KAN

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,
    cat_exog_list=None,
    categorical_cardinalities=None,
    cat_emb_dim="fastai",
    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_monitor="ptl/val_loss",
    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`
`cat_exog_list`	`str list`	exogenous columns (from `hist_exog_list` / `futr_exog_list` / `stat_exog_list`) to embed instead of scale.	`None`
`categorical_cardinalities`	`dict`	mapping from each categorical column to its number of distinct categories.	`None`
`cat_emb_dim`	`str or int`	categorical embedding size strategy (‘fastai’, ‘sqrt’, ‘half’) or an explicit integer.	`‘fastai’`
`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_monitor`	`str`	metric to monitor for early stopping. Valid options: “ptl/val_loss”, “valid_loss”, “train_loss”. Default: “ptl/val_loss”.	`‘ptl/val_loss’`
`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

Getting Started

Capabilities

Tutorials

Use cases

API Reference

1. KAN

`KAN`

`KAN.fit`

`KAN.predict`

Usage Example

2. Auxiliary functions

`KANLinear`

​1. KAN

​KAN

​KAN.fit

​KAN.predict

​Usage Example

​2. Auxiliary functions

​KANLinear

1. KAN

`KAN`

`KAN.fit`

`KAN.predict`

Usage Example

2. Auxiliary functions

`KANLinear`