The Boltzmann target

One distribution, two factors: the grammar supplies parsimony, the learned taste supplies direction, and $\beta$ is the single dial between them.

The target

$$\pi_\beta(x) ;\propto; p_{\text{grammar}}(x);\exp!\big(\beta \cdot \E[u_\theta(\varphi(x))]\big)$$

This is fugue-evo's EvolutionModel with the learned utility plugged in as fitness, so the whole thing becomes an ordinary probabilistic program and typed-MH / SMC drivers apply unchanged.

What each factor does

$p_{\text{grammar}}(x)$ is the parsimony pressure. It is the prior probability of the term under the typed PCFG, not a penalty term. Deeper terms pay more prior mass by construction, because each extra level multiplies in another Bernoulli that came out "processor" plus that node's own parameter draws.

Ad-hoc size penalties in genetic programming need tuning, interact badly with fitness scaling, and leave the target distribution unwritten. Here the target is written down, and the parsimony term is a probability rather than a hyperparameter.

$\exp(\beta \E[u_\theta])$ is the direction. The expectation is over the posterior, so the search climbs the model's mean belief and is not seduced by a single confident-looking draw.

$\beta$

SessionConfig::beta, default 2.0.

One dial for conservatism, which is the practical payoff of writing the target down: there is no explore/exploit schedule to tune, no diversity term, no niching parameter. Tempering the same target is also how tempered SMC would work if it were wired up.

Fitness through the surrogate

SurrogateFitness is the bridge:

impl Fitness for SurrogateFitness {
    fn evaluate(&self, genome: &PatchTree) -> f64 {
        match featurize_memo(genome, &self.phrase, &self.memo, false) {
            Ok((cf, _)) => {
                let phi = self.standardizer.transform(&cf.features.phi());
                self.posterior.utility_mix(&phi).0
            }
            Err(_) => QUARANTINE_FITNESS,
        }
    }
}

Three things in nine lines:

Quarantine is a fitness, not just a filter. QUARANTINE_FITNESS = -50.0, so a pathological candidate contributes a large negative factor to the target and the search learns to avoid the region rather than repeatedly sampling it. That is safety layer 2; hiding alone would leave the search wasting budget somewhere it cannot see is bad.

The standardizer must be the one the observations were made under. $\theta$ is meaningless against any other scaling; see Standardization.

want_audio: false. The surrogate only ever wants $\varphi$; nothing in a refinement generation is played. Asking for samples would undo the memo: a miss would convert 141k f64s it then drops, and a hit would copy a ~565 KB buffer out of the audio tier. Twice per MH step, ~96 times per seed, that is tens of megabytes of churn for a value discarded on the next line.

Why the render memo matters

It is what makes the walk affordable at all.

adaptive_single_site_mh executes the model twice per step: once to re-score the current trace (bit-identically the tree the previous step accepted, and therefore already featurized) and once for the proposal. Without a memo, one render in two is a recomputation of a number the walk already has.

At ~600 ms per render, a 40-step walk from each of 10 seeds is 800 renders without the memo and 400 with it. That is the difference between a generation taking half a minute and taking a minute, per generation, forever.

What is not sampled from this

What ships is not a sample from $\pi_\beta$. Refinement runs a short adaptive single-site MH walk warm-started from each of the best pool members and keeps the final state: local hill-climbing on that target, which is what a candidate pool needs, rather than a draw from it.

Tempered SMC with the crossover population kernel remains the design. The distinction is in Refinement.