from omlt.base import DEFAULT_MODELING_LANGUAGE, OmltConstraintFactory, OmltVarFactory
[docs]
def reduced_space_dense_layer(net_block, net, layer_block, layer, activation):
r"""Add reduced-space formulation of the dense layer to the block.
.. math::
\begin{align*}
\hat z_i &= \sum_{j{=}1}^{M_i} w_{ij} z_j + b_i && \forall i \in N
\end{align*}
"""
# not an input layer, process the expressions
prev_layers = list(net.predecessors(layer))
if len(prev_layers) == 0:
msg = f"Layer {layer} is not an input layer, but has no predecessors."
raise ValueError(msg)
if len(prev_layers) > 1:
msg = f"Layer {layer} has multiple predecessors."
raise ValueError(msg)
prev_layer = prev_layers[0]
prev_layer_block = net_block.layer[id(prev_layer)]
if (
not hasattr(layer_block, "_format")
or layer_block._format == DEFAULT_MODELING_LANGUAGE
):
@layer_block.Expression(layer.output_indexes)
def zhat(b, *output_index):
# dense layers multiply only the last dimension of
# their inputs
expr = 0.0
for (
local_index,
input_index,
) in layer.input_indexes_with_input_layer_indexes:
w = layer.weights[local_index[-1], output_index[-1]]
expr += prev_layer_block.z[input_index] * w
# move this at the end to avoid numpy/pyomo var bug
expr += layer.biases[output_index[-1]]
return expr
@layer_block.Expression(layer.output_indexes)
def z(b, *output_index):
return activation(b.zhat[output_index])
else:
block_lang = layer_block._format
var_factory = OmltVarFactory()
constraint_factory = OmltConstraintFactory()
layer_block.z = var_factory.new_var(layer.output_indexes, lang=block_lang)
layer_block.activation_constraint = constraint_factory.new_constraint(
*layer.output_indexes, lang=block_lang
)
layer_block.zhat = var_factory.new_var(layer.output_indexes, lang=block_lang)
layer_block.weight_constraint = constraint_factory.new_constraint(
*layer.output_indexes, lang=block_lang
)
for output_index in layer.output_indexes:
layer_block.activation_constraint[output_index] = layer_block.z[
output_index
] == activation(layer_block.zhat[output_index], lang=block_lang)
# dense layers multiply only the last dimension of
# their inputs
expr = 0.0
for (
local_index,
input_index,
) in layer.input_indexes_with_input_layer_indexes:
w = layer.weights[local_index[-1], output_index[-1]]
expr += prev_layer_block.z[input_index] * w
# move this at the end to avoid numpy/pyomo var bug
expr += layer.biases[output_index[-1]]
layer_block.weight_constraint[output_index] = (
layer_block.zhat[output_index] == expr
)