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.
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) s…
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 quick…
Hessian based measures of flatness, such as the trace, Frobenius and spectral norms, have been argued, used and shown to relate to generalisation. In this paper we demonstrate that for feed forward neural networks under the cross entropy loss, we would expect low loss solutions with large weights to have small Hessian based measures of flatness. This implies that solutions obtained using $L2$ regularisation should in principle be sharper than those without, despite generalising better. We show this to be true for logistic regression, multi-layer perceptrons, simple convolutional, pre-activated…
University of Oxford（牛津大学）；Facebook AI Research（脸书人工智能研究院）
We study the learning performance of gradient descent when the empirical risk is weakly convex, namely, the smallest negative eigenvalue of the empirical risk's Hessian is bounded in magnitude. By showing that this eigenvalue can control the stability of gradient descent, generalisation error bounds are proven that hold under a wider range of step sizes compared to previous work. Out of sample guarantees are then achieved by decomposing the test error into generalisation, optimisation and approximation errors, each of which can be bounded and traded off with respect to algorithmic parameters, …
Technical University of Munich（慕尼黑工业大学）；fortiss, Forschungsinstitut des Freistaats Bayern（巴伐利亚自由州fortiss研究所）
Recent development of Deep Reinforcement Learning (DRL) has demonstrated superior performance of neural networks in solving challenging problems with large or even continuous state spaces. One specific approach is to deploy neural networks to approximate value functions by minimising the Mean Squared Bellman Error (MSBE) function. Despite great successes of DRL, development of reliable and efficient numerical algorithms to minimise the MSBE is still of great scientific interest and practical demand. Such a challenge is partially due to the underlying optimisation problem being highly non-conve…
A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as the reading site while the latter is used to manipulate visible states' probability. In Generative BM, the samples of visible data imitate the probability distribution of a given data set. In contrast, the visible sites of discriminative BM are treated as Input/Output (I/O) reading sites where the conditional probability of output state is optimized for a give…
Training More Robust Classification Model via Discriminative Loss and Gaussian Noise Injection
Ampere Software Technology（Ampere软件技术公司）；Institut de mathématiques de Toulouse（图卢兹数学研究所）；Institut de Recherche en Informatique de Toulouse（图卢兹计算机研究所）；Laboratoire Jean Alexandre Dieudonné, Université Côte d’Azur（坎特伯雷大学Dieudonné实验室）
NASA Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Cavendish Laboratory（卡文迪许实验室）；Kavli Institute for Cosmology（卡弗里宇宙学研究所）
We present the first public release of our generic neural network training algorithm, called SkyNet. This efficient and robust machine learning tool is able to train large and deep feed-forward neural networks, including autoencoders, for use in a wide range of supervised and unsupervised learning applications, such as regression, classification, density estimation, clustering and dimensionality reduction. SkyNet uses a `pre-training' method to obtain a set of network parameters that has empirically been shown to be close to a good solution, followed by further optimisation using a regularised…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
We recapitulate the Bayesian formulation of neural network based classifiers and show that, while sampling from the posterior does indeed lead to better generalisation than is obtained by standard optimisation of the cost function, even better performance can in general be achieved by sampling finite temperature ($T$) distributions derived from the posterior. Taking the example of two different deep (3 hidden layers) classifiers for MNIST data, we find quite different $T$ values to be appropriate in each case. In particular, for a typical neural network classifier a clear minimum of the test e…
University College London（伦敦大学学院）；University of Oxford（牛津大学）
In this paper, we describe how a patient-specific, ultrasound-probe-induced prostate motion model can be directly generated from a single preoperative MR image. Our motion model allows for sampling from the conditional distribution of dense displacement fields, is encoded by a generative neural network conditioned on a medical image, and accepts random noise as additional input. The generative network is trained by a minimax optimisation with a second discriminative neural network, tasked to distinguish generated samples from training motion data. In this work, we propose that 1) jointly optim…
