> For the complete documentation index, see [llms.txt](https://deeplearning4j.konduit.ai/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://deeplearning4j.konduit.ai/model-import/overview-1/constraints.md).

# Constraints

Keras allows weight constraints to be applied to layer parameters during training. These constraints clip or rescale the weights after each gradient update to keep them within a specified range. DL4J supports all standard Keras constraints via corresponding `LayerConstraint` implementations.

The mapping is implemented in [KerasConstraintUtils](https://github.com/eclipse/deeplearning4j/blob/master/deeplearning4j/deeplearning4j-modelimport/src/main/java/org/deeplearning4j/nn/modelimport/keras/utils/KerasConstraintUtils.java).

## Supported Constraints

| Keras constraint | DL4J LayerConstraint    | Description                                  |
| ---------------- | ----------------------- | -------------------------------------------- |
| `max_norm`       | `MaxNormConstraint`     | Clips incoming weights so                    |
| `non_neg`        | `NonNegativeConstraint` | Forces all weights to be non-negative        |
| `unit_norm`      | `UnitNormConstraint`    | Scales incoming weights to have unit L2 norm |
| `min_max_norm`   | `MinMaxNormConstraint`  | Clips weights so min\_value ≤                |

## Constraint Descriptions

### max\_norm

Clips the incoming weights for each neuron so that their L2 norm does not exceed `max_value`. Applied along the `axis` dimension (default: 0, i.e., incoming connections per unit).

```python
# Keras
from keras.constraints import max_norm
layer = Dense(64, kernel_constraint=max_norm(2.0))
```

```java
// DL4J equivalent
new MaxNormConstraint(2.0, 1)
```

**Keras parameters:**

| Parameter   | Default | Description                   |
| ----------- | ------- | ----------------------------- |
| `max_value` | 2       | Maximum L2 norm value         |
| `axis`      | 0       | Axis along which to constrain |

### non\_neg

Forces all weights to be greater than or equal to zero after each update. Any negative weights are clipped to zero. Useful for non-negative matrix factorisation tasks.

```python
# Keras
from keras.constraints import non_neg
layer = Dense(64, kernel_constraint=non_neg())
```

```java
// DL4J equivalent
new NonNegativeConstraint()
```

### unit\_norm

Scales incoming weights so that their L2 norm equals 1. Effectively normalises the weight vector for each unit.

```python
# Keras
from keras.constraints import unit_norm
layer = Dense(64, kernel_constraint=unit_norm())
```

```java
// DL4J equivalent
new UnitNormConstraint(1)
```

### min\_max\_norm

Clips incoming weights so that their L2 norm is between `min_value` and `max_value`. The `rate` parameter controls the speed of clipping (rate=1.0 applies the constraint exactly; values less than 1.0 apply it more slowly).

```python
# Keras
from keras.constraints import min_max_norm
layer = Dense(64, kernel_constraint=min_max_norm(min_value=0.5, max_value=2.0))
```

```java
// DL4J equivalent
new MinMaxNormConstraint(0.5, 2.0, 1.0, 1)
```

**Keras parameters:**

| Parameter   | Default | Description                             |
| ----------- | ------- | --------------------------------------- |
| `min_value` | 0.0     | Minimum L2 norm value                   |
| `max_value` | 1.0     | Maximum L2 norm value                   |
| `rate`      | 1.0     | Rate at which the constraint is applied |
| `axis`      | 0       | Axis along which to constrain           |

## Usage Example

```java
import org.deeplearning4j.nn.modelimport.keras.KerasModelImport;
import org.deeplearning4j.nn.multilayer.MultiLayerNetwork;

// Constraints are automatically read and applied to the imported network configuration
MultiLayerNetwork model = KerasModelImport.importKerasSequentialModelAndWeights("model.h5");
```

## Notes

* Constraints are only relevant when the imported model is used for **continued training** in DL4J. For inference, constraints have no effect.
* The constraint `axis` parameter from Keras is mapped to the equivalent DL4J axis convention. Verify constraint behaviour when porting models with non-default axis values.
* Custom Python constraint classes cannot be imported.