Quasar periodicity tests drop the DRW null: Nullasar learns noise from light curves and reaches AUC 0.9648 on AR(2) data

Significance in quasar periodicity searches rests on a null hypothesis, the assumed distribution of stochastic variability for a single-black-hole quasar; Nullasar replaces that fixed parametric model with a generative model learned from data. Such tests have generally used the damped random walk (DRW, a stochastic process with a characteristic damping timescale) as the null, and the DRW is known to be incomplete, so a wrong null biases the estimates. On 8,000 synthetic light curves whose true process is AR(2), AR(1) fits leave a small mean absolute lag-1 residual autocorrelation, so individual curves look well fitted, yet the per-frequency relative p-value difference reaches about an order of magnitude in the intermediate band and approaches infinity at the lowest and highest frequencies.

Nullasar is not told the parametric form of the noise; it learns the ensemble-level statistics from a collection of light curves and generates new null realizations conditioned on one observed curve. The method trains a continuous normalizing flow (a generative model defined by an ordinary differential equation) with flow matching, transports Fourier coefficients directly in the frequency domain, and compresses an observed curve into a 128-dimensional conditioning vector with an encoder. On synthetic AR(1) data Nullasar reaches a detection AUC of 0.9273 against 0.9042 for fitting the correct AR(1) per curve; on AR(2) data its three-run mean AUC is 0.9648, versus 0.9180 for fitting AR(2) per curve and 0.9526 for an AR(2) coefficient flow that explicitly uses the population distribution of coefficients.

Periodic signals in the training set sharply degrade Nullasar's detection power, and projecting the conditioning vector onto its leading principal components at inference largely restores it without retraining. AUC is 0.9904 with clean training data and falls to 0.5735 when only 0.5% of training curves carry injected sinusoids; at higher contamination levels AUC stays near 0.5 without a monotonic trend. After the low-rank projection of already trained contaminated models, AUC rises from near chance to 0.92–0.96 and p-values of signal-bearing curves concentrate near zero again, while the clean model's performance is unchanged.

All experiments use synthetic light curves that are uniformly sampled in time, fixed at 256 samples in length, and single-band; these are controlled variability benchmarks rather than a physical calibration to any real quasar survey. The authors propose incorporating time-stamp information into the conditioning or architecture for non-uniform sampling, and list extending the model to longer or variable-length sequences as future work.

The model is highly sensitive to training-set contamination, with 0.5% injected periodic signals enough to push AUC close to chance; the low-rank projection relies on the assumption that contamination is low-rank in the encoding space and contributes much less structural variation than the noise model. The number of retained principal components must be calibrated separately, which the authors suggest doing with a separate model trained on injected signals of known form. The model agrees with the statistical properties examined here, while the extent of agreement in other properties remains open.