AbstractPhil/sd15-geoflow-test-44-1000

sd15-geoflow-test-44-1_000 — Geometric Prior Burn Test

Extreme-repetition burn test of the KSimplex geometric prior on 22 source images for 10,000 total steps. This experiment tests whether the pentachoron-based geometric prior can learn subject-specific anchoring from minimal data with high repetition — analogous to LoRA training but operating in simplex coordinate space rather than weight delta space.

What This Is

A 4.8M parameter geometric prior (0.56% of the frozen 860M SD1.5 UNet) trained on 22 images of a single subject repeated 454× each across 6 aspect-ratio buckets, totaling ~10k samples over ~10k training steps.

The source images are promotional and fan-sourced photographs of actress Terry Farrell as Jadzia Dax from Star Trek: Deep Space Nine.

This answers crucial questions

This is testing the potential for an actual 1000 step lora with small amounts of images. The results are mixed so far.

Architecture

• Base: SD1.5 UNet (frozen) with Lune rectified flow weights from AbstractPhil/tinyflux-experts
• Trainable: KSimplex cross-attention prior — 4 layers of pentachoron-based geometric attention
• Flow: Rectified flow matching with logit-normal timestep sampling, shift=2.5
• Bucketing: 6 AR buckets (576×448, 384×640, 448×576, 704×384, 384×704, 512×512)

Training Details

Bucket	Images	Samples	Steps	Final Loss
576×448	11	4,994	5,000	0.312
384×640	4	1,816	1,818	0.284
448×576	3	1,362	1,363	0.338
704×384	2	908	909	0.216
384×704	1	454	500	0.287
512×512	1	454	500	0.321

Training ran sequentially per bucket with shared geo_prior weights carrying over. Batch size 6, base LR 5e-5 with cosine decay.

Post-Training Analysis

Weight Inspection

Metric	Value	Interpretation
Blend β	0.4991	Nearly 50/50 CLIP vs geometric — barely moved from init
L0 δ	0.268	Minimal deformation
L1 δ	0.272	Minimal deformation
L2 δ	0.296	Slight increase
L3 δ	0.260	Below init (0.25 base + learned offset)

Vertex Weight Entropy (the key signal)

Layer	Trained	Fresh	Δ
L0	1.536	1.511	+0.026
L1	1.330	1.537	−0.208
L2	1.423	1.526	−0.103
L3	1.553	1.560	−0.008

Comparison across all trained models:

Model	L3 vw_entropy	L3 Δ from fresh	Character
Object-relations (50k)	0.243	−1.291	Hard vertex routing
ImageNet (10k)	0.749	−0.868	Moderate sharpening
Characters (50k)	1.277	−0.265	Soft attribute binding
Burn test (22 imgs - 1000 steps)	1.553	−0.008	Slightly established

The burn test shows the geometric prior barely moved from initialization despite 10k steps and 454× repetition. This is the expected result for 22 images of a single subject — there isn't enough compositional diversity to drive simplex specialization.

Branch Point

Recommended branch point: t ≈ 0.68 (much later than object-relations at 0.31 or characters at 0.28).

Analysis Artifacts

Training Analysis

• analysis/01_loss_curves.png — Loss progression across buckets
• analysis/02_entropy_per_layer.png — Attention entropy over training
• analysis/04_entropy_inflection.png — Entropy inflection detection
• analysis/06_volume_sq.png — Simplex volume evolution
• analysis/07_deformation_scale.png — Per-layer deformation scales
• analysis/08_dashboard.png — Combined training dashboard

Post-Training Analysis

• post_analysis/01_timestep_sweep.png — Metrics across noise levels
• post_analysis/02_timestep_inflection.png — Branch point detection
• post_analysis/03_prompt_complexity.png — Simple vs spatial vs complex prompts
• post_analysis/04_trained_vs_fresh.png — Delta from initialization
• post_analysis/06_dashboard.png — Combined post-training dashboard

Sample Images

• samples/baseline/ — Before training
• samples/trained/ — After training, same prompts
• samples/anchor/ — 1person geometric anchor test
• samples/training_*/ — Checkpoint samples per bucket

Key Findings

1. 22 images is below the diversity threshold for geometric specialization. The prior needs compositional variety to develop distinct vertex routing strategies. A single repeated subject gives it nothing to differentiate geometrically.

2. The geo loss converged to −0.047, well below the −0.053 seen in object-relations and characters. The simplex found a valid geometric configuration but a less structured one.

3. L1 showed the most movement (vw_entropy Δ = −0.208), suggesting the prior concentrated subject identity information at the second layer while leaving other layers near-uniform.

4. Blend stayed at 0.499 — the prior learned almost nothing worth asserting over CLIP. In contrast, object-relations moved blend to 0.472 and characters to 0.476.

5. This is NOT a failure — it demonstrates that the geometric prior correctly identifies when there isn't enough structural signal to justify specialization, unlike LoRA which would overfit the weight deltas regardless.

Usage

from sd15_trainer_geo.pipeline import load_pipeline

pipe = load_pipeline(
    geo_repo_id="AbstractPhil/sd15-geoflow-test-44",
    device="cuda",
    dtype=torch.float16,
)
pipe.unet.load_pretrained(
    "AbstractPhil/tinyflux-experts",
    subfolder="",
    filename="sd15-flow-lune-unet.safetensors",
)

License

Dual license:

• Code, architecture, and training methodology: MIT License. The KSimplex geometric prior architecture, training scripts, and analysis tools are freely available for any use.

• Weights and derivative images: The trained weights encode information derived from copyrighted promotional imagery from Star Trek: Deep Space Nine (Paramount/CBS). Generated images from these weights may reproduce likenesses subject to copyright and publicity rights. Users are responsible for ensuring their use of generated imagery complies with applicable intellectual property law. These weights are provided for research and non-commercial use only.

Part of the Geometric Prior Research Series

Model	Dataset	Samples	Steps	L3 vw_entropy
sd15-rectified-geometric-matching	ImageNet subset	10,000	10,000	0.749
sd15-geoflow-object-association	Object relations	50,000	8,333	0.243
sd15-geoflow-characters	Synthetic characters	50,000	8,333	1.277
sd15-geoflow-test-44	Single subject (burn)	9,988	10,090	1.553