> ## Documentation Index
> Fetch the complete documentation index at: https://nixtlaverse.nixtla.io/llms.txt
> Use this file to discover all available pages before exploring further.

> XLinear: A MLP-based model for multivariate forecasting with exogenous features.

# XLinear

XLinear is a MLP-based model for multivariate time series forecasting
that uses gating mechanisms for temporal and cross-channel interactions.
The architecture consists of temporal gating with a global token to capture
global temporal patterns, followed by cross-channel gating to model
dependencies between different time series.

**References**

* [Xinyang, C., et al. "XLinear: A Lightweight and Accurate MLP-Based Model for Long-Term Time Series Forecasting with Exogenous Inputs"](https://arxiv.org/abs/2601.09237)

<img src="https://mintcdn.com/nixtla/SpieC9I5hALUKCn0/neuralforecast/imgs_models/xlinear.png?fit=max&auto=format&n=SpieC9I5hALUKCn0&q=85&s=5e546a3baed90dd263f46447d2d9329f" alt="Figure 1. Architecture of XLinear" width="2596" height="1026" data-path="neuralforecast/imgs_models/xlinear.png" />

*Figure 1. Architecture of XLinear*

## XLinear

### `XLinear`

```python theme={null}
XLinear(
    h,
    input_size,
    n_series,
    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,
    hidden_size=128,
    temporal_ff=256,
    channel_ff=8,
    temporal_dropout=0.0,
    channel_dropout=0.0,
    embed_dropout=0.0,
    head_dropout=0.0,
    use_norm=True,
    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=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: <code>[BaseModel](#neuralforecast.common._base_model.BaseModel)</code>

XLinear

XLinear is a linear-based model for multivariate time series forecasting
that uses gating mechanisms for temporal and cross-channel interactions.
The architecture consists of temporal gating with a global token to capture
global temporal patterns, followed by cross-channel gating to model
dependencies between different time series.

**Parameters:**

| Name | Type | Description | Default |
| - | - | - | - |
| `h` | <code>[int](#int)</code> | Forecast horizon. | *required* |
| `input_size` | <code>[int](#int)</code> | Input size, y=\[1,2,3,4] input\_size=2 -> lags=\[1,2]. | *required* |
| `n_series` | <code>[int](#int)</code> | Number of time series. | *required* |
| `stat_exog_list` | <code>str list</code> | Static exogenous columns. | <code>None</code> |
| `cat_exog_list` | <code>str list</code> | exogenous columns (from `hist_exog_list` / `futr_exog_list` / `stat_exog_list`) to embed instead of scale. | <code>None</code> |
| `categorical_cardinalities` | <code>[dict](#dict)</code> | mapping from each categorical column to its number of distinct categories. | <code>None</code> |
| `cat_emb_dim` | <code>[str](#str) or [int](#int)</code> | categorical embedding size strategy ('fastai', 'sqrt', 'half') or an explicit integer. | <code>'fastai'</code> |
| `hist_exog_list` | <code>str list</code> | Historic exogenous columns. | <code>None</code> |
| `futr_exog_list` | <code>str list</code> | Future exogenous columns. | <code>None</code> |
| `hidden_size` | <code>[int](#int)</code> | Dimension of the model embedding. | <code>128</code> |
| `temporal_ff` | <code>[int](#int)</code> | Dimension of temporal feedforward layer in gating block. | <code>256</code> |
| `channel_ff` | <code>[int](#int)</code> | Dimension of cross-channel feedforward layer in gating block. | <code>8</code> |
| `temporal_dropout` | <code>[float](#float)</code> | Dropout rate for temporal gating. | <code>0.0</code> |
| `channel_dropout` | <code>[float](#float)</code> | Dropout rate for cross-channel gating. | <code>0.0</code> |
| `embed_dropout` | <code>[float](#float)</code> | Dropout rate for embedding projection. | <code>0.0</code> |
| `head_dropout` | <code>[float](#float)</code> | Dropout rate for output head. | <code>0.0</code> |
| `use_norm` | <code>[bool](#bool)</code> | Whether to use RevIN normalization. | <code>True</code> |
| `loss` | <code>PyTorch module</code> | Instantiated train loss class from [losses collection](./losses.pytorch.html). | <code>[MAE](#neuralforecast.losses.pytorch.MAE)()</code> |
| `valid_loss` | <code>PyTorch module</code> | Instantiated valid loss class from [losses collection](./losses.pytorch.html). | <code>None</code> |
| `max_steps` | <code>[int](#int)</code> | Maximum number of training steps. | <code>1000</code> |
| `learning_rate` | <code>[float](#float)</code> | Learning rate between (0, 1). | <code>0.001</code> |
| `num_lr_decays` | <code>[int](#int)</code> | Number of learning rate decays, evenly distributed across max\_steps. | <code>-1</code> |
| `early_stop_patience_steps` | <code>[int](#int)</code> | Number of validation iterations before early stopping. | <code>-1</code> |
| `val_monitor` | <code>[str](#str)</code> | metric to monitor for early stopping. Valid options: "ptl/val\_loss", "valid\_loss", "train\_loss". Default: "ptl/val\_loss". | <code>'ptl/val\_loss'</code> |
| `val_check_steps` | <code>[int](#int)</code> | Number of training steps between every validation loss check. | <code>100</code> |
| `batch_size` | <code>[int](#int)</code> | Number of different series in each batch. | <code>32</code> |
| `valid_batch_size` | <code>[int](#int)</code> | Number of different series in each validation and test batch, if None uses batch\_size. | <code>None</code> |
| `windows_batch_size` | <code>[int](#int)</code> | Number of windows to sample in each training batch. | <code>32</code> |
| `inference_windows_batch_size` | <code>[int](#int)</code> | Number of windows to sample in each inference batch, -1 uses all. | <code>32</code> |
| `start_padding_enabled` | <code>[bool](#bool)</code> | If True, the model will pad the time series with zeros at the beginning. | <code>False</code> |
| `training_data_availability_threshold` | <code>[Union](#Union)\[[float](#float), [List](#List)\[[float](#float)]]</code> | 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). | <code>0.0</code> |
| `step_size` | <code>[int](#int)</code> | Step size between each window of temporal data. | <code>1</code> |
| `scaler_type` | <code>[str](#str)</code> | type of scaler for temporal inputs normalization see [temporal scalers](https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/common/_scalers.py). | <code>'identity'</code> |
| `random_seed` | <code>[int](#int)</code> | Random seed for pytorch initializer and numpy generators. | <code>1</code> |
| `drop_last_loader` | <code>[bool](#bool)</code> | If True, TimeSeriesDataLoader drops last non-full batch. | <code>False</code> |
| `alias` | <code>[str](#str)</code> | Optional custom name of the model. | <code>None</code> |
| `optimizer` | <code>Subclass of 'torch.optim.Optimizer'</code> | Optional user specified optimizer. | <code>None</code> |
| `optimizer_kwargs` | <code>[dict](#dict)</code> | Optional list of parameters used by the user specified optimizer. | <code>None</code> |
| `lr_scheduler` | <code>Subclass of 'torch.optim.lr\_scheduler.LRScheduler'</code> | Optional user specified lr\_scheduler. | <code>None</code> |
| `lr_scheduler_kwargs` | <code>[dict](#dict)</code> | Optional list of parameters used by the user specified lr\_scheduler. | <code>None</code> |
| `dataloader_kwargs` | <code>[dict](#dict)</code> | optional, list of parameters passed into the PyTorch Lightning dataloader by the `TimeSeriesDataLoader`. | <code>None</code> |
| `**trainer_kwargs` | <code>[keyword](#keyword)</code> | trainer arguments inherited from [PyTorch Lightning's trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer). | <code>{}</code> |

<details class="references" open markdown="1">
  <summary>References</summary>

  * [Xinyang, C., et al. "XLinear: A Lightweight and Accurate MLP-Based Model for Long-Term Time Series Forecasting with Exogenous Inputs"](https://arxiv.org/abs/2601.09237)
</details>

#### `XLinear.fit`

```python theme={null}
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](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).

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` | <code>[TimeSeriesDataset](#TimeSeriesDataset)</code> | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `val_size` | <code>[int](#int)</code> | Validation size for temporal cross-validation. | <code>0</code> |
| `random_seed` | <code>[int](#int)</code> | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | <code>None</code> |
| `test_size` | <code>[int](#int)</code> | Test size for temporal cross-validation. | <code>0</code> |

**Returns:**

| Type | Description |
| - | - |
| None | |

#### `XLinear.predict`

```python theme={null}
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` | <code>[TimeSeriesDataset](#TimeSeriesDataset)</code> | NeuralForecast's `TimeSeriesDataset`, see [documentation](./tsdataset.html). | *required* |
| `test_size` | <code>[int](#int)</code> | Test size for temporal cross-validation. | <code>None</code> |
| `step_size` | <code>[int](#int)</code> | Step size between each window. | <code>1</code> |
| `random_seed` | <code>[int](#int)</code> | Random seed for pytorch initializer and numpy generators, overwrites model.**init**'s. | <code>None</code> |
| `quantiles` | <code>[list](#list)</code> | Target quantiles to predict. | <code>None</code> |
| `h` | <code>[int](#int)</code> | Prediction horizon, if None, uses the model's fitted horizon. Defaults to None. | <code>None</code> |
| `explainer_config` | <code>[dict](#dict)</code> | configuration for explanations. | <code>None</code> |
| `**data_module_kwargs` | <code>[dict](#dict)</code> | PL's TimeSeriesDataModule args, see [documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule). | <code>{}</code> |

**Returns:**

| Type | Description |
| - | - |
| None | |

### Usage Example

```python theme={null}
import pandas as pd
import matplotlib.pyplot as plt

from neuralforecast import NeuralForecast
from neuralforecast.models import XLinear
from neuralforecast.losses.pytorch import MAE
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

model = XLinear(h=12, 
            input_size=24,
            n_series=2,
            stat_exog_list=['airline1'],
            hist_exog_list=["y_[lag12]"],
            futr_exog_list=['trend'],            
            loss = MAE(),
            scaler_type='robust',
            learning_rate=1e-3,
            max_steps=200,
            val_check_steps=10,
            early_stop_patience_steps=2)

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
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['XLinear'], c='blue', label='median')
plt.grid()
plt.legend()
plt.plot()
```


## Related topics

- [Forecasting Models](/neuralforecast/docs/capabilities/overview.html.md)
- [NLinear](/neuralforecast/models.nlinear.html.md)
- [DLinear](/neuralforecast/models.dlinear.html.md)
- [Automatic Forecasting](/neuralforecast/models.html.md)
- [Holt Model](/statsforecast/docs/models/holt.html.md)