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

> One of the simplest neural architectures are Multi Layer Perceptrons (`MLP`) composed of stacked Fully Connected Neural Networks trained with backpropagation. Each node in the architecture is capable of modeling non-linear relationships granted by their activation functions. Novel activations like Rectified Linear Units (`ReLU`) have greatly improved the ability to fit deeper networks overcoming gradient vanishing problems that were associated with `Sigmoid` and `TanH` activations. For the forecasting task the last layer is changed to follow a auto-regression problem.<br/><br/>**References**<br/>-[Rosenblatt, F. (1958). "The perceptron: A probabilistic model for information storage and organization in the brain."](https://psycnet.apa.org/record/1959-09865-001)<br/>-[Fukushima, K. (1975). "Cognitron: A self-organizing multilayered neural network."](https://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=PASCAL7750396723)<br/>-[Vinod Nair, Geoffrey E. Hinton (2010). "Rectified Linear Units Improve Restricted Boltzmann Machines"](https://www.cs.toronto.edu/~fritz/absps/reluICML.pdf)<br/>

# MLP

<figure>
  <img src="https://mintcdn.com/nixtla-old-docs/SxdTUKdxfJcIbFeU/neuralforecast/imgs_models/mlp.png?fit=max&auto=format&n=SxdTUKdxfJcIbFeU&q=85&s=14324309ada31938fb02c928e39f107a" alt="Figure 1. Three layer MLP with autorregresive inputs." width="1920" height="1080" data-path="neuralforecast/imgs_models/mlp.png" />

  <figcaption aria-hidden="true">Figure 1. Three layer MLP with
  autorregresive inputs.</figcaption>
</figure>

***

<a href="https://github.com/Nixtla/neuralforecast/blob/main/neuralforecast/models/mlp.py#L16" target="_blank" style={{ float: "right", fontSize: "smaller" }}>source</a>

### MLP

> ```text theme={null}
>  MLP (h, input_size, stat_exog_list=None, hist_exog_list=None,
>       futr_exog_list=None, exclude_insample_y=False, num_layers=2,
>       hidden_size=1024, loss=MAE(), valid_loss=None, max_steps:int=1000,
>       learning_rate:float=0.001, num_lr_decays:int=-1,
>       early_stop_patience_steps:int=-1, val_check_steps:int=100,
>       batch_size:int=32, valid_batch_size:Optional[int]=None,
>       windows_batch_size=1024, inference_windows_batch_size=-1,
>       start_padding_enabled=False, step_size:int=1,
>       scaler_type:str='identity', random_seed:int=1,
>       drop_last_loader:bool=False, alias:Optional[str]=None,
>       optimizer=None, optimizer_kwargs=None, lr_scheduler=None,
>       lr_scheduler_kwargs=None, dataloader_kwargs=None, **trainer_kwargs)
> ```

\*MLP

Simple Multi Layer Perceptron architecture (MLP). This deep neural
network has constant units through its layers, each with ReLU
non-linearities, it is trained using ADAM stochastic gradient descent.
The network accepts static, historic and future exogenous data, flattens
the inputs and learns fully connected relationships against the target
variable.

**Parameters:**<br /> `h`: int, forecast horizon.<br /> `input_size`: int,
considered autorregresive inputs (lags), y=\[1,2,3,4] input\_size=2 ->
lags=\[1,2].<br /> `stat_exog_list`: str list, static exogenous
columns.<br /> `hist_exog_list`: str list, historic exogenous columns.<br />
`futr_exog_list`: str list, future exogenous columns.<br />
`exclude_insample_y`: bool=False, the model skips the autoregressive
features y\[t-input\_size:t] if True.<br /> `num_layers`: int, number of
layers for the MLP.<br /> `hidden_size`: int, number of units for each
layer of the MLP.<br /> `loss`: PyTorch module, instantiated train loss
class from [losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br />
`valid_loss`: PyTorch module=`loss`, instantiated valid loss class from
[losses
collection](https://nixtla.github.io/neuralforecast/losses.pytorch.html).<br />
`max_steps`: int=1000, maximum number of training steps.<br />
`learning_rate`: float=1e-3, Learning rate between (0, 1).<br />
`num_lr_decays`: int=-1, Number of learning rate decays, evenly
distributed across max\_steps.<br /> `early_stop_patience_steps`: int=-1,
Number of validation iterations before early stopping.<br />
`val_check_steps`: int=100, Number of training steps between every
validation loss check.<br /> `batch_size`: int=32, number of different
series in each batch.<br /> `valid_batch_size`: int=None, number of
different series in each validation and test batch, if None uses
batch\_size.<br /> `windows_batch_size`: int=1024, number of windows to
sample in each training batch, default uses all.<br />
`inference_windows_batch_size`: int=-1, number of windows to sample in
each inference batch, -1 uses all.<br /> `start_padding_enabled`:
bool=False, if True, the model will pad the time series with zeros at
the beginning, by input size.<br /> `step_size`: int=1, step size between
each window of temporal data.<br /> `scaler_type`: str=‘identity’, type of
scaler for temporal inputs normalization see [temporal
scalers](https://nixtla.github.io/neuralforecast/common.scalers.html).<br />
`random_seed`: int=1, random\_seed for pytorch initializer and numpy
generators.<br /> `drop_last_loader`: bool=False, if True
`TimeSeriesDataLoader` drops last non-full batch.<br /> `alias`: str,
optional, Custom name of the model.<br /> `optimizer`: Subclass of
‘torch.optim.Optimizer’, optional, user specified optimizer instead of
the default choice (Adam).<br /> `optimizer_kwargs`: dict, optional, list
of parameters used by the user specified `optimizer`.<br />
`lr_scheduler`: Subclass of ‘torch.optim.lr\_scheduler.LRScheduler’,
optional, user specified lr\_scheduler instead of the default choice
(StepLR).<br /> `lr_scheduler_kwargs`: dict, optional, list of parameters
used by the user specified `lr_scheduler`.<br />\
`dataloader_kwargs`: dict, optional, list of parameters passed into the
PyTorch Lightning dataloader by the `TimeSeriesDataLoader`. <br />
`**trainer_kwargs`: int, keyword trainer arguments inherited from
[PyTorch Lighning’s
trainer](https://pytorch-lightning.readthedocs.io/en/stable/api/pytorch_lightning.trainer.trainer.Trainer.html?highlight=trainer).<br />\*

***

### MLP.fit

> ```text theme={null}
>  MLP.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:**<br /> `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).<br />
`val_size`: int, validation size for temporal cross-validation.<br />
`random_seed`: int=None, random\_seed for pytorch initializer and numpy
generators, overwrites model.\_\_init\_\_’s.<br /> `test_size`: int, test
size for temporal cross-validation.<br />\*

***

### MLP.predict

> ```text theme={null}
>  MLP.predict (dataset, test_size=None, step_size=1, random_seed=None,
>               quantiles=None, **data_module_kwargs)
> ```

\*Predict.

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

**Parameters:**<br /> `dataset`: NeuralForecast’s
[`TimeSeriesDataset`](https://nixtlaverse.nixtla.io/neuralforecast/tsdataset.html#timeseriesdataset),
see
[documentation](https://nixtla.github.io/neuralforecast/tsdataset.html).<br />
`test_size`: int=None, test size for temporal cross-validation.<br />
`step_size`: int=1, Step size between each window.<br /> `random_seed`:
int=None, random\_seed for pytorch initializer and numpy generators,
overwrites model.\_\_init\_\_’s.<br /> `quantiles`: list of floats,
optional (default=None), target quantiles to predict. <br />
`**data_module_kwargs`: PL’s TimeSeriesDataModule args, see
[documentation](https://pytorch-lightning.readthedocs.io/en/1.6.1/extensions/datamodules.html#using-a-datamodule).\*

## Usage Example

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

from neuralforecast import NeuralForecast
from neuralforecast.models import MLP
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

model = MLP(h=12, input_size=24,
            loss=DistributionLoss(distribution='Normal', level=[80, 90]),
            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['MLP-median'], c='blue', label='median')
plt.fill_between(x=plot_df['ds'][-12:], 
                 y1=plot_df['MLP-lo-90'][-12:].values, 
                 y2=plot_df['MLP-hi-90'][-12:].values,
                 alpha=0.4, label='level 90')
plt.grid()
plt.legend()
plt.plot()
```