Generative Adversarial Networks (GANs) aim to produce realistic samples by mapping a low-dimensional latent space with known distribution to a high-dimensional data space, exploiting an adversarial training mechanism. However, without an effective characterisation of the generative process, such models face significant challenges in training and architecture selection. In this work, we propose a Topological Data Analysis based approach, using persistent homology, which can provide such a characterisation, where topological information of a data manifold is summarised by its Persistent Diagram and the evolution of its topological features is tracked throughout training. Our approach is applied across multiple GAN architectures using two benchmark datasets, where we demonstrate that conventional metrics such as Fréchet Inception Distance and intrinsic dimension estimates cannot adequately capture the quality of generated samples. Instead, our results confirm that a topological description of the generative process within GANs successfully captures training convergence and mode collapse. Finally, the layer-wise topological analysis determines the role each layer plays in the generative process, and may provide future guidance for refinement of architectures. Code available at https://github.com/bcorrad/genfold25.git .

Foundation models have exhibited unprecedented capabilities across various domains and tasks. Models like CLIP bridge cross-modal representations, while text-to-image diffusion models excel in realistic image generation. While the complexity of these models makes retraining infeasible, their superior performance has driven research to explore how to efficiently use them for downstream tasks. Our work explores how to leverage these models for dense visual prediction tasks, specifically image segmentation. To avoid the annotation cost or training large diffusion models, we constrain our method to be zero-shot and training-free. Our pipeline, dubbed FreeSeg-Diff, uses open-source foundation models to perform open-vocabulary segmentation as follows: (a) retrieving image caption (via BLIP-2) and visual features (via Stable Diffusion), (b) clustering and binarizing features to form class-agnostic object masks, (c) mapping these masks to textual classes using CLIP with open vocabulary support, and (d) refining coarse masks. FreeSeg-Diff surpasses many training-based methods on Pascal VOC and COCO datasets and delivers competitive results against recent weakly-supervised segmentation approaches. We provide experiments demonstrating the superiority of diffusion model features over other pre-trained models. Project page: https://bcorrad.github.io/freesegdiff/.

Recently, generative models for images have garnered remarkable attention, due to their effective generalization ability and their capability to generate highly detailed and realistic content. Indeed, the success of generative networks (e.g., BigGAN, StyleGAN, Diffusion Models) has driven researchers to develop increasingly powerful models. As a result, we have observed an unprecedented improvement in terms of both image resolution and realism, making generated images indistinguishable from real ones. In this work, we focus on a family of generative models known as Stable Diffusion Models (SDMs), which have recently emerged due to their ability to generate images in a multimodal setup (i.e., from a textual prompt) and have outperformed adversarial networks by learning to reverse a diffusion process. Given the complexity of these models that makes it hard to retrain them, researchers started to exploit pre-trained SDMs to perform downstream tasks (e.g., classification and segmentation), where semantics plays a fundamental role. In this context, understanding how well the model preserves semantic information may be crucial to improve its performance. This paper presents an approach aimed at providing insights into the properties of a pre-trained SDM through the semantic lens. In particular, we analyze the features extracted by the U-Net within a SDM to explore whether and how the semantic information of an image is preserved in its internal representation. For this purpose, different distance measures are compared, and an ablation study is performed to select the layer (or combination of layers) of the U-Net that best preserves the semantic information. We also seek to understand whether semantics are preserved when the image undergoes simple transformations (e.g., rotation, flip, scale, padding, crop, and shift) and for a different number of diffusion denoising steps. To evaluate these properties, we consider popular benchmarks for semantic segmentation tasks (e.g., COCO, and Pascal-VOC). Our experiments suggest that the first encoder layer at resolution effectively preserves semantic information. However, increasing inference steps (even for a minimal amount of noise) and applying various image transformations can affect the diffusion U-Net’s internal feature representation. Additionally, we propose some examples taken from a video benchmark (DAVIS dataset), where we investigate if an object instance within a video preserves its internal representation even after several frames. Our findings suggest that the internal object representation remains consistent across multiple frames in a video, as long as the configuration changes are not excessive.

Most Convolutional Neural Networks (CNNs) consist of a number of stages of decreasing spatial resolution and increasing channel dimension between succeeding stages, each stage is composed of convolutional blocks that are repeated a number of times. Previous research on very simple CNNs consisting of a number of convolutional layers in each stage demonstrated that the introduction of feedback loops around convolutional layers can improve results. This paper studies the effectiveness of recursion on convolutional blocks in a more general setting and aims at explaining the results. Four recent models, namely ResNet, Inception, MobileNet and DenseNet are considered in this study. It is found that for all but DenseNet, the recursive version produces results that are similar or better than their feedforward counterpart when the number of convolutional blocks are preserved. To understand this finding and to discriminate the functional behaviors of the feedforward and recursive counterparts, we embark on three investigations: (1) measuring the evolution of the contextualization of the neurons of the last layer using the effective receptive field concept; (2) comparing the position and the size of the global coverage of the networks using class activation maps; and (3) analyzing the evolution of the organization of the feature space prior to the classifier using the Silhouette score. The investigations reveal that the recursion of a convolutional block shares many similarities with the behavior of a sequence of that block, indicating that a recursive alternative consisting of a single physical layer, can be regarded as a “faithful simulation” of its deeper‘feedforward counterpart. We conclude that except for densely connected models, the recursion of convolutional blocks is a safe and powerful alternative enhancing modern network architectures.

Molecule generation has experienced multiple breakthroughs in recent years. While traditional techniques are very reliable they have low space exploration potential; therefore, machine learning techniques are needed to delve deep into the vast space of potential compounds, helping to find new ways of designing candidate molecules. This paper presents a sequential Markovian model based on graph neural networks for molecular generation. The model employs a Breadth–First Search (BFS) ordering strategy and a modular architecture to enhance independence between functions, with a focus on maintaining strict independence at each step of the Markovian process. Experimental results on ZINC (MOSES), ZINC (250 K) and Polymers datasets demonstrate the model’s ability to perform both unconditional and conditional molecule generation while preserving dataset properties. Notably, the step–wise approach achieves state–of–the–art results in terms of uniqueness and validity without using valency masks. • A novel sequential approach to molecular graph generation is presented. • The method exploits Graph Neural Networks to maximize information exploitation. • The employed Markov process and the architecture ensure a flexible learning procedure. • Conditional generation allows tailoring the generated molecules to the objectives of the specific studies. • The experimentation shows that the approach outperforms thestate-of-the-art.

Graph Neural Networks (GNNs) have emerged in recent years as a powerful tool to learn tasks across a wide range of graph domains in a data-driven fashion. Based on a message passing mechanism, GNNs have gained increasing popularity due to their intuitive formulation, closely linked to the Weisfeiler-Lehman (WL) test for graph isomorphism, to which they were demonstrated to be equivalent (Morris et al., 2019 and Xu et al., 2019). From a theoretical point of view, GNNs have been shown to be universal approximators, and their generalization capability - related to the Vapnik Chervonekis (VC) dimension (Scarselli et al., 2018) - has recently been investigated for GNNs with piecewise polynomial activation functions (Morris et al., 2023). The aim of our work is to extend this analysis on the VC dimension of GNNs to other commonly used activation functions, such as the sigmoid and hyperbolic tangent, using the framework of Pfaffian function theory. Bounds are provided with respect to the architecture parameters (depth, number of neurons, input size) as well as with respect to the number of colors resulting from the 1-WL test applied on the graph domain. The theoretical analysis is supported by a preliminary experimental study.

We systematically investigate the expressive power of path-based graph neural networks. While it has been shown that path-based graph neural networks can achieve strong empirical results, an investigation into their expressive power is lacking. Therefore, we propose PATH-WL, a general class of color refinement algorithms based on paths and shortest path distance information. We show that PATH-WL is incomparable to a wide range of expressive graph neural networks, can count cycles, and achieves strong empirical results on the notoriously difficult family of strongly regular graphs. Our theoretical results indicate that PATH-WL forms a new hierarchy of highly expressive graph neural networks.

The ambition to create increasingly realistic images has driven researchers to develop increasingly powerful models, capable of generalizing and generating high-resolution images, even in a multimodal setup (e.g., from textual input). Among the most recent generative networks, Stable Diffusion Models (SDMs) have achieved state-of-the-art showing great generative capabilities but also a high degree of complexity, both in terms of training and interpretability. Indeed, the impressive generalization capability of pre-trained SDMs has pushed researchers to exploit their internal representation to perform downstream tasks (e.g., classification and segmentation). Understanding how well the model preserves semantic information is fundamental to improve its performance. Our approach, namely Diff-Props, analyses the features extracted from the U-Net within Stable Diffusion Model to unveil how Stable Diffusion retains semantic information of an image in a pre-trained setup. Exploiting a set of different distance metrics, Diff-Props aims to analyse how features at different depths contribute to preserving the meaning of the objects in the image.

The Recursive Convolutional Layer (RCL) is a module that wraps a recursive feedback loop around a convolutional layer (CL). The RCL has been proposed to address some of the shortcomings of Convolutional Neural Networks (CNNs), as its unfolding increases the depth of a network without increasing the number of weights. We investigated the “naïve” substitution of CL with RCL on three base models: a 4-CL model, ResNet, DenseNet and their RCL-ized versions: C-FRPN, R-ResNet, and R-DenseNet using five image classification datasets. We find that this one-to-one replacement significantly improves the performances of the 4-CL model, but not those of ResNet or DenseNet. This led us to investigate the implication of the RCL substitution on the 4-CL model which reveals, among a number of properties, that RCLs are particularly efficient in shallow CNNs. We proceeded to re-visit the first set of experiments by gradually transforming the 4-CL model and the C-FRPN into respectively ResNet and R-ResNet, and find that the performance improvement is largely driven by the training regime whereas any depth increase negatively impacts the RCL-ized version. We conclude that the replacement of CLs by RCLs shows great potential in designing high-performance shallow CNNs.

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence. Moreover, the proof of the approximation capability is mostly constructive and allows us to deduce hints on the architecture of GNNs that can achieve the desired approximation.

In the context of deep learning models, attention has recently been paid to studying the surface of the loss function in order to better understand training with methods based on gradient descent. This search for an appropriate description, both analytical and topological, has led to numerous efforts in identifying spurious minima and characterize gradient dynamics. Our work aims to contribute to this field by providing a topological measure for evaluating loss complexity in the case of multilayer neural networks. We compare deep and shallow architectures with common sigmoidal activation functions by deriving upper and lower bounds for the complexity of their respective loss functions and revealing how that complexity is influenced by the number of hidden units, training models, and the activation function used. Additionally, we found that certain variations in the loss function or model architecture, such as adding an ℓ2 regularization term or implementing skip connections in a feedforward network, do not affect loss topology in specific cases.

Abstract Graph neural networks (GNNs) are a broad class of connectionist models for graph processing. Recent studies have shown that GNNs can approximate any function on graphs, modulo the equivalence relation on graphs defined by the Weisfeiler–Lehman (WL) test. However, these results suffer from some limitations, both because they were derived using the Stone–Weierstrass theorem—which is existential in nature—and because they assume that the target function to be approximated must be continuous. Furthermore, all current results are dedicated to graph classification/regression tasks, where the GNN must produce a single output for the whole graph, while also node classification/regression problems, in which an output is returned for each node, are very common. In this paper, we propose an alternative way to demonstrate the approximation capability of GNNs that overcomes these limitations. Indeed, we show that GNNs are universal approximators in probability for node classification/regression tasks, as they can approximate any measurable function that satisfies the 1-WL-equivalence on nodes. The proposed theoretical framework allows the approximation of generic discontinuous target functions and also suggests the GNN architecture that can reach a desired approximation. In addition, we provide a bound on the number of the GNN layers required to achieve the desired degree of approximation, namely $$2r-1$$ 2 r - 1 , where r is the maximum number of nodes for the graphs in the domain.

The development of Convolutional Neural Networks (CNNs) trends towards models with an ever growing number of Convolutional Layers (CLs) and increases the number of trainable parameters significantly. Such models are sensitive to these structural parameters, which implies that large models have to be carefully tuned using hyperparameter optimisation, a process that can be very time consuming. In this paper, we study the usage of Recursive Convolutional Layers (RCLs), a module relying on an algebraic feedback loop wrapped around a CL, which can replace any CL in CNNs. Using three publicly available datasets, CIFAR10, CIFAR100 and SVHN, and a simple model comprised of 4 RCLs, we compare its performances with those obtained by its feedforward counterpart, and exhibit some core properties and use-cases of RCLs. In particular, we show that RCLs can lead to models of better performances, and that reducing the number of modules from four to one lead to a decrease in accuracy of 3.5% on average for models using RCLs, compared to 23% using CLs. Hence, the resulting architecture is much more robust to the addition or the removal of layers. We conclude by relating the effects obtained using additional CLs with those obtained using additional recursion on RCLs, which provides incentives that the latter can simulate an increase of depth but with no extra cost of parameters. Such results point to the potential benefits of either selectively or replacing all CLs by RCLs, in most recently introduced CNNs.

Drug Side-Effects (DSEs) have a high impact on public health, care system costs, and drug discovery processes. Predicting the probability of side-effects, before their occurrence, is fundamental to reduce this impact, in particular on drug discovery. Candidate molecules could be screened before undergoing clinical trials, reducing the costs in time, money, and health of the participants. Drug side-effects are triggered by complex biological processes involving many different entities, from drug structures to protein-protein interactions. To predict their occurrence, it is necessary to integrate data from heterogeneous sources. In this work, such heterogeneous data is integrated into a graph dataset, expressively representing the relational information between different entities, such as drug molecules and genes. The relational nature of the dataset represents an important novelty for drug side-effect predictors. Graph Neural Networks (GNNs) are exploited to predict DSEs on our dataset with very promising results. GNNs are deep learning models that can process graph-structured data, with minimal information loss, and have been applied on a wide variety of biological tasks. Our experimental results confirm the advantage of using relationships between data entities, suggesting interesting future developments in this scope. The experimentation also shows the importance of specific subsets of data in determining associations between drugs and side-effects.

Many real-world domains involve information naturally represented by graphs, where nodes denote basic patterns while edges stand for relationships among them. The graph neural network (GNN) is a machine learning model capable of directly managing graph-structured data. In the original framework, GNNs are inductively trained, adapting their parameters based on a supervised learning environment. However, GNNs can also take advantage of transductive learning, thanks to the natural way they make information flow and spread across the graph, using relationships among patterns. In this paper, we propose a mixed inductive-transductive GNN model, study its properties and introduce an experimental strategy that allows us to understand and distinguish the role of inductive and transductive learning. The preliminary experimental results show interesting properties for the mixed model, highlighting how the peculiarities of the problems and the data can impact on the two learning strategies.

Machine Learning (ML) achievements enabled automatic extraction of actionable information from data in a wide range of decisionmaking scenarios.This demands for improving both ML technical aspects (e.g., design and automation) and human-related metrics (e.g., fairness, robustness, privacy, and explainability), with performance guarantees at both levels.The aforementioned scenario posed three main challenges: (i) Learning from Complex Data (i.e., sequence, tree, and graph data), (ii) Learning Trustworthily, and (iii) Learning Automatically with Guarantees.The focus of this special session is on addressing one or more of these challenges with the final goal of Learning Trustworthily, Automatically, and with Guarantees from Complex Data.

Multi-parametric prostate MRI (mpMRI) is a powerful tool to diagnose prostate cancer, though difficult to interpret even for experienced radiologists. A common radiological procedure is to compare a magnetic resonance image with similarly diagnosed cases. To assist the radiological image interpretation process, computerized Content-Based Image Retrieval systems (CBIRs) can therefore be employed to improve the reporting workflow and increase its accuracy. In this article, we propose a new, supervised siamese deep learning architecture able to handle multi-modal and multi-view MR images with similar PIRADS score. An experimental comparison with well-established deep learning-based CBIRs (namely standard siamese networks and autoencoders) showed significantly improved performance with respect to both diagnostic (ROC-AUC), and information retrieval metrics (Precision-Recall, Discounted Cumulative Gain and Mean Average Precision). Finally, the new proposed multi-view siamese network is general in design, facilitating a broad use in diagnostic medical imaging retrieval.

Anisoptera are a suborder of insects belonging to the order of Odonata, commonly identified with the generic term dragonflies. They are characterized by a long and thin abdomen, two large eyes, and two pairs of transparent wings. Their ability to move the four wings independently allows dragonflies to fly forwards, backwards, to stop suddenly and to hover in mid–air, as well as to achieve high flight performance, with speed up to 50 km per hour. Thanks to these particular skills, many studies have been conducted on dragonflies, also using machine learning techniques. Some analyze the muscular movements of the flight to simulate dragonflies as accurately as possible, while others try to reproduce the neuronal mechanisms of hunting dragonflies. The lack of a consistent database and the difficulties in creating valid tools for such complex tasks have significantly limited the progress in the study of dragonflies. We provide two valuable results in this context: first, a dataset of carefully selected, pre–processed and labeled images, extracted from videos, has been released; then some deep neural network models, namely CNNs and LSTMs, have been trained to accurately distinguish the different phases of dragonfly flight, with very promising results.

During the last decade, deep learning and Convolutional Neural Networks (CNNs) have produced a devastating impact on computer vision, yielding exceptional results on a variety of problems, including analysis of medical images. Recently, these techniques have been extended to 3D images with the downside of a large increase in the computational load. In particular, state-of-the-art CNNs have been used for brain Nuclear Magnetic Resonance (NMR) imaging, with the aim of estimating the patients’ age. In fact, a large discrepancy between the real and the estimated age is a clear alarm for the onset of neurodegenerative diseases, such as some types of early dementia and Alzheimer’s disease. In this paper, we propose an effective alternative to 3D convolutions that guarantees a significant reduction of the computational requirements for this kind of analysis. The proposed architectures achieve comparable results with the competitor 3D methods, requiring only a fraction of the training time and GPU memory.

Recently, researchers in the artificial neural network field have focused their attention on connectionist models composed by several hidden layers. In fact, experimental results and heuristic considerations suggest that deep architectures are more suitable than shallow ones for modern applications, facing very complex problems, e.g., vision and human language understanding. However, the actual theoretical results supporting such a claim are still few and incomplete. In this paper, we propose a new approach to study how the depth of feedforward neural networks impacts on their ability in implementing high complexity functions. First, a new measure based on topological concepts is introduced, aimed at evaluating the complexity of the function implemented by a neural network, used for classification purposes. Then, deep and shallow neural architectures with common sigmoidal activation functions are compared, by deriving upper and lower bounds on their complexity, and studying how the complexity depends on the number of hidden units and the used activation function. The obtained results seem to support the idea that deep networks actually implements functions of higher complexity, so that they are able, with the same number of resources, to address more difficult problems.

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.

Graph Neural Networks (GNNs) are a powerful tool for processing graphs, that represent a natural way to collect information coming from several areas of science and engineering - e.g. data mining, computer vision, molecular chemistry, molecular biology, pattern recognition -, where data are intrinsically organized in entities and relationships among entities. Nevertheless, GNNs suffer, so as recurrent/recursive models, from the long-term dependency problem that makes the learning difficult in deep structures. In this paper, we present a new architecture, called Layered GNN (LGNN), realized by a cascade of GNNs: each layer is fed with the original data and with the state information calculated by the previous layer in the cascade. Intuitively, this allows each GNN to solve a subproblem, related only to those patterns that were misclassified by the previous GNNs. Some experimental results are reported, based on synthetic and real-world datasets, which assess a significant improvement in performances w.r.t. the standard GNN approach.

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

In this paper, we will consider the approximation properties of a recently introduced neural network model called graph neural network (GNN), which can be used to process-structured data inputs, e.g., acyclic graphs, cyclic graphs, and directed or undirected graphs. This class of neural networks implements a function tau(G,n) is an element of IR(m) that maps a graph G and one of its nodes n onto an m-dimensional Euclidean space. We characterize the functions that can be approximated by GNNs, in probability, up to any prescribed degree of precision. This set contains the maps that satisfy a property called preservation of the unfolding equivalence, and includes most of the practically useful functions on graphs; the only known exception is when the input graph contains particular patterns of symmetries when unfolding equivalence may not be preserved. The result can be considered an extension of the universal approximation property established for the classic feedforward neural networks (FNNs). Some experimental examples are used to show the computational capabilities of the proposed model.

Recursive neural networks (RNNs) and graph neural networks (GNNs) are two connectionist models that can directly process graphs. RNNs and GNNs exploit a similar processing framework, but they can be applied to different input domains. RNNs require the input graphs to be directed and acyclic, whereas GNNs can process any kind of graphs. The aim of this paper consists in understanding whether such a difference affects the behaviour of the models on a real application. An experimental comparison on an image classification problem is presented, showing that GNNs outperforms RNNs. Moreover the main differences between the models are also discussed w.r.t. their input domains, their approximation capabilities and their learning algorithms.

The number of XML documents produced and available on the Internet is steadily increasing. It is thus important to devise automatic procedures to extract useful information from them with little or no intervention by a human operator. In this paper, we investigate the efficacy of an unsupervised learning approach, namely self-organising maps (SOMs), for the automatic clustering of XML documents. Specifically, we consider a relatively large corpus of XML formatted data from the INEX initiative and evaluate it using two different self-organising map models. The first model is the classical SOM model, and it requires the XML documents to be represented by real-valued vectors, obtained using a "bag of words" (or better a "bag of tags") approach. The other model is the SOM for structured data (SOM-SD) approach which is able to cluster structured data, and it is possible to feed the model with tree structured representations of the XML documents, thus explicitly preserving the structural information in the documents. The experimental results show that the SOM model exhibits quite a poor performance on this problem domain which requires the ability to encode structural properties of the data. The SOM-SD model, on the other hand, is able to produce a good clustering and generalization performance.

Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically cyclic. In this paper, a methodology is proposed, which allows us to process any cyclic directed graph. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model.

In this article, we present a new approach to page ranking. The page rank of a collection of Web pages can be represented in a parameterized model, and the user requirements can be represented by a set of constraints. For a particular parameterization, namely, a linear combination of the page ranks produced by different forcing functions, and user requirements represented by a set of linear constraints, the problem can be solved using a quadratic programming method. The solution to this problem produces a set of parameters which can be used for ranking all pages in the Web. We show that the method is suitable for building customized versions of PageRank which can be readily adapted to the needs of a vertical search engine or that of a single user.

In several applications the information is naturally represented by graphs. Traditional approaches cope with graphical data structures using a preprocessing phase which transforms the graphs into a set of flat vectors. However, in this way, important topological information may be lost and the achieved results may heavily depend on the preprocessing stage. This paper presents a new neural model, called graph neural network (GNN), capable of directly processing graphs. GNNs extends recursive neural networks and can be applied on most of the practically useful kinds of graphs, including directed, undirected, labelled and cyclic graphs. A learning algorithm for GNNs is proposed and some experiments are discussed which assess the properties of the model.

An artificial neural network model, capable of processing general types of graph structured data, has recently been proposed. This paper applies the new model to the computation of customised page ranks problem in the World Wide Web. The class of customised page ranks that can be implemented in this way is very general and easy because the neural network model is learned by examples. Some preliminary experimental findings show that the model generalizes well over unseen Web pages, and hence, may be suitable for the task of page rank computation on a large Web graph.

Although the interest of a Web page is strictly related to its content and to the subjective readers' cultural background, a measure of the page authority can be provided that only depends on the topological structure of the Web. PageRank is a noticeable way to attach a score to Web pages on the basis of the Web connectivity. In this article, we look inside PageRank to disclose its fundamental properties concerning stability, complexity of computational scheme, and critical role of parameters involved in the computation. Moreover, we introduce a circuit analysis that allows us to understand the distribution of the page score, the way different Web communities interact each other, the role of dangling pages (pages with no outlinks), and the secrets for promotion of Web pages.

In this paper, a new recursive neural network model, able to process directed acyclic graphs with labeled edges, is introduced, in order to address the problem of object detection in images. In fact, the detection is a preliminary step in any object recognition system. The proposed method assumes a graph-based representation of images, that combines both spatial and visual features. In particular, after segmentation, an edge between two nodes stands for the adjacency relationship of two homogeneous regions, the edge label collects information on their relative positions, whereas node labels contain visual and geometric information on each region (area, color, texture, etc.). Such graphs are then processed by the recursive model in order to determine the eventual presence and the position of objects inside the image. Some experiments on face detection, carried out on scenes acquired by an indoor camera, are reported, showing very promising results. The proposed technique is general and can be applied in different object detection systems, since it does not include any a priori knowledge on the particular problem.

The definition of the ordering of the Web pages, returned on a given query, is a crucial topic, which gives rise to the notion of Web visibility. A fundamental contribution towards the conception of appropriate ordering criteria has been given by means of the introduction of PageRank, which takes into account only the hyper-linked structure of the Web, regardless of the content of the pages. We introduce a circuit analysis which allows us to understand the distribution of PageRank, and show some basic results for understanding the way it migrates amongst communities. In particular, we highlight some topological properties which suggest methods for the promotion of Web communities. These results confirm the importance and the effectiveness of PageRank for discovering relevant information but, at the same time, point out its vulnerability to spamming.

In this paper, we consider the possibility of altering the PageRank of web pages, from an administrator's point of view, through the modification of the PageRank equation. It is shown that this problem can be solved using the traditional quadratic programming techniques. In addition, it is shown that the number of parameters can be reduced by clustering web pages together through simple clustering techniques. This problem can be formulated and solved using quadratic programming techniques. It is demonstrated experimentally on a relatively large web data set, viz., the WT10G, that it is possible to modify the PageRanks of the web pages through the proposed method using a set of linear constraints. It is also shown that the PageRank of other pages may be affected; and that the quality of the result depends on the clustering technique used. It is shown that our results compared well with those obtained by a HITS based method.

The prediction of the linguistic origin of surnames is a basic functionality required in the design of high-quality multilanguage speech synthesizers. The assignment of a given string representing a surname to a specific language is typically based on a set of rules which can hardly be written in an explicit form. The approach we propose faces this problem combining a rule-based system with a module based on evidential reasoning and a module based on neural networks. The resulting hybrid system combines the different sources of information, merging both knowledge from experts on linguistics and knowledge automatically acquired using learning from examples. The system has been validated on a large database containing surnames belonging to four different languages, showing its effectiveness for real-world applications.

Content-based search and organization of Web documents poses new issues in information retrieval. We propose a novel approach for the classification of HTML documents based on a structured representation of their contents which are split into logical contexts (paragraphs, sections, anchors, etc.). The classification is performed using Hidden Tree-Markov Models (HTMMs), an extension of Hidden Markov Models for processing structured objects. We report some promising experimental results showing that the use of the structured representation improves the classification accuracy in most of the cases.

Recursive neural networks are conceived for processing graphs and extend the well-known recurrent model for processing sequences. In Frasconi et al. (1998), recursive neural networks can deal only with directed ordered acyclic graphs (DOAGs), in which the children of any given node are ordered. While this assumption is reasonable in some applications, it introduces unnecessary constraints in others. In this paper, it is shown that the constraint on the ordering can be relaxed by using an appropriate weight sharing, that guarantees the independence of the network output with respect to the permutations of the arcs leaving from each node. The method can be used with graphs having low connectivity and, in particular, few outcoming arcs. Some theoretical properties of the proposed architecture are given. They guarantee that the approximation capabilities are maintained, despite the weight sharing.

Recursive neural networks are a new connectionist model introduced for processing graphs. Linear recursive networks are a special subclass where the neurons have linear activation functions. The approximation properties of recursive networks are tightly connected to the possibility of distinguishing the patterns by generating a different internal encoding for each input of the domain. In this paper, it is shown that, even if linear recursive networks can distinguish the patterns of any finite set of trees, such a result requires a prohibitive memory consumption. However, it is also proved that the problem disappears when the domain is restricted to set of trees belonging to special sub-classes.

This paper describes an application to the prediction of the linguistic origin of surnames. The problem can be stated as follows: "Given an input string representing a surname, decide which language the surname belongs to". We present an approach that integrates methodologies from rule-based systems, evidential reasoning, and neural networks. Our hybrid solution maximizes the used information and allows one to deal with aspects of the problem that could have not been solved otherwise. In fact, our predictor exploits both knowledge from experts on languages (by means of a rule-based system) and knowledge automatically acquired by examples (through statistical analysis and a neural network).

Discusses the ability of multilayer perceptrons (MLPs) to model the probability distribution of data in typical pattern recognition and verification problems. It is proven that multilayer perceptrons with sigmoidal units and a number of hidden units less or equal than the number of inputs are unable to model patterns distributed in typical clusters, since these networks draw open separation surfaces in the pattern space. When using more hidden units than inputs, the separation surfaces can be closed but, unfortunately it is proven that determining whether or not a MLP draws closed separation surfaces in the pattern space is NP-hard. The major conclusion of the paper is somewhat opposite to what is believed and reported in many application papers: MLPs are definitely not adequate for applications of pattern recognition requiring a reliable rejection and, especially, they are not adequate for pattern verification tasks.

Given a multilayer perceptron (MLP) with a fixed architecture, there are functions that can be approximated up to any degree of accuracy, without having to increase the number of the hidden nodes. Those functions belong to the closure F of the set F of the maps realizable by the MLP. In this paper, we give a list of maps with this property. In particular, it is proven that 1) rational functions belongs to F for networks with inverse tangent activation function and 2) products of polynomials and exponentials belongs to F for networks with sigmoid activation function. Moreover, for a restricted class of MLP's, we prove that the list is complete and give an analytic definition of F.

Collecting information about the performance of a software process is a necessary step for the assessment of the process quality. Oikos is an environment for the definition and the enactment of software process models. This paper presents the Oikos approach to history recording. We define the events that compose the histories and explain how the events to be monitored can be selected. Finally, we discuss the implementation of the recording mechanism.