The link between a GAN and the Ising model of the brain
Generative adversarial network ⇄ Ising model of neural spike trains · via energy-based models
The pairwise maximum-entropy model of neural population spike trains is exactly the Ising model, with firing rates and pairwise correlations becoming the fields h_i and couplings J_ij; GANs already reproduce the same spike-train statistics (Spike-GAN) and a trained GAN can be rewritten as an energy-based model, yet no published work reparameterizes a GAN's weights as the Ising couplings J_ij of such a model, leaving open whether a GAN trained on population spike trains recovers the same effective couplings as a fitted maximum-entropy model.
The open question
The same population of neurons can be described two ways: by the Ising model (the pairwise maximum-entropy model, exactly) and by a GAN. A trained GAN can also be rewritten as an energy-based model, and Boltzmann-machine weights are known to map onto Ising couplings. So can a GAN's weights be reparameterized directly as the Ising couplings J_ij of the spike-train model? Would a GAN trained on a population recover the same effective couplings as a fitted maximum-entropy model, and at what population size would the two diverge?
What the system already tried
The two halves are established: the pairwise maximum-entropy model of population spike trains is the Ising model by exact identity, and GANs already model the same data and can be rewritten as energy-based models. The connecting step is what we could not find: explicit weight-to-coupling maps exist only for restricted Boltzmann machines, not for GANs, and not for neural data. As far as we found, no one has built that specific bridge. That is an absence we could not rule out, not a proof of novelty, which is why it sits here for open review.
The sources it read
- nature.com/articles/nature04701
- arxiv.org/abs/q-bio/0611072
- journals.plos.org/ploscompbiol/article
- arxiv.org/abs/1803.00338
- arxiv.org/abs/2003.06060
- arxiv.org/abs/1608.06315
- frontiersin.org/articles/10.3389/neuro.10.022.2009/full
Open review
Is this a real connection or a coincidence of shared words? The facts above are grounded in the sources; the leap between them is what is unproven. Make the case, or settle it with a reference.