Kolmogorov–Arnold Transformer: A PyTorch Implementation

ICLR 2025

Yes, I kan!

🎉 This is a PyTorch/GPU implementation of the paper Kolmogorov–Arnold Transformer (KAT), which replace the MLP layers in transformer with KAN layers.

For more technical details, please refer to our ICLR'25 paper.

Kolmogorov–Arnold Transformer
📝[Paper] </>[code] </>[Trition/CUDA kernel]
Xingyi Yang, Xinchao Wang
National University of Singapore
International Conference on Learning Representations (ICLR'25)

🔑 Key Insight:

Vanilla ViT + KAN struggle to scale effectively. We introduce the KAT model, which integrates GR-KANs into transformers for large-scale training scenarios like ImageNet, achieving significant performance improvements.

🎯 Our Solutions:

1. Base Function: Replace B-spline to CUDA-implemented Rational.
2. Group KAN: Share weights among groups of edges for efficiency.
3. Initialization: Maintain activation magnitudes across layers.

✅ Updates

• Release the KAT paper, CUDA implementation and IN-1k training code.
• 🎉🎉🎉🎉 Triton Implementation, on 1D and 2D tasks. This is much easier to install than the CUDA version. Please See https://github.com/Adamdad/rational_kat_cu.
• KAT Detection and segmentation code.
• KAT on NLP tasks.

🛠️ Installation and Dataset

Please find our CUDA implementation in https://github.com/Adamdad/rational_kat_cu.git.

# install torch and other things
pip install timm==1.0.3
pip install wandb # I personally use wandb for results visualizations
git clone https://github.com/Adamdad/rational_kat_cu.git
cd rational_kat_cu
pip install -e .

📦 Data preparation: ImageNet with the following folder structure, you can extract ImageNet by this script

│imagenet/
├──train/
│  ├── n01440764
│  │   ├── n01440764_10026.JPEG
│  │   ├── n01440764_10027.JPEG
│  │   ├── ......
│  ├── ......
├──val/
│  ├── n01440764
│  │   ├── ILSVRC2012_val_00000293.JPEG
│  │   ├── ILSVRC2012_val_00002138.JPEG
│  │   ├── ......
│  ├── ......

Usage

Refer to example.py for a detailed use case demonstrating how to use KAT with timm to classify an image.

📊 Model Checkpoints

Download pre-trained models or access training checkpoints:

🏷️ Model	⚙️ Setup	📦 Param	📈 Top1	🔗 Link
KAT-T	From Scratch	5.7M	74.6	link/huggingface
KAT-T	From ViT	5.7M	75.7	link/huggingface
KAT-S	From Scratch	22.1M	81.2	link/huggingface
KAT-S	From ViT	22.1M	82.0	link/huggingface
KAT-B	From Scratch	86.6M	82.3	link/huggingface
KAT-B	From ViT	86.6M	82.8	link/huggingface

🎓Model Training

All training scripts are under scripts/

bash scripts/train_kat_tiny_8x128.sh

If you want to change the hyper-parameters, can edit

#!/bin/bash
DATA_PATH=/local_home/dataset/imagenet/

bash ./dist_train.sh 8 $DATA_PATH \
    --model kat_tiny_swish_patch16_224 \ # Rationals are initialized to be swish functions 
    -b 128 \
    --opt adamw \
    --lr 1e-3 \
    --weight-decay 0.05 \
    --epochs 300 \
    --mixup 0.8 \
    --cutmix 1.0 \
    --sched cosine \
    --smoothing 0.1 \
    --drop-path 0.1 \
    --aa rand-m9-mstd0.5 \
    --remode pixel --reprob 0.25 \
    --amp \
    --crop-pct 0.875 \
    --mean 0.485 0.456 0.406 \
    --std 0.229 0.224 0.225 \
    --model-ema \
    --model-ema-decay 0.9999 \
    --output output/kat_tiny_swish_patch16_224 \
    --log-wandb

🧪 Evaluation

To evaluate our kat_tiny_patch16_224 models, run:

DATA_PATH=/local_home/dataset/imagenet/
CHECKPOINT_PATH=kat_tiny_patch16_224_1f3ad3b2e69821f3d412f2924cf159a0e266f142d739cb68f68f796f5a0fe289.pth
python validate.py $DATA_PATH --model kat_tiny_patch16_224 \
    --checkpoint $CHECKPOINT_PATH -b 512

###################
Validating in float32. AMP not enabled.
Loaded state_dict from checkpoint 'kat_tiny_patch16_224_1f3ad3b2e69821f3d412f2924cf159a0e266f142d739cb68f68f796f5a0fe289.pth'
Model kat_tiny_patch16_224 created, param count: 5718328
Data processing configuration for current model + dataset:
        input_size: (3, 224, 224)
        interpolation: bicubic
        mean: (0.485, 0.456, 0.406)
        std: (0.229, 0.224, 0.225)
        crop_pct: 0.875
        crop_mode: center
Test: [   0/98]  Time: 3.453s (3.453s,  148.28/s)  Loss:  0.6989 (0.6989)  Acc@1:  84.375 ( 84.375)  Acc@5:  96.875 ( 96.875)
.......
Test: [  90/98]  Time: 0.212s (0.592s,  864.23/s)  Loss:  1.1640 (1.1143)  Acc@1:  71.875 ( 74.270)  Acc@5:  93.750 ( 92.220)
 * Acc@1 74.558 (25.442) Acc@5 92.390 (7.610)
--result
{
    "model": "kat_tiny_patch16_224",
    "top1": 74.558,
    "top1_err": 25.442,
    "top5": 92.39,
    "top5_err": 7.61,
    "param_count": 5.72,
    "img_size": 224,
    "crop_pct": 0.875,
    "interpolation": "bicubic"
}

🙏 Acknowledgments

We extend our gratitude to the authors of rational_activations for their contributions to CUDA rational function implementations that inspired parts of this work. We thank @yuweihao, @florinshen, @Huage001 and @yu-rp for valuable discussions.

📚 Bibtex

If you use this repository, please cite:

@inproceedings{
  yang2025kolmogorovarnold,
  title={Kolmogorov-Arnold Transformer},
  author={Xingyi Yang, Xinchao Wang},
  booktitle={The Thirteenth International Conference on Learning Representations},
  year={2025},
  url={https://openreview.net/forum?id=BCeock53nt}
}