Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.

/pdf/batch-normalization-accelerating-deep-network-training-by-3dkqye6twt.pdf

Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

From the Publisher:
This is the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts, the book examines techniques for modelling probability density functions and the properties and merits of the multi-layer perceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100 exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.

/pdf/neural-networks-for-pattern-recognition-34puigiau1.pdf

Neural networks for pattern recognition

https://sccn.ucsd.edu/eeglab/download/eeglab_jnm03.pdf

EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis.

Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters.

https://www2.econ.iastate.edu/tesfatsi/DeepLearningInNeuralNetworksOverview.JSchmidhuber2015.pdf

Deep learning in neural networks

In this chapter, we discuss a statistical generative model called independent component analysis. It is basically a proper probabilistic formulation of the ideas underpinning sparse coding. It shows how sparse coding can be interpreted as providing a Bayesian prior, and answers some questions which were not properly answered in the sparse coding framework.

/pdf/independent-component-analysis-4eymzc1h2k.pdf

Independent Component Analysis

https://www.cs.helsinki.fi/u/ahyvarin/papers/NN00new.pdf

Independent component analysis: algorithms and applications

We introduce a novel fast algorithm for independent component analysis, which can be used for blind source separation and feature extraction. We show how a neural network learning rule can be transformed into a fixedpoint iteration, which provides an algorithm that is very simple, does not depend on any user-defined parameters, and is fast to converge to the most accurate solution allowed by the data. The algorithm finds, one at a time, all nongaussian independent components, regardless of their probability distributions. The computations can be performed in either batch mode or a semiadaptive manner. The convergence of the algorithm is rigorously proved, and the convergence speed is shown to be cubic. Some comparisons to gradient-based algorithms are made, showing that the new algorithm is usually 10 to 100 times faster, sometimes giving the solution in just a few iterations.

A fast fixed-point algorithm for independent component analysis

A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived. It is shown that the model neuron tends to extract the principal component from a stationary input vector sequence.

Erkki Oja

Papers

Independent Component Analysis

Independent component analysis: algorithms and applications

A fast fixed-point algorithm for independent component analysis

Simplified neuron model as a principal component analyzer

A new curve detection method: randomized Hough transform (RHT)