GyreVI

A variational autoencoder that jointly infers cyclical dynamics and cellular state from single-cell RNA-seq data.

From ~2,000 sparse gene counts per cell, GyreVI places each of 5,422 cells on a circle, its position in the cell cycle. For every gene, it estimates when the gene peaks and how far its unspliced transcripts run ahead of the spliced ones. Every output is scored against an independent protein measurement of each cell's position.

a Two fluorescent reporters give each cell's true position in the cycle; they are never a model input, only the ground truth for scoring. b–c In NUF2, one of the clearest cycling genes, new (unspliced) RNA rises before mature (spliced) RNA, so the two trace a loop. The peak φ and the lead δ (25° here, about 10° for a typical cycling gene) are what GyreVI estimates for every gene.

The encoder maps each cell's counts to θ, its position on the circle, and z, the rest of its state. The decoder turns them back into expected counts, with a peak φ, a lead δ and an amplitude R for each gene.

Result: a simple linear baseline sets the bar, and shows how much signal is left to capture. A phase from PCA on 90 known cell-cycle genes, then a least-squares cosine fit per gene, leads on every quantity.

correlation with ground truth	GyreVI, learned	least squares at GyreVI's phase	CycleVI phase + least squares	Seurat phase + least squares	PCA phase + least squares
cell phase θ	+0.47 ± 0.01	—	+0.44	+0.46	+0.58
gene peak phase φ	+0.71 ± 0.04	+0.77 ± 0.01	+0.77	+0.77	+0.82
unspliced lead δ	+0.60 ± 0.03	+0.82 ± 0.02	+0.93	+0.93	+0.95
gene amplitude R	+0.91 ± 0.01	+0.97 ± <0.01	+0.97	+0.96	+0.98

Spearman correlation (θ after circular alignment), except φ (circular correlation). GyreVI: mean ± sd over 6 paired seeds. The last three columns reproduce with python baselines/two_step.py; the CycleVI column needs CycleVI's output from baselines/run_cyclevi.py first.

The benchmark pinpoints two gaps:

• Phase. GyreVI is trained to follow the PCA phase as a reference, and ends up further from the truth than that reference (+0.47 vs +0.58).
• Gene parameters. Even at the model's own phase, least squares beats its learned parameters (δ: +0.82 vs +0.60).

Why this is useful. The PCA result shows the data hold more phase information than the model extracts (+0.58; a supervised probe reaches +0.68), so the gap is in the model, not the data. The two gaps above say where to look. A natural next step is to anchor the model at the PCA solution and learn only corrections.

Caveat: the per-gene targets are themselves cosine fits at the protein phase, on the same counts, which favours estimators of that form. Kinetics measured independently by metabolic labelling, which this dataset supports, would be the cleaner test.

Phase against published methods

Circular alignment for every method. The oracle is fitted to the labels: a ceiling, not a competitor. GyreVI and the oracle: mean of 6 seeds. With the best of 144 rotations instead (chosen using the labels), every method scores higher and the middle three change order; the PCA leads under both.

Top row: deep models; bottom: simple baselines. GyreVI: the seed closest to the 6-seed mean. The corners are the same point on the circle (0 = 2π).

Confidence

a GyreVI's confidence ρ is calibrated: agreement rises steadily with it. The PCA's radius behaves the same way, and sets the bar here too. b Filtering on either keeps most of the cycle. Filtering on signal brightness keeps a 68° sliver, and agreement falls to zero, because brightness tracks the phase itself.

Checks behind every number

• A simple estimator for every learned quantity, to set the target to beat.
• Paired seeds only: the GPU backend is non-deterministic.
• Range before correlation: a filter correlated with the target truncates it (panel b).
• An external reference for every internal check: a reversed phase frame once passed all of them.

Repository

baselines/two_step.py	the simple estimators above, from this repository alone
circular.py	circular statistics: alignment, circular correlation, resultant length
prepare_battich.py · preprocess.py · gene_selection.py · _constants.py	data preparation
baselines/scvi_baseline.py · baselines/run_cyclevi.py	the oracle, and CycleVI under matched conditions

GyreVI's own code is not yet public; its numbers come from a 6-seed benchmark. Work done at Institut Curie. Data: Battich et al., RPE1-FUCCI (public). License: MIT.