DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly

Reassembly tasks play a fundamental role in many fields and multiple approaches exist to solve specific reassembly problems. In this context, we posit that a general unified model can effectively address them all, irrespective of the input data type (images, 3D, etc.). We introduce DiffAssemble, a Graph Neural Network (GNN)-based architecture that learns to solve reassembly tasks using a diffusion model formulation. Our method treats the elements of a set, whether pieces of 2D patch or 3D object fragments, as nodes of a spatial graph. Training is performed by introducing noise into the position and rotation of the elements and iteratively denoising them to reconstruct the coherent initial pose. DiffAssemble achieves state-of-the-art (SOTA) results in most 2D and 3D reassembly tasks and is the first learning-based approach that solves 2D puzzles for both rotation and translation. Furthermore, we highlight its remarkable reduction in run-time, performing 11 times faster than the quickest optimization-based method for puzzle solving. Code available at https://github.com/IIT-PAVIS/DiffAssemble

Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs

We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed to handle digraphs with weights of arbitrary sign). In addition to its generality, our Quaternionic Laplacian is the only Laplacian to completely preserve the topology of a digraph, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weights without reducing them to a single (directed or undirected) edge as done with other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.

SigMaNet: One Laplacian to Rule Them All

This paper introduces SigMaNet, a generalized Graph Convolutional Network (GCN) capable of handling both undirected and directed graphs with weights not restricted in sign and magnitude. The cornerstone of SigMaNet is the introduction of a generalized Laplacian matrix: the Sign-Magnetic Laplacian ($L^\sigma$). The adoption of such a matrix allows us to bridge a gap in the current literature by extending the theory of spectral GCNs to directed graphs with both positive and negative weights. $L^{\sigma}$ exhibits several desirable properties not enjoyed by the traditional Laplacian matrices on which several state-of-the-art architectures are based. In particular, $L^\sigma$ is completely parameter-free, which is not the case of Laplacian operators such as the Magnetic Laplacian $L^{(q)}$, where the calibration of the parameter q is an essential yet problematic component of the operator. $L^\sigma$ simplifies the approach, while also allowing for a natural interpretation of the signs of the edges in terms of their directions. The versatility of the proposed approach is amply demonstrated experimentally; the proposed network SigMaNet turns out to be competitive in all the tasks we considered, regardless of the graph structure.

Listening to the city, attentively: A Spatio-Temporal Attention Boosted Autoencoder for the Short-Term Flow Prediction Problem

In recent years, the importance of studying traffic flows and making predictions on alternative mobility (sharing services) has become increasingly important, as accurate and timely information on the travel flow is important for the successful implementation of systems that increase the quality of sharing services. This need has been accentuated by the current health crisis that requires alternative transport mobility such as electric bike and electric scooter sharing. Considering the new approaches in the world of deep learning and the difficulty due to the strong spatial and temporal dependence of this problem, we propose a framework, called STREED-Net, with multi-attention (Spatial and Temporal) able to better mining the high-level spatial and temporal features. We conduct experiments on three real datasets to predict the Inflow and Outflow of the different regions into which the city has been divided. The results indicate that the proposed STREED-Net model improves the state-of-the-art for this problem.