Spectrally identifiable phaseless recurrent layer / prediction_report.json

Mechanism confirmed, baseline not beaten

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 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}