Why doesn't continuous-time attention read off period — and should we just feed the model a power spectrum?
A model reads a source's period only to the extent that the period search is done for it. The rungs below pour ever more time information into the model — none, then full continuous time, then an explicit cadence channel — and within-class period reading (ρ_within) barely moves. It only jumps when the search is performed explicitly, by Lomb–Scargle. And that top rung is exactly what "feed it a power spectrum" means, done right: a fine periodogram plus an argmax peak-pick.
ρ_within = within-class Spearman of predicted vs. true log-period — per-source reading with the class-template effect removed. Bars show 95% bootstrap CIs over splits; the dashed line is the Lomb–Scargle ceiling. All numbers from the period-diagnostic study (25,565 ZTF variables).
Contrastive InfoNCE teaches shape and class invariants. Nothing in the loss has a gradient toward "encode the exact period," so the model learns the cheap invariant — what kind of star — and stops.
Reading a period is a search: fold at a trial period, measure dispersion, optimize over trials. Lomb–Scargle and PDM are explicit search algorithms; a fixed-depth feedforward encoder can't run that inner loop. The dispersion landscape is flat with razor-thin spikes, so gradients and smooth attention slide right past the period.
Continuous time as input doesn't move the needle: a pretrained foundation model on flux alone reaches ρ_within ≈ 0.21; our continuous-time transformer on full (t,f,σ) ≈ 0.24; a BiGRU with an explicit Δt channel ≈ 0.26; even handing MOMENT a Δt channel only lifts it to 0.26–0.30. PatchTST on (t,f,σ) ≈ 0.00.