Positive-cycle Jacobian penalty / results.json
Mechanism confirmed, baseline not beaten
1{
2 "device": "cuda",
3 "predictions": {
4 "trace_identity": {
5 "predicted": "tr(K^2)=2ab",
6 "observed": 2.8800000000000003,
7 "expected": 2.8800000000000003,
8 "abs_error": 0.0
9 },
10 "threshold": {
11 "predicted_gamma": 0.8333333333333333,
12 "observed_rho": 1.2000000000000002,
13 "gamma_sweep": [
14 0.35,
15 0.55,
16 0.7,
17 0.74,
18 0.76,
19 0.9,
20 1.1
21 ],
22 "norm_after_30": [
23 4.982860305982785e-12,
24 3.857607756366589e-06,
25 0.005350305513683154,
26 0.028339290517564585,
27 0.06307324131822367,
28 10.062656889073459,
29 4142.074788597609
30 ],
31 "classification": [
32 "decay",
33 "decay",
34 "decay",
35 "decay",
36 "decay",
37 "growth",
38 "growth"
39 ],
40 "theory_log_slopes_at_gamma_0.7_0.9": [
41 -0.17435338714477766,
42 0.0769610411361286
43 ],
44 "observed_log_slopes": [
45 -0.1743533871447778,
46 0.07696104113612844
47 ]
48 },
49 "temperature_scaling": {
50 "predicted_loglog_slope": -2.0,
51 "observed_loglog_slope": -2.0000000000000004,
52 "taus": [
53 0.5,
54 1.0,
55 2.0,
56 4.0
57 ],
58 "normalized_trace": [
59 5.760000000000001,
60 1.4400000000000002,
61 0.36000000000000004,
62 0.09000000000000001
63 ]
64 },
65 "cycle_vanishes_in_dag": {
66 "cycle_trace": 0.0,
67 "predicted": 0.0
68 }
69 },
70 "mini_experiment": {
71 "none": {
72 "final_mse": 0.023448115214705467,
73 "final_loss": 0.007115767803043127,
74 "mean_aux": 0.0,
75 "closed_walk_trace2": 0.6792207360267639,
76 "spectral_proxy": 0.38061052560806274,
77 "seconds": 5.363163948059082
78 },
79 "spectral": {
80 "final_mse": 0.02254125103354454,
81 "final_loss": 0.00795772485435009,
82 "mean_aux": 0.06635072652250529,
83 "closed_walk_trace2": 0.1041954755783081,
84 "spectral_proxy": 0.06258340179920197,
85 "seconds": 4.499120235443115
86 },
87 "cycle": {
88 "final_mse": 0.02341901883482933,
89 "final_loss": 0.007156304083764553,
90 "mean_aux": 0.024760834146291016,
91 "closed_walk_trace2": 0.05696604400873184,
92 "spectral_proxy": 0.06490537524223328,
93 "seconds": 7.007261753082275
94 }
95 }
96}