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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.

@{236,
  author = {Marelie Davel, Marthinus Theunissen, Arnold Pretorius, Etienne Barnard},
  title = {DNNs as layers of cooperating classifiers},
  abstract = {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.},
  year = {2020},
  journal = {The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20)},
  pages = {3725 - 3732},
  month = {07/02-12/02/2020},
  address = {New York},
}

The understanding of generalization in machine learning is in a state of flux. This is partly due to the elatively recent revelation that deep learning models are able to completely memorize training data and still perform appropriately on out-of-sample data, thereby contradicting long-held intuitions about generalization. The phenomenon was brought to light and discussed in a seminal paper by Zhang et al. [24]. We expand upon this work by discussing local attributes of neural network training within the context of a relatively simple and generalizable framework. We describe how various types of noise can be compensated for within the proposed framework in order to allow the global deep learning model to generalize in spite of interpolating spurious function descriptors. Empirically, we support our postulates with experiments involving overparameterized multilayer perceptrons and controlled noise in the training data. The main insights are that deep learning models are optimized for training data modularly, with different regions in the function space dedicated to fitting distinct kinds of sample information. Detrimental overfitting is largely prevented by the fact that different regions in the function space are used for prediction based on the similarity between new input data and that which has been optimized for.

@{284,
  author = {Marthinus Theunissen, Marelie Davel, Etienne Barnard},
  title = {Insights regarding overfitting on noise in deep learning},
  abstract = {The understanding of generalization in machine learning is in a state of flux. This is partly due to the elatively recent revelation that deep learning models are able to completely memorize training data and still perform appropriately on out-of-sample data, thereby contradicting long-held intuitions about generalization. The phenomenon was brought to light and discussed in a seminal paper by Zhang et al. [24]. We expand upon this work by discussing local attributes of neural network training within the context of a relatively simple and generalizable framework. We describe how various types of noise can be compensated for within the proposed framework in order to allow the global deep learning model to generalize in spite of interpolating spurious function descriptors. Empirically, we support our postulates with experiments involving overparameterized multilayer perceptrons and controlled noise in the training data. The main insights are that deep learning models are optimized for training data modularly, with different regions in the function space dedicated to fitting distinct kinds of sample information. Detrimental overfitting is largely prevented by the fact that different regions in the function space are used for prediction based on the similarity between new input data and that which has been optimized for.},
  year = {2019},
  journal = {South African Forum for Artificial Intelligence Research (FAIR)},
  pages = {49-63},
  address = {Cape Town, South Africa},
}

The generalization capabilities of deep neural networks are not well understood, and in particular, the influence of activation functions on generalization has received little theoretical attention. Phenomena such as vanishing gradients, node saturation and network sparsity have been identified as possible factors when comparing different activation functions [1]. We investigate these factors using fully connected feedforward networks on two standard benchmark problems, and find that the most salient differences between networks with sigmoidal and ReLU activations relate to the way that class-distinctive information is propagated through a network.

@{279,
  author = {Arnold Pretorius, Etienne Barnard, Marelie Davel},
  title = {ReLU and sigmoidal activation functions},
  abstract = {The generalization capabilities of deep neural networks are not well understood, and in particular, the influence of activation functions on generalization has received little theoretical attention. Phenomena such as vanishing gradients, node saturation and network sparsity have been identified as possible factors when comparing different activation functions [1]. We investigate these factors using fully connected feedforward networks on two standard benchmark problems, and find that the most salient differences between networks with sigmoidal and ReLU activations relate to the way that class-distinctive information is propagated through a network.},
  year = {2019},
  journal = {South African Forum for Artificial Intelligence Research (FAIR)},
  pages = {37-48},
  month = {04/12-07/12},
  publisher = {CEUR Workshop Proceedings},
  address = {Cape Town, South Africa},
}

Estimating the joint probability density function of a dataset is a central task in many machine learning applications. In this work we address the fundamental problem of kernel bandwidth estimation for variable kernel density estimation in high-dimensional feature spaces. We derive a variable kernel bandwidth estimator by minimizing the leave-one-out entropy objective function and show that this estimator is capable of performing estimation in high-dimensional feature spaces with great success. We compare the performance of this estimator to state-of-the art maximum likelihood estimators on a number of representative high-dimensional machine learning tasks and show that the newly introduced minimum leave-one-out entropy estimator performs optimally on a number of high-dimensional datasets considered.

@{275,
  author = {Christiaan Van der Walt, Etienne Barnard},
  title = {Variable Kernel Density Estimation in High-dimensional Feature Spaces},
  abstract = {Estimating the joint probability density function of a dataset is a central task in many machine learning applications. In this work we address the fundamental problem of kernel bandwidth estimation for variable kernel density estimation in high-dimensional feature spaces. We derive a variable kernel bandwidth estimator by minimizing the leave-one-out entropy objective function and show that this estimator is capable of performing estimation in high-dimensional feature spaces with great success. We compare the performance of this estimator to state-of-the art maximum likelihood estimators on a number of representative high-dimensional machine learning tasks and show that the newly introduced minimum leave-one-out entropy estimator performs optimally on a number of high-dimensional datasets considered.},
  year = {2017},
  journal = {AAAI Conf. on Artificial Intelligence (AAAI-17)},
  pages = {2674-2680},
  month = {04/02-09/04},
}

Automatic speech recognition (ASR) technology has matured over the past few decades and has made significant impacts in a variety of fields, from assistive technologies to commercial products. However, ASR system development is a resource intensive activity and requires language resources in the form of text annotated audio recordings and pronunciation dictionaries. Unfortunately, many languages found in the developing world fall into the resource-scarce category and due to this resource scarcity the deployment of ASR systems in the developing world is severely inhibited. One approach to assist with resource-scarce ASR system development, is to select 'useful' training samples which could reduce the resources needed to collect new corpora. In this work, we propose a new data selection framework which can be used to design a speech recognition corpus. We show for limited data sets, independent of language and bandwidth, the most effective strategy for data selection is frequency-matched selection and that the widely-used maximum entropy methods generally produced the least promising results. In our model, the frequency-matched selection method corresponds to a logarithmic relationship between accuracy and corpus size; we also investigated other model relationships, and found that a hyperbolic relationship (as suggested from simple asymptotic arguments in learning theory) may lead to somewhat better performance under certain conditions.

@article{291,
  author = {Neil Kleynhans, Etienne Barnard},
  title = {Efficient data selection for ASR},
  abstract = {Automatic speech recognition (ASR) technology has matured over the past few decades and has made significant impacts in a variety of fields, from assistive technologies to commercial products. However, ASR system development is a resource intensive activity and requires language resources in the form of text annotated audio recordings and pronunciation dictionaries. Unfortunately, many languages found in the developing world fall into the resource-scarce category and due to this resource scarcity the deployment of ASR systems in the developing world is severely inhibited. One approach to assist with resource-scarce ASR system development, is to select 'useful' training samples which could reduce the resources needed to collect new corpora. In this work, we propose a new data selection framework which can be used to design a speech recognition corpus. We show for limited data sets, independent of language and bandwidth, the most effective strategy for data selection is frequency-matched selection and that the widely-used maximum entropy methods generally produced the least promising results. In our model, the frequency-matched selection method corresponds to a logarithmic relationship between accuracy and corpus size; we also investigated other model relationships, and found that a hyperbolic relationship (as suggested from simple asymptotic arguments in learning theory) may lead to somewhat better performance under certain conditions.},
  year = {2015},
  journal = {Language Resources and Evaluation},
  volume = {49},
  pages = {327-353},
  issue = {2},
  publisher = {Springer Science+Business Media},
  address = {Dordrecht},
  doi = {10.1007/s10579-014-9285-0},
}