One utility, three likelihoods

Every feedback mode conditions the same latent $u$. They differ only in how an answer connects to it.

All three enter as a single factor carrying the total weighted log-likelihood, so from fugue's point of view the model has one observation node regardless of how many kinds of feedback the log contains.

Pairwise duels — Bradley–Terry

$$P(A \succ B) = \sigma\big(u(A) - u(B)\big)$$

Feedback::Duel { a, b, chose_a } => {
    let d = s.utility_mix(a) - s.utility_mix(b);
    log_sigmoid(if *chose_a { d } else { -d })
}

The primary signal: best statistical properties, lowest cognitive load. It identifies $u$ up to an additive constant, which is exactly the right amount of information: a preference relation does not have an origin, and pretending otherwise is what makes absolute ratings drift.

Note that $u$ here is the mixture utility, so a duel across two islands is a comparison of "the drone's best lens's opinion" against "the pluck's best lens's opinion". That this is well-formed is the whole reason for the max form.

log_sigmoid is computed stably as $-\mathrm{softplus}(-v)$ with $\mathrm{softplus}(t) = \max(t,0) + \log(1 + e^{-|t|})$. The naive $\log(1/(1+e^{-v}))$ underflows for moderately confident predictions, which is exactly where a fitted model spends its time.

Keep / kill — a thresholded Bernoulli

$$P(\text{keep}) = \sigma\big(u(x) - \tau_s\big), \qquad \tau_s \sim \mathcal{N}(0,1)$$

$\tau_s$ is a per-session latent, one per session in the log.

No frontend emits this today: Engine::record_keep and its wasm binding exist, but the triage surfaces that would call them are unbuilt, so every log written by the app so far contains duels and stars only.

"Feeling picky today" is therefore modelled rather than treated as noise. A session where you kill almost everything is read as a strict session (a high $\tau_s$) rather than a transformation of your taste. Without the per-session threshold, a strict day and a generous day would average into a meaningless global bar, and both days' data would be degraded by the other's.

One implementation subtlety: reweighting an old observation against a posterior fitted before that session existed finds no $\tau_s$ site, and contributes zero rather than guessing. No threshold site means no threshold evidence.

Star ratings — a cumulative logit

$$P(y = k) = \sigma(c_k - u) - \sigma(c_{k-1} - u)$$

with 0-based cutpoints, $c_{-1} = -\infty$ (so the first term is 0) and $c_{K_{\text{cat}}-1} = +\infty$ (so the last is 1). Six categories by default, hence five cutpoints.

let upper = if k == n_cats - 1 { 1.0 } else { sigmoid(s.cuts[k] - u) };
let lower = if k == 0          { 0.0 } else { sigmoid(s.cuts[k - 1] - u) };
(upper - lower).max(1e-12).ln()

This treats ★★★ as "between two cutpoints" rather than as the number 3, which is the point. A rating is an ordinal judgement, and modelling it as a real number asserts that the gap between 1 and 2 stars equals the gap between 4 and 5, which no rater believes.

Because the cutpoints are fitted, the model absorbs scale drift: a user who becomes harsher moves the cutpoints, not $\theta$. Without that, a change in rating habit would be indistinguishable from a change in taste.

Enforcing the ordering

Cutpoints must be increasing. Rather than constrain the sampler, the model samples unconstrained normals and transforms:

$$c_0 = -2 + 1.5,r_0, \qquad c_j = c_{j-1} + \exp(-0.5 + 0.7,r_j), \quad r_j \sim \mathcal{N}(0,1)$$

The exponential increments are positive by construction, so ordering holds for every draw. No rejection, no constrained kernel, and the generic single-site MH applies unchanged.

The constants place the prior sensibly: $c_0$ near $-2$ (so a 0-star rating means "well below average"), and increments with a median of $e^{-0.5} \approx 0.61$ so the five cutpoints span a few units of utility.

Edit-beats-original

Not a fourth likelihood, but a duel with a provenance tag. Committing a hand edit with my edit is better records Duel { a: edited, b: original, chose_a: true }.

The tag is what makes the claim auditable. Provenance distinguishes:

These make the same claim in the log, and there is no reason to believe they are equally reliable. Calibration scores them separately, which is the only way to find out rather than assume.

Recency weighting

Every observation's log-likelihood is scaled before summing:

$$w_i = 0.5^{,(n - 1 - i)/h}, \qquad h = 150$$

so the newest observation has weight 1 and one $h$ back has weight $\tfrac12$. Default recency_half_life = Some(150.0); None disables forgetting entirely.

$$\log p(\mathcal{D} \mid \theta) = \sum_i w_i , \log p(y_i \mid \theta)$$

Taste is allowed to change, and a model weighting a vote from three sessions ago equally with one from a minute ago would fight the user when it did. The cost is stated plainly: this is not a proper Bayesian posterior over a stationary parameter, it is a tempered/discounted likelihood, chosen because stationarity is the wrong assumption about a person.

Implicit signals are out of scope

Listen time, replays, exports, hover duration: not recorded.

They are cheap to collect and easy to misread: a long listen can mean fascination or confusion, and the two have opposite signs. This version prefers less data that means what it says.

Site count, and what it costs

The model has

$$K \cdot d + S + (n_{\text{stars}} - 1)$$

sample sites. With $d = 40$ and 6 star categories, that is $40K + S + 5$: **45

• $S$** at $K=1$ and 205 + $S$ at $K=5$.

Single-site MH re-executes the whole program on every step, so every site is reconstructed once per step. Two consequences, both measured by auracle-taste/examples/fit_bench.rs:

• The fit is several times slower at the $K$ cap than at the first fit.
• The step budget is fixed, so a mature fit gets proportionally fewer sweeps per site than an early one. Growing $K$ makes the fit both slower and statistically thinner.

That is a real tension in the design, and it is why the address table is hoisted out of the step loop. Building addresses inline cost a format!, a re-allocation and a SipHash per site per step, which measured as the bulk of a mature fit's wall time.