One Rank at a Time: Cascading Error Dynamics in Sequential Learning
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913864382152704 |
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| author | Vandchali, Mahtab Alizadeh Fangshuo Liao Kyrillidis, Anastasios |
| author_facet | Vandchali, Mahtab Alizadeh Fangshuo Liao Kyrillidis, Anastasios |
| contents | Sequential learning -- where complex tasks are broken down into simpler, hierarchical components -- has emerged as a paradigm in AI. This paper views sequential learning through the lens of low-rank linear regression, focusing specifically on how errors propagate when learning rank-1 subspaces sequentially. We present an analysis framework that decomposes the learning process into a series of rank-1 estimation problems, where each subsequent estimation depends on the accuracy of previous steps. Our contribution is a characterization of the error propagation in this sequential process, establishing bounds on how errors -- e.g., due to limited computational budgets and finite precision -- affect the overall model accuracy. We prove that these errors compound in predictable ways, with implications for both algorithmic design and stability guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One Rank at a Time: Cascading Error Dynamics in Sequential Learning Vandchali, Mahtab Alizadeh Fangshuo Liao Kyrillidis, Anastasios Machine Learning Artificial Intelligence Optimization and Control Sequential learning -- where complex tasks are broken down into simpler, hierarchical components -- has emerged as a paradigm in AI. This paper views sequential learning through the lens of low-rank linear regression, focusing specifically on how errors propagate when learning rank-1 subspaces sequentially. We present an analysis framework that decomposes the learning process into a series of rank-1 estimation problems, where each subsequent estimation depends on the accuracy of previous steps. Our contribution is a characterization of the error propagation in this sequential process, establishing bounds on how errors -- e.g., due to limited computational budgets and finite precision -- affect the overall model accuracy. We prove that these errors compound in predictable ways, with implications for both algorithmic design and stability guarantees. |
| title | One Rank at a Time: Cascading Error Dynamics in Sequential Learning |
| topic | Machine Learning Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2505.22602 |