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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.

@article{484,
  author = {Arthur Venter, Marthinus Theunissen, Marelie Davel},
  title = {Pre-interpolation loss behaviour in neural networks},
  abstract = {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.},
  year = {2020},
  journal = {Communications in Computer and Information Science},
  volume = {1342},
  pages = {296-309},
  publisher = {Southern African Conference for Artificial Intelligence Research},
  address = {South Africa},
  isbn = {978-3-030-66151-9},
  doi = {https://doi.org/10.1007/978-3-030-66151-9_19},
}

The understanding of generalisation in machine learning is in a state of flux, in part due to the ability of deep learning models to interpolate noisy training data and still perform appropriately on out-of-sample data, thereby contradicting long-held intuitions about the bias-variance trade off in learning. We expand upon relevant existing work by discussing local attributes of neural network training within the context of a relatively simple framework.We describe how various types of noise can be compensated for within the proposed framework in order to allow the deep learning model to generalise in spite of interpolating spurious function descriptors. Empirically,we support our postulates with experiments involving overparameterised multilayer perceptrons and controlled training data noise. The main insights are that deep learning models are optimised for training data modularly, with different regions in the function space dedicated to fitting distinct types of sample information. Additionally,we show that models tend to fit uncorrupted samples first. Based on this finding, we propose a conjecture to explain an observed instance of the epoch-wise double-descent phenomenon. Our findings suggest that the notion of model capacity needs to be modified to consider the distributed way training data is fitted across sub-units.

@article{394,
  author = {Marthinus Theunissen, Marelie Davel, Etienne Barnard},
  title = {Benign interpolation of noise in deep learning},
  abstract = {The understanding of generalisation in machine learning is in a state of flux, in part due to the ability of deep learning models to interpolate noisy training data and still perform appropriately on out-of-sample data, thereby contradicting long-held intuitions about the bias-variance trade off in learning. We expand upon relevant existing work by discussing local attributes of neural network training within the context of a relatively simple framework.We describe how various types of noise can be compensated for within the proposed framework in order to allow the deep learning model to generalise in spite of interpolating spurious function descriptors. Empirically,we support our postulates with experiments involving overparameterised multilayer perceptrons and controlled training data noise. The main insights are that deep learning models are optimised for training data modularly, with different regions in the function space dedicated to fitting distinct types of sample information. Additionally,we show that models tend to fit uncorrupted samples first. Based on this finding, we propose a conjecture to explain an observed instance of the epoch-wise double-descent phenomenon. Our findings suggest that the notion of model capacity needs to be modified to consider the distributed way training data is fitted across sub-units.},
  year = {2020},
  journal = {South African Computer Journal},
  volume = {32},
  pages = {80-101},
  issue = {2},
  publisher = {South African Institute of Computer Scientists and Information Technologists},
  isbn = {ISSN: 1015-7999; E:2313-7835},
  doi = {https://doi.org/10.18489/sacj.v32i2.833},
}

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},
}