Reversible Mixture of KAN - RMoK

RMoK: Reversible Mixture of Kolmogorov-Arnold Networks. Combines Taylor, Jacobi, and wavelet functions for expressive time series forecasting with reversibility.

Figure 1. Architecture of RMoK.

1. Reversible Mixture of KAN - RMoK

RMoK

RMoK(
    h,
    input_size,
    n_series,
    futr_exog_list=None,
    hist_exog_list=None,
    stat_exog_list=None,
    taylor_order=3,
    jacobi_degree=6,
    wavelet_function="mexican_hat",
    dropout=0.1,
    revin_affine=True,
    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=32,
    inference_windows_batch_size=32,
    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,
    lr_scheduler=None,
    lr_scheduler_kwargs=None,
    dataloader_kwargs=None,
    **trainer_kwargs
)

Bases: BaseModel

Reversible Mixture of KAN

Parameters:

Name	Type	Description	Default
h	int	forecast horizon.	required
input_size	int	autorregresive inputs size, y=[1,2,3,4] input_size=2 -> y_[t-2:t]=[1,2].	required
n_series	int	number of time-series.	required
futr_exog_list	str list	future exogenous columns.	None
hist_exog_list	str list	historic exogenous columns.	None
stat_exog_list	str list	static exogenous columns.	None
taylor_order	int	order of the Taylor polynomial.	3
jacobi_degree	int	degree of the Jacobi polynomial.	6
wavelet_function	str	wavelet function to use in the WaveKAN. Choose from [“mexican_hat”, “morlet”, “dog”, “meyer”, “shannon”]	‘mexican_hat’
dropout	float	dropout rate.	0.1
revin_affine	bool	bool to use affine in RevIn.	True
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.	32
inference_windows_batch_size	int	number of windows to sample in each inference batch, -1 uses all.	32
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
lr_scheduler	Subclass of ‘torch.optim.lr_scheduler.LRScheduler’	optional, user specified lr_scheduler instead of the default choice (StepLR).	None
lr_scheduler_kwargs	dict	optional, list of parameters used by the user specified lr_scheduler.	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.

RMoK.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

RMoK.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 RMoK
from neuralforecast.utils import AirPassengersPanel, AirPassengersStatic
from neuralforecast.losses.pytorch import MSE

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

model = RMoK(h=12,
             input_size=24,
             n_series=2,
             taylor_order=3,
             jacobi_degree=6,
             wavelet_function='mexican_hat',
             dropout=0.1,
             revin_affine=True,
             loss=MSE(),
             valid_loss=MAE(),
             early_stop_patience_steps=3,
             batch_size=32)

fcst = NeuralForecast(models=[model], freq='ME')
fcst.fit(df=Y_train_df, static_df=AirPassengersStatic, val_size=12)
forecasts = fcst.predict(futr_df=Y_test_df)

# Plot predictions
fig, ax = plt.subplots(1, 1, figsize = (20, 7))
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['RMoK'], c='blue', label='Forecast')
ax.set_title('AirPassengers Forecast', fontsize=22)
ax.set_ylabel('Monthly Passengers', fontsize=20)
ax.set_xlabel('Year', fontsize=20)
ax.legend(prop={'size': 15})
ax.grid()

2. Auxiliary functions

WaveKANLayer

WaveKANLayer(
    in_features,
    out_features,
    wavelet_type="mexican_hat",
    with_bn=True,
    device="cpu",
)

Bases: Module

This is a sample code for the simulations of the paper: Bozorgasl, Zavareh and Chen, Hao, Wav-KAN: Wavelet Kolmogorov-Arnold Networks (May, 2024)

https://arxiv.org/abs/2405.12832 and also available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4835325 We used efficient KAN notation and some part of the code:+

TaylorKANLayer

TaylorKANLayer(input_dim, out_dim, order, addbias=True)

Bases: Module

https://github.com/Muyuzhierchengse/TaylorKAN/

JacobiKANLayer

JacobiKANLayer(input_dim, output_dim, degree, a=1.0, b=1.0)

Bases: Module

https://github.com/SpaceLearner/JacobiKAN/blob/main/JacobiKANLayer.py