Spectrally identifiable phaseless recurrent layer / prediction_report.json
Mechanism confirmed, baseline not beaten
1{
2 "prediction_checks": [
3 {
4 "prediction": "Global phase is exactly unobservable",
5 "predicted": "error 0",
6 "observed_max_abs_error": 6.661338147750939e-16
7 },
8 {
9 "prediction": "At least 2n-1=11 local degrees of freedom become identifiable modulo phase once enough times are sampled",
10 "predicted_rank_at_K2_or_more": 11,
11 "observed_ranks": {
12 "1": 6,
13 "2": 11,
14 "3": 11,
15 "4": 11,
16 "5": 11,
17 "6": 11,
18 "7": 11,
19 "8": 11
20 }
21 },
22 {
23 "prediction": "Generic diagonal perturbations improve spectral identifiability conditioning versus nearly constant potential",
24 "predicted": "pair-sum gap and sigma_min(S) increase with potential scale over small scales",
25 "observed_scale_gap_sigma": [
26 [
27 0.02,
28 9.574141116930335e-05,
29 0.002563127302950817
30 ],
31 [
32 0.1,
33 0.0016087870616696698,
34 0.01325704104551373
35 ],
36 [
37 0.3,
38 0.009286181459882137,
39 0.04609205351775604
40 ],
41 [
42 1.0,
43 0.03093639029452433,
44 0.10623320993335798
45 ],
46 [
47 3.0,
48 0.04597004606857613,
49 0.24691854680700215
50 ]
51 ]
52 },
53 {
54 "prediction": "More time samples reduce local noise amplification after the transient sampling regime",
55 "predicted": "1/sigma_min decreases for K>=2 overall",
56 "observed_noise_gain": [
57 [
58 1,
59 1.000000000141043
60 ],
61 [
62 2,
63 5.017408866958467
64 ],
65 [
66 3,
67 2.985295170896411
68 ],
69 [
70 4,
71 1.4874163837223315
72 ],
73 [
74 6,
75 0.8540563661036842
76 ],
77 [
78 8,
79 0.7755764490658387
80 ]
81 ]
82 }
83 ],
84 "classification": {
85 "clean_accuracy": {
86 "phaseless_K6": 0.8777777777777778,
87 "single_time_coordinate_magnitude": 0.6027777777777777
88 },
89 "noisy_test_accuracy_phaseless_K6": 0.8583333333333333,
90 "N": 2400,
91 "train_test": [
92 1680,
93 720
94 ]
95 }
96}