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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.17952 |
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Table of 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.