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Register a new userFenchel Lifted Networks: A Lagrange Relaxation of Neural Network Training
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Despite the recent successes of deep neural networks, the corresponding training problem remains highly non-convex and difficult to optimize. Classes of models have been proposed that introduce greater structure to the objective function at the cost of lifting the dimension of the problem. However, these lifted methods sometimes perform poorly compared to traditional neural networks. In this paper, we introduce a new class of lifted models, Fenchel lifted networks, that enjoy the same benefits as previous lifted models, without suffering a degradation in performance over classical networks. Our model represents activation functions as equivalent biconvex constraints and uses Lagrange Multipliers to arrive at a rigorous lower bound of the traditional neural network training problem. This model is efficiently trained using block-coordinate descent and is parallelizable across data points and/or layers. We compare our model against standard fully connected and convolutional networks and show that we are able to match or beat their performance.
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We investigate the problem of machine learning with mislabeled training data. We try to make the effects of mislabeled training better understood through analysis of the basic model and equations that characterize the problem. This includes results about the ability of the noisy model to make the same decisions as the clean model and the effects of noise on model performance. In addition to providing better insights we also are able to show that the Maximum Likelihood (ML) estimate of the parameters of the noisy model determine those of the clean model. This property is obtained through the use of the ML invariance property and leads to an approach to developing a classifier when training has been mislabeled: namely train the classifier on noisy data and adjust the decision threshold based on the noise levels and/or class priors. We show how our approach to mislabeled training works with multi-layered perceptrons (MLPs).
We propose emph{MaxUp}, an embarrassingly simple, highly effective technique for improving the generalization performance of machine learning models, especially deep neural networks. The idea is to generate a set of augmented data with some random perturbations or transforms and minimize the maximum, or worst case loss over the augmented data. By doing so, we implicitly introduce a smoothness or robustness regularization against the random perturbations, and hence improve the generation performance. For example, in the case of Gaussian perturbation, emph{MaxUp} is asymptotically equivalent to using the gradient norm of the loss as a penalty to encourage smoothness. We test emph{MaxUp} on a range of tasks, including image classification, language modeling, and adversarial certification, on which emph{MaxUp} consistently outperforms the existing best baseline methods, without introducing substantial computational overhead. In particular, we improve ImageNet classification from the state-of-the-art top-1 accuracy $85.5%$ without extra data to $85.8%$. Code will be released soon.
We show new connections between adversarial learning and explainability for deep neural networks (DNNs). One form of explanation of the output of a neural network model in terms of its input features, is a vector of feature-attributions. Two desirable characteristics of an attribution-based explanation are: (1) $textit{sparseness}$: the attributions of irrelevant or weakly relevant features should be negligible, thus resulting in $textit{concise}$ explanations in terms of the significant features, and (2) $textit{stability}$: it should not vary significantly within a small local neighborhood of the input. Our first contribution is a theoretical exploration of how these two properties (when using attributions based on Integrated Gradients, or IG) are related to adversarial training, for a class of 1-layer networks (which includes logistic regression models for binary and multi-class classification); for these networks we show that (a) adversarial training using an $ell_infty$-bounded adversary produces models with sparse attribution vectors, and (b) natural model-training while encouraging stable explanations (via an extra term in the loss function), is equivalent to adversarial training. Our second contribution is an empirical verification of phenomenon (a), which we show, somewhat surprisingly, occurs $textit{not only}$ $textit{in 1-layer networks}$, $textit{but also DNNs}$ $textit{trained on }$ $textit{standard image datasets}$, and extends beyond IG-based attributions, to those based on DeepSHAP: adversarial training with $ell_infty$-bounded perturbations yields significantly sparser attribution vectors, with little degradation in performance on natural test data, compared to natural training. Moreover, the sparseness of the attribution vectors is significantly better than that achievable via $ell_1$-regularized natural training.
Fully quantized training (FQT), which uses low-bitwidth hardware by quantizing the activations, weights, and gradients of a neural network model, is a promising approach to accelerate the training of deep neural networks. One major challenge with FQT is the lack of theoretical understanding, in particular of how gradient quantization impacts convergence properties. In this paper, we address this problem by presenting a statistical framework for analyzing FQT algorithms. We view the quantized gradient of FQT as a stochastic estimator of its full precision counterpart, a procedure known as quantization-aware training (QAT). We show that the FQT gradient is an unbiased estimator of the QAT gradient, and we discuss the impact of gradient quantization on its variance. Inspired by these theoretical results, we develop two novel gradient quantizers, and we show that these have smaller variance than the existing per-tensor quantizer. For training ResNet-50 on ImageNet, our 5-bit block Householder quantizer achieves only 0.5% validation accuracy loss relative to QAT, comparable to the existing INT8 baseline.
Generalisation of a deep neural network (DNN) is one major concern when employing the deep learning approach for solving practical problems. In this paper we propose a new technique, named approximated orthonormal normalisation (AON), to improve the generalisation capacity of a DNN model. Considering a weight matrix W from a particular neural layer in the model, our objective is to design a function h(W) such that its row vectors are approximately orthogonal to each other while allowing the DNN model to fit the training data sufficiently accurate. By doing so, it would avoid co-adaptation among neurons of the same layer to be able to improve network-generalisation capacity. Specifically, at each iteration, we first approximate (WW^T)^(-1/2) using its Taylor expansion before multiplying the matrix W. After that, the matrix product is then normalised by applying the spectral normalisation (SN) technique to obtain h(W). Conceptually speaking, AON is designed to turn orthonormal regularisation into orthonormal normalisation to avoid manual balancing the original and penalty functions. Experimental results show that AON yields promising validation performance compared to orthonormal regularisation.
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