Optimizing chemical properties is a challenging task due to the vastness and complexity of chemical space.Here, we present a generative energy-based architecture for implicit chemical property optimization, designed to efficiently generate molecules that satisfy target properties without explicit conditional generation.We use Graph Energy Based Models and a training approach that does not require property labels.We validated our approach on well-established chemical benchmarks, showing superior results to state-of-the-art methods and demonstrating robustness and efficiency towards de novo drug design.

Generative models of graphs based on discrete Denoising Diffusion Probabilistic Models (DDPMs) offer a principled approach to molecular generation by systematically removing structural noise through iterative atom and bond adjustments. However, existing formulations are fundamentally limited by their inability to adapt the graph size (that is, the number of atoms) during the diffusion process, severely restricting their effectiveness in conditional generation scenarios such as property-driven molecular design, where the targeted property often correlates with the molecular size. In this paper, we reformulate the noising and denoising processes to support monotonic insertion and deletion of nodes. The resulting model, which we call GrIDDD, dynamically grows or shrinks the chemical graph during generation. GrIDDD matches or exceeds the performance of existing graph diffusion models on molecular property targeting despite being trained on a more difficult problem. Furthermore, when applied to molecular optimization, GrIDDD exhibits competitive performance compared to specialized optimization models. This work paves the way for size-adaptive molecular generation with graph diffusion.

BACKGROUND: Protein-protein interaction networks (PPINs) provide a comprehensive view of the intricate biochemical processes that take place in living organisms. In recent years, the size and information content of PPINs have grown thanks to techniques that allow for the functional association of proteins. However, PPINs are static objects that cannot fully describe the dynamics of the protein interactions; these dynamics are usually studied from external sources and can only be added to the PPIN as annotations. In contrast, the time-dependent characteristics of cellular processes are described in Biochemical Pathways (BP), which frame complex networks of chemical reactions as dynamical systems. Their analysis with numerical simulations allows for the study of different dynamical properties. Unfortunately, available BPs cover only a small portion of the interactome, and simulations are often hampered by the unavailability of kinetic parameters or by their computational cost. In this study, we explore the possibility of enriching PPINs with dynamical properties computed from BPs. We focus on the global dynamical property of sensitivity, which measures how a change in the concentration of an input molecular species influences the concentration of an output molecular species at the steady state of the dynamical system. RESULTS: We started with the analysis of BPs via ODE simulations, which enabled us to compute the sensitivity associated with multiple pairs of chemical species. The sensitivity information was then injected into a PPIN, using public ontologies (BioGRID, UniPROT) to map entities at the BP level with nodes at the PPIN level. The resulting annotated PPIN, termed the DyPPIN (Dynamics of PPIN) dataset, was used to train a DGN to predict the sensitivity relationships among PPIN proteins. Our experimental results show that this model can predict these relationships effectively under different use case scenarios. Furthermore, we show that the PPIN structure (i.e., the way the PPIN is "wired") is essential to infer the sensitivity, and that further annotating the PPIN nodes with protein sequence embeddings improves the predictive accuracy. CONCLUSION: To the best of our knowledge, the model proposed in this study is the first that allows performing sensitivity analysis directly on PPINs. Our findings suggest that, despite the high level of abstraction, the structure of the PPIN holds enough information to infer dynamic properties without needing an exact model of the underlying processes. In addition, the designed pipeline is flexible and can be easily integrated into drug design, repurposing, and personalized medicine processes.

Understanding the inductive bias of Deep Graph Networks (DGNs) is crucial because it reveals how these models generalize from training data to unseen data. Discovering these learning assumptions, and their alignment to the task’s characteristics, allows informed architectural design choices and facilitates interpretation. With this goal, we analyze the different inductive biases of DGNs by relating the node-level explanations produced by explainable AI (XAI) methods to known network science measures of lower-order (local) and higher-order (increasingly global) connectivity. We then apply graph signal processing to refine this analysis at the granularity of the graph frequency spectrum spanned by the explanation signals. Our main finding is that different DGNs focus on different regions of the graph frequency spectrum, and in particular, high-frequency DGNs generalize by focusing on lower-order graph connectivity, while low-frequency DGNs generalize by recognizing higher-order graph structures. This characterization is first derived on synthetic benchmarks by showing that explanations align with network science measures sitting at the two extremes of the spectrum (Katz centrality in the high frequencies, and Fiedler eigenvector scores in the low frequencies). Moving to real-world chemical benchmarks, this result is generalized by showing that inductive biases do indeed lie on a continuum that corresponds to sub-regions of the frequency spectrum.

Network quantification (NQ) is the problem of estimating the proportions of nodes belonging to each class in subsets of unlabelled graph nodes. When prior probability shift is at play, this task cannot be effectively addressed by first classifying the nodes and then counting the class predictions. In addition, unlike non-relational quantification, NQ demands enhanced flexibility in order to capture a broad range of connectivity patterns, resilience to the challenge of heterophily, and scalability to large networks. In order to meet these stringent requirements, we introduce XNQ, a novel method that synergizes the flexibility and efficiency of the unsupervised node embeddings computed by randomized recursive Graph Neural Networks, with an Expectation-Maximization algorithm that provides a robust quantification-aware adjustment to the output probabilities of a calibrated node classifier. In an extensive evaluation, in which we also validate the design choices underpinning XNQ through comprehensive ablation experiments, we find that XNQ consistently and significantly improves on the best network quantification methods to date, thereby setting the new state of the art for this challenging task. XNQ also provides a training speed-up of up to 10x–100x over other methods based on graph learning.

Generalization in machine learning involves introducing inductive biases that restrict the solution space of the learning problem, allowing for the inductive leap.In this paper, we show the existence of different inductive biases between convolutional and recursive Deep Graph Networks (DGN) by applying Explainable AI (XAI) methods as model inspection techniques.We show that different architectures can perfectly solve the given tasks by learning different labelling policies.Our results promote the usage of different architectures to address a task and raise warnings on the assessment of XAI techniques as their benchmarks may contain more ground truths than those provided.* Research partly funded by PNRR -M4C2 -Investimento 1.3, Partenariato Esteso PE00000013 -"FAIR -Future Artificial Intelligence Research" -Spoke 1 "Human-centered AI", funded by the European Commission under the NextGeneration EU programme.

In a broad range of real-world machine learning applications, representing examples as graphs is crucial to avoid a loss of information.For this reason, in the last few years, the definition of machine learning methods, particularly neural networks, for graph-structured inputs has been gaining increasing attention.In particular, Deep Graph Networks (DGNs) are nowadays the most commonly adopted models to learn a representation that can be used to address different tasks related to nodes, edges, or even entire graphs.This tutorial paper reviews fundamental concepts and open challenges of graph representation learning and summarizes the contributions that have been accepted for publication to the ESANN 2023 special session on the topic.

MOTIVATION: Dynamical properties of biochemical pathways (BPs) help in understanding the functioning of living cells. Their in silico assessment requires simulating a dynamical system with a large number of parameters such as kinetic constants and species concentrations. Such simulations are based on numerical methods that can be time-expensive for large BPs. Moreover, parameters are often unknown and need to be estimated. RESULTS: We developed a framework for the prediction of dynamical properties of BPs directly from the structure of their graph representation. We represent BPs as Petri nets, which can be automatically generated, for instance, from standard SBML representations. The core of the framework is a neural network for graphs that extracts relevant information directly from the Petri net structure and exploits them to learn the association with the desired dynamical property. We show experimentally that the proposed approach reliably predicts a range of diverse dynamical properties (robustness, monotonicity, and sensitivity) while being faster than numerical methods at prediction time. In synergy with the neural network models, we propose a methodology based on Petri nets arc knock-out that allows the role of each molecule in the occurrence of a certain dynamical property to be better elucidated. The methodology also provides insights useful for interpreting the predictions made by the model. The results support the conjecture often considered in the context of systems biology that the BP structure plays a primary role in the assessment of its dynamical properties. AVAILABILITY AND IMPLEMENTATION: https://github.com/marcopodda/petri-bio (code), https://zenodo.org/record/7610382 (data).

The problem of labeled graph generation is gaining attention in the Deep Learning community. The task is challenging due to the sparse and discrete nature of graph spaces. Several approaches have been proposed in the literature, most of which require to transform the graphs into sequences that encode their structure and labels and to learn the distribution of such sequences through an auto-regressive generative model. Among this family of approaches, we focus on the Graphgen model. The preprocessing phase of Graphgen transforms graphs into unique edge sequences called Depth-First Search (DFS) codes, such that two isomorphic graphs are assigned the same DFS code. Each element of a DFS code is associated with a graph edge: specifically, it is a quintuple comprising one node identifier for each of the two endpoints, their node labels, and the edge label. Graphgen learns to generate such sequences auto-regressively and models the probability of each component of the quintuple independently. While effective, the independence assumption made by the model is too loose to capture the complex label dependencies of real-world graphs precisely. By introducing a novel graph preprocessing approach, we are able to process the labeling information of both nodes and edges jointly. The corresponding model, which we term Graphgen-redux, improves upon the generative performances of Graphgen in a wide range of datasets of chemical and social graphs. In addition, it uses approximately 78% fewer parameters than the vanilla variant and requires 50% fewer epochs of training on average.

Molecule generation is a challenging open problem in cheminformatics. Currently, deep generative approaches addressing the challenge belong to two broad categories, differing in how molecules are represented. One approach encodes molecular graphs as strings of text, and learns their corresponding character-based language model. Another, more expressive, approach operates directly on the molecular graph. In this work, we address two limitations of the former: generation of invalid and duplicate molecules. To improve validity rates, we develop a language model for small molecular substructures called fragments, loosely inspired by the well-known paradigm of Fragment-Based Drug Design. In other words, we generate molecules fragment by fragment, instead of atom by atom. To improve uniqueness rates, we present a frequency-based masking strategy that helps generate molecules with infrequent fragments. We show experimentally that our model largely outperforms other language model-based competitors, reaching state-of-the-art performances typical of graph-based approaches. Moreover, generated molecules display molecular properties similar to those in the training sample, even in absence of explicit task-specific supervision.