A random energy approach to deep learning

We present E NERGY N ET , a new framework for analyzing and building artificial neural network architectures. Our approach adaptively learns the structure of the networks in an unsupervised manner. The methodology is based upon the theoretical guarantees of the energy function of restricted Boltzmann machines (RBM) of infinite number of nodes. We present experimental results to show that the final network adapts to the complexity of a given problem.

Deep learning architectures have been widely fostered throughout the last years, being used in a wide range of applications, such as object recognition, image reconstruction, and signal processing. Nevertheless, such models suffer from a common problem known as overfitting, which limits the network from predicting unseen data effectively. Regularization approaches arise in an attempt to address such a shortcoming. Among them, one can refer to the well-known Dropout, which tac...

In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the hidden layers of DNNs formulate Gibbs distributions; and (iii) the whole architecture of DNNs can be interpreted as a Bayesian neural network. Based on the proposed probabilistic representation, we investigate two fundamental properties of d...

It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, the focus has been on shallow neural networks. A natural question to ask is whether deep neural networks hold any advantage over shallow networks in representing such data. We investigate this question by using unsupervis...

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to arrive at accurate and predictive models. It is hitherto unknown why are deep neural networks easily optimizable. We analyze the energy landscape of a spin glass model of deep neural networks using random matrix theory and algebraic geometry. ...

This is a tutorial and survey paper on Boltzmann Machine (BM), Restricted Boltzmann Machine (RBM), and Deep Belief Network (DBN). We start with the required background on probabilistic graphical models, Markov random field, Gibbs sampling, statistical physics, Ising model, and the Hopfield network. Then, we introduce the structures of BM and RBM. The conditional distributions of visible and hidden variables, Gibbs sampling in RBM for generating variables, training BM and RBM ...

This work maps deep neural networks to classical Ising spin models, allowing them to be described using statistical thermodynamics. The density of states shows that structures emerge in the weights after they have been trained -- well-trained networks span a much wider range of realizable energies compared to poorly trained ones. These structures propagate throughout the entire network and are not observed in individual layers. The energy values correlate to performance on ta...

Thanks to the availability of large scale digital datasets and massive amounts of computational power, deep learning algorithms can learn representations of data by exploiting multiple levels of abstraction. These machine learning methods have greatly improved the state-of-the-art in many challenging cognitive tasks, such as visual object recognition, speech processing, natural language understanding and automatic translation. In particular, one class of deep learning models,...

Throughout the last years, machine learning techniques have been broadly encouraged in the context of deep learning architectures. An exciting algorithm denoted as Restricted Boltzmann Machine relies on energy- and probabilistic-based nature to tackle the most diverse applications, such as classification, reconstruction, and generation of images and signals. Nevertheless, one can see they are not adequately renowned compared to other well-known deep learning techniques, e.g.,...

The success of deep learning in many real-world tasks has triggered an intense effort to understand the power and limitations of deep learning in the training and generalization of complex tasks, so far with limited progress. In this work, we study the statistical mechanics of learning in Deep Linear Neural Networks (DLNNs) in which the input-output function of an individual unit is linear. Despite the linearity of the units, learning in DLNNs is nonlinear, hence studying its...