Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Orthogonal parameterization is a compelling solution to the vanishing gradient problem (VGP) in recurrent neural networks (RNNs). With orthogonal parameters and non-saturated activation functions, gradients in such models are constrained to unit norms. On the other hand, although the traditional vanilla RNNs are seen to have higher memory capacity, they suffer from the VGP and perform badly in many applications. This work proposes Adaptive-Saturated RNNs (asRNN), a variant that dynamically adjusts its saturation level between the two mentioned approaches. Consequently, asRNN enjoys both the capacity of a vanilla RNN and the training stability of orthogonal RNNs. Our experiments show encouraging results of asRNN on challenging sequence learning benchmarks compared to several strong competitors. The research code is accessible at https://github.com/ndminhkhoi46/asRNN/.

A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This ensures eigenvalues with unit norm and thus stable dynamics and training. However this comes at the cost of reduced expressivity due to the limited variety of orthogonal transformations. We propose a novel connectivity structure based on the Schur decomposition and a splitting of the Schur form into normal and non-normal parts. This allows to parametrize matrices with unit-norm eigenspectra without orthogonality constraints on eigenbases. The resulting architecture ensures access to a larger space of spectrally constrained matrices, of which orthogonal matrices are a subset. This crucial difference retains the stability advantages and training speed of orthogonal RNNs while enhancing expressivity, especially on tasks that require computations over ongoing input sequences.