Predictive modeling on web-scale tabular data with billions of instances and hundreds of heterogeneous numerical features faces significant scalability challenges. These features exhibit anisotropy, heavy-tailed distributions, and non-stationarity, creating bottlenecks for models like Gradient Boosting Decision Trees and requiring laborious manual feature engineering. We introduce KMLP, a hybrid deep architecture integrating a shallow Kolmogorov-Arnold Network (KAN) front-end with a Gated Multilayer Perceptron (gMLP) backbone. The KAN front-end uses learnable activation functions to automatically model complex non-linear transformations for each feature, while the gMLP backbone captures high-order interactions. Experiments on public benchmarks and an industrial dataset with billions of samples show KMLP achieves state-of-the-art performance, with advantages over baselines like GBDTs increasing at larger scales, validating KMLP as a scalable deep learning paradigm for large-scale web tabular data.
Figures & tables
Figure 1. Overview of the KMLP-QTL structure. Tabular data features are first processed by QTL for fine-grained numerical representation. The data then flows through the KAN layer to manage feature heterogeneity and complex interactions, followed by stacked gMLP modules to capture deep non-linear interactions. Batch Normalization and Dropout are included in intermediate layers to enhance performance and stability.
Figure 2. Quantile Transformation with Linear interpolation
Dataset
#Train
#Valid
#Test
Tiny
200K
50K
1B
Small
2M
500K
1B
Medium
20M
5M
1B
Large
200M
50M
1B
Ultra Large
2B
50M
1B
Table 1. Statistical Information of the credit scoring dataset. It is a binary classification dataset. We prepared five training and validation sets with different data scales, while the test set is the same, with a proportion of 0.47% for overdues (label=1) in the test set.
Operator
CP
MT
CD
EG
HI
JA
AUC
KS
AUC
KS
AUC
KS
AUC
KS
AUC
KS
AUC
KS
CLR
69.18
28.68
93.35
72.15
85.16
55.18
81.84
48.74
80.03
44.49
87.03
58.66
Quantile
64.22
21.58
92.53
69.99
82.37
51.26
64.65
19.56
79.38
44.17
86.67
57.92
PLE
69.20
28.92
90.98
67.43
84.65
54.15
93.73
72.46
79.39
43.47
85.23
55.00
QTL
69.10
27.76
93.72
73.68
85.20
55.93
99.16
91.87
80.88
46.23
87.30
59.51
Table 2. Comparsion of different numerical preprocessing operators in open public datasets. We highlight the best results in bold. QTL achieved the best performance on 5 out of 6 datasets.
Model
KMLP
LightGBM
Training Resources
8 A100 GPUs
10,000 CPUs
Training Time
10 hours
24 hours
Inference Time
2 hours
2 hours
Table 3. Comparison of Model Training and Inference.We conducted a comparison of model training and inference in terms of time and resource consumption. The training was performed on a large-scale dataset (200M), while the inference was executed on an ultra-large test set (1B Test).
Operator
Valid
Test
AUC
KS
AUC
KS
CLR
95.11
76.34
94.91
75.60
Quantile
95.05
76.51
94.96
75.82
PLE
94.66
75.89
94.73
75.45
QTL
95.20
76.82
95.04
76.08
Table 4. Comparison of different numerical preprocessing operators on the medium-scale financial data.
Methods
Valid
Test
AUC
KS
AUC
KS
LightGBM
95.10
76.16
94.93
75.63
MLP
94.87
75.53
94.71
75.04
gMLP
94.99
75.99
94.86
75.41
KAN
93.15
73.26
93.99
72.86
SAINT
94.79
75.73
94.64
75.24
Table 5. Experimental results on Medium Scale Financial Data. We highlight the best results in bold, and the second-best results with underscores.
Methods
CP
MT
CD
EG
HI
JA
AUC
KS
AUC
KS
AUC
KS
AUC
KS
AUC
KS
AUC
KS
LightGBM
68.98
28.27
92.24
69.89
84.97
55.30
95.05
75.76
79.86
44.16
86.09
56.56
MLP
68.41
27.93
93.59
72.64
84.94
54.88
99.4
93.38
79.71
44.00
86.27
57.22
gMLP
68.23
27.19
93.35
72.66
84.75
54.99
99.56
95.06
79.44
43.69
85.62
56.37
KAN
67.39
25.82
92.10
68.49
84.92
54.91
98.07
85.86
79.32
43.50
86.19
56.85
SAINT
67.41
26.71
92.10
69.37
84.35
53.82
98.95
91.2
78.36
41.78
85.3
55.05
Table 6. Experimental results on Open Public Datasets. Both AUC and KS metrics indicate that the higher the value, the stronger the model’s classification capability; we highlight the best results in bold, and the second best results with underscores.
Figure 3. Data Scale Effects. The KS (left) and AUC (right) of LightGBM and KMLP with different sizes of training sets. When the scale of the training data set is relatively small, LightGBM still performs better than KMLP. However, as the scale of the data set increases, KMLP outperformed LightGBM, achieving a 1.76 improvement in the KS value.
Model Variant
Average AUC
Average KS
AUC
KS
( Open Public Datasets)
(Open Public Datasets)
(Industrial Dataset)
(Industrial Dataset)
KMLP (FULL)
73.62
50.71
95.04
76.08
w.o. QTL
67.12 ( ↓ 6.50)
37.78 ( ↓ 12.93)
94.96 ( ↓ 0.08)
75.82 ( ↓ 0.26)
w.o. gMLP
73.19 ( ↓ 0.43)
50.01 ( ↓ 0.70)
94.71 ( ↓ 0.33)
75.04 ( ↓ 1.04)
w.o. KAN
72.99 ( ↓ 0.63)
49.99 ( ↓ 0.72)
94.86 ( ↓ 0.18)
75.41 ( ↓ 0.67)
Table 7. Ablation Study Performance. The results for the open public datasets are the average across six datasets. The values in parentheses indicate the performance drop compared to the full model, with a downward arrow ↓ representing the decrease.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Abbr
Name
#samples
#features
CP
Click_prediction_small
39948
9
MT
MagicTelescope
13376
10
CD
Credit
16714
10
EG
Eeg-eye-state
14980
14
HI
Higgs
98050
28
JA
Jannis
57580
54
Appendix
Table 8. Statistical Information of open public datasets.
Dataset
Link
CP
https://www.openml.org/d/43901
MT
https://www.openml.org/d/43971
CD
https://www.openml.org/d/45024
EG
https://www.openml.org/d/1471
HI
https://www.openml.org/d/42769
JA
https://www.openml.org/d/41168
Appendix
Table 9. The source of the open public datasets.
Models
Parameter
Values
LightGBM
learning_rate
{0.1,0.01}
num_leaves
{32, 256,512}
subsample
{0.8,0.9,1.0}
colsample_bytree
{0.8, 1.0}
min_child_samples
{10, 100}
#Iterations
{500,1000, 5000}
Appendix
Table 10. Hyperparameter Space. We use Grid Search to find the optimal parameters. Transfomer-model include FT-Transformer, TabNet and SAINT.
School of Mathematical Sciences, Soochow University, No.1 Shizi Street, Suzhou, 215006, Jiangsu Province, China · Digital innovation research center, Duke Kunshan University, No.8 Duke Avenue, Kunshan, 215000, Jiangsu Province, China