Restricted Boltzmann machines (RBMs) are a powerful class of generative models, but their training requires computing a gradient that, unlike supervised backpropagation on typical loss functions, is notoriously difficult even to approximate. Here, we show that properly combining standard gradient updates with an off-gradient direction, constructed from samples of the RBM ground state (mode), improves their training dramatically over traditional gradient methods. This approach, which we call mode training, promotes faster training and stability, in addition to lower converged relative entropy (KL divergence). Along with the proofs of stability and convergence of this method, we also demonstrate its efficacy on synthetic datasets where we can compute KL divergences exactly, as well as on a larger machine learning standard, MNIST. The mode training we suggest is quite versatile, as it can be applied in conjunction with any given gradient method, and is easily extended to more general energy-based neural network structures such as deep, convolutional and unrestricted Boltzmann machines.
Texas A & M University（德克萨斯农工大学）；ABB Corporate Research（ABB企业研究院）；TOTVS Labs（TOTVS实验室）
Dimensionality reduction is considered as an important step for ensuring competitive performance in unsupervised learning such as anomaly detection. Non-negative matrix factorization (NMF) is a popular and widely used method to accomplish this goal. But NMF do not have the provision to include the neighborhood structure information and, as a result, may fail to provide satisfactory performance in presence of nonlinear manifold structure. To address that shortcoming, we propose to consider and incorporate the neighborhood structural similarity information within the NMF framework by modeling th…
OWKIN, Inc.（OWKIN公司）；École Normale Supérieure, PSL University（巴黎文理研究大学巴黎高等师范学院）；Snips（Snips公司）；Université Pierre et Marie Curie, Sorbonne Universités（索邦大学皮埃尔与玛丽·居里大学）；LightOn（LightOn公司）
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which are commonly used as the building blocks for deep architectures neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field approximation of widely-connected systems with weak interactions coming from spin-glass theory. While the TAP approach has been extensively studied for fully-visible binary spin systems, our construction is generalized to latent-variable models, as well as to arbitrarily distributed r…
We introduce Delay Pruning, a simple yet powerful technique to regularize dynamic Boltzmann machines (DyBM). The recently introduced DyBM provides a particularly structured Boltzmann machine, as a generative model of a multi-dimensional time-series. This Boltzmann machine can have infinitely many layers of units but allows exact inference and learning based on its biologically motivated structure. DyBM uses the idea of conduction delays in the form of fixed length first-in first-out (FIFO) queues, with a neuron connected to another via this FIFO queue, and spikes from a pre-synaptic neuron tra…
Universidad Autónoma de Nuevo León（新莱昂自治大学）；Facultad de Ingeniería Mecánica y Eléctrica（机械与电气工程学院）；Facultad de Ciencias Físico Matemáticas（物理数学学院）
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
Georgia Tech Institute of People and Technology（佐治亚理工学院人与技术研究所）
We present a new approach for detecting related crime series, by unsupervised learning of the latent feature embeddings from narratives of crime record via the Gaussian-Bernoulli Restricted Boltzmann Machines (RBM). This is a drastically different approach from prior work on crime analysis, which typically considers only time and location and at most category information. After the embedding, related cases are closer to each other in the Euclidean feature space, and the unrelated cases are far apart, which is a good property can enable subsequent analysis such as detection and clustering of re…
In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights $w_{ij}$ and the bias parameters $θ= ( a_i, b_j) $ that maximize the energy function and assignment element $i$ to element $j$. An application of real problem is presented to show the potentiality of this algorithm.
Deep neural networks (DNNs) provide high image classification accuracy, but experience significant performance degradation when perturbation from various sources are present in the input. The lack of resilience to input perturbations makes DNN less reliable for systems interacting with physical world such as autonomous vehicles, robotics, to name a few, where imperfect input is the normal condition. We present a hybrid deep network architecture with spike-assisted contextual information extraction (ScieNet). ScieNet integrates unsupervised learning using spiking neural network (SNN) for unsupe…
Commercial activity trackers are set to become an essential tool in health research, due to increasing availability in the general population. The corresponding vast amounts of mostly unlabeled data pose a challenge to statistical modeling approaches. To investigate the feasibility of deep learning approaches for unsupervised learning with such data, we examine weekly usage patterns of Fitbit activity trackers with deep Boltzmann machines (DBMs). This method is particularly suitable for modeling complex joint distributions via latent variables. We also chose this specific procedure because it …
Intel Labs（英特尔实验室）；University of California Berkeley（加州大学伯克利分校）
We extend the framework of Boltzmann machines to a network of complex-valued neurons with variable amplitudes, referred to as Complex Amplitude-Phase Boltzmann machine (CAP-BM). The model is capable of performing unsupervised learning on the amplitude and relative phase distribution in complex data. The sampling rule of the Gibbs distribution and the learning rules of the model are presented. Learning in a Complex Amplitude-Phase restricted Boltzmann machine (CAP-RBM) is demonstrated on synthetic complex-valued images, and handwritten MNIST digits transformed by a complex wavelet transform. Sp…
For better classification generative models are used to initialize the model and model features before training a classifier. Typically it is needed to solve separate unsupervised and supervised learning problems. Generative restricted Boltzmann machines and deep belief networks are widely used for unsupervised learning. We developed several supervised models based on DBN in order to improve this two-phase strategy. Modifying the loss function to account for expectation with respect to the underlying generative model, introducing weight bounds, and multi-level programming are applied in model …
A method to control results of gradient descent unsupervised learning in a deep neural network by using evolutionary algorithm is proposed. To process crossover of unsupervisedly trained models, the algorithm evaluates pointwise fitness of individual nodes in neural network. Labeled training data is randomly sampled and breeding process selects nodes by calculating degree of their consistency on different sets of sampled data. This method supervises unsupervised training by evolutionary process. We also introduce modified Restricted Boltzmann Machine which contains repulsive force among nodes …
Unsupervised feature learning has shown impressive results for a wide range of input modalities, in particular for object classification tasks in computer vision. Using a large amount of unlabeled data, unsupervised feature learning methods are utilized to construct high-level representations that are discriminative enough for subsequently trained supervised classification algorithms. However, it has never been \emph{quantitatively} investigated yet how well unsupervised learning methods can find \emph{low-level representations} for image patches without any additional supervision. In this pap…
Unsupervised learning requiring only raw data is not only a fundamental function of the cerebral cortex, but also a foundation for a next generation of artificial neural networks. However, a unified theoretical framework to treat sensory inputs, synapses and neural activity together is still lacking. The computational obstacle originates from the discrete nature of synapses, and complex interactions among these three essential elements of learning. Here, we propose a variational mean-field theory in which the distribution of synaptic weights is considered. The unsupervised learning can then be…
Università del Salento（萨伦托大学）；Universität Zürich（苏黎世大学）；King College London（伦敦国王学院）；Scuola Normale Superiore（比萨高等师范学校）
We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that retrieval is robust for a large class of weight and unit priors, beyond the standard Hopfield scenario. Furthermore we show how the paramagnetic phase boundary is directly related to the optimal size of the…
In recent years, deep learning methods applying unsupervised learning to train deep layers of neural networks have achieved remarkable results in numerous fields. In the past, many genetic algorithms based methods have been successfully applied to training neural networks. In this paper, we extend previous work and propose a GA-assisted method for deep learning. Our experimental results indicate that this GA-assisted approach improves the performance of a deep autoencoder, producing a sparser neural network.
Tufts University（塔夫茨大学）；University of Cambridge（剑桥大学）；City University of Hong Kong（香港城市大学）；Wake Forest University（维克森林大学）
Ash dieback (Hymenoscyphus fraxineus) is an introduced fungal disease that is causing the widespread death of ash trees across Europe. Remote sensing hyperspectral images encode rich structure that has been exploited for the detection of dieback disease in ash trees using supervised machine learning techniques. However, to understand the state of forest health at landscape-scale, accurate unsupervised approaches are needed. This article investigates the use of the unsupervised Diffusion and VCA-Assisted Image Segmentation (D-VIS) clustering algorithm for the detection of ash dieback disease in…
Understanding the results of deep neural networks is an essential step towards wider acceptance of deep learning algorithms. Many approaches address the issue of interpreting artificial neural networks, but often provide divergent explanations. Moreover, different hyperparameters of an explanatory method can lead to conflicting interpretations. In this paper, we propose a technique for aggregating the feature attributions of different explanatory algorithms using Restricted Boltzmann Machines (RBMs) to achieve a more reliable and robust interpretation of deep neural networks. Several challengi…
This study develops an unsupervised learning algorithm for products of expert capsules with dynamic routing. Analogous to binary-valued neurons in Restricted Boltzmann Machines, the magnitude of a squashed capsule firing takes values between zero and one, representing the probability of the capsule being on. This analogy motivates the design of an energy function for capsule networks. In order to have an efficient sampling procedure where hidden layer nodes are not connected, the energy function is made consistent with dynamic routing in the sense of the probability of a capsule firing, and in…
The deep extension of the restricted Boltzmann machine (RBM), known as the deep Boltzmann machine (DBM), is an expressive family of machine learning models which can serve as compact representations of complex probability distributions. However, jointly training DBMs in the unsupervised setting has proven to be a formidable task. A recent technique we have proposed, called mode-assisted training, has shown great success in improving the unsupervised training of RBMs. Here, we show that the performance gains of the mode-assisted training are even more dramatic for DBMs. In fact, DBMs jointly tr…
Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks with two or more hidden units. However, a theoretical study of the permutation symmetry is still lacking. Here, we propose a minimal model with only two hidden units in a restricted Boltzmann machine, which aims to address how the permutation symmetry affects the critical learning data size at which the concept-formation (or spontaneous symmetry breaking in p…
Revealing hidden features in unlabeled data is called unsupervised feature learning, which plays an important role in pretraining a deep neural network. Here we provide a statistical mechanics analysis of the unsupervised learning in a restricted Boltzmann machine with binary synapses. A message passing equation to infer the hidden feature is derived, and furthermore, variants of this equation are analyzed. A statistical analysis by replica theory describes the thermodynamic properties of the model. Our analysis confirms an entropy crisis preceding the non-convergence of the message passing eq…
Interpretation of medical images for diagnosis and treatment of complex disease from high-dimensional and heterogeneous data remains a key challenge in transforming healthcare. In the last few years, both supervised and unsupervised deep learning achieved promising results in the area of medical imaging and image analysis. Unlike supervised learning which is biased towards how it is being supervised and manual efforts to create class label for the algorithm, unsupervised learning derive insights directly from the data itself, group the data and help to make data driven decisions without any ex…
RMIT University（皇家墨尔本理工大学）；The University of Melbourne（墨尔本大学）；Ford Motor Company（福特汽车公司）
Distribution shift between train (source) and test (target) datasets is a common problem encountered in machine learning applications. One approach to resolve this issue is to use the Unsupervised Domain Adaptation (UDA) technique that carries out knowledge transfer from a label-rich source domain to an unlabeled target domain. Outliers that exist in either source or target datasets can introduce additional challenges when using UDA in practice. In this paper, $α$-divergence is used as a measure to minimize the discrepancy between the source and target distributions while inheriting robustness…
Hong Kong University of Science and Technology（香港科技大学）
We are interested in exploring the possibility and benefits of structure learning for deep models. As the first step, this paper investigates the matter for Restricted Boltzmann Machines (RBMs). We conduct the study with Replicated Softmax, a variant of RBMs for unsupervised text analysis. We present a method for learning what we call Sparse Boltzmann Machines, where each hidden unit is connected to a subset of the visible units instead of all of them. Empirical results show that the method yields models with significantly improved model fit and interpretability as compared with RBMs where eac…
Beijing Normal University（北京师范大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Swarma Research（集智研究院）；Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院）；International Centre for Theoretical Physics Asia-Pacific（亚太国际理论物理中心）
Modeling the joint distribution of high-dimensional data is a central task in unsupervised machine learning. In recent years, many interests have been attracted to developing learning models based on tensor networks, which have the advantages of a principle understanding of the expressive power using entanglement properties, and as a bridge connecting classical computation and quantum computation. Despite the great potential, however, existing tensor network models for unsupervised machine learning only work as a proof of principle, as their performance is much worse than the standard models s…
Johannes Gutenberg-University Mainz（美因茨约翰内斯·古腾堡大学）
We propose an alternative method for training a classification model. Using the MNIST set of handwritten digits and Restricted Boltzmann Machines, it is possible to reach a classification performance competitive to semi-supervised learning if we first train a model in an unsupervised fashion on unlabeled data only, and then manually add labels to model samples instead of training data samples with the help of a GUI. This approach can benefit from the fact that model samples can be presented to the human labeler in a video-like fashion, resulting in a higher number of labeled examples. Also, af…
Purdue University（普渡大学）；Oak Ridge National Laboratory（橡树岭国家实验室）
Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate exact gradient of log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), which is much faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results are compared with CD. The classification accuracy …
KTH Royal Institute of Technology（瑞典皇家理工学院）；Stockholm University（斯德哥尔摩大学）
Unsupervised learning of hidden representations has been one of the most vibrant research directions in machine learning in recent years. In this work we study the brain-like Bayesian Confidence Propagating Neural Network (BCPNN) model, recently extended to extract sparse distributed high-dimensional representations. The usefulness and class-dependent separability of the hidden representations when trained on MNIST and Fashion-MNIST datasets is studied using an external linear classifier and compared with other unsupervised learning methods that include restricted Boltzmann machines and autoen…
Nanjing University of Posts and Telecommunications（南京邮电大学）
Domain alignment (DA) has been widely used in unsupervised domain adaptation. Many existing DA methods assume that a low source risk, together with the alignment of distributions of source and target, means a low target risk. In this paper, we show that this does not always hold. We thus propose a novel metric-learning-assisted domain adaptation (MLA-DA) method, which employs a novel triplet loss for helping better feature alignment. We explore the relationship between the second largest probability of a target sample's prediction and its distance to the decision boundary. Based on the relatio…
Glioblastoma is profoundly heterogeneous in microstructure and vasculature, which may lead to tumor regional diversity and distinct treatment response. Although successful in tumor sub-region segmentation and survival prediction, radiomics based on machine learning algorithms, is challenged by its robustness, due to the vague intermediate process and track changes. Also, the weak interpretability of the model poses challenges to clinical application. Here we proposed a machine learning framework to semi-automatically fine-tune the clustering algorithms and quantitatively identify stable sub-re…
Latent truth discovery, LTD for short, refers to the problem of aggregating ltiple claims from various sources in order to estimate the plausibility of atements about entities. In the absence of a ground truth, this problem is highly challenging, when some sources provide conflicting claims and others no claims at all. In this work we provide an unsupervised stochastic inference procedure on top of a model that combines restricted Boltzmann machines with feed-forward neural networks to accurately infer the reliability of sources as well as the plausibility of statements about entities. In comp…
École Normale Supérieure, PSL Research University（巴黎高等师范学院，PSL研究大学）；Université Pierre et Marie Curie, Sorbonne Universités（皮埃尔和玛丽·居里大学，索邦大学）；INRIA Paris（法国国家信息与自动化研究所巴黎中心）
In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine, can be trained in an unsupervised manner on example signals, we demonstrate how this signal model can be used within a Bayesian framework of signal reconstruction. By deriving a message-passing inference for general distribution restricted Boltzmann machines, we are able to integrate these inferred signal models into approximate message passing for compress…
Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；University of Waterloo（滑铁卢大学）
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance-sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generat…
The possibility of employing restricted Boltzmann machine (RBM) for collaborative filtering has been known for about a decade. However, there has been hardly any work on this topic since 2007. This work revisits the application of RBM in recommender systems. RBM based collaborative filtering only used the rating information; this is an unsupervised architecture. This work adds supervision by exploiting user demographic information and item metadata. A network is learned from the representation layer to the labels (metadata). The proposed label consistent RBM formulation improves significantly …
This work presents an unsupervised deep learning scheme that exploiting high-dimensional assisted score-based generative model for color image restoration tasks. Considering that the sample number and internal dimension in score-based generative model have key influence on estimating the gradients of data distribution, two different high-dimensional ways are proposed: The channel-copy transformation increases the sample number and the pixel-scale transformation decreases feasible space dimension. Subsequently, a set of high-dimensional tensors represented by these transformations are used to t…
Imperial College London（帝国理工学院）；King’s College London（伦敦国王学院）
Large-scale automated meta-analysis of neuroimaging data has recently established itself as an important tool in advancing our understanding of human brain function. This research has been pioneered by NeuroSynth, a database collecting both brain activation coordinates and associated text across a large cohort of neuroimaging research papers. One of the fundamental aspects of such meta-analysis is text-mining. To date, word counts and more sophisticated methods such as Latent Dirichlet Allocation have been proposed. In this work we present an unsupervised study of the NeuroSynth text corpus us…
Tianjin University（天津大学）；The Open University（开放大学）；The Hong Kong Polytechnic University（香港理工大学）
Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the scale of data features. This paper aims to address the problem from a new perspective and considers model-oriented dimensionality reduction in parameter spaces of binary multivariate distributions. Specifically, we propose a general parameter reduction criterion, called Confident-In…
Laboratoire de Physique Statistique（统计物理实验室）；CNRS（法国国家科学研究中心）；École Normale Supérieure（巴黎高等师范学院）；PSL Research University（巴黎文理研究大学）；International Centre for Fundamental Physics and its interfaces at Ecole normale supérieure（巴黎高等师范学院基础物理及其交叉学科国际中心）；Sorbonne Universités（索邦大学联盟）；UPMC Univ Paris 06（巴黎第六大学（皮埃尔和玛丽·居里大学））
Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their success is the existence of efficient and practical stochastic algorithms, such as contrastive divergence, for unsupervised training. We propose an alternative deterministic iterative procedure based on an improved mean field method from statistical physics known as the Thouless-Anderson-Palmer approach. We demonstrate that our algorithm provides performance …
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心（CEMS））；The University of Tokyo（东京大学）
Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not directly accessible due to its computational complexity, and Markov-chain sampling is invoked to analyze the learned probability distribution. For training and eventual applications, it is thus desirable to have a sampler that is both accurate and efficient. We highlight that these two goals generally compete with each other and cannot be achieved simultaneously.…
Center for Pattern Recognition and Data Analytics, Deakin University（迪肯大学模式识别与数据分析中心）
The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation learning schemes, restricted Boltzmann machines (RBMs) have proved to be highly effective in unsupervised settings. However, when it comes to parts-based discovery, RBMs do not usually produce satisfactory results. We enhance such capacity of RBMs by introducing nonnegativity into the model weights, resulting in a variant called nonnegative restricted Boltz…
Nagoya University（名古屋大学）；Nagoya University Graduate School of Medicine（名古屋大学医学研究科）
This paper proposes a novel, unsupervised super-resolution (SR) approach for performing the SR of a clinical CT into the resolution level of a micro CT ($μ$CT). The precise non-invasive diagnosis of lung cancer typically utilizes clinical CT data. Due to the resolution limitations of clinical CT (about $0.5 \times 0.5 \times 0.5$ mm$^3$), it is difficult to obtain enough pathological information such as the invasion area at alveoli level. On the other hand, $μ$CT scanning allows the acquisition of volumes of lung specimens with much higher resolution ($50 \times 50 \times 50 μ{\rm m}^3$ or hig…
Peking University（北京大学）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an effic…
LPENS（巴黎高等师范学院物理实验室）；Ecole Normale Supérieure（巴黎高等师范学院）；PSL Research（PSL研究大学）；Blavatnik School of Computer Science（布拉瓦特尼克计算机科学学院）；Tel Aviv University（特拉维夫大学）
Distributions of data or sensory stimuli often enjoy underlying invariances. How and to what extent those symmetries are captured by unsupervised learning methods is a relevant question in machine learning and in computational neuroscience. We study here, through a combination of numerical and analytical tools, the learning dynamics of Restricted Boltzmann Machines (RBM), a neural network paradigm for representation learning. As learning proceeds from a random configuration of the network weights, we show the existence of, and characterize a symmetry-breaking phenomenon, in which the latent va…
Southwest Jiaotong University（西南交通大学）；Leshan Normal University（乐山师范学院）
Restricted Boltzmann machines (RBMs) and their variants are usually trained by contrastive divergence (CD) learning, but the training procedure is an unsupervised learning approach, without any guidances of the background knowledge. To enhance the expression ability of traditional RBMs, in this paper, we propose pairwise constraints restricted Boltzmann machine with Gaussian visible units (pcGRBM) model, in which the learning procedure is guided by pairwise constraints and the process of encoding is conducted under these guidances. The pairwise constraints are encoded in hidden layer features …
Laboratory of Physics of the \'Ecole Normale Sup\'erieure, CNRS UMR 8023 \& PSL Research, Sorbonne Universit\'e, 24 rue Lhomond, 75005 Paris, France
Restricted Boltzmann Machines (RBM) are bi-layer neural networks used for the unsupervised learning of model distributions from data. The bipartite architecture of RBM naturally defines an elegant sampling procedure, called Alternating Gibbs Sampling (AGS), where the configurations of the latent-variable layer are sampled conditional to the data-variable layer, and vice versa. We study here the performance of AGS on several analytically tractable models borrowed from statistical mechanics. We show that standard AGS is not more efficient than classical Metropolis-Hastings (MH) sampling of the e…
Unsupervised neural network learning extracts hidden features from unlabeled training data. This is used as a pretraining step for further supervised learning in deep networks. Hence, understanding unsupervised learning is of fundamental importance. Here, we study the unsupervised learning from a finite number of data, based on the restricted Boltzmann machine learning. Our study inspires an efficient message passing algorithm to infer the hidden feature, and estimate the entropy of candidate features consistent with the data. Our analysis reveals that the learning requires only a few data if …
Limitations of Quantum Advantage in Unsupervised Machine Learning
Centre for High Energy Physics, Indian Institute of Science, Bangalore（高能物理中心，印度科学研究院，班加罗尔）；International Centre for Theoretical Sciences, Bangalore（理论科学国际中心，班加罗尔）
Perimeter Institute for Theoretical Physics（理论物理圆周研究所）；University of Waterloo（滑铁卢大学）
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 unsupervised, generative graphical models to learn the probability distribution of a two-dimensional Ising system. Deep Boltzmann …
Hiroshima City University（广岛市立大学）；Prefectural University of Hiroshima（广岛县立大学）
Restricted Boltzmann Machine (RBM) is a generative stochastic energy-based model of artificial neural network for unsupervised learning. Recently, RBM is well known to be a pre-training method of Deep Learning. In addition to visible and hidden neurons, the structure of RBM has a number of parameters such as the weights between neurons and the coefficients for them. Therefore, we may meet some difficulties to determine an optimal network structure to analyze big data. In order to evade the problem, we investigated the variance of parameters to find an optimal structure during learning. For the…
Laboratory of Physics of the Ecole Normale Supérieure, CNRS & PSL Research（巴黎高等师范学院物理实验室、法国国家科学研究中心及巴黎文理研究大学）
A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning bipartite graphical model that jointly learns a probability distribution over data and extracts their relevant statistical features. As such, RBM were recently proposed for characterizing the patterns of coevolution between amino acids in protein sequences and for designing new sequences. Here, we study how the nature of the features learned by RBM changes with its defining parameters, such as the dimensionality of the representations (size of the hidden layer) and the sparsity of the features. We show that for adequate v…
Universidad Complutense de Madrid（马德里康普顿斯大学）；ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（ICFO光子科学研究所，巴塞罗那科学与技术研究所）；Universitat Politècnica de València（瓦伦西亚理工大学）；ICREA（ICREA（加泰罗尼亚高等研究院））；Adam Mickiewicz University（亚当·密茨凯维奇大学）
We introduce a new family of energy-based probabilistic graphical models for efficient unsupervised learning. Its definition is motivated by the control of the spin-glass properties of the Ising model described by the weights of Boltzmann machines. We use it to learn the Bars and Stripes dataset of various sizes and the MNIST dataset, and show how they quickly achieve the performance offered by standard methods for unsupervised learning. Our results indicate that the standard initialization of Boltzmann machines with random weights equivalent to spin-glass models is an unnecessary bottleneck i…
