What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866909077589721088 |
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| author | Alexander, Yotam De La Vega, Nimrod Razin, Noam Cohen, Nadav |
| author_facet | Alexander, Yotam De La Vega, Nimrod Razin, Noam Cohen, Nadav |
| contents | The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural networks as well as local self-attention models), we address this problem by adopting theoretical tools from quantum physics. Our main theoretical result states that a certain locally connected neural network is capable of accurate prediction over a data distribution if and only if the data distribution admits low quantum entanglement under certain canonical partitions of features. As a practical application of this result, we derive a preprocessing method for enhancing the suitability of a data distribution to locally connected neural networks. Experiments with widespread models over various datasets demonstrate our findings. We hope that our use of quantum entanglement will encourage further adoption of tools from physics for formally reasoning about the relation between deep learning and real-world data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement Alexander, Yotam De La Vega, Nimrod Razin, Noam Cohen, Nadav Machine Learning Artificial Intelligence Quantum Physics The question of what makes a data distribution suitable for deep learning is a fundamental open problem. Focusing on locally connected neural networks (a prevalent family of architectures that includes convolutional and recurrent neural networks as well as local self-attention models), we address this problem by adopting theoretical tools from quantum physics. Our main theoretical result states that a certain locally connected neural network is capable of accurate prediction over a data distribution if and only if the data distribution admits low quantum entanglement under certain canonical partitions of features. As a practical application of this result, we derive a preprocessing method for enhancing the suitability of a data distribution to locally connected neural networks. Experiments with widespread models over various datasets demonstrate our findings. We hope that our use of quantum entanglement will encourage further adoption of tools from physics for formally reasoning about the relation between deep learning and real-world data. |
| title | What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement |
| topic | Machine Learning Artificial Intelligence Quantum Physics |
| url | https://arxiv.org/abs/2303.11249 |