研究人员开发了一种用于复杂函数深度Kolmogorov-Arnold网络（KAN）表示的方法，确保了逐层Lipschitz乘积控制。该方法保证了一个独立于输入维度的域敏感界限，对于标准操作简化为P(KAN) <= 1。研究结果填补了深度KAN堆栈Lipschitz控制方面的空白，并得到了实验验证的支持。 AI
影响 引入了一个改进KAN稳定性和逼近的理论框架，可能影响未来的模型架构。
排序理由 学术论文，详细介绍了一种用于KAN表示的新理论方法。
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arXiv:2604.26444v1 Announce Type: new Abstract: We prove that any continuous function f from [0,1]^n to R representable by a finite computation tree with N internal nodes and compositional sparsity s = O(1) admits a deep Kolmogorov-Arnold Network (KAN) representation. Each intern…
We prove that any continuous function f from [0,1]^n to R representable by a finite computation tree with N internal nodes and compositional sparsity s = O(1) admits a deep Kolmogorov-Arnold Network (KAN) representation. Each internal node is realised by a primitive KAN block wit…
We prove that any continuous function f from [0,1]^n to R representable by a finite computation tree with N internal nodes and compositional sparsity s = O(1) admits a deep Kolmogorov-Arnold Network (KAN) representation. Each internal node is realised by a primitive KAN block wit…