Is network fragmentation a useful complexity measure?
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 16 of its 19 references that are in the map. First posted on arXiv 7 Nov 2024.
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References · 16
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- 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 672
- 2019Fantastic Generalization Measures and Where to Find Themcited by 513
- 2014On the Number of Linear Regions of Deep Neural Networkscited by 381
- 2016On the Expressive Power of Deep Neural Networkscited by 306
- 2018Sensitivity and Generalization in Neural Networks: an Empirical Studycited by 189
- 2019Complexity of Linear Regions in Deep Networkscited by 167
- 2020Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regimecited by 95
- 2022Can Neural Nets Learn the Same Model Twice? Investigating Reproducibility and Double Descent from the Decision Boundary Perspectivecited by 57
- 2019Generalization in Deep Networks: The Role of Distance from Initializationcited by 51
- 2024Neural Redshift: Random Networks are not Random Functionscited by 43
- 2020NeurIPS 2020 Competition: Predicting Generalization in Deep Learningcited by 41
4 more
- 2020Representation Based Complexity Measures for Predicting Generalization in Deep Learningcited by 29
- 2021Predicting Deep Neural Network Generalization with Perturbation Response Curvescited by 14
- 2022Are All Linear Regions Created Equal?cited by 13
- 2023Input margins can predict generalization toocited by 4
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