φ_struct — structural descriptors

Twenty-five dimensions, free to compute.

These cost nothing: no compile, no render, just a walk of the term. That is what makes the screening cascade possible: a structure-only surrogate prunes candidates before the expensive render path. They also capture taste axes audio features cannot fully separate ("likes supersaws", "likes deep modulated chains").

The coordinates

Fourteen family counts:

n_vco  n_supersaw  n_noise  n_wavetable  n_pluck  n_formant
n_filter  n_drive  n_time  n_mod_fx  n_reverb  n_dynamics
n_lfo  n_env  n_rand  n_follow  n_mod_shape  n_mod_logic

Seven term-level numbers:

mod_density  mod_depth_mean  amp_attack  amp_sustain  amp_release
chain_balance  frac_sidechained

Twenty-five in total, appended after the fifteen audio coordinates to give $\varphi \in \R^{40}$.

Families, not one column per module

StructFeatures keeps a raw counter per module kind internally (the Styles tab and the auto-namer both want "two filters", not "two subtractive stages"), but NAMES and to_vec collapse forty-one module kinds into fourteen family counts.

Two reasons.

Nothing meaningful distinguishes them. n_fold, n_distortion and n_bitcrush all answer "how much nonlinear colour". n_chorus, n_phaser, n_flanger, n_tremolo and n_vibrato all answer "how much periodic movement". A user who likes drive does not first decide which drive.

Per-kind columns arrive as near-indicator variables. The prior draws bitcrush at 2.5%, ring mod at 2% and granular at 1.5%, so those columns are zero in ~19 of every 20 pool members. A coefficient fitted on a column that is almost always zero is estimated from a handful of rows, and the Styles tab would render it beside coefficients fitted on hundreds, at the same visual weight.

Measured over 1200 draws, the extreme case: each of the four CV processors appears in under 4% of patches and each of the six combiners in under 1%. A column that is zero in 99 rows of every 100 is not a coefficient, it is a rounding error with a name in the UI.

Sixteen sparse columns would also cost sixteen dimensions of posterior variance for the cold start to pay down before the model says anything at all.

What is deliberately not in φ

size, an exact identity

Every audio node increments exactly one raw counter, so

$$\text{size} \equiv \sum_i n_i \qquad\text{exactly, for every tree}$$

Including it makes the design matrix rank-deficient. The Gaussian prior keeps the posterior proper, so nothing crashes and no test fails, but there is an unidentified ridge along which the MH chain random-walks forever. That wrecks mixing, splits each coefficient arbitrarily between size and the counts (so the per-feature weights the Styles tab renders mean nothing individually), and poisons the taste→grammar proposal tilt, which reads exactly those coefficients.

size − depth would be no better: still an exact linear combination of coordinates already present.

The field is kept for display and naming. It just never reaches the model.

A second, subtler identity

Dropping size alone was not enough, and a VIF sweep caught it: VIF $\approx 10^9$ on every column involved, which is what an exact dependency looks like numerically.

A tree is a forest of source leaves joined by productions that each take some number of audio children, so the leaf count exceeds the total branch count by exactly one:

$$n_{\text{vco}} + n_{\text{supersaw}} + n_{\text{noise}} + n_{\text{wavetable}} + n_{\text{pluck}} + n_{\text{formant}} + n_{\text{silence}}$$ $${} - n_{\text{mix}} - n_{\text{ringmod}} - n_{\text{comp}} - n_{\text{duck}} - n_{\text{gate}} - n_{\text{vocoder}} ;=; 1$$

Silence joins that sum as a source leaf, because that is what it is: it has no children, so it ends a branch exactly as a Vco does. Joining keeps this one equation with one dropped column, and $n_{\text{mix}}$ stays the column dropped. Leaving it outside instead would make the identity exact for a tree with no holes and slack for one with them — near-exact almost always, which is a worse thing to carry than an exact dependency: an exact one is unmistakable in a VIF sweep, and a near-exact one is a large number that looks like a judgment call.

exactly, for every tree. This only became a general statement when the four dynamics productions arrived, each taking two audio subterms exactly as mix and ring mod do.

That is one equation, so exactly one column has to go, and dropping more would remove real dimensions rather than redundant ones. With both binary counts gone, $\varphi$ could not tell a crossfade from a ring modulator at all, which are about as different as two nodes in this grammar get.

So n_mix leaves: it is the one determined by the others, and its proposal tilt is recovered from the source coefficients in the engine's biased_prior. The other five stay, but never as columns of their own: ring mod lives inside n_drive, the vocoder inside n_filter, and comp/duck/gate inside n_dynamics.

Why n_dynamics is still safe

Worth checking rather than assuming, because n_dynamics is exactly $n_{\text{comp}} + n_{\text{duck}} + n_{\text{gate}}$ and it is a retained column, the only family whose members are all on the wrong side of the identity.

It is safe because the identity needs each binary count separately. n_ringmod is only ever visible summed with folds, distortions and bitcrushers; n_vocoder only summed with filters and EQs. No linear combination of the retained columns isolates either, so the equation cannot be reconstructed. n_dynamics supplies three of the six binary terms and nothing supplies the other three.

Confirmed empirically: on the 1200-draw sweep every structural coordinate came back well under 10, with n_dynamics at 1.9.

depth, a weaker but real argument

VIF $\approx 21.7$. Not exact, so the posterior stays proper, but a coefficient that unstable is not individually meaningful, and the Styles tab renders these per-feature weights as though they were. Dropped.

Health of the retained set

Every family coordinate came back under 4 on the 1200-draw sweep, the highest being mod_depth_mean at 3.8. That is the reason the families exist; forty separate module columns would not have managed it.

The three most recent additions: n_mod_shape 1.6, n_mod_logic 1.3, mod_depth_mean 3.8, with mod_density rising from 2.7 to 4.1 as the one visible cost of adding a second modulation-shape coordinate beside it.

Reproduce with:

cargo run -p auracle-features --example pipeline_stats --release -- 1200

The unit coordinates

Seven of the twenty-five are UNIT_NAMES, a subset of NAMES rather than a reordering. Each is either a normalized genome site read straight through (amp_attack, amp_sustain, amp_release, mod_depth_mean) or a ratio that is already in $[0,1]$ (mod_density, chain_balance, frac_sidechained).

The distinction matters for display: these can be rendered as percentages honestly, whereas a family count cannot.

amp_sustain is also the coordinate the 1e30 sentinel killed; see the sentinel.