Adversarial

implementation

Implicit generative models as factors — Mohamed & Lakshminarayanan (arXiv:1610.03483) — and the GAN diagram read as a factor graph.

Sources: code: Adversarial.jl

Theory (CT-ML wiki): Open Game · Bayesian Inversion · Statistical Game · Bayesian Lens · Variational Free Energy · Lens

Three factors, all unidirectional

factor	is	note
NoiseSource	the latent prior $q(z)$, as an emitting factor	generator
GeneratorFactor	$x=G_{\theta }(z)$ — samples out, no density	generator
RatioFactor	$\log r(x)=\log p(x)-\log q(x)$	ratio

Every one has exactly one polarity, so the GAN diagram is a DAG — Lux-shaped, using none of Mycelium’s bidirectionality. That is the finding, not a shortcoming: a generator is a function with no residual behind it. See Three Senses of Implicit.

What it filled in

Two slots LenticulumCore declared and nobody had ever occupied:

• SampleBelief — declared as “the default fallback whenever no conjugate structure is available, which is most of the time”, and never constructed until now.
• pushforward — declared alongside forward and logdensity, never implemented. And for particles it is cheap, against the warning attached to its declaration; see generator §2.

What it exposed

• The combine gap is now reachable. Two SampleBeliefs exist, and Mycelium.combine throws on them — messages.md §1’s oldest recorded blocker, no longer hypothetical.
• And a discriminator is a route around it. A log-density ratio is what importance reweighting needs, and a classifier estimates one without either density. reweight does it; ratio §4 says why it is still not combine (not idempotent, and quality unreported).
• An estimated energy is a new kind of inexactness. Bayesian Lens.md licenses inexact inversions; this factor has an inexact energy, and the free energy has no term for it because the free energy is the thing being estimated. ratio §5.
• AmortisedInversion is literally true for the first time. The discriminator is a network with its own parameters, trained separately — which lens.md calls the structural reason a factor cannot be a Lux layer.

What it cannot do

Train adversarially. The generator descends the same quantity the discriminator ascends, and a Bethe free energy has one sign. The graph holds the GAN’s wiring exactly and its objective not at all — GANs as Two Factors §4 argues the missing structure is Ghani–Hedges–Winschel–Zahn’s open game, a third lens-shaped object beside the parametric lens and the statistical game.

Dependencies: LuxCore, Random, LinearAlgebra. No Lux, no AD, no training loop.

Concept notes: Implicit Generative Models, GANs as Two Factors, Three Senses of Implicit.