Proposals, and the taste tilt

The loop closes here: what the model learns reshapes what the search proposes, not only what it scores.

Moves

Refinement uses fugue's adaptive single-site MH over the trace, so the move set is whatever the trace machinery provides:

Parameter moves perturb one continuous or discrete site.
Structural moves regenerate a subtree, which changes the set of sites and is therefore a reversible-jump move. fugue handles the Jacobian bookkeeping; Auracle does not implement it.

The structural moves are the same lattice as hand edits. One vocabulary, two callers.

The tilt

Once a posterior exists, the grammar's categorical proposal weights are reshaped by what it has learned:

$w'_i ;\propto; w_i \cdot \mathrm{clamp}!\big(e^{\eta t_i},\ \tfrac14,\ 4\big)$

then renormalized. SessionConfig::proposal_tilt is $\eta$ , default 0.6.

pub fn tilt_weights(base: &[f64], tilts: &[f64], eta: f64) -> Vec<f64> {
    let mut out: Vec<f64> = base.iter().zip(tilts)
        .map(|(w, t)| w * (eta * t).exp().clamp(0.25, 4.0))
        .collect();
    let sum: f64 = out.iter().sum();
    if sum > 0.0 { for w in &mut out { *w /= sum; } }
    out
}

The function is pure, which is why the taste→grammar mapping is testable without an MCMC fit. That matters for a mapping this easy to get subtly wrong.

The clamp

$[\tfrac14, 4]$ bounds every multiplier, so no module kind is ever starved or monopolized.

Hollow bars are the prior's own weights; filled bars are the tilted ones. Raise η and the model's opinions start pushing kinds around. Then turn the clamp off: the strongest coefficients drive their kinds toward never being proposed at all. A prior that cannot generate an option can never be argued back into it, because the evidence would have to come from proposing it. Red is a multiplier sitting at a bound.

Without it a confidently-fitted coefficient could drive a kind's proposal weight to effectively zero, and the search would stop being able to discover that it was wrong about that kind. A prior that has been argued out of considering an option cannot be argued back in by evidence it can no longer generate.

Where $t_i$ comes from

biased_prior builds the tilt vector from the posterior, in three steps.

1. Blend the lenses by their pool share.

$\bar\theta = \sum_k \text{share}_k , \theta_k^{\text{mean}}, \qquad \bar\sigma = \sum_k \text{share}_k , \theta_k^{\text{sd}}$

Share-weighted rather than uniform, so an idle lens (one claiming ≈0% of the pool) contributes ≈nothing to how the search proposes. Uniform weighting would let a lens with no evidence steer the search as hard as one with plenty.

2. Shrink each coefficient by its own uncertainty.

$\mathrm{shrink}(\theta, \sigma) = \theta \cdot \frac{|\theta|}{|\theta| + \sigma}$

Regime	Factor
$\sigma \ll$	\theta
$\sigma =$	\theta
$\sigma \gg$	\theta

Same shape as a signal-to-noise weighting, and chosen over a hard significance cut for a specifically musical reason: a cut makes the proposal distribution jump discontinuously as evidence accumulates, and users hear that as the instrument changing its mind. A smooth ramp is a model getting more opinionated; a threshold crossing is a different instrument arriving mid-session. 3. Map coordinates to categorical slots. The source-kind tilts read n_vco, n_supersaw, n_noise, n_wavetable, n_pluck, n_formant directly; processor and modulation tilts read their family coordinates.

The `n_mix` reconstruction

n_mix is not a column of

\varphi

: it was dropped to break an exact linear dependency.

But the search still needs some tilt for the mix production, and biased_prior recovers it from the source coefficients. That is legitimate precisely because of the identity that forced the drop: n_mix is determined by the other counts, so information about it is present in what remains. The dependency that made the column unusable as a regressor is what makes it recoverable as a tilt.

Why tilt proposals rather than only score

A scored-only search is limited by what it happens to generate. If the prior draws bitcrush into 2.5% of terms, then no matter how much the model likes bitcrush, only 2.5% of proposals will contain one and the search has to wait for luck.

Tilting the proposal distribution means the search looks where the model expects to find things. Combined with the clamp, it is a change of emphasis rather than a change of support: every kind stays reachable, and the ones the model believes in get proposed more often.

On detailed balance

Tilting the proposal changes the kernel, not the target. The MH accept/reject step still scores against $\pi_\beta$ , so the stationary distribution is unchanged: a tilted proposal is a better-informed way of exploring the same target, not a different one.

That would matter more if refinement were sampling from $\pi_\beta$ . It is not; it is hill-climbing on it, so in practice the tilt's effect is to make the climb find good regions sooner rather than to change what "correct" means.

Structural taste, specifically

Note that the tilt reads the structural coefficients. That is a deliberate asymmetry: $\varphi_{\text{struct}}$ coordinates map onto grammar productions more or less directly (n_filter ↔ the filter production), whereas an audio coefficient like centroid_mean has no single production to point at. Brightness is a property of the composition, not of a module.

So the audio half of $\theta$ influences the search only through scoring, and the structural half influences both scoring and proposing. Turning centroid_mean into a proposal tilt would require a model of which productions raise brightness, which is a model nobody has fitted.

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