Recurrent Highway Networks

Many sequential processing tasks require complex nonlinear transition functions from one step to the next. However, recurrent neural networks with 'deep' transition functions remain difficult to train, even when using Long Short-Term Memory (LSTM) networks. We introduce a novel theoretical analysis of recurrent networks based on Gersgorin's circle theorem that illuminates several modeling and optimization issues and improves our understanding of the LSTM cell. Based on this analysis we propose Recurrent Highway Networks, which extend the LSTM architecture to allow step-to-step transition depths larger than one. Several language modeling experiments demonstrate that the proposed architecture results in powerful and efficient models. On the Penn Treebank corpus, solely increasing the transition depth from 1 to 10 improves word-level perplexity from 90.6 to 65.4 using the same number of parameters. On the larger Wikipedia datasets for character prediction (text8 and enwik8), RHNs outperform all previous results and achieve an entropy of 1.27 bits per character.Comment: 12 pages, 6 figures, 3 table

Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

Deep learning with asymmetric connections and Hebbian updates

We show that deep networks can be trained using Hebbian updates yielding similar performance to ordinary back-propagation on challenging image datasets. To overcome the unrealistic symmetry in connections between layers, implicit in back-propagation, the feedback weights are separate from the feedforward weights. The feedback weights are also updated with a local rule, the same as the feedforward weights - a weight is updated solely based on the product of activity of the units it connects. With fixed feedback weights as proposed in Lillicrap et. al (2016) performance degrades quickly as the depth of the network increases. If the feedforward and feedback weights are initialized with the same values, as proposed in Zipser and Rumelhart (1990), they remain the same throughout training thus precisely implementing back-propagation. We show that even when the weights are initialized differently and at random, and the algorithm is no longer performing back-propagation, performance is comparable on challenging datasets. We also propose a cost function whose derivative can be represented as a local Hebbian update on the last layer. Convolutional layers are updated with tied weights across space, which is not biologically plausible. We show that similar performance is achieved with untied layers, also known as locally connected layers, corresponding to the connectivity implied by the convolutional layers, but where weights are untied and updated separately. In the linear case we show theoretically that the convergence of the error to zero is accelerated by the update of the feedback weights