Testing

JPC provides a few convenience functions to test different types of PC network (PCN):

• jpc.test_discriminative_pc() for test loss and accuracy of discriminative PCNs;
• jpc.test_generative_pc() for accuracy and output predictions of generative PCNs; and
• jpc.test_hpc() for accuracy of all models (amortiser, generator, & hybrid) as well as output predictions.

jpc.test_discriminative_pc(model: PyTree[typing.Callable], output: typing.Union[jax.Array, numpy.ndarray, numpy.bool, numpy.number, bool, int, float, complex], input: typing.Union[jax.Array, numpy.ndarray, numpy.bool, numpy.number, bool, int, float, complex], *, skip_model: typing.Optional[jaxtyping.PyTree[typing.Callable]] = None, loss: str = 'mse', param_type: str = 'sp') -> typing.Tuple[jaxtyping.Shaped[Array, ''], jaxtyping.Shaped[Array, '']]

Computes test metrics for a discriminative predictive coding network.

Main arguments:

• model: List of callable model (e.g. neural network) layers.
• output: Observation or target of the generative model.
• input: Optional prior of the generative model.

Other arguments:

• skip_model: Optional skip connection model.
• loss: Loss function to use at the output layer. Options are mean squared error "mse" (default) or cross-entropy "ce".
• param_type: Determines the parameterisation. Options are "sp" (standard parameterisation), "mupc" (μPC), or "ntp" (neural tangent parameterisation). See _get_param_scalings() for the specific scalings of these different parameterisations. Defaults to "sp".

Returns:

Test loss and accuracy of output predictions.

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jpc.test_generative_pc(model: PyTree[typing.Callable], output: typing.Union[jax.Array, numpy.ndarray, numpy.bool, numpy.number, bool, int, float, complex], input: typing.Union[jax.Array, numpy.ndarray, numpy.bool, numpy.number, bool, int, float, complex], key: typing.Union[jaxtyping.Key[Array, ''], jaxtyping.UInt32[Array, 2]], layer_sizes: PyTree[int], batch_size: int, *, skip_model: typing.Optional[jaxtyping.PyTree[typing.Callable]] = None, loss_id: str = 'mse', param_type: str = 'sp', sigma: Shaped[Array, ''] = 0.05, ode_solver: AbstractSolver = Heun(), max_t1: int = 500, dt: jaxtyping.Shaped[Array, ''] | int = None, stepsize_controller: AbstractStepSizeController = PIDController(rtol=0.001, atol=0.001), weight_decay: Shaped[Array, ''] = 0.0, spectral_penalty: Shaped[Array, ''] = 0.0, activity_decay: Shaped[Array, ''] = 0.0) -> typing.Tuple[jaxtyping.Shaped[Array, ''], jax.Array]

Computes test metrics for a generative predictive coding network.

Gets output predictions (e.g. of an image given a label) with a feedforward pass and calculates accuracy of inferred input (e.g. of a label given an image).

Main arguments:

• model: List of callable model (e.g. neural network) layers.
• output: Observation or target of the generative model.
• input: Prior of the generative model.
• key: jax.random.PRNGKey for random initialisation of activities.
• layer_sizes: Dimension of all layers (input, hidden and output).
• batch_size: Dimension of data batch for activity initialisation.

Other arguments:

• skip_model: Optional skip connection model.
• loss_id: Loss function to use at the output layer. Options are mean squared error "mse" (default) or cross-entropy "ce".
• param_type: Determines the parameterisation. Options are "sp" (standard parameterisation), "mupc" (μPC), or "ntp" (neural tangent parameterisation). See _get_param_scalings() for the specific scalings of these different parameterisations. Defaults to "sp".
• sigma: Standard deviation for Gaussian to sample activities from. Defaults to 5e-2.
• ode_solver: diffrax ODE solver to be used. Default is Heun, a 2nd order explicit Runge--Kutta method.
• max_t1: Maximum end of integration region (500 by default).
• dt: Integration step size. Defaults to None since the default stepsize_controller will automatically determine it.
• stepsize_controller: diffrax controller for step size integration. Defaults to PIDController. Note that the relative and absolute tolerances of the controller will also determine the steady state to terminate the solver.
• weight_decay: Weight decay for the weights (0 by default).
• spectral_penalty: Weight spectral penalty of the form \(||\mathbf{I} - \mathbf{W}_\ell^T \mathbf{W}_\ell||^2\) (0 by default).
• activity_decay: Activity decay for the activities (0 by default).

Returns:

Accuracy and output predictions.

---

jpc.test_hpc(generator: PyTree[typing.Callable], amortiser: PyTree[typing.Callable], output: typing.Union[jax.Array, numpy.ndarray, numpy.bool, numpy.number, bool, int, float, complex], input: typing.Union[jax.Array, numpy.ndarray, numpy.bool, numpy.number, bool, int, float, complex], key: typing.Union[jaxtyping.Key[Array, ''], jaxtyping.UInt32[Array, 2]], layer_sizes: PyTree[int], batch_size: int, sigma: Shaped[Array, ''] = 0.05, ode_solver: AbstractSolver = Heun(), max_t1: int = 500, dt: jaxtyping.Shaped[Array, ''] | int = None, stepsize_controller: AbstractStepSizeController = PIDController(rtol=0.001, atol=0.001)) -> typing.Tuple[jaxtyping.Shaped[Array, ''], jaxtyping.Shaped[Array, ''], jaxtyping.Shaped[Array, ''], jax.Array]

Computes test metrics for hybrid predictive coding trained in a supervised manner.

Calculates input accuracy of (i) amortiser, (ii) generator, and (iii) hybrid (amortiser + generator). Also returns output predictions (e.g. of an image given a label) with a feedforward pass of the generator.

Note

The input and output of the generator are the output and input of the amortiser, respectively.

Main arguments:

• generator: List of callable layers for the generative model.
• amortiser: List of callable layers for model amortising the inference of the generator.
• output: Observation or target of the generative model.
• input: Optional prior of the generator, target for the amortiser.
• key: jax.random.PRNGKey for random initialisation of activities.
• layer_sizes: Dimension of all layers (input, hidden and output).
• batch_size: Dimension of data batch for initialisation of activities.

Other arguments:

• sigma: Standard deviation for Gaussian to sample activities from. Defaults to 5e-2.
• ode_solver: diffrax ODE solver to be used. Default is Heun, a 2nd order explicit Runge--Kutta method.
• max_t1: Maximum end of integration region (500 by default).
• dt: Integration step size. Defaults to None since the default stepsize_controller will automatically determine it.
• stepsize_controller: diffrax controller for step size integration. Defaults to PIDController. Note that the relative and absolute tolerances of the controller will also determine the steady state to terminate the solver.

Returns:

Accuracies of all models and output predictions.