On the weight dynamics of learning networks
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916231902134272 |
|---|---|
| author | Sharafi, Nahal Martin, Christoph Hallerberg, Sarah |
| author_facet | Sharafi, Nahal Martin, Christoph Hallerberg, Sarah |
| contents | Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution we use the mathematical framework of local stability analysis to gain a deeper understanding of the learning dynamics of feed forward neural networks. Therefore, we derive equations for the tangent operator of the learning dynamics of three-layer networks learning regression tasks. The results are valid for an arbitrary numbers of nodes and arbitrary choices of activation functions. Applying the results to a network learning a regression task, we investigate numerically, how stability indicators relate to the final training-loss. Although the specific results vary with different choices of initial conditions and activation functions, we demonstrate that it is possible to predict the final training loss, by monitoring finite-time Lyapunov exponents or covariant Lyapunov vectors during the training process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the weight dynamics of learning networks Sharafi, Nahal Martin, Christoph Hallerberg, Sarah Machine Learning Chaotic Dynamics Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution we use the mathematical framework of local stability analysis to gain a deeper understanding of the learning dynamics of feed forward neural networks. Therefore, we derive equations for the tangent operator of the learning dynamics of three-layer networks learning regression tasks. The results are valid for an arbitrary numbers of nodes and arbitrary choices of activation functions. Applying the results to a network learning a regression task, we investigate numerically, how stability indicators relate to the final training-loss. Although the specific results vary with different choices of initial conditions and activation functions, we demonstrate that it is possible to predict the final training loss, by monitoring finite-time Lyapunov exponents or covariant Lyapunov vectors during the training process. |
| title | On the weight dynamics of learning networks |
| topic | Machine Learning Chaotic Dynamics |
| url | https://arxiv.org/abs/2405.00743 |