# Weight constraints

Functions that impose constraints on weight values.

constraint_maxnorm(max_value = 2, axis = 0)

constraint_nonneg()

constraint_unitnorm(axis = 0)

constraint_minmaxnorm(min_value = 0, max_value = 1, rate = 1,
axis = 0)

## Arguments

 max_value The maximum norm for the incoming weights. axis The axis along which to calculate weight norms. For instance, in a dense layer the weight matrix has shape input_dim, output_dim, set axis to 0 to constrain each weight vector of length input_dim,. In a convolution 2D layer with dim_ordering="tf", the weight tensor has shape rows, cols, input_depth, output_depth, set axis to c(0, 1, 2) to constrain the weights of each filter tensor of size rows, cols, input_depth. min_value The minimum norm for the incoming weights. rate The rate for enforcing the constraint: weights will be rescaled to yield (1 - rate) * norm + rate * norm.clip(low, high). Effectively, this means that rate=1.0 stands for strict enforcement of the constraint, while rate<1.0 means that weights will be rescaled at each step to slowly move towards a value inside the desired interval.

## Details

• constraint_maxnorm() constrains the weights incident to each hidden unit to have a norm less than or equal to a desired value.

• constraint_nonneg() constraints the weights to be non-negative

• constraint_unitnorm() constrains the weights incident to each hidden unit to have unit norm.

• constraint_minmaxnorm() constrains the weights incident to each hidden unit to have the norm between a lower bound and an upper bound.

## Custom constraints

You can implement your own constraint functions in R. A custom constraint is an R function that takes weights (w) as input and returns modified weights. Note that keras backend() tensor functions (e.g. k_greater_equal()) should be used in the implementation of custom constraints. For example:

nonneg_constraint <- function(w) {
w * k_cast(k_greater_equal(w, 0), k_floatx())
}
layer_dense(units = 32, input_shape = c(784),
kernel_constraint = nonneg_constraint)


Note that models which use custom constraints cannot be serialized using save_model_hdf5(). Rather, the weights of the model should be saved and restored using save_model_weights_hdf5().