Kolmogorov--Arnold Networks for Small Language Models
Kolmogorov-Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering interpretability but facing performance challenges when replacing standard MLPs. Audits of a 10M-parameter B-spline KAN reveal that while most edges can be reconstructed, near-total compression properties are specific to low-capacity bases rather than universal KAN traits. KAN-family and gated variants show improved validation loss on BabyLM compared to GELU MLPs, but this impro
Analysis
TL;DR
- Kolmogorov-Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering interpretability but facing performance challenges when replacing standard MLPs.
- Audits of a 10M-parameter B-spline KAN reveal that while most edges can be reconstructed, near-total compression properties are specific to low-capacity bases rather than universal KAN traits.
- KAN-family and gated variants show improved validation loss on BabyLM compared to GELU MLPs, but this improvement does not translate to standardized benchmarks like BLiMP or Wikitext-103.
- Larger-scale tests indicate that parameter-matched KANs underperform strong MLP baselines, with no consistent advantages in benchmark quality, latency, or generalization.
Why It Matters
This study provides critical empirical evidence regarding the viability of KANs as direct replacements for traditional feed-forward networks in language modeling. For researchers, it highlights the gap between theoretical interpretability benefits and practical performance gains, suggesting that current KAN architectures may not yet offer competitive accuracy over optimized MLPs. Practitioners should temper expectations regarding immediate performance boosts from KANs while recognizing their potential utility in model auditing and interpretability tasks.
Technical Details
- Architecture Audit: The authors analyzed a six-layer, 10M-parameter B-spline KAN, reconstructing 884,736 feed-forward edges, finding 87.8% exceeded a non-linearity score threshold and only 0.4% were inactive.
- Pruning Analysis: Pruning the lowest-activity 20–25% of edges resulted in negligible loss increases, though structured MLP neuron pruning tolerated comparable sparsity levels effectively.
- Benchmark Evaluation: Replacements were evaluated on BabyLM, BLiMP (59,875 pairs), and Wikitext-103, comparing MLP, SwiGLU, grouped Chebyshev, and rational GR-KAN networks.
- Performance Results: While KAN variants improved validation loss on BabyLM, they failed to outperform baselines on standardized benchmarks; a +0.7-point gain on BLiMP reversed on supplementary tests, and a 286M-parameter GR-KAN remained below a SwiGLU ClimbMix baseline.
Industry Insight
- Interpretability vs. Performance Trade-off: Organizations prioritizing model transparency may benefit from small-basis KANs for auditing scalar transformations, but those focused on raw performance should stick to established MLP or SwiGLU architectures.
- Caution in Scaling: The lack of consistent advantage in larger models suggests that simply swapping MLP layers for KAN layers is not a drop-in solution for improving language model capabilities; architectural innovations beyond simple replacement are likely needed.
- Research Direction: Future work should focus on overcoming the limitations observed in low-capacity grids and ensuring that interpretability gains do not come at the cost of significant benchmark degradation.
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