Primary comparison incomplete; no claim about an oscillator advantage is supported.
All networks generate unconditional images in pixel space. They share independent conditional flow matching, AdamW, continuous time conditioning, 4×4 patches, and an EMA sampling checkpoint. MNIST is development data; CIFAR-10 is the final comparison domain. There is no curriculum or augmentation. Classification accuracy, text fill rate, and task-completion accuracy are not applicable; run completion is reported separately from image quality.
Network
Feature computation
Training objective
Role
onn
Coupled 4D unit-vector rotations; four recurrent blocks
Velocity MSE
Proposed generator
dit
Four time-conditioned attention/MLP blocks
Velocity MSE
Parameter-matched transformer
conv
Convolution + SiLU + GroupNorm recurrence
Velocity MSE
Conventional recurrent control
no_coupling
Oscillators with coupling convolution removed
Velocity MSE
Trained removal; lower capacity
no_frequency
Oscillators with natural-frequency term removed
Velocity MSE
Trained removal; slightly lower capacity
Training outcomes
Run
Status
Parameters
Updates
Train seconds
Images/s
Validation MSE
mnist-smoke
step_limit
1.28949e+06
100
33.9622
376.889
2.00869
Distribution and cost measurements
Evaluation
Generated/real N
NFE
KID mean
KID subset SD
FID
Pixel SWD
ms/image
mnist-smoke/validation-check
128/5000
32
—
—
—
1.10101
20.9486
Completeness
Recorded diagnostics: 0. Recorded failed attempts: 0. Completed primary pairs: 0/6. Missing values mean unmeasured, not zero. Individual records and PDFs are in experiments/; raw records remain in the run directories and published artifact manifests.
Glossary
Term
Meaning
Flow matching
Learn a velocity that transports Gaussian noise toward the image distribution.
Oscillator
A hidden vector whose direction changes under natural rotation and learned interactions.
Coupling
A learned convolution that lets hidden oscillators influence one another.
Flow time / internal time
Noise-to-image position / recurrent computation inside one velocity prediction.
NFE
Number of velocity-network evaluations used to generate each image.
KID
Unbiased squared kernel discrepancy between fixed Inception features; smaller is better and estimates may be negative.
KID subset SD
Variation across random metric subsets of one fixed pair of image populations, not across trained models.
FID
Gaussian feature-distribution distance; finite-sample biased, so sample count must accompany it.
Pixel SWD
Wasserstein distance averaged over random pixel-space projections; a MNIST diagnostic, not semantic accuracy.
Seed pair
Two independently initialized architectures using paired data/noise/time stream prefixes.
Confidence interval
A model-based repeated-study procedure; here an approximate t interval across six seed differences.
Sign-flip test
Enumerate all signs of paired differences; exact only under the specified exchangeability/symmetry null.
EMA
Exponential moving average of trainable weights, used for all reported samples.
Ablation / intervention
Retrain with a mechanism removed / perturb a trained model during inference.
Power
Probability of detecting an assumed effect under a planning model; six pairs have about 24% power at effect 0.8.
