training data. To this aim, we approximate the notion of exact match with a theoretically sound mechanism that computes a probability of matching in the input space. Importantly, the model learns to focus on elements of the input that are relevant for the task at hand; by leveraging highlighted portions of the training data, an error boosting technique guides the learning process. In practice, it increases the error associated with relevant parts of the input by a given factor. Remarkable results on text classification tasks confirm the benefits of the proposed approach in both balanced and unbalanced cases, thus being of practical use when labeling new examples is expensive. In addition, by inspecting its weights, it is often possible to gather insights on what the model has learned.

We propose a new Graph Neural Network that combines recent advancements in the field. We give theoretical contributions by proving that the model is strictly more general than the Graph Isomorphism Network and the Gated Graph Neural Network, as it can approximate the same functions and deal with arbitrary edge values. Then, we show how a single node information can flow through the graph unchanged.

The adaptive processing of graph data is a long-standing research topic which has been lately consolidated as a theme of major interest in the deep learning community. The snap increase in the amount and breadth of related research has come at the price of little systematization of knowledge and attention to earlier literature. This work is designed as a tutorial introduction to the field of deep learning for graphs. It favours a consistent and progressive introduction of the main concepts and architectural aspects over an exposition of the most recent literature, for which the reader is referred to available surveys. The paper takes a top-down view to the problem, introducing a generalized formulation of graph representation learning based on a local and iterative approach to structured information processing. It introduces the basic building blocks that can be combined to design novel and effective neural models for graphs. The methodological exposition is complemented by a discussion of interesting research challenges and applications in the field.

Experimental reproducibility and replicability are critical topics in machine learning. Authors have often raised concerns about their lack in scientific publications to improve the quality of the field. Recently, the graph representation learning field has attracted the attention of a wide research community, which resulted in a large stream of works. As such, several Graph Neural Network models have been developed to effectively tackle graph classification. However, experimental procedures often lack rigorousness and are hardly reproducible. Motivated by this, we provide an overview of common practices that should be avoided to fairly compare with the state of the art. To counter this troubling trend, we ran more than 47000 experiments in a controlled and uniform framework to re-evaluate five popular models across nine common benchmarks. Moreover, by comparing GNNs with structure-agnostic baselines we provide convincing evidence that, on some datasets, structural information has not been exploited yet. We believe that this work can contribute to the development of the graph learning field, by providing a much needed grounding for rigorous evaluations of graph classification models., Comment: Extended version of the paper published at the International Conference on Learning Representations (ICLR), 2020. Additional results are shown in the appendix

We introduce the Contextual Graph Markov Model, an approach combining ideas from generative models and neural networks for the processing of graph data. It founds on a constructive methodology to build a deep architecture comprising layers of probabilistic models that learn to encode the structured information in an incremental fashion. Context is diffused in an efficient and scalable way across the graph vertexes and edges. The resulting graph encoding is used in combination with discriminative models to address structure classification benchmarks.