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>, siren_omega_0=30.0, siren_first_layer=False, fourier_features=False, fourier_variables=None, fourier_num_frequencies=6, fourier_base=2.0, fourier_scale=1.0, fourier_frequencies=None, positive=True, name='SpdOperator', parameterization='cholesky', residual=True, 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 operators 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 nuerons in each hidden layer

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

  • siren_omega_0 (float) – Frequency scale for SIREN activations.

  • siren_first_layer (bool) – If True, use a SIREN-style first layer even for non-sine activations.

  • fourier_features (bool) – If True, augment inputs with Fourier features.

  • fourier_variables (iterable of str, optional) – Variable names to augment with Fourier features. Defaults to all inputs.

  • fourier_num_frequencies (int) – Number of frequencies per variable when using Fourier features.

  • fourier_base (float) – Base for geometric progression of Fourier frequencies.

  • fourier_scale (float) – Scaling applied to Fourier frequencies.

  • fourier_frequencies (array-like, optional) – Explicit list of Fourier frequencies. Overrides fourier_num_frequencies.

  • 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 \(S\)).

  • residual (bool) – If True, use residual connections between hidden layers when shapes match.

  • 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)
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