Autoregressive Active Inference: sign conventions, unreachable rules, and an EFE-landscape figure mismatch

While optimising the Advanced Examples/Autoregressive Active Inference notebook (PR #94) I ran into a few things in the message rules that I deliberately did not change, because they look surprising but may well be intentional. Flagging them for @wmkouw rather than "fixing" them.

Everything below was measured on Random.seed!(3), 400 steps, RxInfer 5.5.2 / ReactiveMP 6.4.0.

1. Two sign conventions that cancel (not a bug — but please add a comment)

Two places look mutually inconsistent:

• prod(::ClosedProd, ::MvLocationScaleT, ::unBoltzmann) uses Q(y) = -logpdf(left, y) - right.G(y), whereas the analogous prod(::ClosedProd, ::AbstractMvNormal, ::unBoltzmann) uses + right.G(u). Since logpdf(::unBoltzmann) = -G, the product's negative log density "should" be -logpdf(left) + right.G.
• The :outprev1 rules return G(outprev1) = logpdf(marx_predictive(...), m_star) — a positive log density as an energy, where -logpdf would be conventional.

They turn out to be a compensating pair. Flipping both is bit-identical to flipping neither; flipping either one alone breaks the agent completely:

prod sign	:outprev1 sign	waypoints reached
- (current)	+ (current)	3/3 — switches at [103, 129, 144]
+	+	0/3
-	-	0/3
+	-	3/3 — switches at [103, 129, 144]

So the code is self-consistent and correct as written. The risk is purely that a future reader (or a linter, or me) "fixes" one half in isolation and silently destroys the agent — I very nearly did. Would you consider a short comment at both sites noting that the sign convention is paired?

2. mutualinfo disagrees with the rules — the EFE landscape figure plots the wrong surface

In the "standalone predictive / EFE functions" cell:

mutualinfo(Σ) = 1 / 2 * logdet(Σ)

but every :in rule uses MI = -1/2*logdet(Σ), and the notebook's own markdown states the EFE as

$$G(u) = \underbrace{-\tfrac12\log\det\Sigma}_{\text{epistemic}} + \dots$$

mutualinfo is used only by efe_landscape, so the "Expected free energy at step N" heatmap plots a different function than the agent minimises, and its white argmin marker is not the agent's chosen action. Unlike item 1 this one does not cancel — nothing else consumes it.

I verified that flipping it changes only the figure: trajectory and waypoint switches are identical (3/3, [103, 129, 144]). I left it as-is so this PR stays behaviour-preserving — happy to flip it in a follow-up if you agree it is a typo.

3. Latent UndefVarError in one :outprev1 rule

One of the eight :outprev1 rules had arguments named m_inprev1 / m_inprev2 but its body referenced mode(q_inprev1) / mode(q_inprev2). It would have thrown UndefVarError if it ever dispatched. It never does in practice (see below), and PR #94 fixes it incidentally by generating the rule wrappers from their signatures.

4. 34 of the 42 MARX rules never fire

Instrumenting every rule with a dispatch counter, only 8 are ever reached:

rule	hits
:out	17250
:in	17160
:inprev1	11010
:outprev1	8790
:inprev2	6660
:Φ (conjugate)	4500
:outprev2	2700
:Φ (uninformative)	120

The other 34 are dead under this model and constraint set. I kept all of them in PR #94 (they cost nothing at runtime and may be needed for other configurations), but if they were written defensively during development it may be worth pruning them. Your call — you would know which are load-bearing for variants of the model.

5. The planner was under-converging (fixed in #93, but worth a sanity check)

mode(::unBoltzmann) used Fminbox(LBFGS()) with Optim.Options(outer_iterations=100, iterations=1). Comparing it in situ against a properly converged solve on identical inputs, it returned a strictly worse minimum in 5739 of 9270 calls (mean ΔG = −0.80 in favour of the converged solve), and never a better one.

So the published trajectory was shaped partly by the optimiser stopping early. With it converging properly the agent reaches the waypoints noticeably sooner (steps 103/129/144 rather than late in the trial), and all 10 validation seeds still reach 3/3. Could you sanity-check that the new behaviour is what you expect scientifically? It is a real change to the figures, even though it is strictly better EFE minimisation.

🤖 Generated with Claude Code

Start with the Advanced Examples/Autoregressive Active Inference notebook and reproduce the Random.seed!(3), 400-step run using the stated RxInfer and ReactiveMP versions. Inspect the standalone predictive/EFE functions, MARX rules, and mode(::unBoltzmann), including PR #94. Done means the maintainers have resolved or documented the sign and mutualinfo mismatch, checked the latent error and unreachable rules, and validated the optimizer's changed trajectory.