# Kolmogorov--Arnold Networks for Small Language Models

arXiv: https://arxiv.org/abs/2607.15525 · HTML: https://mlsanity.com/paper/2607.15525/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [BLiMP: The Benchmark of Linguistic Minimal Pairs for English](https://mlsanity.com/paper/1912.00582/) (2019)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models](https://mlsanity.com/paper/2403.19647/) (2024)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation](https://mlsanity.com/paper/2405.07200/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [Elements of World Knowledge (EWoK): A Cognition-Inspired Framework for Evaluating Basic World Knowledge in Language Models](https://mlsanity.com/paper/2405.09605/) (2024)
- [A Practitioner's Guide to Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2510.25781/) (2025)
- [Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate](https://mlsanity.com/paper/2604.21174/) (2026)

## Abstract (arXiv)

Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks. We test these claims separately. In a six-layer, 10M-parameter B-spline KAN, we reconstruct all 884,736 feed-forward edges: 87.8% exceed (NLS>0.1) and 0.4% are inactive. Pruning the lowest-activity 20--25% causes negligible loss increase, although structured MLP neuron pruning tolerates comparable sparsity. The audit replicates on BabyLM, but grid-size sweeps show that near-total fPCA compression and high closed-form-fit coverage are properties of the low-capacity grid-2 basis, not universal KAN behavior. For replacement, we evaluate MLP, SwiGLU, grouped Chebyshev, and rational GR-KAN networks on BabyLM. The KAN-family and gated variants improve validation loss over the GELU MLP, but this ordering does not transfer to standardized benchmarks: across ten seeds and 59,875 BLiMP pairs, accuracies span 62.4--63.1%, EWoK remains at chance, and a (+0.7)-point GR-KAN effect on BLiMP reverses on the supplement. Larger tests are also cautionary: parameter-matched MLPEdge underperforms the MLP on Wikitext-103, and 286M-parameter GR-KAN remains below a SwiGLU ClimbMix baseline after stabilization. Thus, small-basis KANs provide a practical, corpus-transferable interface for auditing learned scalar transformations, but the tested replacements show no consistent benchmark, quality, or latency advantage over strong MLP baselines.