Tian Theunissen

2024

Mouton, C. ., Rabe, R. ., Haasbroek, D. G., Theunissen, M. W., Potgieter, H. ., & Davel, M. H. (2024). Is network fragmentation a useful complexity measure?. NeurIPS 2024 Workshop SciForDL.

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27_Is_network_fragmentation_a_.pdf

It has been observed that the input space of deep neural network classifiers can exhibit ‘fragmentation’, where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the double descent curve, achieving a maximum at the interpolation regime. We study this phenomenon in the context of image classification and ask whether fragmentation could be predictive of generalization performance. Using a fragmentation-based complexity measure, we show this to be possible by achieving good performance on the PGDL (Predicting Generalization in Deep Learning) benchmark. In addition, we report on new observations related to fragmentation, namely (i) fragmentation is not limited to the input space but occurs in the hidden representations as well, (ii) fragmentation follows the trends in the validation error throughout training, and (iii) fragmentation is not a direct result of increased weight norms. Together, this indicates that fragmentation is a phenomenon worth investigating further when studying the generalization ability of deep neural networks.

@misc{514,
  author = {Coenraad Mouton and Randle Rabe and Daniël Haasbroek and Marthinus Theunissen and Harmen Potgieter and Marelie Davel},
  title = {Is network fragmentation a useful complexity measure?},
  abstract = {It has been observed that the input space of deep neural network classifiers can exhibit ‘fragmentation’, where the model function rapidly changes class as the input space is traversed. The severity of this fragmentation tends to follow the double descent curve, achieving a maximum at the interpolation regime. We study this phenomenon in the context of image classification and ask whether fragmentation could be predictive of generalization performance. Using a fragmentation-based complexity measure, we show this to be possible by achieving good performance on the PGDL (Predicting Generalization in Deep Learning) benchmark. In addition, we report on new observations related to fragmentation, namely (i) fragmentation is not limited to the input space but occurs in the hidden representations as well, (ii) fragmentation follows the trends in the validation error throughout training, and (iii) fragmentation is not a direct result of increased weight norms. Together, this indicates that fragmentation is a phenomenon worth investigating further when studying the generalization ability of deep neural networks.},
  year = {2024},
  journal = {NeurIPS 2024 Workshop SciForDL},
  month = {12/2024},
}

Mouton, C. ., Theunissen, M. W., & Davel, M. H. (2024). Input margins can predict generalization too. In In Proceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence (AAAI’24/IAAI’24/E. AAAI Conference on Artificial Intelligence (AAAI).

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29351-Article Text-33405-1-2-20240324 (2).pdf

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

@inbook{512,
  author = {Coenraad Mouton and Marthinus Theunissen and Marelie Davel},
  title = {Input margins can predict generalization too},
  abstract = {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},
  year = {2024},
  journal = {In Proceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence (AAAI&#039;24/IAAI&#039;24/E},
  pages = {14379 - 14387},
  month = {20 February 2024},
  publisher = {AAAI Conference on Artificial Intelligence (AAAI)},
}

2023

Davel, M. H., Lotz, S. ., Theunissen, M. W., De Villiers, A. ., Grant, C. ., Rabe, R. ., & Conacher, C. . (2023). Knowledge Discovery in Time Series Data. In Deep Learning Indaba 2023.

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DLI_poster_2023.pdf

• Complex time series data often encountered in scientific and engineering domains. • Deep learning (DL) is particularly successful here: – large data sets, multivariate input and/or ouput, – highly complex sequences of interactions. • Model interpretability: – Ability to understand a model’s decisions in a given context [1]. – Techniques typically not originally developed for time series data. – Time series interpretations themselves become uninterpretable. • Knowledge Discovery: – DL has potential to reveal interesting patterns in large data sets. – Potential to produce novel insights about the task itself [2, 3]. • ‘know-it’: Collaborative project that studies knowledge discovery in time series data.

@{507,
  author = {Marelie Davel and Stefan Lotz and Marthinus Theunissen and Almaro De Villiers and Chara Grant and Randle Rabe and Cleo Conacher},
  title = {Knowledge Discovery in Time Series Data},
  abstract = {• Complex time series data often encountered in scientific and engineering domains.
• Deep learning (DL) is particularly successful here:
– large data sets, multivariate input and/or ouput,
– highly complex sequences of interactions.
• Model interpretability:
– Ability to understand a model’s decisions in a given context [1].
– Techniques typically not originally developed for time series data.
– Time series interpretations themselves become uninterpretable.
• Knowledge Discovery:
– DL has potential to reveal interesting patterns in large data sets.
– Potential to produce novel insights about the task itself [2, 3].
• ‘know-it’: Collaborative project that studies knowledge discovery in
time series data.},
  year = {2023},
  journal = {Deep Learning Indaba 2023},
  month = {September 2023},
}

2022

Theunissen, M. W., Mouton, C. ., & Davel, M. H. (2022). The Missing Margin: How Sample Corruption Affects Distance to the Boundary in ANNs. In Artificial Intelligence Research (SACAIR 2022), Communications in Computer and Information Science (Vol. 1734). Springer, Cham. http://doi.org/ https://doi.org/10.48550/arXiv.2302.06925

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2302.06925.pdf

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.

@inbook{505,
  author = {Marthinus Theunissen and Coenraad Mouton and Marelie Davel},
  title = {The Missing Margin: How Sample Corruption Affects Distance to the Boundary in ANNs},
  abstract = {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.},
  year = {2022},
  journal = {Artificial Intelligence Research (SACAIR 2022), Communications in Computer and Information Science},
  volume = {1734},
  pages = {78 - 92},
  month = {November 2022},
  publisher = {Springer, Cham},
  doi = {https://doi.org/10.48550/arXiv.2302.06925},
}

2020

Venter, A. E., Theunissen, M. W., & Davel, M. H. (2020). Pre-interpolation loss behaviour in neural networks. Communications in Computer and Information Science, 1342. http://doi.org/https://doi.org/10.1007/978-3-030-66151-9_19

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Pre-interpolation-loss-behaviour-venter_0.pdf

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 and Marthinus Theunissen and 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},
}

Theunissen, M. W., Davel, M. H., & Barnard, E. . (2020). Benign interpolation of noise in deep learning. South African Computer Journal, 32(2). http://doi.org/https://doi.org/10.18489/sacj.v32i2.833

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Benign-interpolation-theunissen.pdf

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 and Marelie Davel and 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},
}

Davel, M. H., Theunissen, M. W., Pretorius, A. P., & Barnard, E. . (2020). DNNs as layers of cooperating classifiers. In The Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20). New York.

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Published (shortened) version

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 and Marthinus Theunissen and Arnold Pretorius and 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},
}

2019

Theunissen, M. W., Davel, M. H., & Barnard, E. . (2019). Insights regarding overfitting on noise in deep learning. In South African Forum for Artificial Intelligence Research (FAIR). Cape Town, South Africa.

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Insights regarding overfitting on noise in deep learning

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 and Marelie Davel and 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},
}