Effectively learning from sequential data is a longstanding goal of Artificial Intelligence, especially in the case of long sequences. From the dawn of Machine Learning, several researchers have pursued algorithms and architectures capable of processing sequences of patterns, retaining information about past inputs while still leveraging future data, without losing precious long-term dependencies and correlations. While such an ultimate goal is inspired by the human hallmark of continuous real-time processing of sensory information, several solutions have simplified the learning paradigm by artificially limiting the processed context or dealing with sequences of limited length, given in advance. These solutions were further emphasized by the ubiquity of Transformers, which initially overshadowed the role of Recurrent Neural Nets. However, recurrent networks are currently experiencing a strong recent revival due to the growing popularity of (deep) State-Space models and novel instances of large-context Transformers, which are both based on recurrent computations that aim to go beyond several limits of currently ubiquitous technologies. The fast development of Large Language Models has renewed the interest in efficient solutions to process data over time. This survey provides an in-depth summary of the latest approaches that are based on recurrent models for sequential data processing. A complete taxonomy of recent trends in architectural and algorithmic solutions is reported and discussed, guiding researchers in this appealing research field. The emerging picture suggests that there is room for exploring novel routes, constituted by learning algorithms that depart from the standard Backpropagation Through Time, towards a more realistic scenario where patterns are effectively processed online, leveraging local-forward computations, and opening new directions for research on this topic.

Abstract Explainability in artificial intelligence (XAI) remains a crucial aspect for fostering trust and understanding in machine learning models. Current visual explanation techniques, such as gradient-based or class-activation-based methods, often exhibit a strong dependence on specific model architectures. Conversely, perturbation-based methods, despite being model-agnostic, are computationally expensive as they require evaluating models on a large number of forward passes. We introduce Foveation-based Explanations (FovEx), a novel XAI method inspired by human vision, which combines biologically inspired foveation-based transformations with gradient-driven overt attention to iteratively select locations of interest. These locations are selected to maximize the performance of the model to be explained with respect to the downstream task and then combined to generate an attribution map. We provide a thorough evaluation with qualitative and quantitative assessments on established benchmarks. Our method achieves state-of-the-art performance on both transformers (on 4 out of 5 metrics) and convolutional models (on 3 out of 5 metrics), demonstrating its versatility among various architectures. Furthermore, we show the alignment between the explanation map produced by FovEx and human gaze patterns (+14% in NSS compared to RISE, +203% in NSS compared to GradCAM). This comparison enhances our confidence in FovEx’s ability to close the interpretation gap between humans and machines.

Correction: International Journal of Computer Vision (2025) 133:7437–7459

Learning with neural networks from a continuous stream of visual information presents several challenges due to the non-i.i.d. nature of the data. However, it also offers novel opportunities to develop representations that are consistent with the information flow. In this paper we investigate the case of unsupervised continual learning of pixel-wise features subject to multiple motion-induced constraints, therefore named motion-conjugated feature representations. Differently from existing approaches, motion is not a given signal (either ground-truth or estimated by external modules), but is the outcome of a progressive and autonomous learning process, occurring at various levels of the feature hierarchy. Multiple motion flows are estimated with neural networks and characterized by different levels of abstractions, spanning from traditional optical flow to other latent signals originating from higher-level features, hence called higher-order motions. Continuously learning to develop consistent multi-order flows and representations is prone to trivial solutions, which we counteract by introducing a self-supervised contrastive loss, spatially-aware and based on flow-induced similarity. We assess our model on photorealistic synthetic streams and real-world videos, comparing to pre-trained state-of-the art feature extractors (also based on Transformers) and to recent unsupervised learning models, significantly outperforming these alternatives.

Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the Pontryagin Maximum Principle. In both approaches, Hamiltonian equations offer an interpretation of optimality through auxiliary variables known as costates. However, Hamiltonian equations are rarely used due to their reliance on forward-backward algorithms across the entire temporal domain. This paper introduces a novel neural-based approach to optimal control. Neural networks are employed not only for implementing state dynamics but also for estimating costate variables. The parameters of the latter network are determined at each time step using a newly introduced local policy referred to as the time-reversed generalized Riccati equation. This policy is inspired by a result discussed in the Linear Quadratic (LQ) problem, which we conjecture stabilizes state dynamics. We support this conjecture by discussing experimental results from a range of optimal control case studies.

Efficiently learning unsupervised pixel-wise visual representations is crucial for training agents that can perceive their environment without relying on heavy human supervision or abundant annotated data. Motivated by recent work that promotes motion as a key source of information in representation learning, we propose a novel instance of contrastive criterions over time and space. In our architecture, pixel-wise motion field and representations are extracted by neural models, trained from scratch in an integrated fashion. Learning proceeds online over time, exploiting also a momentum-based moving average to update the feature extractor, without replaying any large buffers of past data. Experiments on real-world videos and on a recently introduced benchmark, with photorealistic streams generated from a 3D environment, confirm that the proposed model can learn to estimate motion and jointly develop representations. Our model nicely encodes the variable appearance of the visual information in space and time, significantly overcoming a recent approach and it also compares favourably with convolutional and Transformer-based networks, offline-pre-trained on large collections of supervised and unsupervised images.

Graph drawing techniques have been developed in the last few years with the purpose of producing esthetically pleasing node-link layouts. Recently, the employment of differentiable loss functions has paved the road to the massive usage of gradient descent and related optimization algorithms. In this article, we propose a novel framework for the development of Graph Neural Drawers (GNDs), machines that rely on neural computation for constructing efficient and complex maps. GND is Graph Neural Networks (GNNs) whose learning process can be driven by any provided loss function, such as the ones commonly employed in Graph Drawing. Moreover, we prove that this mechanism can be guided by loss functions computed by means of feedforward neural networks, on the basis of supervision hints that express beauty properties, like the minimization of crossing edges. In this context, we show that GNNs can nicely be enriched by positional features to deal also with unlabeled vertexes. We provide a proof-of-concept by constructing a loss function for the edge crossing and provide quantitative and qualitative comparisons among different GNN models working under the proposed framework.

The intrinsic difficulty in adapting deep learning models to non-stationary environments limits the applicability of neural networks to real-world tasks. This issue is critical in practical supervised learning settings, such as the ones in which a pre-trained model computes projections toward a latent space where different task predictors are sequentially learned over time. As a matter of fact, incrementally fine-tuning the whole model to better adapt to new tasks usually results in catastrophic forgetting, with decreasing performance over the past experiences and losing valuable knowledge from the pretraining stage. In this paper, we propose a novel strategy to make the fine-tuning procedure more effective, by avoiding to update the pre-trained part of the network and learning not only the usual classification head, but also a set of newly-introduced learnable parameters that are responsible for transforming the input data. This process allows the network to effectively leverage the pre-training knowledge and find a good trade-off between plasticity and stability with modest computational efforts, thus especially suitable for on-the-edge settings. Our experiments on four image classification problems in a continual learning setting confirm the quality of the proposed approach when compared to several fine-tuning procedures and to popular continual learning methods.

In this paper, we present PARTIME, a software library written in Python and based on PyTorch, designed specifically to speed up neural networks whenever data is continuously streamed over time, for both learning and inference. Existing libraries are designed to exploit data-level parallelism, assuming that samples are batched, a condition that is not naturally met in applications that are based on streamed data. Differently, PARTIME starts processing each data sample at the time in which it becomes available from the stream. PARTIME wraps the code that implements a feed-forward multi-layer network and it distributes the layer-wise processing among multiple devices, such as Graphics Processing Units (GPUs). Thanks to its pipeline-based computational scheme, PARTIME allows the devices to perform computations in parallel. At inference time this results in scaling capabilities that are theoretically linear with respect to the number of devices. During the learning stage, PARTIME can leverage the non-i.i.d. nature of the streamed data with samples that are smoothly evolving over time for efficient gradient computations. Experiments are performed in order to empirically compare PARTIME with classic non-parallel neural computations in online learning, distributing operations on up to 8 NVIDIA GPUs, showing significant speedups that are almost linear in the number of devices, mitigating the impact of the data transfer overhead.

Devising intelligent agents able to live in an environment and learn by observing the surroundings is a longstanding goal of Artificial Intelligence. From a bare Machine Learning perspective, challenges arise when the agent is prevented from leveraging large fully-annotated dataset, but rather the interactions with supervisory signals are sparsely distributed over space and time. This paper proposes a novel neural-network-based approach to progressively and autonomously develop pixel-wise representations in a video stream. The proposed method is based on a human-like attention mechanism that allows the agent to learn by observing what is moving in the attended locations. Spatio-temporal stochastic coherence along the attention trajectory, paired with a contrastive term, leads to an unsupervised learning criterion that naturally copes with the considered setting. Differently from most existing works, the learned representations are used in open-set class-incremental classification of each frame pixel, relying on few supervisions. Our experiments leverage 3D virtual environments and they show that the proposed agents can learn to distinguish objects just by observing the video stream. Inheriting features from state-of-the art models is not as powerful as one might expect.

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.

In the last few years, the scientific community showed a remarkable and increasing interest towards 3D Virtual Environments, training and testing Machine Learning-based models in realistic virtual worlds. On one hand, these environments could also become a mean to study the weaknesses of Machine Learning algorithms, or to simulate training settings that allow Machine Learning models to gain robustness to 3D adversarial attacks. On the other hand, their growing popularity might also attract those that aim at creating adversarial conditions to invalidate the benchmarking process, especially in the case of public environments that allow the contribution from a large community of people. Most of the existing Adversarial Machine Learning approaches are focused on static images, and little work has been done in studying how to deal with 3D environments and how a 3D object should be altered to fool a classifier that observes it. In this paper, we study how to craft adversarial 3D objects by altering their textures, using a tool chain composed of easily accessible elements. We show that it is possible, and indeed simple, to create adversarial objects using off-the-shelf limited surrogate renderers that can compute gradients with respect to the parameters of the rendering process, and, to a certain extent, to transfer the attacks to more advanced 3D engines. We propose a saliency-based attack that intersects the two classes of renderers in order to focus the alteration to those texture elements that are estimated to be effective in the target engine, evaluating its impact in popular neural classifiers.

In the last decade, motivated by the success of Deep Learning, the scientific community proposed several approaches to make the learning procedure of Neural Networks more effective. When focussing on the way in which the training data are provided to the learning machine, we can distinguish between the classic random selection of stochastic gradient-based optimization and more involved techniques that devise curricula to organize data, and progressively increase the complexity of the training set. In this paper, we propose a novel training procedure named Friendly Training that, differently from the aforementioned approaches, involves altering the training examples in order to help the model to better fulfil its learning criterion. The model is allowed to “simplify” those examples that are too hard to be classified at a certain stage of the training procedure. The data transformation is controlled by a developmental plan that progressively reduces its impact during training, until it completely vanishes. In a sense, this is the opposite of what is commonly done in order to increase robustness against adversarial examples, i.e., Adversarial Training. Experiments on multiple datasets are provided, showing that Friendly Training yields improvements with respect to informed data sub-selection routines and random selection, especially in deep convolutional architectures. Results suggest that adapting the input data is a feasible way to stabilize learning and improve the generalization skills of the network.

In many real world applications, data are characterized by a complex structure, that can be naturally encoded as a graph.In the last years, the popularity of deep learning techniques has renewed the interest in neural models able to process complex patterns.In particular, inspired by the Graph Neural Network (GNN) model, different architectures have been proposed to extend the original GNN scheme.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.In this paper, we propose a novel approach to the state computation and the learning algorithm for GNNs, based on a constraint optimisation 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.The proposed approach is compared experimentally with other popular models for processing graphs.

Recently, researchers in Machine Learning algorithms, Computer Vision scientists, engineers and others, showed a growing interest in 3D simulators as a mean to artificially create experimental settings that are very close to those in the real world. However, most of the existing platforms to interface algorithms with 3D environments are often designed to setup navigation-related experiments, to study physical interactions, or to handle ad-hoc cases that are not thought to be customized, sometimes lacking a strong photorealistic appearance and an easy-to-use software interface. In this paper, we present a novel platform, SAILenv, that is specifically designed to be simple and customizable, and that allows researchers to experiment visual recognition in virtual 3D scenes. A few lines of code are needed to interface every algorithm with the virtual world, and non-3D-graphics experts can easily customize the 3D environment itself, exploiting a collection of photorealistic objects. Our framework yields pixel-level semantic and instance labeling, depth, and, to the best of our knowledge, it is the only one that provides motion-related information directly inherited from the 3D engine. The client-server communication operates at a low level, avoiding the overhead of HTTP-based data exchanges. We perform experiments using a state-of-the-art object detector trained on real-world images, showing that it is able to recognize the photorealistic 3D objects of our environment. The computational burden of the optical flow compares favourably with the estimation performed using modern GPU-based convolutional networks or more classic implementations. We believe that the scientific community will benefit from the easiness and high-quality of our framework to evaluate newly proposed algorithms in their own customized realistic conditions.

In this paper we study a constraint-based representation of neural network architectures. We cast the learning problem in the Lagrangian framework and we investigate a simple optimization procedure that is well suited to fulfil the so-called architectural constraints, learning from the available supervisions. The computational structure of the proposed Local Propagation (LP) algorithm is based on the search for saddle points in the adjoint space composed of weights, neural outputs, and Lagrange multipliers. All the updates of the model variables are locally performed, so that LP is fully parallelizable over the neural units, circumventing the classic problem of gradient vanishing in deep networks. The implementation of popular neural models is described in the context of LP, together with those conditions that trace a natural connection with Backpropagation. We also investigate the setting in which we tolerate bounded violations of the architectural constraints, and we provide experimental evidence that LP is a feasible approach to train shallow and deep networks, opening the road to further investigations on more complex architectures, easily describable by constraints.

Unsupervised learning from continuous visual streams is a challenging problem that cannot be naturally and efficiently managed in the classic batch-mode setting of computation. The information stream must be carefully processed accordingly to an appropriate spatio-temporal distribution of the visual data, while most approaches of learning commonly assume uniform probability density. In this paper we focus on unsupervised learning for transferring visual information in a truly online setting by using a computational model that is inspired to the principle of least action in physics. The maximization of the mutual information is carried out by a temporal process which yields online estimation of the entropy terms. The model, which is based on second-order differential equations, maximizes the information transfer from the input to a discrete space of symbols related to the visual features of the input, whose computation is supported by hidden neurons. In order to better structure the input probability distribution, we use a human-like focus of attention model that, coherently with the information maximization model, is also based on second-order differential equations. We provide experimental results to support the theory by showing that the spatio-temporal filtering induced by the focus of attention allows the system to globally transfer more information from the input stream over the focused areas and, in some contexts, over the whole frames with respect to the unfiltered case that yields uniform probability distributions.