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** Published:**

A crucial role for the success of the Artificial Neural Networks (ANN) processing scheme has been played by the feed-forward propagation of signals. The input patterns undergo a series of stacked parametrized transformations, which foster deep feature extraction and an increasing representational power. Each artificial neural network layer aggregates information from its incoming connections, projects it to another space, and immediately propagates it to the next layer.

Since its introduction in the ’80s, BackPropagation (BP) is considered to be the **de facto** algorithm for training neural nets. The weights associated to the connections between the network layers are updated due to the backward pass, that is a straightforward derivation of the chain rule for the computation of the derivatives in a composition of functions. This computation requires to store all the intermediate values of the process. Moreover, it implies the use of non-local information, since the activity of one neuron has the ability to affect all the subsequent units up to the last output layer.

However, learning in the human brain can be considered a continuous, life-long and gradual process in which neuron activations fire, leveraging local information, both in space, e.g neighboring neurons, and time, e.g. previous states.

Short description of portfolio item number 1

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Published in *8th IAPR TC3 Workshop, ANNPR 2018*, 2018

8th IAPR TC3 Workshop, ANNPR 2018 - Inductive–Transductive Learning GNNs

Recommended citation: Rossi, A., Tiezzi, M., Dimitri, G. M., Bianchini, M., Maggini, M., & Scarselli, F. (2018, September). "Inductive–transductive learning with graph neural networks. " IAPR Workshop on Artificial Neural Networks in Pattern Recognition (pp. 201-212). Springer, Cham. *8th IAPR TC3 Workshop, ANNPR 2018* __https://link.springer.com/chapter/10.1007%2F978-3-319-99978-4_16__

Published in *27th International Conference on Artificial Neural Networks, Rhodes, Greece*, 2018

27th International Conference on Artificial Neural Networks, ICANN18 - Video Surveillance of Highway Traffic Events by Deep Learning Architectures

Recommended citation: Tiezzi, M., Melacci, S., Maggini, M., & Frosini, A. (2018, October). "Video Surveillance of Highway Traffic Events by Deep Learning Architectures. " International Conference on Artificial Neural Networks (pp. 584-593). Springer, Cham. *27th International Conference on Artificial Neural Networks, ICANN18* __https://link.springer.com/chapter/10.1007%2F978-3-030-01424-7_57__

Published in *AAAI20 - DLGMA Workshop paper*, 2020

AAAI20 - DLGMA Workshop paper - LPGNN

Recommended citation: Matteo Tiezzi, Giuseppe Marra, Stefano Melacci, Marco Maggini and Marco Gori (2020). "Lagrangian Propagation Graph Neural Networks " *AAAI20 - DLGMA Workshop* __https://deep-learning-graphs.bitbucket.io/dlg-aaai20/__

Published in *IJCNN2020 - Accepted for publishing*, 2020

IJCNN2020 - Local Propagation

Recommended citation: Giuseppe Marra, Matteo Tiezzi, Stefano Melacci, Alessandro Betti, Marco Maggini and Marco Gori (2020). "Local Propagation in Constraint-based Neural Network " *IJCNN2020* __https://ieeexplore.ieee.org/document/9207043__

Published in *ECAI2020*, 2020

ECAI2020 - LPGNN

Recommended citation: Matteo Tiezzi, Giuseppe Marra, Stefano Melacci, Marco Maggini and Marco Gori (2020). "A Lagrangian Approach to Information Propagation in Graph Neural Networks; *ECAI2020 -* __http://ebooks.iospress.nl/publication/55057__

Published in *ICML20 - GRL+ Workshop paper*, 2020

ICML20 - GRL+ Workshop paper - DeepLPGNN

Recommended citation: Matteo Tiezzi, Giuseppe Marra, Stefano Melacci and Marco Maggini (2020). "Deep Lagrangian Propagation in Graph Neural Networks " *ICML20 - GRL+ Workshop* __https://grlplus.github.io/papers/51.pdf__

Published in *NeurIPS2020*, 2020

NeurIPS2020 - Focus

Recommended citation: Matteo Tiezzi, Stefano Melacci, Alessandro Betti, Marco Maggini, Marco Gori (2020). "Focus of Attention Improves Information Transfer in Visual Features " *NeurIPS2020* __https://papers.nips.cc/paper/2020/hash/fc2dc7d20994a777cfd5e6de734fe254-Abstract.html__

Published in *TPAMI*, 2021

TPAMI - Deep LP-GNNs

Recommended citation: Matteo Tiezzi, Giuseppe Marra, Stefano Melacci, Marco Maggini (2021). "Deep Constraint-based Propagation in Graph Neural Networks " *TPAMI* __https://doi.org/10.1109/TPAMI.2021.3073504__

, *Italy, University of Siena, SAILab*, 2018

The Graph Neural Network (GNN) is a connectionist model particularly suited for problems whose domain can be represented by a set of patterns and relationships between them.

, *Italy, University of Siena, SAILab*, 2020

SAILenv is a Virtual Environment powered by Unity3D. It includes 3 pre-built scenes with full pixel-wise annotations. SAILenv is capable of generating frames at real-time speed, complete with pixel-wise annotations, optical flow and depth.

, *Italy, University of Siena, SAILab*, 2020

The Graph Neural Network (GNN) is a connectionist model particularly suited for problems whose domain can be represented by a set of patterns and relationships between them.

, *Italy, University of Siena, SAILab*, 2020

Lagrangian Propagation Graph Neural Network - LP-GNN

** Published:**

Convolutional neural networks that are used to recognize shapes typically use one or more layers of learned feature detectors that produce scalar outputs, interleaved with subsampling.

** Published:**

In image classification an image with a single object is the focus and the task is to say what it contains. But when we look at the world around us, we carry out far more complex tasks. There are multiple overlapping objects, different backgrounds and we not only classify these different objects but also identify their boundaries, differences, and relations among them. This task fall under the name of object detection and instance segmentation.

** Published:**

Adversarial examples are defined as “inputs to machine learning models that an attacker has intentionally designed to cause the model to make a mistake”. Indeed, in the computer vision scenario it has been shown that well-crafted perturbation to input images can induce classification errors, such as confusing a cat with a computer. In general, adversarial attacks are designed to degrade the performances of models or to prompt the prediction of specific output classes. In this recent work, the authors introduce a framework in which the goal of adversarial attacks is to reprogram the target model to perform a completely new task. This is accomplished by optimizing for a single adversarial perturbation that can be added to all test-time inputs. In such a way, the target model performs a task chosen by the adversary when processing these inputs—even if it was not trained on this task.

** Published:**

The ability to decompose visual scenes in terms of abstract building blocks is crucial for general intelligence. These basic building blocks are capable to represent meaningful properties, interactions and other relations across scenes.

** Published:**

GNNs exploit a set of state variables, each assigned to a graph node, and a diffusion mechanism of the states among neighbor nodes, to implement an iterative procedure to compute the fixed point of the (learnable) state transition function. We propose a novel approach to the state computation and the learning algorithm for GNNs, based on a constraint optimization task solved in the Lagrangian framework. The state convergence procedure is implicitly expressed by the constraint satisfaction mechanism and does not require a separate iterative phase for each epoch of the learning procedure. In fact, the computational structure is based on the search for saddle points of the Lagrangian in the adjoint space composed of weights, neural outputs (node states), and Lagrange multipliers.

** Published:**

One characteristic that sets humans apart from modern learning-based computer vision algorithms is the ability to acquire knowledge about the world and use that knowledge to reason about the visual world. Humans can learn about the characteristics of objects and the relationships that occur between them to learn a large variety of visual concepts, often with few examples.

** Published:**

My spotlight presentation for the Lagrangian Propagation Graph Neural Network paper at the AAAI20-DLGMA Workshop.

** Published:**

On Mutual Information Maximization for Representation Learning - An excursus into Deep InfoMax, its variants and their lacks

** Published:**

Deep Lagrangian Propagation in Graph Neural Networks

** Published:**

Several real-world applications are characterized by data that exhibit a complex structure that can be represented using graphs. The popularity of deep learning techniques renewed the interest in neural architectures able to process these patterns, inspired by the Graph Neural Network(GNN) model, proposed by SAILab. In this talk, I will present the original GNN model, recent evolutions (GCN, GATs, …) and our implementation framework in Tensorflow and PyTorch. The original GNNs encode the state of the nodes of the graph by means of an iterative diffusion procedure that, during the learning stage, must be computed at every epoch, until the fixed point of a learnable state transition function is reached, propagating the information among the neighbouring nodes. We propose a novel approach to learning in GNNs, based on constrained optimization in the Lagrangian framework, named Lagrangian Propagation Graph Neural Networks. Learning both the transition function and the node states is the outcome of a joint process, in which the state convergence procedure is implicitly expressed by a constraint satisfaction mechanism, avoiding iterative epoch-wise procedures and the network unfolding. Our computational structure searches for saddle points of the Lagrangian in the adjoint space composed of weights, nodes state variables and Lagrange multipliers. This process is further enhanced by multiple layers of constraints that accelerate the diffusion process. An experimental analysis shows that the proposed approach compares favourably with popular models on several benchmarks.