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Graph Neural Networks have proven to be very valuable models for the solution of a wide variety of problems on molecular graphs, as well as in many other research fields involving graph-structured data. Molecules are heterogeneous graphs composed of atoms of different species. Composite graph neural networks process heterogeneous graphs with multiple-state-updating networks, each one dedicated to a particular node type. This approach allows for the extraction of information from s graph more efficiently than standard graph neural networks that distinguish node types through a one-hot encoded type of vector. We carried out extensive experimentation on eight molecular graph datasets and on a large number of both classification and regression tasks. The results we obtained clearly show that composite graph neural networks are far more efficient in this setting than standard graph neural networks.

The popularity of deep learning techniques renewed the interest in neural architectures able to process complex structures that can be represented using graphs, inspired by Graph Neural Networks (GNNs). We focus our attention on the originally proposed GNN model of Scarselli et al. 2009, which encodes 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. 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.

This paper analyzes the practical issues and reports some results on a theory in which learning is modeled as a continuous temporal process driven by laws describing the interactions of intelligent agents with their own environment. The classic regularization framework is paired with the idea of temporal manifolds by introducing the principle of least cognitive action, which is inspired by the related principle of mechanics. The introduction of the counterparts of the kinetic and potential energy leads to an interpretation of learning as a dissipative process. As an example, we apply the theory to supervised learning in neural networks and show that the corresponding Euler-Lagrange differential equations can be connected to the classic gradient descent algorithm on the supervised pairs. We give preliminary experiments to confirm the soundness of the theory., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

In this paper we present Similarity Neural Networks (SNNs), a neural network model able to learn a similarity measure for pairs of patterns, exploiting a binary supervision on their similarity/dissimilarity relationships. Pairwise relationships, also referred to as pairwise constraints, generally contain less information than class labels, but, in some contexts, are easier to obtain from human supervisors. The SNN architecture guarantees the basic properties of a similarity measure (symmetry and non negativity) and it can deal with non-transitivity of the similarity criterion. Unlike the majority of the metric learning algorithms proposed so far, it can model non-linear relationships among data still providing a natural out-of-sample extension to novel pairs of patterns. The theoretical properties of SNNs and their application to Semi-Supervised Clustering are investigated. In particular, we introduce a novel technique that allows the clustering algorithm to compute the optimal representatives of a data partition by means of backpropagation on the input layer, biased by a L(2) norm regularizer. An extensive set of experimental results are provided to compare SNNs with the most popular similarity learning algorithms. Both on benchmarks and real world data, SNNs and SNN-based clustering show improved performances, assessing the advantage of the proposed neural network approach to similarity measure learning., (Copyright © 2011 Elsevier Ltd. All rights reserved.)

Relevance ranking consists in sorting a set of objects with respect to a given criterion. However, in personalized retrieval systems, the relevance criteria may usually vary among different users and may not be predefined. In this case, ranking algorithms that adapt their behavior from users' feedbacks must be devised. Two main approaches are proposed in the literature for learning to rank: the use of a scoring function, learned by examples, that evaluates a feature-based representation of each object yielding an absolute relevance score, a pairwise approach, where a preference function is learned to determine the object that has to be ranked first in a given pair. In this paper, we present a preference learning method for learning to rank. A neural network, the comparative neural network (CmpNN), is trained from examples to approximate the comparison function for a pair of objects. The CmpNN adopts a particular architecture designed to implement the symmetries naturally present in a preference function. The learned preference function can be embedded as the comparator into a classical sorting algorithm to provide a global ranking of a set of objects. To improve the ranking performances, an active-learning procedure is devised, that aims at selecting the most informative patterns in the training set. The proposed algorithm is evaluated on the LETOR dataset showing promising performances in comparison with other state-of-the-art algorithms.

In this paper, we introduce a new recursive neural network model able to process directed acyclic graphs with labelled edges. The model uses a state transition function which considers the edge labels and is independent both from the number and the order of the children of each node. The computational capabilities of the new recursive architecture are assessed. Moreover, in order to test the proposed architecture on a practical challenging application, the problem of object detection in images is also addressed. In fact, the localization of target objects is a preliminary step in any recognition system. The proposed technique is general and can be applied in different detection systems, since it does not exploit any a priori knowledge on the particular problem. Some experiments on face detection, carried out on scenes acquired by an indoor camera, are reported, showing very promising results.

Background: The Bispectral Index (BIS) is a proprietary index of anaesthesia depth, which is correlated with the level of consciousness and probability of intraoperative recall. The present study investigates the use of a neural network technique to obtain a non-proprietary index of the depth of anaesthesia from the processed EEG data., Methods: Two hundred patients, who underwent general abdominal surgery, were recruited for our trial. For anaesthesia we used a total i.v. technique, tracheal intubation, and artificial ventilation. Fourteen EEG variables, including the BIS, were extracted from the EEG, monitored with an EEG computerized monitor, and then stored on a computer. Data from 150 patients were used to train the neural network. All the variables, excluding the BIS, were used as input data in the neural network. The output targets of the network were provided by anaesthesia scores ranging from 10 to 100 assigned by the anaesthesiologist according to the observer's assessment of alertness and sedation (OAA/S) and other clinical means of assessing depth of anaesthesia. Data from the other 50 patients were used to test the model and for statistical analysis., Results: The artificial neural network was successfully trained to predict an anaesthesia depth index, the NED (neural network evaluated depth), ranging from 0 to 100. The correlation coefficient between the NED and the BIS over the test set was 0.94 (P<0.0001)., Conclusion: We have developed a neural network model, which evaluates 13 processed EEG parameters to produce an index of anaesthesia depth, which correlates very well with the BIS during total i.v. anaesthesia with propofol.