Trajectory growth lower bounds for random sparse deep ReLU networks Article Swipe
Ilan Price
,
Jared Tanner
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1109/icmla52953.2021.00165
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1109/icmla52953.2021.00165
This paper considers the growth in the length of one-dimensional trajectories as they are passed through deep ReLU neural networks, which, among other things, is one measure of the expressivity of deep networks. We generalise existing results, providing an alternative, simpler method for lower bounding expected trajectory growth through random networks, for a more general class of weights distributions, including sparsely connected networks. We illustrate this approach by deriving bounds for sparse-Gaussian, sparse-uniform, and sparse-discrete-valued random nets. We prove that trajectory growth can remain exponential in depth with these new distributions, including their sparse variants, with the sparsity parameter appearing in the base of the exponent.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1109/icmla52953.2021.00165
- OA Status
- green
- Cited By
- 2
- References
- 31
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2990405359
All OpenAlex metadata
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https://openalex.org/W2990405359Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1109/icmla52953.2021.00165Digital Object Identifier
- Title
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Trajectory growth lower bounds for random sparse deep ReLU networksWork 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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2021-12-01Full publication date if available
- Authors
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Ilan Price, Jared TannerList of authors in order
- Landing page
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https://doi.org/10.1109/icmla52953.2021.00165Publisher 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/1911.10651Direct OA link when available
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Bounding overwatch, Trajectory, Gaussian, Exponent, Computer science, Class (philosophy), Algorithm, Mathematics, Torus, Applied mathematics, Artificial intelligence, Geometry, Physics, Quantum mechanics, Astronomy, Linguistics, PhilosophyTop concepts (fields/topics) attached by OpenAlex
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2Total citation count in OpenAlex
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2024: 1, 2021: 1Per-year citation counts (last 5 years)
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31Number of works referenced by this work
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.among | 21 |
| abstract_inverted_index.class | 55 |
| abstract_inverted_index.depth | 86 |
| abstract_inverted_index.lower | 43 |
| abstract_inverted_index.nets. | 76 |
| abstract_inverted_index.other | 22 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.prove | 78 |
| abstract_inverted_index.their | 92 |
| abstract_inverted_index.these | 88 |
| abstract_inverted_index.bounds | 69 |
| abstract_inverted_index.growth | 4, 47, 81 |
| abstract_inverted_index.length | 7 |
| abstract_inverted_index.method | 41 |
| abstract_inverted_index.neural | 18 |
| abstract_inverted_index.passed | 14 |
| abstract_inverted_index.random | 49, 75 |
| abstract_inverted_index.remain | 83 |
| abstract_inverted_index.sparse | 93 |
| abstract_inverted_index.which, | 20 |
| abstract_inverted_index.general | 54 |
| abstract_inverted_index.measure | 26 |
| abstract_inverted_index.simpler | 40 |
| abstract_inverted_index.things, | 23 |
| abstract_inverted_index.through | 15, 48 |
| abstract_inverted_index.weights | 57 |
| abstract_inverted_index.approach | 66 |
| abstract_inverted_index.bounding | 44 |
| abstract_inverted_index.deriving | 68 |
| abstract_inverted_index.existing | 35 |
| abstract_inverted_index.expected | 45 |
| abstract_inverted_index.results, | 36 |
| abstract_inverted_index.sparsely | 60 |
| abstract_inverted_index.sparsity | 97 |
| abstract_inverted_index.appearing | 99 |
| abstract_inverted_index.connected | 61 |
| abstract_inverted_index.considers | 2 |
| abstract_inverted_index.exponent. | 105 |
| abstract_inverted_index.including | 59, 91 |
| abstract_inverted_index.networks, | 19, 50 |
| abstract_inverted_index.networks. | 32, 62 |
| abstract_inverted_index.parameter | 98 |
| abstract_inverted_index.providing | 37 |
| abstract_inverted_index.variants, | 94 |
| abstract_inverted_index.generalise | 34 |
| abstract_inverted_index.illustrate | 64 |
| abstract_inverted_index.trajectory | 46, 80 |
| abstract_inverted_index.exponential | 84 |
| abstract_inverted_index.alternative, | 39 |
| abstract_inverted_index.expressivity | 29 |
| abstract_inverted_index.trajectories | 10 |
| abstract_inverted_index.distributions, | 58, 90 |
| abstract_inverted_index.one-dimensional | 9 |
| abstract_inverted_index.sparse-uniform, | 72 |
| abstract_inverted_index.sparse-Gaussian, | 71 |
| abstract_inverted_index.sparse-discrete-valued | 74 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.45161892 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |