KAN

KAN: Kolmogorov-Arnold Networks for time series forecasting. MLP alternative using learnable activation functions for improved non-linear pattern modeling.

Kolmogorov-Arnold Networks (KANs) are an alternative to Multi-Layer Perceptrons (MLPs). This model uses KANs similarly as our MLP model.

References

• Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljačić, Thomas Y. Hou, Max Tegmark. “KAN: Kolmogorov–Arnold Networks”

Figure 1. KAN compared to MLP.

1. KAN

KAN

KAN(
    h,
    input_size,
    grid_size=5,
    spline_order=3,
    scale_noise=0.1,
    scale_base=1.0,
    scale_spline=1.0,
    enable_standalone_scale_spline=True,
    grid_eps=0.02,
    grid_range=[-1, 1],
    n_hidden_layers=1,
    hidden_size=512,
    stat_exog_list=None,
    hist_exog_list=None,
    futr_exog_list=None,
    exclude_insample_y=False,
    loss=MAE(),
    valid_loss=None,
    max_steps=1000,
    learning_rate=0.001,
    num_lr_decays=-1,
    early_stop_patience_steps=-1,
    val_check_steps=100,
    batch_size=32,
    valid_batch_size=None,
    windows_batch_size=1024,
    inference_windows_batch_size=-1,
    start_padding_enabled=False,
    training_data_availability_threshold=0.0,
    step_size=1,
    scaler_type="identity",
    random_seed=1,
    drop_last_loader=False,
    alias=None,
    optimizer=None,
    optimizer_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)

Bases: BaseModel

KAN

Simple Kolmogorov-Arnold Network (KAN). This network uses the Kolmogorov-Arnold approximation theorem, where splines are learned to approximate more complex functions. Unlike the MLP, the non-linear function are learned at the edges, and the nodes simply sum the different learned functions.

Parameters:

Name	Type	Description	Default
h	int	forecast horizon.	required
input_size	int	considered autorregresive inputs (lags), y=[1,2,3,4] input_size=2 -> lags=[1,2].	required
grid_size	int	number of intervals used by the splines to approximate the function.	5
spline_order	int	order of the B-splines.	3
scale_noise	float	regularization coefficient for the splines.	0.1
scale_base	float	scaling coefficient for the base function.	1.0
scale_spline	float	scaling coefficient for the splines.	1.0
enable_standalone_scale_spline	bool	whether each spline is scaled individually.	True
grid_eps	float	used for numerical stability.	0.02
grid_range	list	range of the grid used for spline approximation.	[-1, 1]
n_hidden_layers	int	number of hidden layers for the KAN.	1
hidden_size	int or list	number of units for each hidden layer of the KAN. If an integer, all hidden layers will have the same size. Use a list to specify the size of each hidden layer.	512
stat_exog_list	str list	static exogenous columns.	None
hist_exog_list	str list	historic exogenous columns.	None
futr_exog_list	str list	future exogenous columns.	None
exclude_insample_y	bool	the model skips the autoregressive features y[t-input_size:t] if True.	False
loss	PyTorch module	instantiated train loss class from losses collection.	MAE()
valid_loss	PyTorch module	instantiated valid loss class from losses collection.	None
max_steps	int	maximum number of training steps.	1000
learning_rate	float	Learning rate between (0, 1).	0.001
num_lr_decays	int	Number of learning rate decays, evenly distributed across max_steps.	-1
early_stop_patience_steps	int	Number of validation iterations before early stopping.	-1
val_check_steps	int	Number of training steps between every validation loss check.	100
batch_size	int	number of different series in each batch.	32
valid_batch_size	int	number of different series in each validation and test batch, if None uses batch_size.	None
windows_batch_size	int	number of windows to sample in each training batch, default uses all.	1024
inference_windows_batch_size	int	number of windows to sample in each inference batch, -1 uses all.	-1
start_padding_enabled	bool	if True, the model will pad the time series with zeros at the beginning, by input size.	False
training_data_availability_threshold	Union[float, List[float]]	minimum fraction of valid data points required for training windows. Single float applies to both insample and outsample; list of two floats specifies [insample_fraction, outsample_fraction]. Default 0.0 allows windows with only 1 valid data point (current behavior).	0.0
step_size	int	step size between each window of temporal data.	1
scaler_type	str	type of scaler for temporal inputs normalization see temporal scalers.	‘identity’
random_seed	int	random_seed for pytorch initializer and numpy generators.	1
drop_last_loader	bool	if True TimeSeriesDataLoader drops last non-full batch.	False
alias	str	optional, Custom name of the model.	None
optimizer	Subclass of ‘torch.optim.Optimizer’	optional, user specified optimizer instead of the default choice (Adam).	None
optimizer_kwargs	dict	optional, list of parameters used by the user specified optimizer.	None
dataloader_kwargs	dict	optional, list of parameters passed into the PyTorch Lightning dataloader by the TimeSeriesDataLoader.	None
**trainer_kwargs	int	keyword trainer arguments inherited from PyTorch Lighning’s trainer.

KAN.fit

fit(
    dataset, val_size=0, test_size=0, random_seed=None, distributed_config=None
)

Fit.

The fit method, optimizes the neural network’s weights using the initialization parameters (learning_rate, windows_batch_size, …) and the loss function as defined during the initialization. Within fit we use a PyTorch Lightning Trainer that inherits the initialization’s self.trainer_kwargs, to customize its inputs, see PL’s trainer arguments.

The method is designed to be compatible with SKLearn-like classes and in particular to be compatible with the StatsForecast library.

By default the model is not saving training checkpoints to protect disk memory, to get them change enable_checkpointing=True in __init__.

Parameters:

Name	Type	Description	Default
dataset	TimeSeriesDataset	NeuralForecast’s TimeSeriesDataset, see documentation.	required
val_size	int	Validation size for temporal cross-validation.	0
random_seed	int	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	None
test_size	int	Test size for temporal cross-validation.	0

Returns:

Type	Description
None

KAN.predict

predict(
    dataset,
    test_size=None,
    step_size=1,
    random_seed=None,
    quantiles=None,
    h=None,
    explainer_config=None,
    **data_module_kwargs
)

Predict.

Neural network prediction with PL’s Trainer execution of predict_step.

Parameters:

Name	Type	Description	Default
dataset	TimeSeriesDataset	NeuralForecast’s TimeSeriesDataset, see documentation.	required
test_size	int	Test size for temporal cross-validation.	None
step_size	int	Step size between each window.	1
random_seed	int	Random seed for pytorch initializer and numpy generators, overwrites model.init’s.	None
quantiles	list	Target quantiles to predict.	None
h	int	Prediction horizon, if None, uses the model’s fitted horizon. Defaults to None.	None
explainer_config	dict	configuration for explanations.	None
**data_module_kwargs	dict	PL’s TimeSeriesDataModule args, see documentation.

Returns:

Type	Description
None

Usage Example

import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import KAN
from neuralforecast.losses.pytorch import DistributionLoss
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic

Y_train_df = AirPassengersPanel[AirPassengersPanel.ds<AirPassengersPanel['ds'].values[-12]] # 132 train
Y_test_df = AirPassengersPanel[AirPassengersPanel.ds>=AirPassengersPanel['ds'].values[-12]].reset_index(drop=True) # 12 test

fcst = NeuralForecast(
    models=[
            KAN(h=12,
                input_size=24,
                loss = DistributionLoss(distribution="Normal"),
                max_steps=100,
                scaler_type='standard',
                futr_exog_list=['y_[lag12]'],
                hist_exog_list=None,
                stat_exog_list=['airline1'],
                ),     
    ],
    freq='ME'
)
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic)
forecasts = fcst.predict(futr_df=Y_test_df)

# Plot quantile predictions
Y_hat_df = forecasts.reset_index(drop=False).drop(columns=['unique_id','ds'])
plot_df = pd.concat([Y_test_df, Y_hat_df], axis=1)
plot_df = pd.concat([Y_train_df, plot_df])

plot_df = plot_df[plot_df.unique_id=='Airline1'].drop('unique_id', axis=1)
plt.plot(plot_df['ds'], plot_df['y'], c='black', label='True')
plt.plot(plot_df['ds'], plot_df['KAN-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['KAN-lo-90'][-12:].values,
                 y2=plot_df['KAN-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.legend()
plt.grid()

2. Auxiliary functions

KANLinear

KANLinear(
    in_features,
    out_features,
    grid_size=5,
    spline_order=3,
    scale_noise=0.1,
    scale_base=1.0,
    scale_spline=1.0,
    enable_standalone_scale_spline=True,
    base_activation=torch.nn.SiLU,
    grid_eps=0.02,
    grid_range=[-1, 1],
)

Bases: Module

KANLinear