In this paper, we present GGSD, a novel graph generative model based on 1) the spectral decomposition of the graph Laplacian matrix and 2) a diffusion process. Specifically, we propose to use a denoising model to sample eigenvectors and eigenvalues from which we can reconstruct the graph Laplacian and adjacency matrix. Using the Laplacian spectrum allows us to naturally capture the structural characteristics of the graph and work directly in the node space while avoiding the quadratic complexity bottleneck that limits the applicability of other diffusion-based methods. This, in turn, is accomplished by truncating the spectrum, which, as we show in our experiments, results in a faster yet accurate generative process, and by designing a novel transformer-based architecture linear in the number of nodes. Our permutation invariant model can also handle node features by concatenating them to the eigenvectors of each node. An extensive set of experiments on both synthetic and real-world graphs demonstrates the strengths of our model against state-of-the-art alternatives.

The convolution operator at the core of many modern neural architectures can effectively be seen as performing a dot product between an input matrix and a filter. While this is readily applicable to data such as images, which can be represented as regular grids in the Euclidean space, extending the convolution operator to work on graphs proves more challenging, due to their irregular structure. In this article, we propose to use graph kernels, i.e., kernel functions that compute an inner product on graphs, to extend the standard convolution operator to the graph domain. This allows us to define an entirely structural model that does not require computing the embedding of the input graph. Our architecture allows to plug-in any type of graph kernels and has the added benefit of providing some interpretability in terms of the structural masks that are learned during the training process, similar to what happens for convolutional masks in traditional convolutional neural networks (CNNs). We perform an extensive ablation study to investigate the model hyperparameters' impact and show that our model achieves competitive performance on standard graph classification and regression datasets.

Understanding the behavior of deep neural networks for Information Retrieval (IR) is crucial to improve trust in these effective models. Current popular approaches to diagnose the predictions made by deep neural networks are mainly based on: i) the adherence of the retrieval model to some axiomatic property of the IR system, ii) the generation of free-text explanations, or iii) feature importance attributions. In this work, we propose a novel approach that analyzes the changes of document and query embeddings in the latent space and that might explain the inner workings of IR large pre-trained language models. In particular, we focus on predicting query/document relevance, and we characterize the predictions by analyzing the topological arrangement of the embeddings in their latent space and their evolution while passing through the layers of the network. We show that there exists a link between the embedding adjustment and the predicted score, based on how tokens cluster in the embedding space. This novel approach, grounded in the query and document tokens interplay over the latent space, provides a new perspective on neural ranker explanation and a promising strategy for improving the efficiency of the models and Query Performance Prediction (QPP).

Abstract The Average Mixing Kernel Signature is a novel spectral signature for points on non-rigid three-dimensional shapes. It is based on a quantum exploration process of the shape surface, where the average transition probabilities between the points of the shape are summarised in the finite-time average mixing kernel. A band-filtered spectral analysis of this kernel then yields the AMKS. Crucially, we show that opting for a finite time-evolution allows the signature to account for a mixing of the Laplacian eigenspaces, similar to what is observed in the presence of noise, explaining the increased noise robustness of this signature when compared to alternative signatures. We perform an extensive experimental analysis of the AMKS under a wide range of problem scenarios, evaluating the performance of our descriptor under different sources of noise (vertex jitter and topological), shape representations (mesh and point clouds), as well as when only a partial view of the shape is available. Our experiments show that the AMKS consistently outperforms two of the most widely used spectral signatures, the Heat Kernel Signature and the Wave Kernel Signature, and suggest that the AMKS should be the signature of choice for various compute vision problems, including as input of deep convolutional architectures for shape analysis.

In this paper, we present a novel thermodynamic framework for graphs that can be used to analyze time evolving networks, relating the thermodynamics variables to macroscopic changes in network topology, and linking major structural transition to phase changes in the thermodynamic picture. We start from a recent quantum-mechanical characterization of the structure of a network relating the graph Laplacian to a density operator and resulting in a characterization of the network's entropy. Then we adopt a Schrödinger picture of the dynamics of the network, resulting in an estimation of a hidden time-varying Hamiltonian from the data, from which we derive a measure of Energy exchange. From these variables, using the thermodynamic identity, we obtain temperature under the assumption of constant volume of the system. Evaluation of real-world data shows that the thermodynamic variables thus extracted are effective in detecting critical events occurring during network evolution.

Non-rigid 3D shape retrieval is an active and important research topic in content based object retrieval. This problem is often cast in terms of the shapes intrinsic geometry due to its invariance to a wide range of non-rigid deformations. In this paper, we devise a novel generative model for shape retrieval based on the spectral representation of the Laplacian of a mesh. Contrary to common use, our approach avoids the ubiquitous correspondence problem by transforming the eigenvectors of the Laplacian to a density in the spectral-embedding space which is estimated nonparametrically. We show that this model can efficiently be learned from a set of 3D meshes. The experimental results on the SHREC'14 benchmark show the effectiveness of the approach compared to the state-of-the-art.