File size: 3,051 Bytes
535348a
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
{
  "model": "google/gemma-2-9b-it",
  "theta": 10000,
  "gamma_pred": 0.99999561666838,
  "C_theory": 9.2103,
  "distances": [
    10,
    20,
    30,
    50,
    100,
    200,
    500,
    1000,
    2000
  ],
  "distances_fit": [
    30,
    50,
    100,
    200,
    500,
    1000,
    2000
  ],
  "d_min_fit": 30,
  "n_prompts_per_distance": 150,
  "seeds": [
    42,
    123,
    7
  ],
  "attn_by_distance": {
    "10": {
      "mean_across_seeds": 0.01131202671935575,
      "std_across_seeds": 0.0004384004663510598,
      "per_seed_means": [
        0.01191513662226498,
        0.011134915679382781,
        0.010886027856419483
      ]
    },
    "20": {
      "mean_across_seeds": 0.007342287618666887,
      "std_across_seeds": 0.000120221270640251,
      "per_seed_means": [
        0.0071971141314134,
        0.007338237394578755,
        0.007491511330008507
      ]
    },
    "30": {
      "mean_across_seeds": 0.005608218560616176,
      "std_across_seeds": 0.00012586673790719274,
      "per_seed_means": [
        0.005452117463573813,
        0.00576035007291163,
        0.005612188145363082
      ]
    },
    "50": {
      "mean_across_seeds": 0.004600468463678327,
      "std_across_seeds": 0.00029442297838144305,
      "per_seed_means": [
        0.004994370874483138,
        0.004286649797577411,
        0.004520384718974432
      ]
    },
    "100": {
      "mean_across_seeds": 0.0025041243884091576,
      "std_across_seeds": 0.00013270791219153536,
      "per_seed_means": [
        0.0026802454908223202,
        0.0024722163340387244,
        0.0023599113403664283
      ]
    },
    "200": {
      "mean_across_seeds": 0.0011723479800275526,
      "std_across_seeds": 0.00010549223246344652,
      "per_seed_means": [
        0.00103700214473065,
        0.0012943720275264544,
        0.0011856697678255539
      ]
    },
    "500": {
      "mean_across_seeds": 0.00037003465085743104,
      "std_across_seeds": 6.662525937622196e-05,
      "per_seed_means": [
        0.00031459913613313497,
        0.0004637339629213481,
        0.00033177085351780987
      ]
    },
    "1000": {
      "mean_across_seeds": 0.0001858278461845152,
      "std_across_seeds": 5.3211896888022095e-06,
      "per_seed_means": [
        0.00019292063060371827,
        0.00018445904356970762,
        0.00018010386438011968
      ]
    },
    "2000": {
      "mean_across_seeds": 4.510536613654242e-05,
      "std_across_seeds": 1.884703048218177e-06,
      "per_seed_means": [
        4.538706549889563e-05,
        4.266916409202774e-05,
        4.725986881870389e-05
      ]
    }
  },
  "fit_power_law": {
    "gamma": 1.1347958464287666,
    "log_A": -0.9640958037685541,
    "R2": 0.976472,
    "n_points": 7
  },
  "fit_exponential": {
    "lambda": 0.002322719608941013,
    "log_A": -5.827234742708562,
    "R2": 0.881621,
    "n_points": 7
  },
  "delta_R2_power_minus_exp": 0.0949,
  "gamma_CI_95": {
    "lo": 0.9244744962120605,
    "hi": 1.331560490527999
  },
  "decision": "ANOMALY: long-context training effect"
}