A Treatise On FST Lattice Based MMI Training

Maximum mutual information (MMI) has become one of the two de facto methods for sequence-level training of speech recognition acoustic models. This paper aims to isolate, identify and bring forward the implicit modelling decisions induced by the design implementation of standard finite state transducer (FST) lattice based MMI training framework. The paper particularly investigates the necessity to maintain a preselected numerator alignment and raises the importance of determinizing FST denominator lattices on the fly. The efficacy of employing on the fly FST lattice determinization is mathematically shown to guarantee discrimination at the hypothesis level and is empirically shown through training deep CNN models on a 18K hours Mandarin dataset and on a 2.8K hours English dataset. On assistant and dictation tasks, the approach achieves between 2.3-4.6% relative WER reduction (WERR) over the standard FST lattice based approach.

A Distributed Optimisation Framework Combining Natural Gradient with Hessian-Free for Discriminative Sequence Training

This paper presents a novel natural gradient and Hessian-free (NGHF) optimisation framework for neural network training that can operate efficiently in a distributed manner. It relies on the linear conjugate gradient (CG) algorithm to combine the natural gradient (NG) method with local curvature information from Hessian-free (HF) or other second-order methods. A solution to a numerical issue in CG allows effective parameter updates to be generated with far fewer CG iterations than usually used (e.g. 5-8 instead of 200). This work also presents a novel preconditioning approach to improve the progress made by individual CG iterations for models with shared parameters. Although applicable to other training losses and model structures, NGHF is investigated in this paper for lattice-based discriminative sequence training for hybrid hidden Markov model acoustic models using a standard recurrent neural network, long short-term memory, and time delay neural network models for output probability calculation. Automatic speech recognition experiments are reported on the multi-genre broadcast data set for a range of different acoustic model types. These experiments show that NGHF achieves larger word error rate reductions than standard stochastic gradient descent or Adam, while requiring orders of magnitude fewer parameter updates.

Combining Natural Gradient with Hessian Free Methods for Sequence Training

This paper presents a new optimisation approach to train Deep Neural Networks (DNNs) with discriminative sequence criteria. At each iteration, the method combines information from the Natural Gradient (NG) direction with local curvature information of the error surface that enables better paths on the parameter manifold to be traversed. The method is derived using an alternative derivation of Taylor's theorem using the concepts of manifolds, tangent vectors and directional derivatives from the perspective of Information Geometry. The efficacy of the method is shown within a Hessian Free (HF) style optimisation framework to sequence train both standard fully-connected DNNs and Time Delay Neural Networks as speech recognition acoustic models. It is shown that for the same number of updates the proposed approach achieves larger reductions in the word error rate (WER) than both NG and HF, and also leads to a lower WER than standard stochastic gradient descent. The paper also addresses the issue of over-fitting due to mismatch between training criterion and Word Error Rate (WER) that primarily arises during sequence training of ReLU-DNN models.

A Common Framework for Natural Gradient and Taylor based Optimisation using Manifold Theory

This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods with the method of NG.

Sequence Training of DNN Acoustic Models With Natural Gradient

Deep Neural Network (DNN) acoustic models often use discriminative sequence training that optimises an objective function that better approximates the word error rate (WER) than frame-based training. Sequence training is normally implemented using Stochastic Gradient Descent (SGD) or Hessian Free (HF) training. This paper proposes an alternative batch style optimisation framework that employs a Natural Gradient (NG) approach to traverse through the parameter space. By correcting the gradient according to the local curvature of the KL-divergence, the NG optimisation process converges more quickly than HF. Furthermore, the proposed NG approach can be applied to any sequence discriminative training criterion. The efficacy of the NG method is shown using experiments on a Multi-Genre Broadcast (MGB) transcription task that demonstrates both the computational efficiency and the accuracy of the resulting DNN models.