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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.17952 |
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| _version_ | 1866917283931095040 |
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| author | Lou, Hu Gao, Yin-Jun Zhang, Dong-Xiao Du, Tai-Jiao Zhang, Jun-Jie Zhang, Jia-Rui |
| author_facet | Lou, Hu Gao, Yin-Jun Zhang, Dong-Xiao Du, Tai-Jiao Zhang, Jun-Jie Zhang, Jia-Rui |
| contents | One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered by flat loss landscapes induced by parameter-space symmetries, leading to slow convergence and poor generalization, particularly for high-frequency components. Inspired by the principle of \emph{symmetry breaking} in physics, this paper proposes a hardware-friendly approach for function approximation through \emph{input-space expansion}. The core idea involves augmenting the original one-dimensional input (e.g., $x$) with constant values (e.g., $π$) to form a higher-dimensional vector (e.g., $[π, π, x, π, π]$), effectively breaking parameter symmetries without increasing the network's parameter count. We evaluate the method on ten representative one-dimensional functions, including smooth, discontinuous, high-frequency, and non-differentiable functions. Experimental results demonstrate that input-space expansion significantly accelerates training convergence (reducing LBFGS iterations by 12\% on average) and enhances approximation accuracy (reducing final MSE by 66.3\% for the optimal 5D expansion). Ablation studies further reveal the effects of different expansion dimensions and constant selections, with $π$ consistently outperforming other constants. Our work proposes a low-cost, efficient, and hardware-friendly technique for algorithm design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hardware-Friendly Input Expansion for Accelerating Function Approximation Lou, Hu Gao, Yin-Jun Zhang, Dong-Xiao Du, Tai-Jiao Zhang, Jun-Jie Zhang, Jia-Rui Machine Learning One-dimensional function approximation is a fundamental problem in scientific computing and engineering applications. While neural networks possess powerful universal approximation capabilities, their optimization process is often hindered by flat loss landscapes induced by parameter-space symmetries, leading to slow convergence and poor generalization, particularly for high-frequency components. Inspired by the principle of \emph{symmetry breaking} in physics, this paper proposes a hardware-friendly approach for function approximation through \emph{input-space expansion}. The core idea involves augmenting the original one-dimensional input (e.g., $x$) with constant values (e.g., $π$) to form a higher-dimensional vector (e.g., $[π, π, x, π, π]$), effectively breaking parameter symmetries without increasing the network's parameter count. We evaluate the method on ten representative one-dimensional functions, including smooth, discontinuous, high-frequency, and non-differentiable functions. Experimental results demonstrate that input-space expansion significantly accelerates training convergence (reducing LBFGS iterations by 12\% on average) and enhances approximation accuracy (reducing final MSE by 66.3\% for the optimal 5D expansion). Ablation studies further reveal the effects of different expansion dimensions and constant selections, with $π$ consistently outperforming other constants. Our work proposes a low-cost, efficient, and hardware-friendly technique for algorithm design. |
| title | Hardware-Friendly Input Expansion for Accelerating Function Approximation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.17952 |