Monotonicity: error at each prefix, v5.5 against the new version

Updated 2026-10-30 18:04; built by sections/monotonic/ (README.txt there).

Does the error always fall as atoms are added? One encode per object and version, every atom kept, decoded at 23–27 prefixes on a 128³ grid; a rise is a step up of more than 0.5 % in Chamfer. parts="tracked-fit", 256 layers, N 64, M 24; the 12 objects of the other pages, one run each. v5.5 is 7ccd2a39. The new version is the v5.5-encoder-fixes branch (ca4ad834): a part's centre stored with its first shape atom (decision 33), plus decision 32 and the changes to _parts.py in that branch. It keeps more parts (jogger 78 → 183, shoe 35 → 162), so this compares the two versions, not decision 33 alone.

Twelve log-log panels of Chamfer against atoms for v5.5 and the new version; rises are ringed, all at 64 atoms or fewer — Chamfer against atoms, log-log, one panel per object. Ringed: rises of more than 0.5 %.

Monotonicity: from 64 atoms up the error falls at every step on all 12 objects in both versions (largest rise above that: +0.07 %). Below it neither version is monotone: 6 rises on 5 objects in v5.5 (worst +30 %, dog bowl), 4 rises on 3 objects in the new version (worst +25 %, mug ace); the rises move rather than go away. Low budgets: the new version is mixed: much better on the dino (surface from 8 atoms, against 32) and the horse, worse on others (flower pot 3.1× at 8 atoms, serving bowl 2.3× at 16, mug 1.6× at 32), and the spring needs 192 atoms for a surface, against 128. From 256 atoms: the two versions stay within 13 % of each other; the shoe and the jogger, where the part count jumps, are 5–13 % worse in the new version at 512–4096 atoms. All atoms: the new version is better on 10 objects (by up to 13 %) and identical on the spring and the knot.

object	parts	first surface, atoms	rises	worst rise	new / v5.5 at 32 atoms	at 64	at 256	at 1024	at 4096	all atoms
mug	10 → 13	8 → 8	0 → 0	– → –	1.64	1.17	1.04	0.95	0.91	0.87
mug ace	11 → 13	8 → 8	1 → 1	+2.2 % → +24.8 %	1.22	1.15	1.03	0.99	0.97	0.94
bowl	7 → 9	8 → 8	0 → 0	– → –	1.74	1.39	1.03	1.00	1.00	0.99
bowl serving	6 → 7	8 → 8	0 → 0	– → –	1.14	0.98	0.98	0.94	0.90	0.88
bowl dog	7 → 8	8 → 8	1 → 2	+30.2 % → +11.3 %	1.03	1.00	0.90	1.01	0.99	0.99
flower pot	7 → 13	8 → 8	0 → 0	– → –	1.02	1.21	1.04	1.02	0.98	0.97
shoe	35 → 162	8 → 8	2 → 0	+1.7 % → –	1.22	0.87	1.03	1.05	1.07	0.94
jogger	78 → 183	8 → 8	1 → 0	+0.5 % → –	1.19	0.74	0.90	1.09	1.07	0.90
dino	34 → 49	32 → 8	0 → 0	– → –	0.44	0.68	0.96	1.00	0.97	0.93
horse	20 → 21	12 → 8	1 → 1	+1.3 % → +1.1 %	0.87	0.72	1.00	1.01	1.01	0.99
spring	33 → 33	128 → 192	0 → 0	– → –	–	–	0.99	1.00	1.00	1.00
knot	12 → 12	48 → 48	0 → 0	– → –	–	1.00	1.00	1.00	1.00	1.00

Pairs read v5.5 → new. Ratios below 1 favour the new version; – where a version has no surface.

The horse in detail

One encode of the horse per version (parts="tracked-fit", 256 layers, N 64, M 24, every atom), decoded on a 128³ grid at 25 prefixes. Current version: v5.5 (7ccd2a39), 20 parts, 55446 atoms. New: the v5.5-encoder-fixes branch (ca4ad834), where a part's centre is stored with its first shape atom (decision 33), 21 parts, 55587 atoms. Chamfer and p95 in % of the diagonal. One object, one run.

Log-log plots of Chamfer and p95 error against atoms for v5.5 and the new version; the curves coincide from about 256 atoms; each has one small rise below 16 atoms — Error against atoms, log-log. Ringed: the steps where the error rises.

Horse decoded at 8 to 128 atoms: the same atoms in the current order (top, no surface at 8 atoms) and with each part's centre ranked with its first shape atom (bottom), beside the ground truth — The order alone: one encode (21 parts) with the same atoms and values, decoded at 8–128 atoms. Top, the order before decision 33; bottom, each part's centre ranked with its first shape atom, which draws a surface at 8 atoms and the legs earlier. A prototype of the reorder, so its numbers differ slightly from the new version's curve above (4.54 % against 4.35 % at 8 atoms).

Low budgets: the new order gives a surface at 8 atoms (4.35 %, v5.5 has none) and a lower error at every prefix up to 192 atoms (1.15 % against 1.59 % at 64 atoms). Monotonicity: neither version is strictly monotone. v5.5 rises once, 12→16 atoms (+1.3 %); the new version rises once by a similar amount, 8→12 (+1.1 %), then stays flat at 12→16 (+0.01 %) and 24→32 (−0.04 %). Every later step falls in both. High budgets: from 256 atoms the two agree within 0.72 % at every prefix.

atoms	Chamfer %, v5.5	Chamfer %, new	new / v5.5	p95 %, v5.5	p95 %, new
8	no surface	4.35354	–	no surface	19.8558
12	5.77074	4.40320	0.763	23.7055	19.9997
16	5.84442	4.40363	0.753	23.9786	19.9924
24	4.53730	3.44166	0.759	19.7809	19.0409
32	3.95969	3.44032	0.869	19.7744	19.0403
48	2.53916	2.31850	0.913	12.4394	11.7793
64	1.59039	1.15085	0.724	4.9730	2.5835
96	0.66047	0.61468	0.931	1.7994	1.7010
128	0.55002	0.51241	0.932	1.4820	1.3688
192	0.41112	0.40691	0.990	1.1773	1.1516
256	0.32143	0.32154	1.000	0.8792	0.8787
384	0.24405	0.24414	1.000	0.6700	0.6656
512	0.19781	0.19913	1.007	0.5429	0.5419
768	0.14641	0.14685	1.003	0.4062	0.4097
1024	0.11595	0.11678	1.007	0.3160	0.3187
1536	0.08724	0.08716	0.999	0.2380	0.2359
2048	0.07110	0.07134	1.003	0.1937	0.1951
3072	0.05496	0.05529	1.006	0.1502	0.1512
4096	0.04587	0.04614	1.006	0.1270	0.1278
6144	0.03669	0.03653	0.996	0.1040	0.1027
8192	0.03134	0.03134	1.000	0.0907	0.0903
12288	0.02674	0.02665	0.997	0.0813	0.0816
16384	0.02480	0.02473	0.997	0.0786	0.0789
24576	0.02342	0.02346	1.002	0.0776	0.0776
55446	0.02312	–	–	0.0772	–
55587	–	0.02295	–	–	0.0766