Input margins can predict generalization too

Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or its representation internal to the network. While margins have been shown to be correlated with the generalization ability of a model when measured at its hidden representations (hidden margins), no such link between large margins and generalization has been established for input margins. We show that while input margins are not generally predictive of generalization, they can be if the search space is appropriately constrained. We develop such a measure based on input margins, which we refer to as `constrained margins'. The predictive power of this new measure is demonstrated on the 'Predicting Generalization in Deep Learning' (PGDL) dataset and contrasted with hidden representation margins. We find that constrained margins achieve highly competitive scores and outperform other margin measurements in general. This provides a novel insight on the relationship between generalization and classification margins, and highlights the importance of considering the data manifold for investigations of generalization in DNNs.

The Missing Margin: How Sample Corruption Affects Distance to the Boundary in ANNs

Classification margins are commonly used to estimate the generalization ability of machine learning models. We present an empirical study of these margins in artificial neural networks. A global estimate of margin size is usually used in the literature. In this work, we point out seldom considered nuances regarding classification margins. Notably, we demonstrate that some types of training samples are modelled with consistently small margins while affecting generalization in different ways. By showing a link with the minimum distance to a different-target sample and the remoteness of samples from one another, we provide a plausible explanation for this observation. We support our findings with an analysis of fully-connected networks trained on noise-corrupted MNIST data, as well as convolutional networks trained on noise-corrupted CIFAR10 data.

Efficient acoustic feature transformation in mismatched environments using a Guided-GAN

We propose a new framework to improve automatic speech recognition (ASR) systems in resource-scarce environments using a generative adversarial network (GAN) operating on acoustic input features. The GAN is used to enhance the features of mismatched data prior to decoding, or can optionally be used to fine-tune the acoustic model. We achieve improvements that are comparable to multi-style training (MTR), but at a lower computational cost. With less than one hour of data, an ASR system trained on good quality data, and evaluated on mismatched audio is improved by between 11.5% and 19.7% relative word error rate (WER). Experiments demonstrate that the framework can be very useful in under-resourced environments where training data and computational resources are limited. The GAN does not require parallel training data, because it utilises a baseline acoustic model to provide an additional loss term that guides the generator to create acoustic features that are better classified by the baseline.

Multi-style Training for South African Call Centre Audio

Mismatched data is a challenging problem for automatic speech recognition (ASR) systems. One of the most common techniques used to address mismatched data is multi-style training (MTR), a form of data augmentation that attempts to transform the training data to be more representative of the testing data; and to learn robust representations applicable to different conditions. This task can be very challenging if the test conditions are unknown. We explore the impact of different MTR styles on system performance when testing conditions are different from training conditions in the context of deep neural network hidden Markov model (DNN-HMM) ASR systems. A controlled environment is created using the LibriSpeech corpus, where we isolate the effect of different MTR styles on final system performance. We evaluate our findings on a South African call centre dataset that contains noisy, WAV49-encoded audio.

Exploring layerwise decision making in DNNs

While deep neural networks (DNNs) have become a standard architecture for many machine learning tasks, their internal decision-making process and general interpretability is still poorly understood. Conversely, common decision trees are easily interpretable and theoretically well understood. We show that by encoding the discrete sample activation values of nodes as a binary representation, we are able to extract a decision tree explaining the classification procedure of each layer in a ReLU-activated multilayer perceptron (MLP). We then combine these decision trees with existing feature attribution techniques in order to produce an interpretation of each layer of a model. Finally, we provide an analysis of the generated interpretations, the behaviour of the binary encodings and how these relate to sample groupings created during the training process of the neural network.

Tracking translation invariance in CNNs

Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity maps to quantify how sensitive a standard CNN is to a translated input. We propose the use of Cosine Similarity as sensitivity metric over Euclidean Distance, and discuss the importance of restricting the dimensionality of either of these metrics when comparing architectures. Our main focus is to investigate the effect of different architectural components of a standard CNN on that network's sensitivity to translation. By varying convolutional kernel sizes and amounts of zero padding, we control the size of the feature maps produced, allowing us to quantify the extent to which these elements influence translation invariance. We also measure translation invariance at different locations within the CNN to determine the extent to which convolutional and fully connected layers, respectively, contribute to the translation invariance of a CNN as a whole. Our analysis indicates that both convolutional kernel size and feature map size have a systematic influence on translation invariance. We also see that convolutional layers contribute less than expected to translation invariance, when not specifically forced to do so.

Stride and Translation Invariance in CNNs

Convolutional Neural Networks have become the standard for image classification tasks, however, these architectures are not invariant to translations of the input image. This lack of invariance is attributed to the use of stride which ignores the sampling theorem, and fully connected layers which lack spatial reasoning. We show that stride can greatly benefit translation invariance given that it is combined with sufficient similarity between neighbouring pixels, a characteristic which we refer to as local homogeneity. We also observe that this characteristic is dataset-specific and dictates the relationship between pooling kernel size and stride required for translation invariance. Furthermore we find that a trade-off exists between generalization and translation invariance in the case of pooling kernel size, as larger kernel sizes lead to better invariance but poorer generalization. Finally we explore the efficacy of other solutions proposed, namely global average pooling, anti-aliasing, and data augmentation, both empirically and through the lens of local homogeneity.

Pre-interpolation loss behaviour in neural networks

When training neural networks as classifiers, it is common to observe an increase in average test loss while still maintaining or improving the overall classification accuracy on the same dataset. In spite of the ubiquity of this phenomenon, it has not been well studied and is often dismissively attributed to an increase in borderline correct classifications. We present an empirical investigation that shows how this phenomenon is actually a result of the differential manner by which test samples are processed. In essence: test loss does not increase overall, but only for a small minority of samples. Large representational capacities allow losses to decrease for the vast majority of test samples at the cost of extreme increases for others. This effect seems to be mainly caused by increased parameter values relating to the correctly processed sample features. Our findings contribute to the practical understanding of a common behaviour of deep neural networks. We also discuss the implications of this work for network optimisation and generalisation.

DNNs as Layers of Cooperating Classifiers

A robust theoretical framework that can describe and predict the generalization ability of deep neural networks (DNNs) in general circumstances remains elusive. Classical attempts have produced complexity metrics that rely heavily on global measures of compactness and capacity with little investigation into the effects of sub-component collaboration. We demonstrate intriguing regularities in the activation patterns of the hidden nodes within fully-connected feedforward networks. By tracing the origin of these patterns, we show how such networks can be viewed as the combination of two information processing systems: one continuous and one discrete. We describe how these two systems arise naturally from the gradient-based optimization process, and demonstrate the classification ability of the two systems, individually and in collaboration. This perspective on DNN classification offers a novel way to think about generalization, in which different subsets of the training data are used to train distinct classifiers; those classifiers are then combined to perform the classification task, and their consistency is crucial for accurate classification.