Learned Cloth Optimizer · ablations of November 2026

LeCO ablation results

Every model is trained for 500,000 steps with the same data and then runs the same test scene. This page shows which changes still give a usable solver at inference, and which do not.

Data as of 2026-11-12 23:42 UTC Trainings finished 30 of 31 Inference runs finished 199 of 199

Findings

A per-vertex step scale does not work at inference. Every model with a per-node scale breaks within the first 60 to 180 of 4,040 steps. This holds at 5, 10 and 30 iterations, with DAT and without DAT, with per-node gradient normalization, with the gradient magnitude input, and with a ring context of 1 to 32 rings. The truncated scale does not rescue them: the positions stay finite, but more than 5 % of the edges are badly stretched after 60 to 180 steps.
Per-node gradient normalization with a global scale works. It finishes every setting. At 5 iterations it is at least as good as the baseline (end distance 21 to 26 mm against 32 to 49 mm, depth 1.6 to 2.9 mm against 1.8 to 10.3 mm). At 10 and 30 iterations the two are equal. Two runs per model are not enough to call it better, and on the criteria of the paper (gradient norm and residual ratio per step) it is level with the baseline.
The gradient magnitude input does not help. With global normalization it makes the 5-iteration result clearly worse (109 to 116 mm from the reference at 25 % of the sequence). At 10 iterations it equals the baseline. With per-node normalization the result is about the same as the baseline.
Width 96 or more is safe. Below 96 the 5-iteration solver is not reliable. Widths 96, 128, 192 and 256 give the same quality. Width 64 keeps good edge numbers but loses a garment at 5 iterations. Width 32 breaks, width 24 gives NaN, width 16 ends far off. At 10 iterations every width finishes. No width above 96 is better than 96.
The other ablations confirm the main design. Each removed input makes the result worse or unstable. The per-iteration scale and the model without scale finish, but with lower accuracy. A context window of 3 equals the baseline within the run-to-run spread.
A context window of 5 gives the closest 5-iteration result. Its end distance is 20 to 21 mm, against 32 to 49 mm for the baseline and 21 to 26 mm for per-node normalization. It costs 5 message-passing rounds per iteration, so it is not a free gain.
The fixed-state test of the code base separates two things. Almost every model can solve a single time step in 30 iterations, also the per-node scale models. Their failure appears only in rollouts. From a cold start the per-node normalization with the magnitude input is the fastest model (6 % of the energy decrease missing after 5 iterations, baseline 31 %).
On the criteria of the paper no ablation beats the baseline at 5 iterations. Objective, gradient norm and residual ratio per time step are level for all stable models. At 10 iterations the larger context windows are about 30 % lower; at 30 iterations all are equal.

Still open: the model without iteration (in training).

How to read the tables

Test

Scene dlayers_00396 (layered dress on a moving body), 4,040 solver steps. DAT is on with dynamic collision detection. “5 it · 15 mm” means 5 network iterations per step and a 15 mm collision query radius. Every model runs on the same PyTorch network path. Each line in a cell is one run.

Numbers

edge: Largest edge stretch in the run (length / rest length). The baseline reaches about 2 to 6.
depth: Deepest body penetration in the run, in mm.
dist.: Median vertex distance to the reference, in mm, at 25 % of the sequence / at the end. The reference is the released checkpoint at 30 iterations.

Outcome

OK: Finished, close to the reference (below 50 mm at 25 % and below 150 mm at the end).
far off: Finished, but far from the reference. lost means more than 1 m: a garment left the body.
NaN: Positions became NaN at this step.
broken: Stopped at this step: more than 5 % of the edges were badly stretched.
time limit: No result: the run was too slow on a GPU shared with trainings. It is shown only if no rerun gave a result.

Criteria of the paper

The three criteria of the paper, recorded at every time step of the rollout on dlayers_00396 (4,040 steps, DAT on, 15 mm): the objective G after K iterations, the gradient norm ‖∇_XG‖₂ over the free vertices, and the gradient norm after K iterations divided by the gradient norm at the start of the step. The recorder is the one of the code base (experiments/ablation_statistics/run.py), changed only to accept a sewn scene. Both gradients use the final contact set of the step. Each metric has its mean and its median over the steps. A run counts as failed when any value becomes non-finite, as in the summary script of the code base. Green is 30 % or more below the baseline, red is 50 % or more above; G has no colour.

K = 5 iterations per time step

Model	G		‖∇_XG‖₂		‖∇_XG^(K)‖₂ / ‖∇_XG⁽⁰⁾‖₂
Model	mean	median	mean	median	mean	median
Baseline (width 96)`width_96`	5.048	4.934	5.60	0.96	0.179	0.123
Normalization × scale
Per-node normalization`norm_node_scale_global`	5.034	4.937	5.02	1.19	0.174	0.127
Per-node scale`scale_per_node_scale`	failed non-finite at step 50 of 4,040
Both per node`norm_node_scale_node`	failed non-finite at step 107 of 4,040
Baseline + magnitude`network_inputs_w_gradient_magnitude`	4.290	4.174	10.17	3.77	0.118	0.063
Per-node normalization + magnitude`mag_norm_node_scale_global`	5.372	5.000	17.93	1.02	0.201	0.133
Per-node scale + magnitude`mag_norm_global_scale_node`	failed non-finite at step 48 of 4,040
Both per node + magnitude`mag_norm_node_scale_node`	failed non-finite at step 100 of 4,040
Per-node scale with ring context
1-ring context`scale_per_node_ring1`	failed non-finite at step 100 of 4,040
2-ring context`scale_per_node_ring2`	failed non-finite at step 151 of 4,040
4-ring context`scale_per_node_ring4`	failed non-finite at step 118 of 4,040
8-ring context`scale_per_node_ring8`	failed non-finite at step 158 of 4,040
16-ring context`scale_per_node_ring16`	failed non-finite at step 203 of 4,040
32-ring context`scale_per_node_ring32`	failed non-finite at step 418 of 4,040
Width
Width 16`width_16`	failed non-finite at step 3,370 of 4,040
Width 24`width_24`	failed non-finite at step 421 of 4,040
Width 32`width_32`	failed non-finite at step 419 of 4,040
Width 64`width_64`	4.747	4.310	14.73	8.81	0.167	0.125
Width 128`width_128`	5.033	4.889	5.90	1.14	0.203	0.145
Width 192`width_192`	5.014	4.868	5.68	1.15	0.180	0.127
Width 256`width_256`	5.184	5.358	6.41	1.06	0.194	0.127
Step scale
Per-iteration scale`scale_per_iteration_scale`	5.252	4.933	20.69	5.64	0.246	0.146
No scale`scale_wo_scale`	5.191	5.268	11.96	3.92	0.189	0.098
Inputs
No current gradient`network_inputs_wo_current_gradients`	9.602	7.772	100	79.88	0.716	0.721
No previous gradient`network_inputs_wo_previous_gradients`	5.366	4.747	25.59	14.10	0.326	0.234
No gradients`network_inputs_wo_gradients`	3496	225	4249	755	1.000	1.000
No last update`network_inputs_wo_displacements`	5.642	5.298	26.46	13.62	0.366	0.359
Last update / RMS`network_inputs_RMS_displacements`	failed non-finite at step 252 of 4,040
Context window
Depth 3`context_window_context_window_3`	5.025	4.920	4.82	1.00	0.213	0.162
Depth 5`context_window_context_windows_5`	5.032	4.930	4.38	0.86	0.204	0.159

K = 10 iterations per time step

Model	G		‖∇_XG‖₂		‖∇_XG^(K)‖₂ / ‖∇_XG⁽⁰⁾‖₂
Model	mean	median	mean	median	mean	median
Baseline (width 96)`width_96`	5.021	4.917	1.17	0.19	0.060	0.037
Normalization × scale
Per-node normalization`norm_node_scale_global`	5.034	4.925	1.29	0.16	0.049	0.034
Per-node scale`scale_per_node_scale`	failed non-finite at step 29 of 4,040
Both per node`norm_node_scale_node`	failed non-finite at step 65 of 4,040
Baseline + magnitude`network_inputs_w_gradient_magnitude`	5.022	4.913	1.71	0.25	0.075	0.048
Per-node normalization + magnitude`mag_norm_node_scale_global`	5.029	4.928	1.10	0.21	0.059	0.039
Per-node scale + magnitude`mag_norm_global_scale_node`	failed non-finite at step 32 of 4,040
Both per node + magnitude`mag_norm_node_scale_node`	failed non-finite at step 39 of 4,040
Per-node scale with ring context
1-ring context`scale_per_node_ring1`	failed non-finite at step 53 of 4,040
2-ring context`scale_per_node_ring2`	failed non-finite at step 78 of 4,040
4-ring context`scale_per_node_ring4`	failed non-finite at step 68 of 4,040
8-ring context`scale_per_node_ring8`	failed non-finite at step 80 of 4,040
16-ring context`scale_per_node_ring16`	failed non-finite at step 115 of 4,040
32-ring context`scale_per_node_ring32`	failed non-finite at step 242 of 4,040
Width
Width 16`width_16`	4.797	4.848	4.50	0.47	0.084	0.051
Width 24`width_24`	5.027	5.034	6.75	0.44	0.125	0.071
Width 32`width_32`	5.018	4.873	3.91	0.29	0.110	0.052
Width 64`width_64`	5.011	4.913	2.20	0.27	0.081	0.044
Width 128`width_128`	5.028	4.927	1.69	0.19	0.057	0.036
Width 192`width_192`	5.022	4.916	1.37	0.20	0.051	0.034
Width 256`width_256`	5.018	4.912	1.50	0.18	0.056	0.034
Step scale
Per-iteration scale`scale_per_iteration_scale`	4.928	4.936	7.86	2.61	0.246	0.082
No scale`scale_wo_scale`	5.053	4.941	5.48	0.74	0.128	0.052
Inputs
No current gradient`network_inputs_wo_current_gradients`	failed non-finite at step 58 of 4,040
No previous gradient`network_inputs_wo_previous_gradients`	5.010	4.983	5.20	0.59	0.128	0.056
No gradients`network_inputs_wo_gradients`	3504	237	4298	811	1.000	1.000
No last update`network_inputs_wo_displacements`	5.160	5.198	7.68	1.72	0.181	0.132
Last update / RMS`network_inputs_RMS_displacements`	failed non-finite at step 273 of 4,040
Context window
Depth 3`context_window_context_window_3`	5.018	4.915	0.84	0.14	0.038	0.024
Depth 5`context_window_context_windows_5`	5.017	4.915	0.54	0.13	0.034	0.021

K = 30 iterations per time step

Model	G		‖∇_XG‖₂		‖∇_XG^(K)‖₂ / ‖∇_XG⁽⁰⁾‖₂
Model	mean	median	mean	median	mean	median
Baseline (width 96)`width_96`	5.022	4.918	0.52	0.01	0.007	0.002
Normalization × scale
Per-node normalization`norm_node_scale_global`	5.022	4.918	0.29	0.02	0.006	0.003
Per-node scale`scale_per_node_scale`	failed non-finite at step 10 of 4,040
Both per node`norm_node_scale_node`	failed non-finite at step 41 of 4,040
Baseline + magnitude`network_inputs_w_gradient_magnitude`	5.024	4.918	0.84	0.01	0.008	0.003
Per-node normalization + magnitude`mag_norm_node_scale_global`	5.026	4.919	0.15	0.02	0.006	0.003
Per-node scale + magnitude`mag_norm_global_scale_node`	failed non-finite at step 14 of 4,040
Both per node + magnitude`mag_norm_node_scale_node`	failed non-finite at step 29 of 4,040
Per-node scale with ring context
1-ring context`scale_per_node_ring1`	failed non-finite at step 17 of 4,040
2-ring context`scale_per_node_ring2`	failed non-finite at step 26 of 4,040
4-ring context`scale_per_node_ring4`	failed non-finite at step 21 of 4,040
8-ring context`scale_per_node_ring8`	failed non-finite at step 33 of 4,040
16-ring context`scale_per_node_ring16`	failed non-finite at step 51 of 4,040
32-ring context`scale_per_node_ring32`	failed non-finite at step 82 of 4,040
Width
Width 16`width_16`	5.004	4.913	1.36	0.04	0.021	0.006
Width 24`width_24`	5.022	4.917	0.56	0.02	0.012	0.004
Width 32`width_32`	5.024	4.917	0.31	0.02	0.010	0.004
Width 64`width_64`	5.022	4.917	0.76	0.02	0.008	0.003
Width 128`width_128`	5.024	4.919	0.65	0.01	0.007	0.002
Width 192`width_192`	5.022	4.918	0.16	0.01	0.004	0.002
Width 256`width_256`	5.023	4.919	0.44	0.01	0.005	0.001
Step scale
Per-iteration scale`scale_per_iteration_scale`	5.044	5.032	6.09	1.01	0.241	0.031
No scale`scale_wo_scale`	5.001	4.816	1.56	0.38	0.089	0.045
Inputs
No current gradient`network_inputs_wo_current_gradients`	failed non-finite at step 702 of 4,040
No previous gradient`network_inputs_wo_previous_gradients`	4.919	4.777	0.84	0.03	0.034	0.005
No gradients`network_inputs_wo_gradients`	3504	237	4298	811	1.000	1.000
No last update`network_inputs_wo_displacements`	5.023	5.016	2.19	0.17	0.068	0.021
Last update / RMS`network_inputs_RMS_displacements`	failed non-finite at step 856 of 4,040
Context window
Depth 3`context_window_context_window_3`	5.021	4.918	0.38	0.01	0.005	0.002
Depth 5`context_window_context_windows_5`	5.022	4.918	0.16	0.01	0.004	0.001

Reading

At 5 iterations no stable model is clearly below the baseline in gradient norm or in the residual ratio. Per-node normalization is level with it (median ratio 0.127 against 0.123), and so are widths 128 to 256 and both context windows. The magnitude input has a lower ratio but a 4 times larger gradient norm: its run drifted away, so its start gradients are larger and its ratio is not comparable.
At 10 iterations the context windows 3 and 5 are about 30 % lower in median gradient norm and ratio. The other stable models stay level with the baseline.
At 30 iterations all stable models with the full inputs are equal: median gradient norm about 0.01 to 0.02, median ratio 0.001 to 0.004.
Failed by the strict rule: every per-node scale model at every K, the last update divided by its RMS, the model without the current gradient at 10 and 30 iterations, and widths 16, 24 and 32 at 5 iterations.
The mean gradient norm is several times the median in every row. A few steps with large gradients dominate the mean, so the median is the steadier number.
G is comparable only while the trajectories stay together. A garment that slides down lowers G: width 64 and the magnitude input at 5 iterations have the lowest G and are the runs that ended far from the reference.

Fixed-state test

The direct test of the code base (experiments/checkpoints/checkpoint_progress.py). Every model solves the same 300 saved states, each one time step, with fresh optimizer history. The states come from two motions of the repository's test split, simulated by the baseline at 60 iterations. Numbers are in percent; lower is better. “5 it”, “10 it”, “30 it”: share of the energy decrease that is still missing, median over the states. 100 % of the decrease is what the baseline reaches after 60 iterations on the same state. A value above 100 means the energy went up. “resid.”: gradient norm after 10 iterations relative to the start. “failed”: share of states with a non-finite result. Green is clearly better than the baseline, red is clearly worse. Two limits. The optimizer starts cold in every state (step scale 1e-4, no history), so the 5-iteration column mostly shows how fast a model finds its step size; in a rollout the history carries over. The trainings used all motions (split: all), so this is a like-for-like loss on fixed states, not a held-out test.

Model	Without DAT (as in training)					With DAT
Model	5 it	10 it	30 it	resid. 10 it	failed	5 it	10 it	30 it	resid. 10 it	failed
Baseline (width 96)`width_96`	31.1	6.0	0.0	63.2	0	14.0	3.8	0.0	24.8	0
Normalization × scale
Per-node normalization`norm_node_scale_global`	65.9	10.3	0.1	62.0	0	28.8	7.0	0.0	23.2	0
Per-node scale`scale_per_node_scale`	>999	230	0.4	97.9	0	440	37.9	0.1	31.8	0
Both per node`norm_node_scale_node`	510	44.4	0.1	74.6	0	134	13.4	0.0	24.7	0
Baseline + magnitude`network_inputs_w_gradient_magnitude`	11.8	2.7	0.1	59.5	0	8.8	2.6	0.0	27.7	0
Per-node normalization + magnitude`mag_norm_node_scale_global`	6.2	1.0	0.0	41.3	0	6.1	1.1	0.0	19.4	0
Per-node scale + magnitude`mag_norm_global_scale_node`	12.8	1.9	0.3	54.1	0	10.4	1.9	0.1	24.4	0
Both per node + magnitude`mag_norm_node_scale_node`	106	6.9	0.2	64.7	0	34.9	3.8	0.1	23.9	0
Per-node scale with ring context
1-ring context`scale_per_node_ring1`	313	34.0	0.0	75.1	0	110	9.7	0.1	28.4	0
2-ring context`scale_per_node_ring2`	225	13.8	0.1	76.1	0	58.6	5.5	0.1	30.2	0
4-ring context`scale_per_node_ring4`	124	13.6	0.1	81.7	0	40.0	5.1	0.0	28.2	0
8-ring context`scale_per_node_ring8`	127	9.0	0.0	73.5	0	44.8	4.3	0.0	27.0	0
16-ring context`scale_per_node_ring16`	70.4	4.9	0.0	74.4	0	22.1	2.3	0.0	25.4	0
32-ring context`scale_per_node_ring32`	53.1	4.7	0.0	67.0	0	22.3	3.1	0.0	25.6	0
Width
Width 16`width_16`	41.0	4.8	0.5	67.4	0	21.9	5.5	0.2	26.3	0
Width 24`width_24`	28.7	2.8	0.2	68.7	0	13.6	2.8	0.1	23.9	0
Width 32`width_32`	23.7	3.0	0.0	73.1	0	14.8	2.5	0.0	27.4	0
Width 64`width_64`	33.0	4.1	0.1	67.5	0	14.5	3.4	0.0	25.8	0
Width 128`width_128`	31.9	2.4	0.0	57.1	0	14.2	2.1	0.0	24.4	0
Width 192`width_192`	31.5	2.3	0.0	66.8	0	13.1	2.2	0.0	24.4	0
Width 256`width_256`	22.7	2.0	0.0	62.4	0	11.7	1.8	0.0	24.7	0
Step scale
Per-iteration scale`scale_per_iteration_scale`	147	7.8	0.1	95.8	0	20.7	3.9	0.0	28.6	0
No scale`scale_wo_scale`	>999	200	5.0	138	0	72.7	11.9	2.1	34.6	0
Inputs
No current gradient`network_inputs_wo_current_gradients`	93.5	18.1	5.2	84.0	0	51.5	19.7	5.5	52.8	0
No previous gradient`network_inputs_wo_previous_gradients`	11.1	1.8	0.5	51.7	0	15.7	2.7	0.1	24.7	0
No gradients`network_inputs_wo_gradients`	126	126	126	108	0	108	108	108	101	0
No last update`network_inputs_wo_displacements`	208	29.3	0.8	87.9	0	24.1	8.4	0.6	28.2	0
Last update / RMS`network_inputs_RMS_displacements`	87.9	9.9	0.0	93.5	0	24.8	3.3	0.0	33.4	0
Context window
Depth 3`context_window_context_window_3`	21.7	2.4	0.0	59.9	0	10.5	1.1	0.0	24.1	0
Depth 5`context_window_context_windows_5`	21.9	1.3	0.1	59.5	0	12.3	1.4	0.0	21.8	0

Reading

All models except three solve a single step: after 30 iterations they reach the same energy as the baseline. The exceptions are the model without gradient inputs (it never lowers the energy), the model without the current gradient and the model without a step scale (each 5 % missing).
Per-node scale models do not fail here. They start badly (after 5 iterations the energy is far above the start) and are level with the baseline after 30 iterations. Their rollouts break within 200 steps. So the per-node scale can solve one step from a cold start; the failure is in the rollout, where the scale carries over from step to step. More rings make the cold start better: 1 ring 34 % missing after 10 iterations, 32 rings 5 %.
Fastest from a cold start: per-node normalization with the magnitude input (6 % missing after 5 iterations, baseline 31 %). The magnitude input alone and the model without the previous gradient are also faster than the baseline here.
Per-node normalization without the magnitude input is slower from a cold start (66 % missing after 5 iterations), although its rollouts are the best. The magnitude input removes this.
Width has a small effect: 16 is the slowest; 96 to 256 are equal after 10 iterations.
The ranking differs from the rollout tables. A cold start rewards a fast step-size search; a rollout rewards stability over thousands of steps. Both are needed.

Gradient normalization × step scale

Gradient normalization: the gradient input is divided by the RMS of the whole mesh (global) or by the size of the gradient of that vertex (per node). Step scale: one learned scale per axis for the whole mesh (global) or one per vertex (per node). Magnitude input: log10 of the divisor as one more input channel.

Without the gradient magnitude input

global scale

per-node scale

global normalization

width_96

5 it OK10 it OK5 it 7 mm OK30 it OK

scale_per_node_scale

5 it NaN10 it NaN5 it 7 mm NaN30 it NaN

per-node normalization

norm_node_scale_global

5 it OK10 it OK5 it 7 mm OK30 it OK

norm_node_scale_node

5 it NaN10 it NaN5 it 7 mm NaN30 it NaN

With the gradient magnitude input

global scale

per-node scale

global normalization

network_inputs_w_gradient_magnitude

5 it far off10 it OK5 it 7 mm NaN

mag_norm_global_scale_node

5 it NaN10 it NaN5 it 7 mm NaN

per-node normalization

mag_norm_node_scale_global

5 it OK10 it OK5 it 7 mm OK

mag_norm_node_scale_node

5 it NaN10 it NaN5 it 7 mm NaN

Variant	5 it · 15 mm edgedepthdist.	10 it · 15 mm edgedepthdist.	5 it · 7 mm edgedepthdist.	30 it · 15 mm edgedepthdist.
Baseline`width_96`	OK6.110.311 / 49 OK2.71.810 / 32	OK1.97.46 / 11	OK4.11.215 / 47	OK1.95.73 / 5
Per-node normalization`norm_node_scale_global`	OK4.72.911 / 26 OK4.21.610 / 21	OK2.25.95 / 5	OK4.02.617 / 123	OK1.96.83 / 4
Per-node scale`scale_per_node_scale`	NaN · step 60 NaN · step 60	NaN · step 60	NaN · step 60	NaN · step 60
Both per node`norm_node_scale_node`	NaN · step 120 NaN · step 120	NaN · step 60	NaN · step 120	NaN · step 60
Baseline + magnitude`network_inputs_w_gradient_magnitude`	far off7.931.7116 / 202 far off9.210.3109 / 255	OK1.95.17 / 10	NaN · step 4040	–
Per-node normalization + magnitude`mag_norm_node_scale_global`	OK7.810.813 / 61 OK7.16.513 / 50	OK2.63.36 / 10	OK7.84.322 / 42	–
Per-node scale + magnitude`mag_norm_global_scale_node`	NaN · step 60 NaN · step 60	NaN · step 60	NaN · step 60	–
Both per node + magnitude`mag_norm_node_scale_node`	NaN · step 120 NaN · step 120	NaN · step 60	NaN · step 120	–

Reading

The column decides the result. Both models with a global scale work. All models with a per-node scale fail, with either normalization.
Per-node normalization with a global scale is better than the baseline row at 5 iterations and equal to it at 10 and 30 iterations. At 7 mm its end distance is larger (123 mm against 47 mm); one run each.
The magnitude input makes the baseline worse at 5 iterations and changes nothing at 10 iterations. With per-node normalization it changes little.

Per-node step scale: k-ring context and truncated scale

The scale head of a vertex reads the mean of its k-ring neighbourhood (network.scale_context_rings). “cut s” means solver.truncated_scale: true: at inference the per-vertex scale follows the DAT cut. All these models were trained without DAT.

Variant	5 it · 15 mm	5 it · 15 mm · cut s	10 it · 15 mm	10 it · 15 mm · cut s	5 it · 7 mm	5 it · 7 mm · cut s	30 it · 15 mm	30 it · 15 mm · cut s
Per-node scaleno neighbourhood`scale_per_node_scale`	NaN · step 60 NaN · step 60	broken · step 120 broken · step 120	NaN · step 60	broken · step 120	NaN · step 60	broken · step 120	NaN · step 60	broken · step 60
1-ring context`scale_per_node_ring1`	NaN · step 120 NaN · step 120	broken · step 180 broken · step 120	NaN · step 60	broken · step 120	NaN · step 120	broken · step 120	NaN · step 60	broken · step 60
2-ring context`scale_per_node_ring2`	NaN · step 180 NaN · step 180	broken · step 360 broken · step 180	NaN · step 120	broken · step 240	NaN · step 180	broken · step 300	NaN · step 60	broken · step 60
4-ring context`scale_per_node_ring4`	NaN · step 180 NaN · step 180	broken · step 300 broken · step 180	NaN · step 120	broken · step 120	NaN · step 180	broken · step 180	NaN · step 60	broken · step 60
8-ring context`scale_per_node_ring8`	NaN · step 180 NaN · step 180	broken · step 180 broken · step 180	NaN · step 120	broken · step 120	NaN · step 180	broken · step 240	NaN · step 60	broken · step 120
16-ring context`scale_per_node_ring16`	broken · step 240 NaN · step 240	broken · step 240 broken · step 240	NaN · step 120	broken · step 120	NaN · step 240	broken · step 240	NaN · step 60	broken · step 120
32-ring context`scale_per_node_ring32`	broken · step 300 NaN · step 300	broken · step 300 broken · step 360	NaN · step 300	broken · step 240	broken · step 360	broken · step 300	NaN · step 120	broken · step 120

Check without DAT

Variant	5 it · no DAT edgedepthdist.	30 it · no DAT edgedepthdist.
Baseline`width_96`	OK4.62.427 / 69	OK2.04.18 / 18
Per-node normalization`norm_node_scale_global`	OK3.74.116 / 31	OK1.95.58 / 18
Per-node scale`scale_per_node_scale`	NaN · step 60	NaN · step 60
Both per node`norm_node_scale_node`	broken · step 180	broken · step 120

Reading

No per-node scale model survives 200 steps. A neighbourhood of 1 to 32 rings for the scale head does not change this.
With the truncated scale the run no longer gives NaN, but the mesh is badly stretched at the first checks. So the cut is not the only cause.
DAT is not the cause: the same models also break without DAT, where the global-scale models run without problems.
The trainings already show the problem (see the last table): per-node scale runs restart 1.1 to 2.8 times as many episodes as the baseline. A larger ring count lowers this number.
The cause is not yet known.

Latent width

Same network and training, only the latent width changes. Width 96 is the main configuration.

Variant	5 it · 15 mm edgedepthdist.	10 it · 15 mm edgedepthdist.	5 it · 7 mm edgedepthdist.	30 it · 15 mm edgedepthdist.
Width 16`width_16`	far off12.614.1156 / 179 far off10.97.6165 / 164	OK5.23.326 / 40	far off8.817.7137 / 157	–
Width 24`width_24`	NaN · step 420 NaN · step 480 NaN · step 480	OK4.63.538 / 114	NaN · step 1200	–
Width 32`width_32`	broken · step 240 broken · step 360	OK3.01.311 / 51	broken · step 240	–
Width 64`width_64`	lost4.31.5250 / 5.2 m lost4.21.3230 / 7.5 m	OK1.94.88 / 14	lost8.21.488 / 7.1 m	–
Width 96baseline`width_96`	OK6.110.311 / 49 OK2.71.810 / 32	OK1.97.46 / 11	OK4.11.215 / 47	OK1.95.73 / 5
Width 128`width_128`	OK6.04.513 / 44 OK9.016.115 / 54	OK1.95.87 / 9	OK7.011.414 / 48	–
Width 192`width_192`	OK4.13.48 / 34 OK6.07.88 / 39	OK1.96.04 / 8	OK5.95.311 / 53	OK1.95.73 / 4
Width 256`width_256`	OK6.55.017 / 46 OK5.311.717 / 43	OK1.95.010 / 14	OK8.111.918 / 53	–

Reading

At 10 iterations widths 64 to 256 are equal (end distance 8 to 14 mm).
At 5 iterations only widths 96, 128, 192 and 256 stay on the reference. Width 64 keeps the mesh intact but a garment slides off the body.
Widths 16 to 32 need 10 iterations to finish, and 16 and 24 are then less accurate.
Widths 128, 192 and 256 give no clear gain over 96 on this scene.

Step scale mode

The scale ablations of ablations/2026_11.md.

Variant	5 it · 15 mm edgedepthdist.	10 it · 15 mm edgedepthdist.	5 it · 7 mm edgedepthdist.	30 it · 15 mm edgedepthdist.
Global scalebaseline`width_96`	OK6.110.311 / 49 OK2.71.810 / 32	OK1.97.46 / 11	OK4.11.215 / 47	OK1.95.73 / 5
Per-iteration scale`scale_per_iteration_scale`	far off7.16.5100 / 167 far off8.425.7119 / 181	OK5.42.523 / 80	far off9.511.250 / 163	–
Per-node scale`scale_per_node_scale`	NaN · step 60 NaN · step 60	NaN · step 60	NaN · step 60	NaN · step 60
No scale`scale_wo_scale`	OK5.34.738 / 76 broken · step 2160	OK4.64.931 / 56	OK7.27.138 / 106	–
No iterationno scale, 1 iteration per step`scale_wo_iteration`	training step 423,400 of 500,000

Reading

The global scale is the best mode.
The per-iteration scale finishes every run but ends far from the reference at 5 iterations.
Without a scale, one of the two runs at 5 iterations and 15 mm breaks. The runs that finish are about 3 times as far from the reference at 25 % of the sequence.
The model without iteration is still in training. It needs its own test with 1 iteration per step.

Network inputs

One input removed or changed at a time.

Variant	5 it · 15 mm edgedepthdist.	10 it · 15 mm edgedepthdist.	5 it · 7 mm edgedepthdist.	30 it · 15 mm edgedepthdist.
All inputsbaseline`width_96`	OK6.110.311 / 49 OK2.71.810 / 32	OK1.97.46 / 11	OK4.11.215 / 47	OK1.95.73 / 5
No current gradient`network_inputs_wo_current_gradients`	NaN · step 2220 NaN · step 2160	NaN · step 120	NaN · step 1320	–
No previous gradient`network_inputs_wo_previous_gradients`	lost7.019.1180 / 8.7 m NaN · step 3900	OK4.26.623 / 68	far off5.35.8164 / 242	–
No gradientscurrent and previous removed`network_inputs_wo_gradients`	broken · step 2220	broken · step 2400	–	–
No last update`network_inputs_wo_displacements`	broken · step 1740 OK11.423.629 / 90	OK6.03.312 / 34	broken · step 1200	–
Last update / RMSinstead of / step scale`network_inputs_RMS_displacements`	NaN · step 360 NaN · step 180	NaN · step 2340	OK4.214.515 / 78	–
+ gradient magnitude`network_inputs_w_gradient_magnitude`	far off7.931.7116 / 202 far off9.210.3109 / 255	OK1.95.17 / 10	NaN · step 4040	–

Reading

Without the current gradient the solver gives NaN in every setting.
Without the previous gradient the 5-iteration runs end far from the reference; one loses a garment and one gives NaN. At 10 iterations it finishes.
Without both gradients the mesh breaks at 5 and at 10 iterations. This model also did not learn (see the training table).
Without the last update it breaks in two of three runs at 5 iterations. At 10 iterations it finishes.
The last update divided by its RMS (instead of by the step scale) gives NaN at 15 mm.
The gradient magnitude as an added input makes the 5-iteration result worse.

Context window

Number of message-passing rounds per iteration.

Variant	5 it · 15 mm edgedepthdist.	10 it · 15 mm edgedepthdist.	5 it · 7 mm edgedepthdist.	30 it · 15 mm edgedepthdist.
Depth 1baseline`width_96`	OK6.110.311 / 49 OK2.71.810 / 32	OK1.97.46 / 11	OK4.11.215 / 47	OK1.95.73 / 5
Depth 3shared weights`context_window_context_window_3`	OK3.817.711 / 71 OK4.54.512 / 42	OK2.28.04 / 5	OK3.11.719 / 42	–
Depth 5shared weights`context_window_context_windows_5`	OK3.90.89 / 20 OK4.81.89 / 21	OK2.15.03 / 6	OK5.40.512 / 33	OK2.46.33 / 4

Reading

Depth 3 equals the baseline within the run-to-run spread.
Depth 5 is closer to the reference than the baseline at 5 iterations (end distance 20 to 21 mm against 32 to 49 mm) and equal at 10 and 30 iterations.
Depth 3 and 5 cost 3 and 5 message-passing rounds per iteration. A fair comparison needs equal time, which this page does not have.

Training side

Loss: median over the last 50,000 steps of the logged loss (energy after the update; the samples change, so small differences mean nothing). Restarts: how often the training pool started a new episode. Each run sees the same data, so more restarts than the baseline mean that more rollouts were cut short.

Run	State	Loss	Restarts per 1,000 steps	vs. baseline
`width_16`	done	0.58	37	1.0×
`width_24`	done	0.51	36	1.0×
`width_32`	done	0.46	36	1.0×
`width_64`	done	0.43	36	1.0×
`width_96`	done	0.23	36	1.0×
`width_128`	done	0.22	36	1.0×
`width_192`	done	0.31	36	1.0×
`width_256`	done	0.31	36	1.0×
`norm_node_scale_global`	done	0.20	36	1.0×
`scale_per_node_scale`	done	1.73	100	2.8×
`norm_node_scale_node`	done	1.72	68	1.9×
`network_inputs_w_gradient_magnitude`	done	0.44	36	1.0×
`mag_norm_node_scale_global`	done	0.23	35	1.0×
`mag_norm_global_scale_node`	done	1.55	94	2.6×
`mag_norm_node_scale_node`	done	0.87	60	1.7×
`scale_per_node_ring1`	done	0.88	64	1.8×
`scale_per_node_ring2`	done	0.81	52	1.5×
`scale_per_node_ring4`	done	0.62	50	1.4×
`scale_per_node_ring8`	done	0.42	41	1.1×
`scale_per_node_ring16`	done	0.21	37	1.0×
`scale_per_node_ring32`	done	0.26	36	1.0×
`scale_per_iteration_scale`	done	0.35	36	1.0×
`scale_wo_scale`	done	0.41	36	1.0×
`scale_wo_iteration`	training 85 %	3.47	743	20.7×
`network_inputs_wo_current_gradients`	done	1.09	39	1.1×
`network_inputs_wo_previous_gradients`	done	0.35	35	1.0×
`network_inputs_wo_gradients`	done	109.43	258	7.2×
`network_inputs_wo_displacements`	done	0.56	37	1.0×
`network_inputs_RMS_displacements`	done	0.39	36	1.0×
`context_window_context_window_3`	done	0.38	36	1.0×
`context_window_context_windows_5`	done	0.28	36	1.0×

Reading

All global-scale runs restart about 36 episodes per 1,000 steps. This is the normal rate.
Per-node scale runs restart more often: 100 for the plain per-node scale, 41 to 64 with a ring context.
The model without gradient inputs did not learn (loss above 100). The model without iteration restarts most often.
The loss alone does not predict the inference result: widths 32 and 64 have a normal loss but fail at 5 iterations.