Foundations of support constraint machines.

The mathematical foundations of a new theory for the design of intelligent agents are presented. The proposed learning paradigm is centered around the concept of constraint, representing the interactions with the environment, and the parsimony principle. The classical regularization framework of kernel machines is naturally extended to the case in which the agents interact with a richer environment, where abstract granules of knowledge, compactly described by different linguistic formalisms, can be translated into the unified notion of constraint for defining the hypothesis set. Constrained variational calculus is exploited to derive general representation theorems that provide a description of the optimal body of the agent (i.e., the functional structure of the optimal solution to the learning problem), which is the basis for devising new learning algorithms. We show that regardless of the kind of constraints, the optimal body of the agent is a support constraint machine (SCM) based on representer theorems that extend classical results for kernel machines and provide new representations. In a sense, the expressiveness of constraints yields a semantic-based regularization theory, which strongly restricts the hypothesis set of classical regularization. Some guidelines to unify continuous and discrete computational mechanisms are given so as to accommodate in the same framework various kinds of stimuli, for example, supervised examples and logic predicates. The proposed view of learning from constraints incorporates classical learning from examples and extends naturally to the case in which the examples are subsets of the input space, which is related to learning propositional logic clauses.

Deep Constraint-Based Propagation in 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.

Domain Knowledge Alleviates Adversarial Attacks in Multi-Label Classifiers.

Adversarial attacks on machine learning-based classifiers, along with defense mechanisms, have been widely studied in the context of single-label classification problems. In this paper, we shift the attention to multi-label classification, where the availability of domain knowledge on the relationships among the considered classes may offer a natural way to spot incoherent predictions, i.e., predictions associated to adversarial examples lying outside of the training data distribution. We explore this intuition in a framework in which first-order logic knowledge is converted into constraints and injected into a semi-supervised learning problem. Within this setting, the constrained classifier learns to fulfill the domain knowledge over the marginal distribution, and can naturally reject samples with incoherent predictions. Even though our method does not exploit any knowledge of attacks during training, our experimental analysis surprisingly unveils that domain-knowledge constraints can help detect adversarial examples effectively, especially if such constraints are not known to the attacker. We show how to implement an adaptive attack exploiting knowledge of the constraints and, in a specifically-designed setting, we provide experimental comparisons with popular state-of-the-art attacks. We believe that our approach may provide a significant step towards designing more robust multi-label classifiers.

A language modeling-like approach to sketching.

Sketching is a universal communication tool that, despite its simplicity, is able to efficiently express a large variety of concepts and, in some limited contexts, it can be even more immediate and effective than natural language. In this paper we explore the feasibility of using neural networks to approach sketching in the same way they are commonly used in Language Modeling. We propose a novel approach to what we refer to as "Sketch Modeling", in which a neural network is exploited to learn a probabilistic model that estimates the probability of sketches. We focus on simple sketches and, in particular, on the case in which sketches are represented as sequences of segments. Segments and sequences can be either given - when the sketches are originally drawn in this format - or automatically generated from the input drawing by means of a procedure that we designed to create short sequences, loosely inspired by the human behavior. A Recurrent Neural Network is used to learn the sketch model and, afterward, the network is seeded with an incomplete sketch that it is asked to complete, generating one segment at each time step. We propose a set of measures to evaluate the outcome of a Beam Search-based generation procedure, showing how they can be used to identify the most promising generations. Our experimental analysis assesses the feasibility of this way of modeling sketches, also in the case in which several different categories of sketches are considered.

Visual Features and Their Own Optical Flow.

Symmetries, invariances and conservation equations have always been an invaluable guide in Science to model natural phenomena through simple yet effective relations. For instance, in computer vision, translation equivariance is typically a built-in property of neural architectures that are used to solve visual tasks; networks with computational layers implementing such a property are known as Convolutional Neural Networks (CNNs). This kind of mathematical symmetry, as well as many others that have been recently studied, are typically generated by some underlying group of transformations (translations in the case of CNNs, rotations, etc.) and are particularly suitable to process highly structured data such as molecules or chemical compounds which are known to possess those specific symmetries. When dealing with video streams, common built-in equivariances are able to handle only a small fraction of the broad spectrum of transformations encoded in the visual stimulus and, therefore, the corresponding neural architectures have to resort to a huge amount of supervision in order to achieve good generalization capabilities. In the paper we formulate a theory on the development of visual features that is based on the idea that movement itself provides trajectories on which to impose consistency. We introduce the principle of Material Point Invariance which states that each visual feature is invariant with respect to the associated optical flow, so that features and corresponding velocities are an indissoluble pair. Then, we discuss the interaction of features and velocities and show that certain motion invariance traits could be regarded as a generalization of the classical concept of affordance. These analyses of feature-velocity interactions and their invariance properties leads to a visual field theory which expresses the dynamical constraints of motion coherence and might lead to discover the joint evolution of the visual features along with the associated optical flows.

Gravitational models explain shifts on human visual attention.

Visual attention refers to the human brain's ability to select relevant sensory information for preferential processing, improving performance in visual and cognitive tasks. It proceeds in two phases. One in which visual feature maps are acquired and processed in parallel. Another where the information from these maps is merged in order to select a single location to be attended for further and more complex computations and reasoning. Its computational description is challenging, especially if the temporal dynamics of the process are taken into account. Numerous methods to estimate saliency have been proposed in the last 3 decades. They achieve almost perfect performance in estimating saliency at the pixel level, but the way they generate shifts in visual attention fully depends on winner-take-all (WTA) circuitry. WTA is implemented by the biological hardware in order to select a location with maximum saliency, towards which to direct overt attention. In this paper we propose a gravitational model to describe the attentional shifts. Every single feature acts as an attractor and the shifts are the result of the joint effects of the attractors. In the current framework, the assumption of a single, centralized saliency map is no longer necessary, though still plausible. Quantitative results on two large image datasets show that this model predicts shifts more accurately than winner-take-all.

Learning in Text Streams: Discovery and Disambiguation of Entity and Relation Instances.

We consider a scenario where an artificial agent is reading a stream of text composed of a set of narrations, and it is informed about the identity of some of the individuals that are mentioned in the text portion that is currently being read. The agent is expected to learn to follow the narrations, thus disambiguating mentions and discovering new individuals. We focus on the case in which individuals are entities and relations and propose an end-to-end trainable memory network that learns to discover and disambiguate them in an online manner, performing one-shot learning and dealing with a small number of sparse supervisions. Our system builds a not-given-in-advance knowledge base, and it improves its skills while reading the unsupervised text. The model deals with abrupt changes in the narration, considering their effects when resolving coreferences. We showcase the strong disambiguation and discovery skills of our model on a corpus of Wikipedia documents and on a newly introduced data set that we make publicly available.

Asynchronous Distributed Learning From Constraints.

In this brief, the extension of the framework of Learning from Constraints (LfC) to a distributed setting where multiple parties, connected over the network, contribute to the learning process is studied. LfC relies on the generic notion of "constraint" to inject knowledge into the learning problem, and, due to its generality, it deals with possibly nonconvex constraints, enforced either in a hard or soft way. Motivated by recent progresses in the field of distributed and constrained nonconvex optimization, we apply the (distributed) asynchronous method of multipliers (ASYMM) to LfC. The study shows that such a method allows us to support scenarios where selected constraints (i.e., knowledge), data, and outcomes of the learning process can be locally stored in each computational node without being shared with the rest of the network, opening the road to further investigations into privacy-preserving LfC. Constraints act as a bridge between what is shared over the net and what is private to each node, and no central authority is required. We demonstrate the applicability of these ideas in two distributed real-world settings in the context of digit recognition and document classification.

Cognitive Action Laws: The Case of Visual Features.

This paper proposes a theory for understanding perceptual learning processes within the general framework of laws of nature. Artificial neural networks are regarded as systems whose connections are Lagrangian variables, namely, functions depending on time. They are used to minimize the cognitive action, an appropriate functional index that measures the agent interactions with the environment. The cognitive action contains a potential and a kinetic term that nicely resemble the classic formulation of regularization in machine learning. A special choice of the functional index, which leads to the fourth-order differential equations-Cognitive Action Laws (CAL)-exhibits a structure that mirrors classic formulation of machine learning. In particular, unlike the action of mechanics, the stationarity condition corresponds with the global minimum. Moreover, it is proven that typical asymptotic learning conditions on the weights can coexist with the initialization provided that the system dynamics is driven under a policy referred to as information overloading control. Finally, the theory is experimented for the problem of feature extraction in computer vision.

Gravitational Laws of Focus of Attention.

The understanding of the mechanisms behind focus of attention in a visual scene is a problem of great interest in visual perception and computer vision. In this paper, we describe a model of scanpath as a dynamic process which can be interpreted as a variational law somehow related to mechanics, where the focus of attention is subject to a gravitational field. The distributed virtual mass that drives eye movements is associated with the presence of details and motion in the video. Unlike most current models, the proposed approach does not estimate directly the saliency map, but the prediction of eye movements allows us to integrate over time the positions of interest. The process of inhibition-of-return is also supported in the same dynamic model with the purpose of simulating fixations and saccades. The differential equations of motion of the proposed model are numerically integrated to simulate scanpaths on both images and videos. Experimental results for the tasks of saliency and scanpath prediction on a wide collection of datasets are presented to support the theory. Top level performances are achieved especially in the prediction of scanpaths, which is the primary purpose of the proposed model.

Learning visual features under motion invariance.

Humans are continuously exposed to a stream of visual data with a natural temporal structure. However, most successful computer vision algorithms work at image level, completely discarding the precious information carried by motion. In this paper, we claim that processing visual streams naturally leads to formulate the motion invariance principle, which enables the construction of a new theory of learning that originates from variational principles, just like in physics. Such principled approach is well suited for a discussion on a number of interesting questions that arise in vision, and it offers a well-posed computational scheme for the discovery of convolutional filters over the retina. Differently from traditional convolutional networks, which need massive supervision, the proposed theory offers a truly new scenario for the unsupervised processing of video signals, where features are extracted in a multi-layer architecture with motion invariance. While the theory enables the implementation of novel computer vision systems, it also sheds light on the role of information-based principles to drive possible biological solutions.

Learning With Mixed Hard/Soft Pointwise Constraints.

A learning paradigm is proposed and investigated, in which the classical framework of learning from examples is enhanced by the introduction of hard pointwise constraints, i.e., constraints imposed on a finite set of examples that cannot be violated. Such constraints arise, e.g., when requiring coherent decisions of classifiers acting on different views of the same pattern. The classical examples of supervised learning, which can be violated at the cost of some penalization (quantified by the choice of a suitable loss function) play the role of soft pointwise constraints. Constrained variational calculus is exploited to derive a representer theorem that provides a description of the functional structure of the optimal solution to the proposed learning paradigm. It is shown that such an optimal solution can be represented in terms of a set of support constraints, which generalize the concept of support vectors and open the doors to a novel learning paradigm, called support constraint machines. The general theory is applied to derive the representation of the optimal solution to the problem of learning from hard linear pointwise constraints combined with soft pointwise constraints induced by supervised examples. In some cases, closed-form optimal solutions are obtained.

Learning with box kernels.

Supervised examples and prior knowledge on regions of the input space have been profitably integrated in kernel machines to improve the performance of classifiers in different real-world contexts. The proposed solutions, which rely on the unified supervision of points and sets, have been mostly based on specific optimization schemes in which, as usual, the kernel function operates on points only. In this paper, arguments from variational calculus are used to support the choice of a special class of kernels, referred to as box kernels, which emerges directly from the choice of the kernel function associated with a regularization operator. It is proven that there is no need to search for kernels to incorporate the structure deriving from the supervision of regions of the input space, because the optimal kernel arises as a consequence of the chosen regularization operator. Although most of the given results hold for sets, we focus attention on boxes, whose labeling is associated with their propositional description. Based on different assumptions, some representer theorems are given that dictate the structure of the solution in terms of box kernel expansion. Successful results are given for problems of medical diagnosis, image, and text categorization.

Constraint verification with kernel machines.

Based on a recently proposed framework of learning from constraints using kernel-based representations, in this brief, we naturally extend its application to the case of inferences on new constraints. We give examples for polynomials and first-order logic by showing how new constraints can be checked on the basis of given premises and data samples. Interestingly, this gives rise to a perceptual logic scheme in which the inference mechanisms do not rely only on formal schemes, but also on the data probability distribution. It is claimed that when using a properly relaxed computational checking approach, the complementary role of data samples makes it possible to break the complexity barriers of related formal checking mechanisms.

Unsupervised learning by minimal entropy encoding.

Following basic principles of information-theoretic learning, in this paper, we propose a novel approach to data clustering, referred to as minimal entropy encoding (MEE), which is based on a set of functions (features) projecting each input onto a minimum entropy configuration (code). Inspired by traditional parsimony principles, we seek solutions in reproducing kernel Hilbert spaces and then we prove that the encoding functions are expressed in terms of kernel expansion. In order to avoid trivial solutions, the developed features must be as different as possible by means of a soft constraint on the empirical estimation of the entropy associated with the encoding functions. This leads to an unconstrained optimization problem that can be efficiently solved by conjugate gradient. We also investigate an optimization strategy based on concave-convex algorithms. The relationships with maximum margin clustering are studied, showing that MEE overcomes some of its critical issues, such as the lack of a multiclass extension and the need to face problems with a large number of constraints. A massive evaluation on several benchmarks of the proposed approach shows improvements over state-of-the-art techniques, both in terms of accuracy and computational complexity.

Learning from pairwise constraints by Similarity Neural Networks.

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.