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Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discovery
Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discovery
Published: 12 May 2026 · Updated: 13 July 2026
Read the original sourceThe Critique
The paper's findings challenge the KAN hype, but they don't explore the fundamental question: why does the Kolmogorov-Arnold representation theorem fail to translate to neural network performance? The theorem guarantees that any continuous function can be represented, but the paper shows learnability issues. They miss that this reveals a crucial distinction between approximation theory (what functions CAN be represented) and learning theory (what functions CAN BE LEARNED from data). This is a profound insight for neural network theory that the paper under-emphasizes.
Why It Matters
The distinction between representability and learnability affects how we evaluate all neural architecture proposals based on mathematical theorems. If KANs can represent but not learn, this undermines a common justification for architecture design.