nnopinf.operators.SpdOperator#

class nnopinf.operators.SpdOperator(acts_on, depends_on, n_hidden_layers, n_neurons_per_layer, activation=<built-in method tanh of type object>, positive=True, name='SpdOperator', parameterization='cholesky', layer_norm=True)[source]#

Bases: Module

\(f: (v,x) \mapsto L(v)L(v)^T x\)

Constructs an SPD (or NPD) operator \(f: (v,x) \mapsto L(v)L(v)^Tx = A(v)x\) such that \(x^T A(v) x >= 0\)

Parameters:

  • acts_on (nnopinf.Variable) – The state the operator acts on, i.e., the x in A(v) x

  • depends_on (tuple of nnopinf.Variable) – The variables the operator depends on, i.e., the v in A(v) x

  • n_hidden_layers (int) – Number of hidden layers in the network

  • n_neurons_per_layer (int) – Number of neurons in each hidden layer

  • activation (PyTorch activation function (e.g., torch.nn.functional.relu)) – Activation function used at each hidden layer.

  • positive (bool) – If operator is SPD or NPD

  • parameterization (str) – SPD parameterization. Supported values are "cholesky" (default, uses \(L L^T\)) and "matrix_exp" (uses \(\exp(S)\) with symmetric \(S\)).

  • layer_norm (bool) – If True, apply LayerNorm after each hidden linear layer.

  • name (string) – Operator name. Used when saving to file

Examples

>>> import nnopinf
>>> import nnopinf.operators
>>> x_input = nnopinf.Variable(size=3,name="x")
>>> mu_input = nnopinf.Variable(size=2,name="mu")
>>> NpdMlp = nnopinf.operators.SpdOperator(acts_on=x_input,depends_on=(x_input,mu_input,),n_hidden_layers=2,n_neurons_per_layer=2,positive=False)
forward(inputs, return_jacobian=False)[source]#

Forward pass of operator

Parameters:

  • inputs (dict(str, np.array)) – Dictionary of input data in the form of arrays referenced by the variable name, i.e., inputs[‘x’] = np.ones(3)

  • return_jacobian (bool, optional) – If True, return the (approximate) Jacobian in addition to the output.

Examples

>>> import nnopinf
>>> import nnopinf.operators
>>> import numpy as np
>>> x_input = nnopinf.Variable(size=3,name="x")
>>> mu_input = nnopinf.Variable(size=2,name="mu")
>>> NpdMlp = nnopinf.operators.SpdOperator(acts_on=x_input,depends_on=(x_input,mu_input,),n_hidden_layers=2,n_neurons_per_layer=2,positive=False)
>>> inputs = {}
>>> inputs['x'] = np.random.normal(3)
>>> inputs['mu'] = np.random.normal(2)
>>> Av,A = NpdMlp.forward(inputs,True)
set_scalings(input_scalings_dict, output_scaling)[source]#

Apply input and output scaling factors to the SPD operator.

Parameters:

  • input_scalings_dict (dict) – Mapping from variable name to the corresponding feature-wise input scaling vector.

  • output_scaling (tensor-like) – Feature-wise scaling vector for the operator output.

Show Source