Learning Functions of Halfspaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910046598725632 |
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| author | Alman, Josh Patel, Shyamal Servedio, Rocco A. |
| author_facet | Alman, Josh Patel, Shyamal Servedio, Rocco A. |
| contents | We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log n)^{O(k)}}$. This is the first algorithm that can PAC learn even intersections of two halfspaces in time $2^{o(n)}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning Functions of Halfspaces Alman, Josh Patel, Shyamal Servedio, Rocco A. Data Structures and Algorithms Computational Complexity We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log n)^{O(k)}}$. This is the first algorithm that can PAC learn even intersections of two halfspaces in time $2^{o(n)}.$ |
| title | Learning Functions of Halfspaces |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2603.08700 |