A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Randomly chosen primary hidden units and derived secondary units reduce neural network complexity.
Study examines dependence properties of Bayesian neural network units in finite-width networks.
Study on hidden units in finite Bayesian neural networks and their tail properties.
RBM models reveal how hidden unit tail behavior affects pattern reconstruction.
Deep belief networks can approximate any multivariate density with binary hidden units.
We establish upper bounds for the minimal number of hidden units for which a binary stochastic feedforward network with sigmoid activation probabilities and a single hidden layer is a universal approximator of Markov kernels. We show that each possible probabilistic assignment of the states of output units, given t…
Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using regularization upon the activation possibilities of hidden unit…
New MBL hidden Born machine learns various tasks.
A neural network with a single hidden layer can't represent certain multivariable functions.
The problem of attributing a deep network's prediction to its \emph{input/base} features is well-studied. We introduce the notion of \emph{conductance} to extend the notion of attribution to the understanding the importance of \emph{hidden} units. Informally, the conductance of a hidden unit of a deep network is the \e…
Deep learning is the state-of-the-art in fields such as visual object recognition and speech recognition. This learning uses a large number of layers, huge number of units, and connections. Therefore, overfitting is a serious problem. To avoid this problem, dropout learning is proposed. Dropout learning neglects some i…
We study layered neural networks of rectified linear units (ReLU) in a modelling framework for stochastic training processes. The comparison with sigmoidal activation functions is in the center of interest. We compute typical learning curves for shallow networks with K hidden units in matching student teacher scenarios…
The infinite restricted Boltzmann machine (iRBM) is an extension of the classic RBM. It enjoys a good property of automatically deciding the size of the hidden layer according to specific training data. With sufficient training, the iRBM can achieve a competitive performance with that of the classic RBM. However, the c…
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 sy…
New method reduces overfitting in deep neural networks by measuring and regulating hidden unit diversity.
We propose a novel quantum model for the restricted Boltzmann machine (RBM), in which the visible units remain classical whereas the hidden units are quantized as noninteracting fermions. The free motion of the fermions is parametrically coupled to the classical signal of the visible units. This model possesses a quant…
Lipschitz RNNs improve stability and performance in various tasks.
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
Structural RBM reduces parameters for image denoising and classification.
The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions , then a standard feedforward neural network with one hidden layer is able to approximate any continuous multivariate function to any given approximation threshold …
This work tackles the problem of learning a set of language specific acoustic units from unlabeled speech recordings given a set of labeled recordings from other languages. Our approach may be described by the following two steps procedure: first the model learns the notion of acoustic units from the labelled data and …
State of the art Deep Neural Networks (DNN) can now achieve above human level accuracy on image classification tasks. However their outstanding performances come along with a complex inference mechanism making them arduously interpretable models. In order to understand the underlying prediction rules of DNNs, Dhamdhere…
Background: Statistical mechanics results (Dauphin et al. (2014); Choromanska et al. (2015)) suggest that local minima with high error are exponentially rare in high dimensions. However, to prove low error guarantees for Multilayer Neural Networks (MNNs), previous works so far required either a heavily modified MNN mod…
We develop a new approach to learn the parameters of regression models with hidden variables. In a nutshell, we estimate the gradient of the regression function at a set of random points, and cluster the estimated gradients. The centers of the clusters are used as estimates for the parameters of hidden units. We justif…
We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We use this to show that the maximal Kullback-Leibler divergence to the RBM model w…
We introduce dropout compaction, a novel method for training feed-forward neural networks which realizes the performance gains of training a large model with dropout regularization, yet extracts a compact neural network for run-time efficiency. In the proposed method, we introduce a sparsity-inducing prior on the per u…
Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep learning. In this paper, we propose a new building block -- distributed random models…
The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters advancing conventional randomized approaches constrained with a fixed scope of rand…
Focusing on the grand-canonical extension of the ordinary restricted Boltzmann machine, we suggest an energy-based model for feature extraction that uses a layer of hidden units with varying size. By an appropriate choice of the chemical potential and given a sufficiently large number of hidden resources the generative…
Recurrent neural networks (RNNs) have been drawing much attention with great success in many applications like speech recognition and neural machine translation. Long short-term memory (LSTM) is one of the most popular RNN units in deep learning applications. LSTM transforms the input and the previous hidden states to …
This paper describes a novel energy-based probabilistic distribution that represents complex-valued data and explains how to apply it to direct feature extraction from complex-valued spectra. The proposed model, the complex-valued restricted Boltzmann machine (CRBM), is designed to deal with complex-valued visible unit…
New methods detect modular structure in neural networks, revealing surprising effects of dropout.
We present a novel neural network algorithm, the Tensor Switching (TS) network, which generalizes the Rectified Linear Unit (ReLU) nonlinearity to tensor-valued hidden units. The TS network copies its entire input vector to different locations in an expanded representation, with the location determined by its hidden un…
Study on neural networks' performance under different normalizations as N grows.
Bayesian units improve speech recognition with minimal parameters.
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where finding a factorization corresponds to finding edges in different layers and valu…
Mathematical methods characterize RNNs' asymptotics as hidden units and data grow.
CRUs model irregular time series with continuous hidden states.
Traditionally, deep learning algorithms update the network weights whereas the network architecture is chosen manually, using a process of trial and error. In this work, we propose two novel approaches that automatically update the network structure while also learning its weights. The novelty of our approach lies in o…
In this work, we propose an infinite restricted Boltzmann machine~(RBM), whose maximum likelihood estimation~(MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each ite…
George Cybenko's landmark 1989 paper showed that there exists a feedforward neural network, with exactly one hidden layer (and a finite number of neurons), that can arbitrarily approximate a given continuous function on the unit hypercube. The paper did not address how to find the weight/parameters of such a networ…
Recurrent Neural Networks (RNNs), which are a powerful scheme for modeling temporal and sequential data need to capture long-term dependencies on datasets and represent them in hidden layers with a powerful model to capture more information from inputs. For modeling long-term dependencies in a dataset, the gating mecha…
Bayesian SHMM models speech units from unannotated speech.
Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this problem, based on the eigenvectors of both the second order moment matrix and t…
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Bolt…
Improves TTS accuracy by correcting context-dependent units.
New framework analyzes deep neural networks using feature probabilities.
New term ADS describes how machine learning can change user behavior.