arXiv research

Wide neural networks' last hidden layers split into groups of redundant neurons.

This paper explores loss landscapes of sparse neural networks, finding unique characteristics compared to dense networks.

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

Wide hidden layer TCM nets capacity analyzed using RDT and fl RDT.

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…

LIFE framework improves model accuracy and interpretability.

Single wide layer followed by a pyramidal structure ensures global convergence in deep networks.

Does over-parameterization eliminate sub-optimal local minima for neural networks? An affirmative answer was given by a classical result in [59] for 1-hidden-layer wide neural networks. A few recent works have extended the setting to multi-layer neural networks, but none of them has proved every local minimum is global…

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…

Enhanced ELM reduces randomness in neural network training.

Bounds neural network output distribution to Gaussian for random initialization.

Two-layer CNNs can overfit well if initialized correctly.

Combining Bayesian nonparametrics and a forward model selection strategy, we construct parsimonious Bayesian deep networks (PBDNs) that infer capacity-regularized network architectures from the data and require neither cross-validation nor fine-tuning when training the model. One of the two essential components of a PB…

Softmax policy gradient achieves global optimality in wide neural networks with entropy regularization.

In the recent literature the important role of depth in deep learning has been emphasized. In this paper we argue that sufficient width of a feedforward network is equally important by answering the simple question under which conditions the decision regions of a neural network are connected. It turns out that for a cl…

We study how finite Bayesian neural networks adapt their hidden representations.

Despite the effectiveness of multitask deep neural network (MTDNN), there is a limited theoretical understanding on how the information is shared across different tasks in MTDNN. In this work, we establish a formal connection between MTDNN with infinitely-wide hidden layers and multitask Gaussian Process (GP). We deriv…

New CFNN architecture approximates functions with machine accuracy.

Nowadays, deep learning can be employed to a wide ranges of fields including medicine, engineering, etc. In deep learning, Convolutional Neural Network (CNN) is extensively used in the pattern and sequence recognition, video analysis, natural language processing, spam detection, topic categorization, regression analysi…

Study analyzes error in ReLU networks with local connections.

Improved DNN calibration without sacrificing accuracy.

Spotlight method finds hidden errors in deep learning models.

It is widely believed that the backpropagation algorithm is essential for learning good feature detectors in early layers of artificial neural networks, so that these detectors are useful for the task performed by the higher layers of that neural network. At the same time, the traditional form of backpropagation is bio…

Long Short-Term Memory (LSTM) is a well-known method used widely on sequence learning and time series prediction. In this paper we deployed stacked LSTM model in an application of weather forecasting. We propose a 2-layer spatio-temporal stacked LSTM model which consists of independent LSTM models per location in the f…

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…

We prove that for an $L$-layer fully-connected linear neural network, if the width of every hidden layer is $\tildeΩ(L \cdot r \cdot d_{\mathrm{out}} \cdot κ^3 )$, where $r$ and $κ$ are the rank and the condition number of the input data, and $d_{\mathrm{out}}$ is the output dimension, then gradient descent with Gaussi…

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

To infer multilayer deep representations of high-dimensional discrete and nonnegative real vectors, we propose an augmentable gamma belief network (GBN) that factorizes each of its hidden layers into the product of a sparse connection weight matrix and the nonnegative real hidden units of the next layer. The GBN's hidd…

Deep neural networks with heavy-tailed weights converge to stable distributions.

Deep Gaussian processes reduce uncertainty in porous media flow modeling.

Formula found for neural network error with fixed weights.

This study uses neural networks to solve interpolation problems with sparse, infinitely wide layers.

Universal MLPs with a single hidden layer can learn any function.

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

Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single…

Normalization methods play an important role in enhancing the performance of deep learning while their theoretical understandings have been limited. To theoretically elucidate the effectiveness of normalization, we quantify the geometry of the parameter space determined by the Fisher information matrix (FIM), which als…

Long short-term memory (LSTM) has been widely used for sequential data modeling. Researchers have increased LSTM depth by stacking LSTM cells to improve performance. This incurs model redundancy, increases run-time delay, and makes the LSTMs more prone to overfitting. To address these problems, we propose a hidden-laye…

Transferability of learned features between tasks can massively reduce the cost of training a neural network on a novel task. We investigate the effect of network width on learned features using activation atlases --- a visualization technique that captures features the entire hidden state responds to, as opposed to in…

Deep linear ResNets converge globally with certain transformations.

Chemical networks outperform spiking neural networks in classification tasks.

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…

Binary autoencoder with sparse hidden layer preserves information and zero reconstruction error.

Analysis of gradient descent on wide neural networks reveals strong generalization.

The muti-layer information bottleneck (IB) problem, where information is propagated (or successively refined) from layer to layer, is considered. Based on information forwarded by the preceding layer, each stage of the network is required to preserve a certain level of relevance with regards to a specific hidden variab…

Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so-called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. One key feature of the neural networks used in the…

New method amplifies hidden structure in complex networks.

This paper extends depth separation results to piece-wise oscillatory functions.

While the optimization problem behind deep neural networks is highly non-convex, it is frequently observed in practice that training deep networks seems possible without getting stuck in suboptimal points. It has been argued that this is the case as all local minima are close to being globally optimal. We show that thi…