On the Initialisation of Wide Low-Rank Feedforward Neural Networks Article Swipe
Thiziri Nait Saada
,
Jared Tanner
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2301.13710
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2301.13710
The edge-of-chaos dynamics of wide randomly initialized low-rank feedforward networks are analyzed. Formulae for the optimal weight and bias variances are extended from the full-rank to low-rank setting and are shown to follow from multiplicative scaling. The principle second order effect, the variance of the input-output Jacobian, is derived and shown to increase as the rank to width ratio decreases. These results inform practitioners how to randomly initialize feedforward networks with a reduced number of learnable parameters while in the same ambient dimension, allowing reductions in the computational cost and memory constraints of the associated network.
Related Topics
Concepts
Rank (graph theory)
Feed forward
Jacobian matrix and determinant
Multiplicative function
Feedforward neural network
Dimension (graph theory)
Variance (accounting)
Artificial neural network
Inverse
Computer science
Enhanced Data Rates for GSM Evolution
Mathematics
Algorithm
Applied mathematics
Artificial intelligence
Combinatorics
Mathematical analysis
Engineering
Geometry
Business
Control engineering
Accounting
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2301.13710
- https://arxiv.org/pdf/2301.13710
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4318908232
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4318908232Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2301.13710Digital Object Identifier
- Title
-
On the Initialisation of Wide Low-Rank Feedforward Neural NetworksWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-01-31Full publication date if available
- Authors
-
Thiziri Nait Saada, Jared TannerList of authors in order
- Landing page
-
https://arxiv.org/abs/2301.13710Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2301.13710Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2301.13710Direct OA link when available
- Concepts
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Rank (graph theory), Feed forward, Jacobian matrix and determinant, Multiplicative function, Feedforward neural network, Dimension (graph theory), Variance (accounting), Artificial neural network, Inverse, Computer science, Enhanced Data Rates for GSM Evolution, Mathematics, Algorithm, Applied mathematics, Artificial intelligence, Combinatorics, Mathematical analysis, Engineering, Geometry, Business, Control engineering, AccountingTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.computational | 87 |
| abstract_inverted_index.edge-of-chaos | 1 |
| abstract_inverted_index.practitioners | 63 |
| abstract_inverted_index.multiplicative | 34 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |