KAF_icml466_SupplementaryMaterials

Figure s1: KAF overall framework description

Figure s2: Compare two models : KAF/MLP (Updated Figure 1)

Table s1: Comparison of Experiment 4.2 after regularization is turned on

MODEL	DATASETS	FEATURE MIXER	#PARAM.	FLOPS	TOP-1 (ORIGINAL)	TOP-1 (W/ REG.)
ResNet/18	CIFAR-10	MLP	11.1M	0.56G	91.19	91.32
		KAF	12.0M	0.63G	91.72	91.88
		GPKAN	11.3M	0.56G	90.98	91.15
		FAN	8M	0.42G	90.69	90.82
		KAN	-	-	-	-
MLP_Mixer/S	ImageNet1k	MLP	18.2M	3.8G	63.5	63.7
		KAF	18.8M	4.2G	64.7	65.0
		GPKAN	18.8M	4.0G	62.9	63.2
		FAN	15.7M	3.2G	58.2	58.6
		KAN	-	-	-	-
ViT-T/16	ImageNet1K	MLP	5.7M	1.08G	72.3	72.5
		KAF	5.9M	1.12G	73.2	73.5
		GPKAN	5.7M	1.13G	74.6	74.8
		FAN	4.2M	0.96G	65.7	66.0
		KAN	-	-	-	-
MLP_KAN (Deit)	Cifar100	MLP	1.3M	0.12G	49.0	49.3
		KAF	1.4M	0.15G	53.8	54.2
		KAN	1.9M	0.19G	51.2	51.6
		GPKAN	1.4M	0.14G	54.3	54.6
		FAN	1M	0.1G	46.7	47.1

Table s2: Experiment 4.1 t-test results of visual dataset

Dataset	KAF vs MLP (p-value)	KAN vs MLP (p-value)	KAF vs MLP (Significance)	KAN vs MLP (Significance)
MNIST	0.03	0.08	Significant	Not Significant
EMNIST	0.02	0.10	Significant	Not Significant
KMNIST	0.04	0.09	Significant	Not Significant
CIFAR-10	0.01	0.07	Significant	Not Significant
CIFAR-100	0.02	0.12	Significant	Not Significant
SVHN	0.03	0.11	Significant	Not Significant
Bean Dataset	0.02	0.06	Significant	Significant
AG News	0.01	0.05	Significant	Significant

Table s3: Noise Robustness Experiment Results (Corrected High-Frequency Noise Scenario)

Noise Type	Noise Level (SNR)	Architecture	Model	Test RMSE (Mean ± STD)	Training Time (s)
Gaussian Noise	10dB	FNO	MLP	1.23e-2 ± 8.7e-4	0.8
			KAF	9.8e-3 ± 6.2e-4	0.9
			KAN	7.1e-3 ± 4.5e-4	1.2
Gaussian Noise	20dB	PINN	MLP	8.4e-3 ± 5.3e-4	1.1
			KAF	6.7e-3 ± 4.1e-4	1.3
			KAN	5.2e-3 ± 3.2e-4	1.6
Impulse Noise (20% Corruption)	-	FNO	MLP	1.5e-2 ± 1.1e-3	0.8
			KAF	1.1e-2 ± 8.5e-4	0.9
			KAN	8.9e-3 ± 6.7e-4	1.2
High-Frequency Noise (Fourier Domain)	30dB	PINN	MLP	9.7e-3 ± 7.2e-4	1.1
			KAF	5.5e-3 ± 3.8e-4	1.2
			KAN	5.8e-3 ± 4.1e-4	1.6