arXiv subjects

Marco Gori

Publications and source records attributed to Marco Gori.

87 records · Page 5Linked to original sources

arXiv2019

Integrating Learning and Reasoning with Deep Logic Models

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take consistent and robust decisions in complex environments. The integration of deep learning and logic reasoning is still an open-research problem and it is considered to be the key for the development of real intelligent agents. This paper presents Deep Logic Models, which are deep graphical models integrating deep learning and logic reasoning both for learning and inference. Deep Logic Models create an end-to-end differentiable architecture, where deep learners are embedded into a network implementing a continuous relaxation of the logic knowledge. The learning process allows to jointly learn the weights of the deep learners and the meta-parameters controlling the high-level reasoning. The experimental results show that the proposed methodology overtakes the limitations of the other approaches that have been proposed to bridge deep learning and reasoning.

cs.LG↗

arXiv2018

On a Convex Logic Fragment for Learning and Reasoning

In this paper we introduce the convex fragment of Łukasiewicz Logic and discuss its possible applications in different learning schemes. Indeed, the provided theoretical results are highly general, because they can be exploited in any learning framework involving logical constraints. The method is of particular interest since the fragment guarantees to deal with convex constraints, which are shown to be equivalent to a set of linear constraints. Within this framework, we are able to formulate learning with kernel machines as well as collective classification as a quadratic programming problem.

cs.LO↗

arXiv2018

Coherence Constraints in Facial Expression Recognition

Recognizing facial expressions from static images or video sequences is a widely studied but still challenging problem. The recent progresses obtained by deep neural architectures, or by ensembles of heterogeneous models, have shown that integrating multiple input representations leads to state-of-the-art results. In particular, the appearance and the shape of the input face, or the representations of some face parts, are commonly used to boost the quality of the recognizer. This paper investigates the application of Convolutional Neural Networks (CNNs) with the aim of building a versatile recognizer of expressions in static images that can be further applied to video sequences. We first study the importance of different face parts in the recognition task, focussing on appearance and shape-related features. Then we cast the learning problem in the Semi-Supervised setting, exploiting video data, where only a few frames are supervised. The unsupervised portion of the training data is used to enforce three types of coherence, namely temporal coherence, coherence among the predictions on the face parts and coherence between appearance and shape-based representation. Our experimental analysis shows that coherence constraints can improve the quality of the expression recognizer, thus offering a suitable basis to profitably exploit unsupervised video sequences. Finally we present some examples with occlusions where the shape-based predictor performs better than the appearance one.

cs.CV↗

arXiv2018

Learning Neuron Non-Linearities with Kernel-Based Deep Neural Networks

The effectiveness of deep neural architectures has been widely supported in terms of both experimental and foundational principles. There is also clear evidence that the activation function (e.g. the rectifier and the LSTM units) plays a crucial role in the complexity of learning. Based on this remark, this paper discusses an optimal selection of the neuron non-linearity in a functional framework that is inspired from classic regularization arguments. It is shown that the best activation function is represented by a kernel expansion in the training set, that can be effectively approximated over an opportune set of points modeling 1-D clusters. The idea can be naturally extended to recurrent networks, where the expressiveness of kernel-based activation functions turns out to be a crucial ingredient to capture long-term dependencies. We give experimental evidence of this property by a set of challenging experiments, where we compare the results with neural architectures based on state of the art LSTM cells.

cs.LG↗

arXiv2018

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. 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 forth-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.

cs.CV↗

arXiv2018

Backpropagation and Biological Plausibility

By and large, Backpropagation (BP) is regarded as one of the most important neural computation algorithms at the basis of the progress in machine learning, including the recent advances in deep learning. However, its computational structure has been the source of many debates on its arguable biological plausibility. In this paper, it is shown that when framing supervised learning in the Lagrangian framework, while one can see a natural emergence of Backpropagation, biologically plausible local algorithms can also be devised that are based on the search for saddle points in the learning adjoint space composed of weights, neural outputs, and Lagrangian multipliers. This might open the doors to a truly novel class of learning algorithms where, because of the introduction of the notion of support neurons, the optimization scheme also plays a fundamental role in the construction of the architecture.

cs.AI↗

arXiv2018

Generalization in quasi-periodic environments

By and large the behavior of stochastic gradient is regarded as a challenging problem, and it is often presented in the framework of statistical machine learning. This paper offers a novel view on the analysis of on-line models of learning that arises when dealing with a generalized version of stochastic gradient that is based on dissipative dynamics. In order to face the complex evolution of these models, a systematic treatment is proposed which is based on energy balance equations that are derived by means of the Caldirola-Kanai (CK) Hamiltonian. According to these equations, learning can be regarded as an ordering process which corresponds with the decrement of the loss function. Finally, the main results established in this paper is that in the case of quasi-periodic environments, where the pattern novelty is progressively limited as time goes by, the system dynamics yields an asymptotically consistent solution in the weight space, that is the solution maps similar patterns to the same decision.

cs.LG↗

arXiv2018

Motion Invariance in Visual Environments

The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams, just as happens in nature. In this paper, we claim that their processing naturally leads to formulate the motion invariance principle, which enables the construction of a new theory of visual learning based on convolutional features. The theory addresses a number of intriguing questions that arise in natural vision, and offers a well-posed computational scheme for the discovery of convolutional filters over the retina. They are driven by the Euler-Lagrange differential equations derived from the principle of least cognitive action, that parallels laws of mechanics. Unlike traditional convolutional networks, which need massive supervision, the proposed theory offers a truly new scenario in which feature learning takes place by unsupervised processing of video signals. An experimental report of the theory is presented where we show that features extracted under motion invariance yield an improvement that can be assessed by measuring information-based indexes.

cs.CV↗

arXiv2018

Visual Attention driven by Convolutional Features

The understanding of where humans look in a scene is a problem of great interest in visual perception and computer vision. When eye-tracking devices are not a viable option, models of human attention can be used to predict fixations. In this paper we give two contribution. First, we show a model of visual attention that is simply based on deep convolutional neural networks trained for object classification tasks. A method for visualizing saliency maps is defined which is evaluated in a saliency prediction task. Second, we integrate the information of these maps with a bottom-up differential model of eye-movements to simulate visual attention scanpaths. Results on saliency prediction and scores of similarity with human scanpaths demonstrate the effectiveness of this model.

cs.CV↗

arXiv2018

Trees in the Real Field

This paper proposes an algebraic view of trees which opens the doors to an alternative computational scheme with respect to classic algorithms. In particular, it is shown that this view is very well-suited for machine learning and computational linguistics.

cs.DM↗

arXiv2018

Convolutional Networks in Visual Environments

The puzzle of computer vision might find new challenging solutions when we realize that most successful methods are working at image level, which is remarkably more difficult than processing directly visual streams. In this paper, we claim that their processing naturally leads to formulate the motion invariance principle, which enables the construction of a new theory of learning with convolutional networks. The theory addresses a number of intriguing questions that arise in natural vision, and offers a well-posed computational scheme for the discovery of convolutional filters over the retina. They are driven by differential equations derived from the principle of least cognitive action. Unlike traditional convolutional networks, which need massive supervision, the proposed theory offers a truly new scenario in which feature learning takes place by unsupervised processing of video signals. It is pointed out that an opportune blurring of the video, along the interleaving of segments of null signal, make it possible to conceive a novel learning mechanism that yields the minimum of the cognitive action. Basically, while the theory enables the implementation of novel computer vision systems, it is also provides an intriguing explanation of the solution that evolution has discovered for humans, where it looks like that the video blurring in newborns and the day-night rhythm seem to emerge in a general computational framework, regardless of biology.

cs.CV↗

arXiv2017

The principle of cognitive action - Preliminary experimental analysis

In this document we shows a first implementation and some preliminary results of a new theory, facing Machine Learning problems in the frameworks of Classical Mechanics and Variational Calculus. We give a general formulation of the problem and then we studies basic behaviors of the model on simple practical implementations.

cs.LG↗

arXiv2017

Collapsing of dimensionality

We analyze a new approach to Machine Learning coming from a modification of classical regularization networks by casting the process in the time dimension, leading to a sort of collapse of dimensionality in the problem of learning the model parameters. This approach allows the definition of a online learning algorithm that progressively accumulates the knowledge provided in the input trajectory. The regularization principle leads to a solution based on a dynamical system that is paired with a procedure to develop a graph structure that stores the input regularities acquired from the temporal evolution. We report an extensive experimental exploration on the behavior of the parameter of the proposed model and an evaluation on artificial dataset.

cs.LG↗

arXiv2016

LQG Online Learning

Optimal control theory and machine learning techniques are combined to formulate and solve in closed form an optimal control formulation of online learning from supervised examples with regularization of the updates. The connections with the classical Linear Quadratic Gaussian (LQG) optimal control problem, of which the proposed learning paradigm is a non-trivial variation as it involves random matrices, are investigated. The obtained optimal solutions are compared with the Kalman-filter estimate of the parameter vector to be learned. It is shown that the proposed algorithm is less sensitive to outliers with respect to the Kalman estimate (thanks to the presence of the regularization term), thus providing smoother estimates with respect to time. The basic formulation of the proposed online-learning framework refers to a discrete-time setting with a finite learning horizon and a linear model. Various extensions are investigated, including the infinite learning horizon and, via the so-called "kernel trick", the case of nonlinear models.

math.OC↗

arXiv2014

Learning to see like children: proof of concept

In the last few years we have seen a growing interest in machine learning approaches to computer vision and, especially, to semantic labeling. Nowadays state of the art systems use deep learning on millions of labeled images with very successful results on benchmarks, though it is unlikely to expect similar results in unrestricted visual environments. Most learning schemes essentially ignore the inherent sequential structure of videos: this might be a critical issue, since any visual recognition process is remarkably more complex when shuffling video frames. Based on this remark, we propose a re-foundation of the communication protocol between visual agents and the environment, which is referred to as learning to see like children. Like for human interaction, visual concepts are acquired by the agents solely by processing their own visual stream along with human supervisions on selected pixels. We give a proof of concept that remarkable semantic labeling can emerge within this protocol by using only a few supervised examples. This is made possible by exploiting a constraint of motion coherent labeling that virtually offers tons of supervisions. Additional visual constraints, including those associated with object supervisions, are used within the context of learning from constraints. The framework is extended in the direction of lifelong learning, so as our visual agents live in their own visual environment without distinguishing learning and test set. Learning takes place in deep architectures under a progressive developmental scheme. In order to evaluate our Developmental Visual Agents (DVAs), in addition to classic benchmarks, we open the doors of our lab, allowing people to evaluate DVAs by crowd-sourcing. Such assessment mechanism might result in a paradigm shift in methodologies and algorithms for computer vision, encouraging truly novel solutions within the proposed framework.

cs.CV↗