Memory Capacity

Archived TotalMC tables for the HypercubeESN linear memory-capacity diagnostic. Story, how to run, and at-a-glance peaks: MemoryCapacity.md.

These tables are not auto-synced to whatever main() currently has checked in. Single-seed peaks are indicative; use RunSeedSurvey (or Appendix B) before locking an op-point for other tasks.

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Reference campaign protocol

Knob	Value
dim	5 … 12 (one grid each; N = F = 2dim)
Spectral radius	0.90 · 0.95 · 1.00
Leak	1.0 (singleton → M × sr pivot) for main grids
history_depth M	1, 2, 4, 8, 16, 32, 40, 48, 56, 64
input_scaling	0.06
Reservoir seed	47397376 (main grids + Appendix A)
Meter	warmup 4000 · collect 25000 · Kmax 4000 · ridge 1e-4 · train_frac 0.7 · input_seed 0xc0ffee

Every main-grid cell early-stopped (e); no open-tail undercount.

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TotalMC grids (M × sr)

Leak = 1.0, is = 0.06, seed = 47397376. Bold = best cell in that dim table.

dim 5 · N = 32

M \ sr	0.90	0.95	1.00
1	18.83	19.38	18.70
2	22.34	24.29	22.26
4	29.47	30.08	27.52
8	29.75	29.82	27.95
16	29.92	29.83	28.53
32	29.76	29.95	26.55
40	29.75	30.05	29.11
48	28.85	30.09	24.88
56	25.98	29.99	25.44
64	23.86	29.91	26.66

dim 6 · N = 64

M \ sr	0.90	0.95	1.00
1	20.96	23.23	23.15
2	27.52	31.12	33.20
4	37.67	45.34	48.14
8	39.36	49.64	58.70
16	49.27	61.55	59.60
32	50.93	61.76	59.46
40	44.89	61.55	59.71
48	45.75	61.59	42.70
56	47.00	61.65	59.55
64	40.90	61.54	40.24

dim 7 · N = 128

M \ sr	0.90	0.95	1.00
1	22.34	24.24	24.65
2	35.07	41.39	45.10
4	49.91	67.92	78.83
8	55.12	81.98	93.46
16	59.29	90.48	122.91
32	61.33	104.08	121.21
40	53.68	103.13	122.34
48	47.86	105.96	108.56
56	55.34	106.68	124.62
64	54.62	106.53	124.64

dim 8 · N = 256

M \ sr	0.90	0.95	1.00
1	30.04	34.05	35.74
2	39.37	49.70	59.37
4	46.92	63.31	86.76
8	60.28	91.28	158.25
16	66.58	108.63	233.33
32	63.71	121.43	243.35
40	68.91	123.07	249.44
48	51.03	130.70	168.82
56	55.92	127.95	248.86
64	61.47	125.86	169.56

dim 9 · N = 512

M \ sr	0.90	0.95	1.00
1	37.33	43.69	45.16
2	43.28	54.38	65.15
4	51.68	69.96	95.52
8	65.89	110.94	213.56
16	69.96	127.05	324.50
32	67.91	135.18	477.04
40	77.10	149.55	481.27
48	49.62	147.02	309.77
56	56.01	143.77	424.23
64	63.76	132.22	495.00

dim 10 · N = 1024

M \ sr	0.90	0.95	1.00
1	35.93	42.98	49.36
2	50.08	63.46	78.43
4	43.39	54.40	72.57
8	71.58	117.84	225.87
16	75.09	122.94	285.13
32	74.37	157.72	623.22
40	78.99	149.15	819.29
48	73.12	158.69	554.54
56	56.26	156.23	725.92
64	63.99	149.58	566.92

dim 11 · N = 2048

M \ sr	0.90	0.95	1.00
1	37.06	45.57	54.74
2	48.96	62.63	78.93
4	55.85	74.90	108.23
8	69.78	106.15	207.41
16	75.40	119.18	257.84
32	79.88	150.05	779.48
40	79.65	149.93	591.12
48	74.03	164.95	904.21
56	57.34	162.10	954.07
64	64.00	161.70	993.28

dim 12 · N = 4096

M \ sr	0.90	0.95	1.00
1	36.65	44.54	54.32
2	46.45	59.81	79.88
4	66.04	98.97	145.26
8	73.74	117.07	230.21
16	75.38	123.31	322.10
32	85.52	144.80	514.89
40	80.25	165.03	1045.04
48	88.98	175.15	1346.06
56	59.50	170.18	1169.33
64	64.00	171.42	1383.41

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Appendix A — dim 10 leak × sr × M

Same meter and seed family as the main tables (is = 0.06, seed = 47397376, warmup 4000 / collect 25000 / Kmax 4000 / ridge 1e-4). dim = 10 only (N = F = 1024). Grid: 3 sr × 5 leak × 10 M = 150 cells; all early-stopped (e), none open-tail.

Axis	Values
sr	0.90 · 0.95 · 1.00
leak	0.60 · 0.70 · 0.80 · 0.90 · 1.00
M	1, 2, 4, 8, 16, 32, 40, 48, 56, 64

The leak = 1.00 column matches the dim 10 main-grid row for each M (that campaign held leak fixed at 1.0). Bold = best cell within that M block.

Reading tip. At shallow M, higher leak almost always wins. At deep M and sr = 1.00, mid/high leak still dominates through M = 40, but at M = 48 and M = 64 the peak shifts off leak = 1.00 (leak 0.90 beats 1.00). Do not assume leak = 1 is optimal for every depth.

Peak by M (dim 10)

M	Peak TotalMC	at sr	at leak
1	49.36	1.00	1.00
2	78.43	1.00	1.00
4	72.57	1.00	1.00
8	225.87	1.00	1.00
16	285.13	1.00	1.00
32	623.22	1.00	1.00
40	819.29	1.00	1.00
48	621.07	1.00	0.90
56	725.92	1.00	1.00
64	684.51	1.00	0.90

Overall peak for this appendix: 819.29 (M = 40, sr = 1.00, leak = 1.00).

M = 1

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	17.19	19.31	22.31	27.21	35.93
0.95	19.67	22.19	25.94	32.13	42.98
1.00	22.76	25.81	30.48	37.99	49.36

M = 2

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	23.79	27.36	31.90	38.60	50.08
0.95	27.89	32.25	38.06	46.98	63.46
1.00	32.18	37.72	45.30	57.16	78.43

M = 4

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	24.73	27.78	31.41	36.20	43.39
0.95	29.36	33.34	38.12	44.62	54.40
1.00	35.34	40.70	47.67	57.44	72.57

M = 8

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	41.34	46.53	52.49	60.27	71.58
0.95	57.77	66.93	78.24	93.57	117.84
1.00	85.27	102.57	125.73	161.05	225.87

M = 16

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	50.30	55.29	60.61	67.32	75.09
0.95	72.30	81.21	91.39	104.56	122.94
1.00	123.51	146.46	176.01	217.22	285.13

M = 32

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	54.38	60.60	64.77	68.38	74.37
0.95	104.00	114.84	126.79	141.16	157.72
1.00	256.39	307.32	373.77	467.69	623.22

M = 40

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	54.01	60.34	68.64	75.99	78.99
0.95	103.66	114.15	125.15	137.11	149.15
1.00	351.21	421.86	511.22	639.40	819.29

M = 48

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	50.33	52.26	56.02	63.20	73.12
0.95	112.95	122.37	134.20	146.26	158.69
1.00	382.93	452.86	518.02	621.07	554.54

M = 56

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	55.38	55.90	56.01	56.07	56.26
0.95	114.66	123.59	132.98	145.97	156.23
1.00	390.28	467.13	563.69	694.10	725.92

M = 64

sr \ leak	0.60	0.70	0.80	0.90	1.00
0.90	58.86	62.58	63.70	63.95	63.99
0.95	110.19	122.52	130.59	137.98	149.58
1.00	499.15	579.49	625.09	684.51	566.92

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Appendix B — dim 10 seed survey (M = 30–34)

Seed-to-seed variance at dim = 10 (N = F = 1024), sr = 1.00, is = 0.06. Fine M grid around the deep-memory knee (not the coarse pow2 / M∈{40,48,…} grid of the main tables). Leak near full (0.95 · 0.98 · 1.00). Ten reservoir seeds of the form 73896+k × (k+2) for k = 0…9 (same family as the NARMA multi-seed pools). All cells early-stopped.

Axis	Values
dim	10
sr	1.00 (fixed)
leak	0.95 · 0.98 · 1.00
M	30 · 31 · 32 · 33 · 34
Seeds	10 (table below)

Note from the run log: “M = 30 appears to be the best choice” as a coarse pick in this band. Per-seed peaks (below) actually land most often at M = 31 or 33, not 30 — M = 30 is solid but rarely the max. Prefer the peak-by-seed table when locking an op-point.

Qual labels (from the source log, per seed overall): GREAT · GOOD · POOR.

Peak by seed (best cell in that seed’s 5 × 3 grid)

Seed expr	Seed	Qual	Peak TotalMC	at M	at leak
73896×2	147792	GREAT	696.23	33	1.00
73897×3	221691	GREAT	785.23	31	1.00
73898×4	295592	GREAT	674.80	33	0.98
73899×5	369495	GOOD	626.32	33	1.00
73900×6	443400	GREAT	729.77	33	1.00
73901×7	517307	GREAT	739.65	34	1.00
73902×8	591216	GOOD	651.26	34	0.98
73903×9	665127	GOOD	669.60	31	1.00
73904×10	739040	POOR	705.36	34	1.00
73905×11	812955	GREAT	774.68	33	1.00

Across these ten seeds at sr = 1.00: best peak 785.23 (seed 221691, M = 31, leak = 1.00); weakest peak 626.32 (seed 369495, M = 33, leak = 1.00). Spread is large — single-seed main tables can sit anywhere in this band.

Per-seed grids (M × leak)

Seed 147792 (73896×2) · GREAT

M \ leak	0.95	0.98	1.00
30	509.84	548.35	577.39
31	598.72	643.71	693.75
32	428.55	456.98	488.60
33	595.63	642.84	696.23
34	543.15	584.15	631.16

Seed 221691 (73897×3) · GREAT

M \ leak	0.95	0.98	1.00
30	518.46	561.16	609.22
31	660.24	718.82	785.23
32	558.88	603.52	651.99
33	692.71	737.69	768.18
34	656.01	688.22	728.18

Seed 295592 (73898×4) · GREAT

M \ leak	0.95	0.98	1.00
30	513.05	552.79	600.44
31	528.76	570.75	616.54
32	484.33	519.68	559.73
33	625.69	674.80	672.66
34	420.22	447.81	478.01

Seed 369495 (73899×5) · GOOD

M \ leak	0.95	0.98	1.00
30	421.28	449.79	482.28
31	451.24	482.46	517.71
32	487.91	524.02	564.49
33	591.88	612.08	626.32
34	448.44	479.10	513.29

Seed 443400 (73900×6) · GREAT

M \ leak	0.95	0.98	1.00
30	481.92	518.48	561.72
31	579.59	631.88	670.04
32	498.17	529.99	569.55
33	645.39	699.61	729.77
34	514.84	552.35	594.85

Seed 517307 (73901×7) · GREAT

M \ leak	0.95	0.98	1.00
30	440.41	471.85	506.00
31	487.02	522.36	563.10
32	409.53	436.22	466.08
33	562.76	605.00	653.64
34	649.97	705.47	739.65

Seed 591216 (73902×8) · GOOD

M \ leak	0.95	0.98	1.00
30	448.49	480.42	516.30
31	534.89	577.57	626.91
32	472.44	505.54	542.95
33	529.31	568.39	613.68
34	603.37	651.26	621.68

Seed 665127 (73903×9) · GOOD

M \ leak	0.95	0.98	1.00
30	484.74	521.33	563.15
31	566.82	614.76	669.60
32	547.33	590.99	640.40
33	517.78	557.72	601.61
34	471.61	504.43	538.95

Seed 739040 (73904×10) · POOR

M \ leak	0.95	0.98	1.00
30	558.47	604.24	631.65
31	531.34	572.91	621.37
32	466.55	499.60	534.09
33	405.44	431.58	460.34
34	598.88	647.45	705.36

Seed 812955 (73905×11) · GREAT

M \ leak	0.95	0.98	1.00
30	471.60	506.17	546.15
31	582.27	630.47	665.95
32	507.02	545.62	590.02
33	680.79	740.67	774.68
34	426.21	454.90	485.76