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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.11743 |
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| _version_ | 1866929348749033472 |
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| author | Fu, Jingwen Zhang, Zhizheng Lu, Yan Zheng, Nanning |
| author_facet | Fu, Jingwen Zhang, Zhizheng Lu, Yan Zheng, Nanning |
| contents | Compositional Generalization (CG) embodies the ability to comprehend novel combinations of familiar concepts, representing a significant cognitive leap in human intellectual advancement. Despite its critical importance, the deep neural network (DNN) faces challenges in addressing the compositional generalization problem, prompting considerable research interest. However, existing theories often rely on task-specific assumptions, constraining the comprehensive understanding of CG. This study aims to explore compositional generalization from a task-agnostic perspective, offering a complementary viewpoint to task-specific analyses. The primary challenge is to define CG without overly restricting its scope, a feat achieved by identifying its fundamental characteristics and basing the definition on them. Using this definition, we seek to answer the question "what does the ultimate solution to CG look like?" through the following theoretical findings: 1) the first No Free Lunch theorem in CG, indicating the absence of general solutions; 2) a novel generalization bound applicable to any CG problem, specifying the conditions for an effective CG solution; and 3) the introduction of the generative effect to enhance understanding of CG problems and their solutions. This paper's significance lies in providing a general theory for CG problems, which, when combined with prior theorems under task-specific scenarios, can lead to a comprehensive understanding of CG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A General Theory for Compositional Generalization Fu, Jingwen Zhang, Zhizheng Lu, Yan Zheng, Nanning Machine Learning Compositional Generalization (CG) embodies the ability to comprehend novel combinations of familiar concepts, representing a significant cognitive leap in human intellectual advancement. Despite its critical importance, the deep neural network (DNN) faces challenges in addressing the compositional generalization problem, prompting considerable research interest. However, existing theories often rely on task-specific assumptions, constraining the comprehensive understanding of CG. This study aims to explore compositional generalization from a task-agnostic perspective, offering a complementary viewpoint to task-specific analyses. The primary challenge is to define CG without overly restricting its scope, a feat achieved by identifying its fundamental characteristics and basing the definition on them. Using this definition, we seek to answer the question "what does the ultimate solution to CG look like?" through the following theoretical findings: 1) the first No Free Lunch theorem in CG, indicating the absence of general solutions; 2) a novel generalization bound applicable to any CG problem, specifying the conditions for an effective CG solution; and 3) the introduction of the generative effect to enhance understanding of CG problems and their solutions. This paper's significance lies in providing a general theory for CG problems, which, when combined with prior theorems under task-specific scenarios, can lead to a comprehensive understanding of CG. |
| title | A General Theory for Compositional Generalization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.11743 |