Investigating the locality of neural network training dynamics. Article Swipe
A fundamental quest in the theory of deep-learning is to understand the properties of the trajectories in the weight space that a learning algorithm takes. One such property that had very recently been isolated is that of ($S_{\rm rel}$), which quantifies the propagation of influence of a sampled data point on the prediction at another data point. In this work, we perform a comprehensive study of local elasticity by providing new theoretical insights and more careful empirical evidence of this property in a variety of settings. Firstly, specific to the classification setting, we suggest a new definition of the original idea of $S_{\rm rel}$. Via experiments on state-of-the-art neural networks training on SVHN, CIFAR-10 and CIFAR-100 we demonstrate how our new $S_{\rm rel}$ detects the property of the weight updates preferring to make changes in predictions within the same class of the sampled data. Next, we demonstrate via examples of neural nets doing regression that the original $S_{\rm rel}$ reveals a $2-$phase behaviour: that their training proceeds via an initial elastic phase when $S_{\rm rel}$ changes rapidly and an eventual inelastic phase when $S_{\rm rel}$ remains large. Lastly, we give multiple examples of learning via gradient flows for which one can get a closed-form expression of the original $S_{\rm rel}$ function. By studying the plots of these derived formulas we given a theoretical demonstration of some of the experimentally detected properties of $S_{\rm rel}$ in the regression setting.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/pdf/2111.01166.pdf
- OA Status
- green
- Cited By
- 1
- References
- 13
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3208382036
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- OpenAlex ID
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https://openalex.org/W3208382036Canonical identifier for this work in OpenAlex
- Title
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Investigating the locality of neural network training dynamics.Work title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-11-02Full publication date if available
- Authors
-
Soham Dan, Phanideep Gampa, Anirbit MukherjeeList of authors in order
- Landing page
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https://arxiv.org/pdf/2111.01166.pdfPublisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2111.01166.pdfDirect OA link when available
- Concepts
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Locality, Property (philosophy), Artificial neural network, Artificial intelligence, Point (geometry), Computer science, Class (philosophy), Machine learning, Function (biology), Mathematics, Algorithm, Geometry, Epistemology, Evolutionary biology, Biology, Philosophy, LinguisticsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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13Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.quantifies | 42 |
| abstract_inverted_index.regression | 155, 238 |
| abstract_inverted_index.understand | 10 |
| abstract_inverted_index.closed-form | 205 |
| abstract_inverted_index.demonstrate | 119, 148 |
| abstract_inverted_index.experiments | 107 |
| abstract_inverted_index.fundamental | 1 |
| abstract_inverted_index.predictions | 137 |
| abstract_inverted_index.propagation | 44 |
| abstract_inverted_index.theoretical | 73, 224 |
| abstract_inverted_index.trajectories | 15 |
| abstract_inverted_index.comprehensive | 65 |
| abstract_inverted_index.deep-learning | 7 |
| abstract_inverted_index.demonstration | 225 |
| abstract_inverted_index.classification | 92 |
| abstract_inverted_index.experimentally | 230 |
| abstract_inverted_index.state-of-the-art | 109 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |