Kolmogorov-Arnold Networks hit dimension curse on arbitrary targets
Source published ·Modelwire updated
Original coverage: arXiv cs.LG ↗·How Modelwire adds context
The development
A new theoretical analysis challenges the architectural advantages claimed for Kolmogorov-Arnold Networks, revealing that their dimension-independent approximation properties depend heavily on the structure of the target function rather than the model itself. Researchers prove that standard spline-KANs face exponential scaling penalties on arbitrary high-dimensional problems, matching limitations already known in MLPs. This work matters because KANs have attracted significant attention as a potential alternative to transformers for scientific computing and function approximation. The findings suggest the hype around KANs may conflate favorable properties of specific problem classes with genuine architectural breakthroughs, forcing practitioners to recalibrate expectations about when KANs outperform conventional networks.
Modelwire’s AI-generated summary of coverage from arXiv cs.LG.
Modelwire analysis
Skeptical readOur AI-generated reading of the wider context and the next developments to watch.
The paper's core finding isn't that KANs have limits (expected), but that their claimed dimension-independence is a property of the problem, not the architecture. This means KAN advocates have been attributing favorable results on structured problems to the model itself rather than to the input structure.
This echoes a pattern we've covered repeatedly: metric selection and comparison methodology matter more than the metric itself ("A Better Metric Will Not Save You" from October 9), and architectural choices often mask brittle mechanisms that fail under distribution shift ("Premature Floods in Recurrent Algorithmic Reasoners" from October 10, and "Why Linear Models Can Still Work" from the same period). The KAN story is another instance where a model's performance on a curated set of problems gets mistaken for general superiority. We've also seen this with synthetic benchmarks that overfit to their generators ("PATTERN Can Be Solved from Memory" from October 10). The difference here is that KANs aren't failing on a specific benchmark; they're failing on the theoretical promise itself.
If papers claiming KAN superiority on scientific computing tasks (PDEs, symbolic regression) from 2026-2027 explicitly restrict claims to low-dimensional or structured problem classes, the field has absorbed this critique. If they continue making dimension-agnostic claims without qualification, this arXiv result has been ignored by practitioners despite the evidence.
This interpretation is generated from the summary above and the archive coverage cited below. Our methodology · Report an error
Coverage behind this analysis
These archive entries ground the connection in our analysis. They are ordered by source publication date, with links to our coverage and the original sources.
·arXiv cs.CL
How you group data matters more than which metric you choose
A new arXiv paper challenges the foundational assumptions behind representational similarity analysis, a family of metrics widely used to compare neural network representations across models and architectures. The authors demonstrate that the choice of which conditions to compare matters far more than which mathematical invariance property the metric preserves. Testing across vowel acoustics in 27…
MentionsKolmogorov-Arnold Networks · MLPs · spline-KANs
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Modelwire summarizes, we don’t republish. arXiv cs.LG originally reported this story as “Kolmogorov-Arnold Networks: Curse of Dimensionality and Structural Bias”. The full content lives on arxiv.org. If you’re a publisher and want a different summarization policy for your work, see our takedown page.