GPFA Port Notes

The local MATLAB reference is /Users/jonathanhuml/Desktop/gpfa-matlab. The Python Elephant reference is: https://github.com/NeuralEnsemble/elephant/tree/master/elephant/gpfa.

The implementation in zynamics.models.gpfa is being moved toward the Elephant Python structure while keeping tensors in PyTorch:

• gpfaEngine.m: initialize gamma, eps, C, d, and diagonal R.
• fastfa.m: initialize C, d, and R with factor analysis.
• exactInferenceWithLL.m: run the GPFA E-step and compute likelihood.
• em.m: update C, d, R, then learn GP kernel parameters.
• learnGPparams.m and grad_betgam.m: update each RBF gamma from posterior autocovariance sufficient statistics.

Current Elephant-aligned choices:

• Elephant uses sklearn.decomposition.FactorAnalysis; zynamics ports the same FA EM objective in torch to avoid adding sklearn to the model dependency surface.
• Elephant uses SciPy L-BFGS-B for grad_betgam; zynamics uses PyTorch autograd with torch.optim.LBFGS on the equivalent objective.
• Elephant exposes both raw latent trajectories and latent_variable_orth. Zynamics now returns raw latents in ModelOutput.latents and orthonormalized latents plus Corth in ModelOutput.extras.

Orthonormalization is postprocessing for latent visualization. It should not change decoded firing-rate predictions unless the latent trajectories and the loading matrix are transformed consistently.

The benchmark epoch definition is unchanged: one GPFA epoch is one full E-step, one C/d/R M-step, and the associated gamma optimization using the E-step sufficient statistics.