# L1Decay¶

class paddle.regularizer. L1Decay ( coeff=0.0 ) [source]

Implement the L1 Weight Decay Regularization, which encourages the weights to be sparse.

It can be set in ParamAttr or `optimizer` (such as Momentum ). When set in `ParamAttr` , it only takes effect for trainable parameters in this layer. When set in `optimizer` , it takes effect for all trainable parameters. When set together, `ParamAttr` has higher priority than `optimizer` , which means that for a trainable parameter, if regularizer is defined in its ParamAttr, then the regularizer in Optimizer will be ignored. Otherwise the regularizer in Optimizer will be used.

In the implementation, the loss function of L1 Weight Decay Regularization is as follows:

\[loss = coeff * reduce\_sum(abs(x))\]
Parameters

coeff (float, optional) – regularization coeff. Default:0.0.

Examples

```>>> # Example1: set Regularizer in optimizer
>>> import paddle
>>> from paddle.regularizer import L1Decay

>>> linear = paddle.nn.Linear(10, 10)
>>> inp = paddle.rand(shape=[10, 10], dtype="float32")
>>> out = linear(inp)
>>> loss = paddle.mean(out)
>>> beta1 = paddle.to_tensor([0.9], dtype="float32")
>>> beta2 = paddle.to_tensor([0.99], dtype="float32")
>>> momentum = paddle.optimizer.Momentum(
...     learning_rate=0.1,
...     parameters=linear.parameters(),
...     weight_decay=L1Decay(0.0001))
>>> back = out.backward()
>>> momentum.step()
>>> momentum.clear_grad()
```
```>>> # Example2: set Regularizer in parameters
>>> # Set L1 regularization in parameters.
>>> # Global regularizer does not take effect on my_conv2d for this case.
>>> from paddle.nn import Conv2D
>>> from paddle import ParamAttr
>>> from paddle.regularizer import L1Decay

>>> my_conv2d = Conv2D(
...         in_channels=10,
...         out_channels=10,
...         kernel_size=1,
...         stride=1,
...         padding=0,
...         weight_attr=ParamAttr(regularizer=L1Decay(coeff=0.01)),
...         bias_attr=False)
```