GNCN-PDH (Ororbia & Kifer, 2020/2022)

This circuit implements one of the models proposed in (Ororbia & Kifer, 2022) [1]. Specifically, this model is unsupervised and can be used to process sensory pattern (row) vector(s) x to infer internal latent states. This class offers, beyond settling and update routines, a projection function by which ancestral sampling may be carried out given the underlying directed generative model formed by this NGC system.

The GNCN-PDH is graphically depicted by the following graph:

class ngclearn.museum.gncn_pdh.GNCN_PDH(args)

Structure for constructing the model proposed in:

Ororbia, A., and Kifer, D. The neural coding framework for learning generative models. Nature Communications 13, 2064 (2022).

This model, under the NGC computational framework, is referred to as the GNCN-t1-Sigma/Friston, according to the naming convention in (Ororbia & Kifer 2022).

Historical Note:

(The arXiv paper that preceded the publication above is shown below:)

Ororbia, Alexander, and Daniel Kifer. “The neural coding framework for

learning generative models.” arXiv preprint arXiv:2012.03405 (2020).

Node Name Structure:

z3 -(z3-mu2)-> mu2 ;e2; z2 -(z2-mu1)-> mu1 ;e1; z1 -(z1-mu0-)-> mu0 ;e0; z0

z3 -(z3-mu1)-> mu1; z2 -(z2-mu0)-> mu0

e2 -> e2 * Sigma2; e1 -> e1 * Sigma1 // Precision weighting

z3 -> z3 * Lat3; z2 -> z2 * Lat2; z1 -> z1 * Lat1 // Lateral competition

e2 -(e2-z3)-> z3; e1 -(e1-z2)-> z2; e0 -(e0-z1)-> z1 // Error feedback

Parameters

args – a Config dictionary containing necessary meta-parameters for the GNCN-PDH

DEFINITION NOTE:

args should contain values for the following:

* batch_size - the fixed batch-size to be fed into this model

* z_top_dim: # of latent variables in layer z3 (top-most layer)

* z_dim: # of latent variables in layers z1 and z2

* x_dim: # of latent variables in layer z0 or sensory x

* seed: number to control determinism of weight initialization

* wght_sd: standard deviation of Gaussian initialization of weights

* beta: latent state update factor

* leak: strength of the leak variable in the latent states

* K: # of steps to take when conducting iterative inference/settling

* act_fx: activation function for layers z1, z2, and z3

* out_fx: activation function for layer mu0 (prediction of z0) (Default: sigmoid)

* n_group: number of neurons w/in a competition group for z2 and z2 (sizes of z2 and z1 should be divisible by this number)

* n_top_group: number of neurons w/in a competition group for z3 (size of z3 should be divisible by this number)

* alpha_scale: the strength of self-excitation

* beta_scale: the strength of cross-inhibition

project(z_sample)

Run projection scheme to get a sample of the underlying directed generative model given the clamped variable z_sample

Parameters

z_sample – the input noise sample to project through the NGC graph

Returns

x_sample (sample(s) of the underlying generative model)

settle(x, calc_update=True)

Run an iterative settling process to find latent states given clamped input and output variables

Parameters

• x – sensory input to reconstruct/predict

• calc_update – if True, computes synaptic updates @ end of settling process (Default = True)

Returns

x_hat (predicted x)

calc_updates(avg_update=True, decay_rate=- 1.0)

Calculate adjustments to parameters under this given model and its current internal state values

Returns

delta, a list of synaptic matrix updates (that follow order of .theta)

clear()

Clears the states/values of the stateful nodes in this NGC system

References:
[1] Ororbia, A., and Kifer, D. The neural coding framework for learning generative models. Nature Communications 13, 2064 (2022).