arXiv research

Two-layer CNNs can overfit well if initialized correctly.

Deep Convolutional Neural Networks (CNN) enforces supervised information only at the output layer, and hidden layers are trained by back propagating the prediction error from the output layer without explicit supervision. We propose a supervised feature learning approach, Label Consistent Neural Network, which enforces…

ReLU networks trained with MILPs match deep learning accuracy.

Proposes BATer for improved adversarial example detection.

Bounds neural network output distribution to Gaussian for random initialization.

A neural network with a single hidden layer can't represent certain multivariable functions.

3-layer NTK models generalize better than 2-layer models, especially with large input dimensions.

This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network, the entire collection of hidden layer node states from the training dataset is …

Inserts proximal mapping into deep networks for better regularization.

Deep Gaussian processes reduce uncertainty in porous media flow modeling.

Artificial neural networks are most commonly trained with the back-propagation algorithm, where the gradient for learning is provided by back-propagating the error, layer by layer, from the output layer to the hidden layers. A recently discovered method called feedback-alignment shows that the weights used for propagat…

There has recently been much work on the "wide limit" of neural networks, where Bayesian neural networks (BNNs) are shown to converge to a Gaussian process (GP) as all hidden layers are sent to infinite width. However, these results do not apply to architectures that require one or more of the hidden layers to remain n…

We study the problem of learning one-hidden-layer neural networks with Rectified Linear Unit (ReLU) activation function, where the inputs are sampled from standard Gaussian distribution and the outputs are generated from a noisy teacher network. We analyze the performance of gradient descent for training such kind of n…

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an update direction for the weights. An alternative approach is to train the network …

Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We continue the work by firstly introducing a third transformation to normalize the scal…

Enhanced ELM reduces randomness in neural network training.

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 $n$ output units, given t…

Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship between large number of parameters, we failed to understand how they could achie…

Generative model initializes 2-layer network weights for small datasets.

We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our a…

We consider the problem of inferring the input and hidden variables of a stochastic multi-layer neural network from an observation of the output. The hidden variables in each layer are represented as matrices. This problem applies to signal recovery via deep generative prior models, multi-task and mixed regression and …

Hysteresis phenomena have been observed in different branches of physics and engineering sciences. Therefore, several models have been proposed for hysteresis simulation in different fields; however, almost neither of them can be utilized universally. In this paper by inspiring of Preisach Neural Network which was insp…

In this paper we propose a method to model speaker and session variability and able to generate likelihood ratios using neural networks in an end-to-end phrase dependent speaker verification system. As in Joint Factor Analysis, the model uses tied hidden variables to model speaker and session variability and a MAP adap…

Study on deep neural networks using concentration inequalities and optimal stopping.

Study clarifies Bayesian generalization error in CBM for 3-layered linear neural networks.

Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane. For complex data with multimodal distributions this transformation is difficult t…

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural netwo…

We analyze multi-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations. We rigorously establish the limiting behavior of the multi-layer neural network output. The limit procedure is valid for any number of hidde…

For linear classifiers, the relationship between (normalized) output margin and generalization is captured in a clear and simple bound -- a large output margin implies good generalization. Unfortunately, for deep models, this relationship is less clear: existing analyses of the output margin give complicated bounds whi…

A new neural network initialization method is proposed for faster and more accurate training.

We consider deep linear networks with arbitrary convex differentiable loss. We provide a short and elementary proof of the fact that all local minima are global minima if the hidden layers are either 1) at least as wide as the input layer, or 2) at least as wide as the output layer. This result is the strongest possibl…

Deep linear ResNets converge globally with certain transformations.

Gradient descent proves global convergence for deep networks with a single wide layer.

Introduces fuzzy layers to enhance deep learning performance.

Neural networks can approximate any continuous function with a single hidden layer.

Extreme learning machine (ELM) is a new single hidden layer feedback neural network. The weights of the input layer and the biases of neurons in hidden layer are randomly generated, the weights of the output layer can be analytically determined. ELM has been achieved good results for a large number of classification ta…

We consider the problem of learning a one-hidden-layer neural network with non-overlapping convolutional layer and ReLU activation, i.e., $f(\mathbf{Z}, \mathbf{w}, \mathbf{a}) = \sum_j a_jσ(\mathbf{w}^T\mathbf{Z}_j)$, in which both the convolutional weights $\mathbf{w}$ and the output weights $\mathbf{a}$ are paramete…

This paper introduces a novel approach to measuring privacy risks in deep computer vision models based on intermediate outputs.

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…

Interpreting the prediction mechanism of complex models is currently one of the most important tasks in the machine learning field, especially with layered neural networks, which have achieved high predictive performance with various practical data sets. To reveal the global structure of a trained neural network in an …

Deep neural networks (DNNs) are vulnerable to subtle adversarial perturbations applied to the input. These adversarial perturbations, though imperceptible, can easily mislead the DNN. In this work, we take a control theoretic approach to the problem of robustness in DNNs. We treat each individual layer of the DNN as a …

Hierarchical nucleation patterns emerge in deep neural network layers.

We use smoothed analysis techniques to provide guarantees on the training loss of Multilayer Neural Networks (MNNs) at differentiable local minima. Specifically, we examine MNNs with piecewise linear activation functions, quadratic loss and a single output, under mild over-parametrization. We prove that for a MNN with …

RVFL NNs perform well without direct links and output bias for regression.

Normalization effects on deep neural networks impact output variance and test accuracy.

Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here we focus on the sequence lear…

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…

Researchers analyze how RNNs solve intent detection tasks using dynamical systems theory.