| # Experiment ledger and glossary |
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| Primary comparison incomplete; no claim about an oscillator advantage is supported. |
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| 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. |
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| | 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 | |
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| ## Training outcomes |
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| | Run | Status | Parameters | Updates | Train seconds | Images/s | Validation MSE | |
| | --- | --- | --- | --- | --- | --- | --- | |
| | mnist-smoke | step_limit | 1.28949e+06 | 100 | 33.9622 | 376.889 | 2.00869 | |
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| ## Distribution and cost measurements |
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| | 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 | |
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| ## Completeness |
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| 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. |
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| ## Glossary |
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| | 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. | |
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