Global convergence of SGD on two layer neural nets Article Swipe
Pulkit Gopalani
,
Anirbit Mukherjee
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1093/imaiai/iaae035
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1093/imaiai/iaae035
In this note, we consider appropriately regularized $\ell _{2}-$empirical risk of depth $2$ nets with any number of gates and show bounds on how the empirical loss evolves for Stochastic Gradient Descent (SGD) iterates on it—for arbitrary data and if the activation is adequately smooth and bounded like sigmoid and tanh. This, in turn, leads to a proof of global convergence of SGD for a special class of initializations. We also prove an exponentially fast convergence rate for continuous time SGD that also applies to smooth unbounded activations like SoftPlus. Our key idea is to show the existence of Frobenius norm regularized loss functions on constant-sized neural nets that are ‘Villani functions’ and thus be able to build on recent progress with analyzing SGD on such objectives. Most critically, the amount of regularization required for our analysis is independent of the size of the net.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1093/imaiai/iaae035
- https://academic.oup.com/imaiai/article-pdf/14/1/iaae035/61510614/iaae035.pdf
- OA Status
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- Cited By
- 1
- References
- 90
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4406626549
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https://doi.org/10.1093/imaiai/iaae035Digital Object Identifier
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Global convergence of SGD on two layer neural netsWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-01-15Full publication date if available
- Authors
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Pulkit Gopalani, Anirbit MukherjeeList of authors in order
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https://doi.org/10.1093/imaiai/iaae035Publisher landing page
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https://academic.oup.com/imaiai/article-pdf/14/1/iaae035/61510614/iaae035.pdfDirect link to full text PDF
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hybridOpen access status per OpenAlex
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https://academic.oup.com/imaiai/article-pdf/14/1/iaae035/61510614/iaae035.pdfDirect OA link when available
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Convergence (economics), Layer (electronics), Political science, Computer science, Economics, Nanotechnology, Materials science, MacroeconomicsTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.Gradient | 31 |
| abstract_inverted_index.analysis | 137 |
| abstract_inverted_index.consider | 5 |
| abstract_inverted_index.iterates | 34 |
| abstract_inverted_index.it—for | 36 |
| abstract_inverted_index.progress | 121 |
| abstract_inverted_index.required | 134 |
| abstract_inverted_index.Frobenius | 100 |
| abstract_inverted_index.SoftPlus. | 90 |
| abstract_inverted_index.analyzing | 123 |
| abstract_inverted_index.arbitrary | 37 |
| abstract_inverted_index.empirical | 26 |
| abstract_inverted_index.existence | 98 |
| abstract_inverted_index.functions | 104 |
| abstract_inverted_index.unbounded | 87 |
| abstract_inverted_index.Stochastic | 30 |
| abstract_inverted_index.activation | 42 |
| abstract_inverted_index.adequately | 44 |
| abstract_inverted_index.continuous | 79 |
| abstract_inverted_index.‘Villani | 111 |
| abstract_inverted_index.activations | 88 |
| abstract_inverted_index.convergence | 61, 76 |
| abstract_inverted_index.critically, | 129 |
| abstract_inverted_index.independent | 139 |
| abstract_inverted_index.objectives. | 127 |
| abstract_inverted_index.regularized | 7, 102 |
| abstract_inverted_index.functions’ | 112 |
| abstract_inverted_index.appropriately | 6 |
| abstract_inverted_index.exponentially | 74 |
| abstract_inverted_index.constant-sized | 106 |
| abstract_inverted_index.regularization | 133 |
| abstract_inverted_index._{2}-$empirical | 9 |
| abstract_inverted_index.initializations. | 69 |
| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 91 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.92557293 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |