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Register a new userHow does Weight Correlation Affect the Generalisation Ability of Deep Neural Networks
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Gaojie Jin
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper studies the novel concept of weight correlation in deep neural networks and discusses its impact on the networks generalisation ability. For fully-connected layers, the weight correlation is defined as the average cosine similarity between weight vectors of neurons, and for convolutional layers, the weight correlation is defined as the cosine similarity between filter matrices. Theoretically, we show that, weight correlation can, and should, be incorporated into the PAC Bayesian framework for the generalisation of neural networks, and the resulting generalisation bound is monotonic with respect to the weight correlation. We formulate a new complexity measure, which lifts the PAC Bayes measure with weight correlation, and experimentally confirm that it is able to rank the generalisation errors of a set of networks more precisely than existing measures. More importantly, we develop a new regulariser for training, and provide extensive experiments that show that the generalisation error can be greatly reduced with our novel approach.
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Unsupervised domain adaptation (UDA) aims to train a target classifier with labeled samples from the source domain and unlabeled samples from the target domain. Classical UDA learning bounds show that target risk is upper bounded by three terms: source risk, distribution discrepancy, and combined risk. Based on the assumption that the combined risk is a small fixed value, methods based on this bound train a target classifier by only minimizing estimators of the source risk and the distribution discrepancy. However, the combined risk may increase when minimizing both estimators, which makes the target risk uncontrollable. Hence the target classifier cannot achieve ideal performance if we fail to control the combined risk. To control the combined risk, the key challenge takes root in the unavailability of the labeled samples in the target domain. To address this key challenge, we propose a method named E-MixNet. E-MixNet employs enhanced mixup, a generic vicinal distribution, on the labeled source samples and pseudo-labeled target samples to calculate a proxy of the combined risk. Experiments show that the proxy can effectively curb the increase of the combined risk when minimizing the source risk and distribution discrepancy. Furthermore, we show that if the proxy of the combined risk is added into loss functions of four representative UDA methods, their performance is also improved.
Model-Agnostic Meta-Learning (MAML) has become increasingly popular for training models that can quickly adapt to new tasks via one or few stochastic gradient descent steps. However, the MAML objective is significantly more difficult to optimize compared to standard Empirical Risk Minimization (ERM), and little is understood about how much MAML improves over ERM in terms of the fast adaptability of their solutions in various scenarios. We analytically address this issue in a linear regression setting consisting of a mixture of easy and hard tasks, where hardness is related to the condition number of the tasks loss function. Specifically, we prove that in order for MAML to achieve substantial gain over ERM, (i) there must be some discrepancy in hardness among the tasks, and (ii) the optimal solutions of the hard tasks must be closely packed with the center far from the center of the easy tasks optimal solutions. We also give numerical and analytical results suggesting that these insights also apply to two-layer neural networks. Finally, we provide few-shot image classification experiments that support our insights for when MAML should be used and emphasize the importance of training MAML on hard tasks in practice.
Although neural networks are widely used, it remains challenging to formally verify the safety and robustness of neural networks in real-world applications. Existing methods are designed to verify the network before use, which is limited to relatively simple specifications and fixed networks. These methods are not ready to be applied to real-world problems with complex and/or dynamically changing specifications and networks. To effectively handle dynamically changing specifications and networks, the verification needs to be performed online when these changes take place. However, it is still challenging to run existing verification algorithms online. Our key insight is that we can leverage the temporal dependencies of these changes to accelerate the verification process, e.g., by warm starting new online verification using previous verified results. This paper establishes a novel framework for scalable online verification to solve real-world verification problems with dynamically changing specifications and/or networks, known as domain shift and weight shift respectively. We propose three types of techniques (branch management, perturbation tolerance analysis, and incremental computation) to accelerate the online verification of deep neural networks. Experiment results show that our online verification algorithm is up to two orders of magnitude faster than existing verification algorithms, and thus can scale to real-world applications.
It is observed in the literature that data augmentation can significantly mitigate membership inference (MI) attack. However, in this work, we challenge this observation by proposing new MI attacks to utilize the information of augmented data. MI attack is widely used to measure the models information leakage of the training set. We establish the optimal membership inference when the model is trained with augmented data, which inspires us to formulate the MI attack as a set classification problem, i.e., classifying a set of augmented instances instead of a single data point, and design input permutation invariant features. Empirically, we demonstrate that the proposed approach universally outperforms original methods when the model is trained with data augmentation. Even further, we show that the proposed approach can achieve higher MI attack success rates on models trained with some data augmentation than the existing methods on models trained without data augmentation. Notably, we achieve a 70.1% MI attack success rate on CIFAR10 against a wide residual network while the previous best approach only attains 61.9%. This suggests the privacy risk of models trained with data augmentation could be largely underestimated.
Understanding the role of (stochastic) gradient descent (SGD) in the training and generalisation of deep neural networks (DNNs) with ReLU activation has been the object study in the recent past. In this paper, we make use of deep gated networks (DGNs) as a framework to obtain insights about DNNs with ReLU activation. In DGNs, a single neuronal unit has two components namely the pre-activation input (equal to the inner product the weights of the layer and the previous layer outputs), and a gating value which belongs to $[0,1]$ and the output of the neuronal unit is equal to the multiplication of pre-activation input and the gating value. The standard DNN with ReLU activation, is a special case of the DGNs, wherein the gating value is $1/0$ based on whether or not the pre-activation input is positive or negative. We theoretically analyse and experiment with several variants of DGNs, each variant suited to understand a particular aspect of either training or generalisation in DNNs with ReLU activation. Our theory throws light on two questions namely i) why increasing depth till a point helps in training and ii) why increasing depth beyond a point hurts training? We also present experimental evidence to show that gate adaptation, i.e., the change of gating value through the course of training is key for generalisation.
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