{
  "features": [
    "Size",
    "Rooms",
    "Age"
  ],
  "beta": [
    2.0,
    1.0,
    -0.2
  ],
  "data_seed": 20260925,
  "train_count": 2048,
  "test_count": 4096,
  "learning_rate": 0.03,
  "init_std": 0.4,
  "seeds": [
    7,
    11,
    23,
    42,
    101
  ],
  "python": "3.12.13",
  "numpy": "2.2.6",
  "samples": [
    [
      -1.6027412862938757,
      1.2390995448269142,
      -0.4491768625389556
    ],
    [
      -1.3621541511427544,
      0.28710498276863516,
      -0.6802800764685906
    ],
    [
      -0.44791497017847526,
      0.49888061223803293,
      1.6134771537402908
    ],
    [
      0.6258432307664017,
      -1.460163945407345,
      1.2223830209674569
    ],
    [
      0.9930597164652513,
      -0.1758457567015752,
      -1.5757618889439766
    ],
    [
      1.4609901864306183,
      -1.2688237585032454,
      -1.1243592198439631
    ],
    [
      0.5510637092989192,
      -1.2034209259625614,
      0.87573996343305
    ],
    [
      -0.3291503000481144,
      -1.6359140369464187,
      0.2563604980151104
    ],
    [
      -0.4550377644173529,
      1.4698297553959945,
      0.4949799790032574
    ],
    [
      1.5715381230054262,
      0.13865645057097642,
      1.315406700591661
    ],
    [
      -0.05326512665526284,
      0.1259390409706267,
      -1.394761596592899
    ],
    [
      -0.3447623730608682,
      -0.9054995865900591,
      -0.3259275492362579
    ],
    [
      -0.8825464455059675,
      -1.7107940942959956,
      1.5181184235802805
    ],
    [
      -0.6538420022938489,
      -0.8988992510906814,
      0.16738018267885124
    ],
    [
      0.6201950715766267,
      -1.0110086598142072,
      -1.0332326844388953
    ],
    [
      -0.7842052440006175,
      -1.4950016359312932,
      -1.5985806720955005
    ],
    [
      -1.491585386520527,
      0.7196355525057521,
      0.6343864651225415
    ],
    [
      0.3116855312761446,
      1.5276603727624312,
      -1.4475361229629806
    ],
    [
      0.5155001016653968,
      -1.2405883035912844,
      0.0819139849639583
    ],
    [
      1.4312856944605024,
      -0.7121905577838894,
      -0.04785009373888727
    ],
    [
      -0.6389496675028088,
      0.6457479315618775,
      -1.3051140924173183
    ],
    [
      -1.5597236989798968,
      -1.0083199559921479,
      0.35122261164826396
    ],
    [
      -1.6231335406513607,
      0.40916342771517167,
      -1.3673623575994012
    ],
    [
      -0.60165232491345,
      0.9863556853987698,
      0.9124124650812626
    ],
    [
      0.34210628554855305,
      0.6575105954407348,
      1.1395255357177225
    ],
    [
      0.8728987172053184,
      0.22113437534221547,
      -0.2573138682139273
    ],
    [
      0.24907170064496054,
      0.43315913470600664,
      -0.24326929397961572
    ],
    [
      -1.4380462405600127,
      0.7059431208233593,
      -0.2684488944215788
    ],
    [
      0.8801138492019009,
      -1.501847187664889,
      1.1361160852506065
    ],
    [
      -1.2943929534038885,
      -0.8520797311996899,
      -0.2608974865219822
    ],
    [
      0.37033504529434325,
      -0.7695292430089876,
      -1.171893251001565
    ],
    [
      -1.7138312310955859,
      0.8908643214661591,
      -0.7180289077530715
    ],
    [
      -1.2885494535852686,
      -0.3895816095695819,
      -1.5808743260244595
    ],
    [
      -0.07241700581177013,
      -1.2763023551284585,
      -1.2347016913613744
    ],
    [
      -1.070830461390846,
      -1.1989692555228868,
      -1.584026777859611
    ],
    [
      1.0756404840802438,
      -1.3410590953863326,
      0.3338693532109689
    ],
    [
      -0.1096353405609205,
      -1.598437940864994,
      0.13863359418482957
    ],
    [
      -0.9673836439588337,
      -0.8651805155858334,
      -0.23028204283483045
    ],
    [
      -1.4142265944720114,
      1.0772560002896387,
      -1.3656376300222757
    ],
    [
      -1.04992455520614,
      1.0676638675793164,
      0.21220185511155187
    ],
    [
      -1.031402550728014,
      -0.7565479032220885,
      -0.6773108036732454
    ],
    [
      -0.266145920853905,
      -0.7389231345342511,
      1.536883783503213
    ],
    [
      -1.192985491372274,
      -0.9971739448573788,
      0.6091889065183831
    ],
    [
      -1.2066233759749445,
      -0.7173512560281867,
      -0.6382931098281872
    ],
    [
      0.1722427996800524,
      1.0026360384388018,
      1.3994264719239191
    ],
    [
      -1.6324481654789553,
      0.4416134184084024,
      1.6906544588040235
    ],
    [
      -0.4347122676763673,
      -1.4186204269267935,
      1.5748959946416359
    ],
    [
      1.6504986288700585,
      -0.003060309491823343,
      1.2192535132364886
    ],
    [
      -0.5865564429616243,
      1.266807218096722,
      -1.573294317223093
    ],
    [
      -0.041298708269083884,
      -0.05219410570319716,
      -0.19124191598311202
    ],
    [
      -0.07359185900623788,
      -1.6210877883865058,
      0.17611197911748366
    ],
    [
      -0.5644787233807429,
      -0.8621598843749372,
      -0.8229997736099046
    ],
    [
      1.067203642283269,
      1.6243144909274139,
      1.1739376417621816
    ],
    [
      0.7169703288026774,
      0.9271858269997044,
      -1.3746657555370754
    ],
    [
      1.7025118577203928,
      0.059856922130799406,
      0.8194284719302045
    ],
    [
      1.2481038389282388,
      1.3458477900840724,
      0.01709898732768811
    ],
    [
      -1.40963960745743,
      -0.8847424736539878,
      -0.886028883615319
    ],
    [
      -1.2180752589259058,
      -0.6428331028892036,
      -0.34092974589006
    ],
    [
      -1.568476205588499,
      -0.7559427366420663,
      -1.7283790861364439
    ],
    [
      -1.1314612535345163,
      -1.2343850433166026,
      0.9138415163059457
    ],
    [
      1.6073411490182332,
      0.008651986884682827,
      0.6166997654335558
    ],
    [
      -1.4434689386462338,
      1.4044784422588061,
      -0.3483202661775109
    ],
    [
      -1.554967461125589,
      1.5180921662475373,
      1.2782483724699314
    ],
    [
      1.6818507081621386,
      -0.18036379413522585,
      -1.463778555510791
    ],
    [
      1.0832836415205245,
      -1.6147762613648653,
      -1.4725337344881144
    ],
    [
      1.4545293464061175,
      0.9444024009638459,
      -1.4685599036490427
    ],
    [
      -0.44306815238492914,
      -0.5528989112248621,
      0.23112993911849333
    ],
    [
      -0.7983036609376583,
      -0.8217878757509905,
      -0.021706451180515396
    ],
    [
      -1.2805935548901979,
      -0.33151683765649387,
      -0.6912123846010132
    ],
    [
      -0.6244738407007011,
      -0.12776714344124485,
      1.2860314999258948
    ],
    [
      -0.38758203033380534,
      -0.8250048500406445,
      -1.2979543551552626
    ],
    [
      -0.21854803483539764,
      0.9715770433089106,
      -0.23975499523900723
    ],
    [
      1.5796148051910301,
      -0.5920019528979845,
      -1.6629366829201433
    ],
    [
      0.053680511822378874,
      -0.548160615461434,
      1.5041159806718052
    ],
    [
      1.4047918208199013,
      0.6975885794814607,
      0.3353474086288992
    ],
    [
      0.7182967616882436,
      1.4047923377616565,
      -1.6585528689098188
    ],
    [
      -0.6138343424421404,
      1.1118242297936352,
      0.2992825090539686
    ],
    [
      1.1555351025670513,
      1.225754849695189,
      0.04581417450422465
    ],
    [
      -0.7089633687592056,
      -1.6563395376197751,
      -0.24272670950567932
    ],
    [
      -0.07729096935944835,
      0.6340799993398418,
      -0.7139392410898369
    ],
    [
      0.30295332180974066,
      0.11328280177145977,
      -1.1625732606522483
    ],
    [
      1.3037396645624897,
      -0.7178142833894401,
      -1.6983863053407426
    ],
    [
      -1.5828035589516263,
      0.8763094447542255,
      -0.9626643548428319
    ],
    [
      0.48906455600241605,
      1.546460724466558,
      -0.31000282632941323
    ],
    [
      -0.02715099600780957,
      -0.18032380289881078,
      -0.7362452220618023
    ],
    [
      -0.6744083325160124,
      1.5650395739921432,
      0.16157303139246038
    ],
    [
      1.237457418729635,
      -0.8559883651815978,
      0.4039587606859536
    ],
    [
      -0.20872660552568423,
      -0.8757654285029846,
      1.5127204459814174
    ],
    [
      -1.149638394991827,
      0.5440682691139762,
      1.4588298332424658
    ],
    [
      -1.393820583348766,
      1.0564609431912504,
      -1.5788725775980352
    ],
    [
      0.5120080850516908,
      -0.42371238736063965,
      1.084022639603194
    ],
    [
      -1.0147651117148362,
      1.0251448175425333,
      1.598934182749745
    ],
    [
      -0.14497860127054096,
      -0.2888999074720453,
      0.06288677926519837
    ],
    [
      1.3251914161201244,
      0.7399545274134525,
      -0.6342470343188396
    ],
    [
      0.11290435022453282,
      0.24880507839669352,
      1.1012428259731917
    ],
    [
      1.6744926784993828,
      -0.40801206829204517,
      0.49126289364813536
    ],
    [
      -0.8463113818938783,
      -0.5678837969755275,
      1.5953388887493776
    ],
    [
      1.6288317717705203,
      1.0004963362858574,
      0.8119542301078484
    ],
    [
      -1.7174310505576973,
      0.24885760705463822,
      0.6835669704312086
    ],
    [
      0.6564090872115234,
      -0.48386733045093755,
      -0.9634469711804619
    ],
    [
      -1.5274660428246225,
      -0.24093680932788253,
      1.4814399561299014
    ],
    [
      -0.6461942062416335,
      0.6828344665149011,
      -1.595403508134732
    ],
    [
      0.24532283467988036,
      -0.7097907636547514,
      -0.7682975521866187
    ],
    [
      -0.5784084494605846,
      -0.7309216840205022,
      0.470993077178786
    ],
    [
      -0.6308148268962217,
      -1.5488294497452464,
      0.46542891265091635
    ],
    [
      -1.6713922903941476,
      1.6105940809229997,
      1.6614093919205941
    ],
    [
      -0.2824602559090763,
      1.461520490660663,
      -1.451056299053709
    ],
    [
      0.39045504204392767,
      0.9149632656795728,
      0.8989011397075606
    ],
    [
      -0.9306526056788749,
      0.9196311516959987,
      -0.2080304645035682
    ],
    [
      -1.2956443792066947,
      0.2847355907388618,
      -0.993218991761509
    ],
    [
      0.33563316599885473,
      1.2386445310327656,
      0.4713943505604945
    ],
    [
      -0.22530649594810215,
      -0.5805885852419124,
      1.7100375897220803
    ],
    [
      1.4022183393333902,
      0.8129785140847767,
      -0.6579830596653573
    ],
    [
      -0.23570042372057087,
      1.1324446276477884,
      0.20003938816677191
    ],
    [
      1.3528107106496665,
      -0.9798895916333262,
      -0.8658117066971411
    ],
    [
      0.25532545348029534,
      1.5174130204463872,
      -0.28828864827143086
    ],
    [
      1.0835349519223154,
      1.17187992721647,
      1.182000192289269
    ],
    [
      -1.2452028091576346,
      0.03470419709448036,
      -0.04221789793276365
    ],
    [
      1.218908761790237,
      0.1545881979272401,
      0.524598597990054
    ],
    [
      1.3312713869271828,
      -1.00113730413802,
      0.05116687295529809
    ],
    [
      1.1711292807865914,
      0.20860123878134296,
      -0.4835818978720503
    ],
    [
      1.588148537412153,
      -0.901990205300221,
      -0.547754351219192
    ],
    [
      -1.1475057276385652,
      0.23795865464893118,
      -1.2573004185807046
    ],
    [
      -0.05723413910968422,
      0.10530208905739391,
      0.2516548330566952
    ],
    [
      -0.39184622330031105,
      1.4549809992157807,
      -1.632643947038947
    ],
    [
      0.5993856450819544,
      -1.1796823927202147,
      -1.1854775402989
    ],
    [
      1.6908931572520212,
      1.2474011965225684,
      -1.3122427182764453
    ],
    [
      1.2677861894473876,
      -0.01794857585273779,
      0.27115828695836175
    ],
    [
      1.3911673353675895,
      0.41874110651441043,
      1.3730471480013575
    ],
    [
      -1.254378617041562,
      -1.2284788749494866,
      0.3221118770389655
    ],
    [
      -0.527444374892412,
      0.24734664333200196,
      -1.080266290116523
    ],
    [
      -0.8284747027145486,
      -0.025352467119268418,
      -0.8935032729552261
    ],
    [
      -0.9329804484226908,
      -1.537730096762363,
      0.9067389768288101
    ],
    [
      0.7899139272255287,
      -0.020301979268181336,
      -0.6034033268879926
    ],
    [
      -0.6918018701544202,
      -0.3393664325603247,
      -1.414008973465113
    ],
    [
      -0.31238438560245774,
      -1.0183779088343974,
      -0.4827074944732497
    ],
    [
      -1.1216761910178668,
      0.48727195034176374,
      0.35552745262619156
    ],
    [
      -0.32168735708426377,
      1.0658001800229884,
      0.8670155581904231
    ],
    [
      -0.08221701690768568,
      1.6685115416856298,
      -0.21173901742850565
    ],
    [
      0.47747428429927874,
      -0.2935394018026647,
      -1.3985125256025128
    ],
    [
      1.3313795942658224,
      0.5315606991777226,
      1.5057921481194931
    ],
    [
      -1.001622913112409,
      1.266708305088247,
      0.35170176618124716
    ],
    [
      -0.3912734731152345,
      -0.5049647993073374,
      -0.36911853295765407
    ],
    [
      -0.5088558460570036,
      1.0187486348004922,
      0.35891699189490067
    ],
    [
      1.5559160875320432,
      1.1388870023909332,
      -1.4188798393919364
    ],
    [
      0.5308753066078493,
      1.5323400210187494,
      1.4024673275124653
    ],
    [
      1.0981477699531386,
      -1.125959220713869,
      1.5699192486654283
    ],
    [
      0.20355833507534138,
      -0.9504102273131464,
      0.15290184667282825
    ],
    [
      -1.691528085867756,
      0.14504184826445377,
      -0.12676683895389407
    ],
    [
      1.4654013118021636,
      -1.656361789872944,
      0.9459029317607013
    ],
    [
      0.5424969046272983,
      -1.4626315549614297,
      -1.3338960051925082
    ],
    [
      0.0926795233360378,
      1.4125588195034382,
      -1.6294601866880902
    ],
    [
      0.08655073402580671,
      -0.3523845940434971,
      -1.395323722364627
    ],
    [
      -0.5953780014568204,
      -0.475080534029245,
      -0.1555940633890307
    ],
    [
      -0.29503014298360397,
      0.6444340530311332,
      -1.4985158444254192
    ],
    [
      -1.1026851313445662,
      -1.2136582772281974,
      -0.803824230987716
    ],
    [
      -0.2208835210824569,
      0.6200810611561098,
      1.7020994178837912
    ],
    [
      -0.6759676635898617,
      0.9543542415713411,
      -0.23569963748588485
    ],
    [
      1.0492068119146616,
      -1.200809538893167,
      -0.4025227507353084
    ],
    [
      0.002475074563893065,
      -1.5649983009602357,
      1.3218244280722717
    ]
  ],
  "runs": [
    {
      "seed": 7,
      "width": 1,
      "steps": 178,
      "train_mse": 7.450742884601912e-21,
      "test_mse": 7.588781485764599e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.0004920613429930297,
          0.11949821500338796,
          -0.10965514214488703
        ],
        [
          -0.3562367355029097,
          -0.18186831406868903,
          -0.396658621998585
        ],
        [
          0.024057441038975395,
          0.5360860982218134,
          -0.19688260742053187
        ]
      ],
      "W1": [
        [
          0.524209429168092,
          0.299847666805365,
          -0.2994901162939712
        ],
        [
          -1.1170330232255925,
          -0.43072632971924046,
          -0.09770000198263336
        ],
        [
          0.0749575017878812,
          0.5345937240944139,
          -0.24754961684870508
        ]
      ],
      "W2": [
        [
          -0.6960872314811346,
          1.0785456281253543,
          -0.22440513956942135
        ]
      ],
      "W3": [
        [
          -1.260646615594275
        ]
      ],
      "B": [
        [
          -1.586487422588018,
          -0.7932437113581345,
          0.15864874222011624
        ]
      ],
      "effective_weights": [
        1.9999999999684692,
        1.0000000000650744,
        -0.1999999999480781
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.007767835768285101,
          0.001202304234978014,
          -0.006798827128827969
        ],
        "pca": [
          [
            -0.44937170864826476,
            0.860971115985556,
            -0.23831450838152107
          ],
          [
            0.32745603837007925,
            0.4069473536796713,
            0.8527405198934114
          ],
          [
            0.8311664155880651,
            0.30515993965738586,
            -0.4648008184446196
          ]
        ],
        "singular_values": [
          63.87613478775151,
          25.05819707356973,
          9.65064278408469
        ],
        "variance_share": [
          0.8498194547564187,
          0.13078232468123993,
          0.01939822056234126
        ],
        "pc_feature_correlations": [
          [
            -0.8832657313073673,
            -0.47224604307589707,
            0.0642258118638534
          ],
          [
            -0.3948640661972989,
            0.6780094172882382,
            -0.6376918257564154
          ],
          [
            0.2519897516051923,
            -0.5943724325451505,
            -0.743296200127347
          ]
        ],
        "probe": [
          [
            0.9493148364067898,
            -1.6962395805010393,
            -3.3756496026406455
          ],
          [
            -0.5132046040609435,
            -0.6413316186528195,
            -1.5403796551000466
          ],
          [
            -0.9459530695372846,
            2.3052553944746066,
            0.652268379467994
          ],
          [
            -2.6454533008646308e-17,
            -7.45931094670027e-17,
            -4.5102810375396984e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000007,
          1.0000000000000002,
          0.9999999999999999
        ]
      },
      "h2": {
        "rank": 1,
        "mean": [
          0.008229523021610938
        ],
        "pca": [
          [
            1.0
          ]
        ],
        "singular_values": [
          82.72509039092351
        ],
        "variance_share": [
          1.0
        ],
        "pc_feature_correlations": [
          [
            -0.8899387785138503,
            -0.457572263696653,
            0.07320636777129676
          ]
        ],
        "probe": [
          [
            -0.4998096285817143,
            -0.25459344683054425,
            0.0321695580058196
          ],
          [
            0.0025534164261270666,
            -0.001172815519122386,
            0.019670086669981122
          ]
        ],
        "probe_r2": [
          0.791974143172993,
          0.20927995105605635,
          0.0018459047316331523
        ],
        "population_linear_probe_r2": [
          0.7936507936284061,
          0.19841269843918075,
          0.007936507932413519
        ]
      },
      "history": [
        [
          0,
          5.320466197704518
        ],
        [
          25,
          5.2421604460360705
        ],
        [
          50,
          0.166184436437363
        ],
        [
          75,
          1.997666985752018e-05
        ],
        [
          100,
          3.5134903618524325e-09
        ],
        [
          125,
          6.351374294585207e-13
        ],
        [
          150,
          1.1530295257636739e-16
        ],
        [
          175,
          2.0945299740553428e-20
        ],
        [
          178,
          7.450742884601912e-21
        ]
      ]
    },
    {
      "seed": 11,
      "width": 1,
      "steps": 154,
      "train_mse": 8.820830604550152e-21,
      "test_mse": 9.210594466810716e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.013677106901273668,
          0.5438990161239847,
          0.489888431434373
        ],
        [
          -0.204122830715067,
          -0.11918780444257884,
          -0.2109536772133701
        ],
        [
          0.22789054302878406,
          -0.02242577561824704,
          0.29875424650261756
        ]
      ],
      "W1": [
        [
          0.759813429443176,
          0.6570442565525403,
          0.03701733588798358
        ],
        [
          -0.8868446093280581,
          -0.20752483493419943,
          0.22553531342143596
        ],
        [
          0.31399793263189596,
          -0.014018504306849373,
          0.2392647662772112
        ]
      ],
      "W2": [
        [
          -0.9893292447914938,
          1.0696417603454544,
          -0.127790979540461
        ]
      ],
      "W3": [
        [
          -1.149136168111373
        ]
      ],
      "B": [
        [
          -1.7404377787927028,
          -0.8702188894870656,
          0.17404377785783243
        ]
      ],
      "effective_weights": [
        1.999999999958116,
        1.000000000083301,
        -0.19999999997117657
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.0025944258259199843,
          0.006557479266898052,
          0.004325746919567408
        ],
        "pca": [
          [
            0.724676368357114,
            -0.6600561845250609,
            0.19791410868092002
          ],
          [
            0.665871367271873,
            0.7446822210069867,
            0.04542809663179667
          ],
          [
            -0.1773682141541452,
            0.09886467006125191,
            0.9791661215654109
          ]
        ],
        "singular_values": [
          62.62778037083362,
          16.433024835228863,
          13.767808999477209
        ],
        "variance_share": [
          0.8951131679218014,
          0.06162812141039274,
          0.04325871066780591
        ],
        "pc_feature_correlations": [
          [
            0.8891605968098366,
            0.4644418899905098,
            -0.039870028986439154
          ],
          [
            -0.35538055781954436,
            0.7521598377378411,
            0.5256296193937126
          ],
          [
            0.29190484999118965,
            -0.5034618183626243,
            0.8277810965043862
          ]
        ],
        "probe": [
          [
            -0.30288493388078114,
            1.8437467905377243,
            0.5055145279839175
          ],
          [
            -1.0275588362437589,
            1.1086470995820794,
            1.4134673050298439
          ],
          [
            1.0154558120044386,
            -1.3302822236140202,
            2.768900818864972
          ],
          [
            4.336808689942018e-19,
            8.196568423990414e-17,
            3.8250652645288596e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000002,
          0.9999999999999997,
          0.9999999999999998
        ]
      },
      "h2": {
        "rank": 1,
        "mean": [
          0.009028103573402967
        ],
        "pca": [
          [
            1.0
          ]
        ],
        "singular_values": [
          90.75260889008769
        ],
        "variance_share": [
          1.0
        ],
        "pc_feature_correlations": [
          [
            -0.8899387785087401,
            -0.4575722637047366,
            0.07320636778178277
          ]
        ],
        "probe": [
          [
            -0.4555989872703344,
            -0.2320733933702261,
            0.029324001005367396
          ],
          [
            0.002553416426305109,
            -0.0011728155189881092,
            0.019670086669922024
          ]
        ],
        "probe_r2": [
          0.7919741431638907,
          0.20927995106343666,
          0.0018459047331839118
        ],
        "population_linear_probe_r2": [
          0.7936507936195148,
          0.19841269844624498,
          0.007936507934239988
        ]
      },
      "history": [
        [
          0,
          5.756869756046955
        ],
        [
          25,
          3.3744034117134714
        ],
        [
          50,
          0.0005355135458026103
        ],
        [
          75,
          4.175754137372462e-08
        ],
        [
          100,
          3.734472404485789e-12
        ],
        [
          125,
          3.6756911533718275e-16
        ],
        [
          150,
          3.8161385540504975e-20
        ],
        [
          154,
          8.820830604550152e-21
        ]
      ]
    },
    {
      "seed": 23,
      "width": 1,
      "steps": 204,
      "train_mse": 8.703565136734554e-21,
      "test_mse": 8.872649433993864e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.2213042355554955,
          0.08704024368778956,
          -0.023195995146610474
        ],
        [
          -0.9275744378886263,
          0.1725976670835402,
          -0.8505119137803527
        ],
        [
          0.3639684868090537,
          0.24238622920256547,
          0.3320226594313664
        ]
      ],
      "W1": [
        [
          -0.029014448766084368,
          -0.10829782145032871,
          0.19303314968228674
        ],
        [
          -1.3779959276980196,
          -0.24221717893210973,
          -0.287538582474463
        ],
        [
          0.8248458488606164,
          0.680570246031885,
          -0.30571506457608316
        ]
      ],
      "W2": [
        [
          0.31271433446569624,
          0.6562231115548708,
          -0.9840046554265194
        ]
      ],
      "W3": [
        [
          -1.1594215233879874
        ]
      ],
      "B": [
        [
          -1.724998164707796,
          -0.8624990824299428,
          0.1724998164261293
        ]
      ],
      "effective_weights": [
        1.9999999999669955,
        1.0000000000716656,
        -0.199999999944931
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.0042472555945635305,
          -0.0027910982345741913,
          -0.009605055918311907
        ],
        "pca": [
          [
            0.03263604532666627,
            0.810772874133077,
            -0.5844503701046183
          ],
          [
            -0.3257348894342267,
            0.561462915258766,
            0.7606945356675043
          ],
          [
            0.9448977036434726,
            0.16554981534002872,
            0.2824209416636353
          ]
        ],
        "singular_values": [
          79.55752809584921,
          28.468332924358307,
          3.219122805610817
        ],
        "variance_share": [
          0.8852049317399829,
          0.11334577473220209,
          0.001449293527814987
        ],
        "pc_feature_correlations": [
          [
            -0.9366243963870595,
            -0.3599477128939534,
            -0.0464608325897582
          ],
          [
            -0.22454138831031042,
            0.6633580850713041,
            -0.7292395667444632
          ],
          [
            -0.28777119443501725,
            0.6787280727165019,
            0.6517094076213716
          ]
        ],
        "probe": [
          [
            -3.415194184359289,
            8.336674468344178,
            9.344269154509101
          ],
          [
            -1.2441323282171883,
            1.9036236723942868,
            0.8809910793363283
          ],
          [
            -0.9862439868161692,
            3.473460752245737,
            1.8004830118926942
          ],
          [
            -3.9898639947466563e-17,
            1.0408340855860843e-16,
            9.020562075079397e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000013,
          1.0000000000000004,
          0.9999999999999992
        ]
      },
      "h2": {
        "rank": 1,
        "mean": [
          0.008948014277662997
        ],
        "pca": [
          [
            1.0
          ]
        ],
        "singular_values": [
          89.94753256035528
        ],
        "variance_share": [
          1.0
        ],
        "pc_feature_correlations": [
          [
            -0.8899387785126794,
            -0.4575722636992561,
            0.07320636776992322
          ]
        ],
        "probe": [
          [
            -0.4596768307666957,
            -0.23415056869925616,
            0.02958646577680137
          ],
          [
            0.0025534164261023138,
            -0.0011728155191217354,
            0.019670086669988623
          ]
        ],
        "probe_r2": [
          0.7919741431709091,
          0.2092799510584351,
          0.0018459047314265398
        ],
        "population_linear_probe_r2": [
          0.7936507936262867,
          0.19841269844155895,
          0.007936507932154255
        ]
      },
      "history": [
        [
          0,
          5.2569733399494964
        ],
        [
          25,
          0.5749823970791115
        ],
        [
          50,
          0.00040507523862007093
        ],
        [
          75,
          4.32904110382933e-07
        ],
        [
          100,
          8.721842007112467e-10
        ],
        [
          125,
          1.9590549359392643e-12
        ],
        [
          150,
          4.451791121289097e-15
        ],
        [
          175,
          1.0128078975892642e-17
        ],
        [
          200,
          2.3044615066422052e-20
        ],
        [
          204,
          8.703565136734554e-21
        ]
      ]
    },
    {
      "seed": 42,
      "width": 1,
      "steps": 154,
      "train_mse": 8.838822707215783e-21,
      "test_mse": 8.721434870709988e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.12188683190177255,
          -0.41599364249619825,
          0.30018047832258293
        ],
        [
          0.3762258865564856,
          -0.7804140754615346,
          -0.5208718027449273
        ],
        [
          0.05113616126691415,
          -0.1264970369374329,
          -0.006720463001715519
        ]
      ],
      "W1": [
        [
          -0.615287371400666,
          -0.8862421255577297,
          0.06380454084459863
        ],
        [
          0.9749367079889462,
          -0.40777247913269093,
          -0.3666999133352643
        ],
        [
          0.6083679500233765,
          0.22538399821961805,
          0.16020066283171144
        ]
      ],
      "W2": [
        [
          -0.9966639361993261,
          0.5809645101128034,
          0.7178307503818678
        ]
      ],
      "W3": [
        [
          1.2373606834851691
        ]
      ],
      "B": [
        [
          1.6163435824952708,
          0.8081717912732713,
          -0.16163435832263762
        ]
      ],
      "effective_weights": [
        1.9999999999832152,
        1.0000000000233285,
        -0.20000000008878563
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.0051278820608821616,
          -0.007498184784488988,
          0.0015080987763829688
        ],
        "pca": [
          [
            0.6591429661757084,
            -0.5910045309576165,
            -0.46502063882010336
          ],
          [
            0.6349666775643912,
            0.768700166314493,
            -0.07692446094000094
          ],
          [
            0.4029241473576978,
            -0.24456839267501196,
            0.8819514911719541
          ]
        ],
        "singular_values": [
          62.693070297792616,
          42.788206296986566,
          12.227162181792599
        ],
        "variance_share": [
          0.6649608991236107,
          0.30974563311101944,
          0.025293467765370004
        ],
        "pc_feature_correlations": [
          [
            -0.9326035740270937,
            -0.34507898010658894,
            0.11708198985383304
          ],
          [
            0.3027088801898148,
            -0.9133290046215257,
            -0.23516113970656297
          ],
          [
            0.2085098875590675,
            -0.23294796655987507,
            0.9586601999846375
          ]
        ],
        "probe": [
          [
            0.048753080939688366,
            -1.0674197671158363,
            1.3165958196077256
          ],
          [
            0.44004773809758824,
            -0.3866561570948136,
            -1.1271166206488918
          ],
          [
            0.9878535873842941,
            -0.4599266311734346,
            3.1378249768503563
          ],
          [
            -2.3418766925686896e-17,
            3.2959746043559335e-17,
            4.336808689942018e-18
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.000000000000001,
          1.0,
          1.0
        ]
      },
      "h2": {
        "rank": 1,
        "mean": [
          -0.008384394692919702
        ],
        "pca": [
          [
            1.0
          ]
        ],
        "singular_values": [
          84.28189663535817
        ],
        "variance_share": [
          1.0
        ],
        "pc_feature_correlations": [
          [
            0.8899387785168511,
            0.45757226367839204,
            -0.07320636783305481
          ]
        ],
        "probe": [
          [
            0.4905774354091318,
            0.24989074453709723,
            -0.03157534064704983
          ],
          [
            0.0025534164272015135,
            -0.0011728155186590153,
            0.019670086669636783
          ]
        ],
        "probe_r2": [
          0.791974143178322,
          0.20927995103933672,
          0.0018459047407972662
        ],
        "population_linear_probe_r2": [
          0.793650793635105,
          0.19841269842136391,
          0.007936507943530742
        ]
      },
      "history": [
        [
          0,
          5.306455099650673
        ],
        [
          25,
          5.0541902285787295
        ],
        [
          50,
          0.0070963897288215064
        ],
        [
          75,
          3.096060802077023e-07
        ],
        [
          100,
          1.5975118055767194e-11
        ],
        [
          125,
          8.27474182057341e-16
        ],
        [
          150,
          4.2864613329680975e-20
        ],
        [
          154,
          8.838822707215783e-21
        ]
      ]
    },
    {
      "seed": 101,
      "width": 1,
      "steps": 149,
      "train_mse": 9.041843506839136e-21,
      "test_mse": 9.138775920458937e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          -0.31606099998520587,
          -0.8138501927327492,
          0.2413206987699059
        ],
        [
          0.29771781195196473,
          -0.12387471994650855,
          0.1469285491782161
        ],
        [
          0.684157716591058,
          0.42431913602632554,
          0.2830556083224302
        ]
      ],
      "W1": [
        [
          -0.8980121582343443,
          -0.8384435551872013,
          0.31317426409528804
        ],
        [
          0.7746538201677184,
          -0.09050952209949532,
          0.09034012644135676
        ],
        [
          0.6381534820920526,
          0.34835273428843827,
          0.2721275039907589
        ]
      ],
      "W2": [
        [
          0.936777114036392,
          -0.7778326232321328,
          -0.23434390763117316
        ]
      ],
      "W3": [
        [
          -1.255228314879381
        ]
      ],
      "B": [
        [
          -1.5933356316601017,
          -0.796667815895698,
          0.15933356311753955
        ]
      ],
      "effective_weights": [
        1.9999999999659837,
        1.000000000065394,
        -0.19999999993575665
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.01038380668144984,
          0.0008884114128290202,
          0.0032910205356273302
        ],
        "pca": [
          [
            0.7865284247570924,
            -0.4020886068674667,
            -0.46871930755677876
          ],
          [
            0.5797273890695885,
            0.7422930018657181,
            0.33603162610644005
          ],
          [
            0.2128125734341942,
            -0.5360278459264596,
            0.8169363236995618
          ]
        ],
        "singular_values": [
          71.44482425697919,
          27.44050469560295,
          13.249392072026462
        ],
        "variance_share": [
          0.846089089031102,
          0.12481268892599634,
          0.02909822204290174
        ],
        "pc_feature_correlations": [
          [
            -0.8570098538695006,
            -0.522341931608726,
            0.039980567492929546
          ],
          [
            0.4382800020353377,
            -0.7090332583204012,
            0.5703698349390155
          ],
          [
            -0.2612875615046995,
            0.5103986498434059,
            0.8005505400850327
          ]
        ],
        "probe": [
          [
            -0.19936931460118756,
            -0.5442773773395122,
            1.164265758867844
          ],
          [
            1.1985489581827167,
            -1.5786929480681526,
            -0.7897628240767062
          ],
          [
            -0.16844944142996754,
            1.1504643340395417,
            2.5970517157464315
          ],
          [
            -4.5102810375396984e-17,
            1.0061396160665481e-16,
            1.2836953722228372e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999999,
          0.9999999999999996,
          1.0
        ]
      },
      "h2": {
        "rank": 1,
        "mean": [
          0.00826504646359691
        ],
        "pca": [
          [
            1.0
          ]
        ],
        "singular_values": [
          83.08218034098498
        ],
        "variance_share": [
          1.0
        ],
        "pc_feature_correlations": [
          [
            -0.8899387785140656,
            -0.45757226369728593,
            0.0732063677659602
          ]
        ],
        "probe": [
          [
            -0.4976614303210479,
            -0.2534991958032738,
            0.032031292182103696
          ],
          [
            0.0025534164260345603,
            -0.001172815519167092,
            0.019670086670010908
          ]
        ],
        "probe_r2": [
          0.7919741431733782,
          0.20927995105663566,
          0.0018459047308438947
        ],
        "population_linear_probe_r2": [
          0.7936507936286742,
          0.19841269843986786,
          0.007936507931458038
        ]
      },
      "history": [
        [
          0,
          5.4786750667595125
        ],
        [
          25,
          0.001684423861458176
        ],
        [
          50,
          5.194622419670958e-07
        ],
        [
          75,
          1.7192331707321904e-10
        ],
        [
          100,
          5.778967784642381e-14
        ],
        [
          125,
          1.9476725016803507e-17
        ],
        [
          149,
          9.041843506839136e-21
        ]
      ]
    },
    {
      "seed": 7,
      "width": 2,
      "steps": 149,
      "train_mse": 9.397688136194641e-21,
      "test_mse": 9.865033249079265e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.0004920613429930297,
          0.11949821500338796,
          -0.10965514214488703
        ],
        [
          -0.3562367355029097,
          -0.18186831406868903,
          -0.396658621998585
        ],
        [
          0.024057441038975395,
          0.5360860982218134,
          -0.19688260742053187
        ]
      ],
      "W1": [
        [
          -0.48412509667680315,
          0.0374981798074796,
          -0.1293205672494728
        ],
        [
          0.06420377694052423,
          -0.025990214285124644,
          -0.39684087239823257
        ],
        [
          1.0877293112421074,
          0.6738670831306797,
          -0.1444242999527369
        ]
      ],
      "W2": [
        [
          -0.44902745828680524,
          0.0498427543336956,
          0.7663734000533818
        ],
        [
          0.2894245873271528,
          -0.12577032211912817,
          -0.8712382856625619
        ]
      ],
      "W3": [
        [
          0.8642448633667922,
          -0.9936630888112614
        ]
      ],
      "B": [
        [
          1.0541923653293177,
          0.49830067144788615,
          -0.07239409830138435
        ],
        [
          -1.095864056418969,
          -0.5729771094323199,
          0.13831023204130768
        ]
      ],
      "effective_weights": [
        1.9999999999548628,
        1.0000000000877263,
        -0.19999999997941015
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.0019453992127916194,
          -0.00792616174717548,
          -0.006777886490302991
        ],
        "pca": [
          [
            -0.2976379646178729,
            0.04958762531545591,
            0.9533901139794265
          ],
          [
            0.5040734620792785,
            0.8562588427197181,
            0.11283057693595011
          ],
          [
            0.8107537152832173,
            -0.5141613187316438,
            0.27985094510220415
          ]
        ],
        "singular_values": [
          62.56992407550422,
          19.73717886893496,
          11.688417366056894
        ],
        "variance_share": [
          0.881523282411394,
          0.08771476114550947,
          0.030761956443096573
        ],
        "pc_feature_correlations": [
          [
            0.8785020785519115,
            0.4796571079628104,
            -0.07308161096153598
          ],
          [
            -0.1760913062771683,
            0.18349712149103375,
            -0.9743241876098958
          ],
          [
            -0.4382537223152293,
            0.866357471612307,
            0.19243167870986563
          ]
        ],
        "probe": [
          [
            -1.7341605516917216,
            2.7011665163348293,
            -0.45747191493178313
          ],
          [
            0.5226638326787424,
            -1.3467063647449458,
            -2.347141853720762
          ],
          [
            0.11665803414459741,
            1.2817215841275569,
            -0.06506973958290363
          ],
          [
            -1.496198998029996e-17,
            -2.0816681711721685e-17,
            2.2551405187698492e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000009,
          1.0,
          1.0000000000000002
        ]
      },
      "h2": {
        "rank": 2,
        "mean": [
          -0.004715915983650015,
          0.006338983757988783
        ],
        "pca": [
          [
            -0.6848938232534352,
            0.7286428829469839
          ],
          [
            0.7286428829469839,
            0.6848938232534352
          ]
        ],
        "singular_values": [
          79.24898682074479,
          2.4463538293604157
        ],
        "variance_share": [
          0.9990479988778779,
          0.0009520011221221603
        ],
        "pc_feature_correlations": [
          [
            -0.8903704668267598,
            -0.4569039171810548,
            0.07223891115877681
          ],
          [
            0.33443571929815663,
            -0.547472245885841,
            0.7829551180832273
          ]
        ],
        "probe": [
          [
            4.816268618697559,
            -6.626636211462729,
            10.70828080993674
          ],
          [
            3.810747740908671,
            -6.593022858378442,
            10.110678558539721
          ],
          [
            -0.0030029282936522694,
            0.007274407036870781,
            0.006342752252353253
          ]
        ],
        "probe_r2": [
          0.9137945845987286,
          0.4990801963143161,
          0.615287107887606
        ],
        "population_linear_probe_r2": [
          0.9117352216452566,
          0.4820441916785719,
          0.6062205866761724
        ]
      },
      "history": [
        [
          0,
          5.751131180269082
        ],
        [
          25,
          0.261126416846615
        ],
        [
          50,
          2.2517736541880276e-05
        ],
        [
          75,
          2.8739532172008467e-09
        ],
        [
          100,
          3.772479829294096e-13
        ],
        [
          125,
          4.977813303426e-17
        ],
        [
          149,
          9.397688136194641e-21
        ]
      ],
      "null_direction": [
        -0.29709388811408294,
        0.7196914674507605,
        0.6275184565603054
      ],
      "intervention_delta": 0.25,
      "intervention_effects": [
        0.4999999999887157,
        0.25000000002193157,
        -0.049999999994852495
      ],
      "basis_transform": [
        [
          1.0,
          2.0
        ],
        [
          0.0,
          0.3
        ]
      ],
      "transformed": {
        "rank": 2,
        "mean": [
          0.007962051532327518,
          0.0019016951273966244
        ],
        "pca": [
          [
            0.9625186226119115,
            0.2712155989711298
          ],
          [
            -0.2712155989711298,
            0.9625186226119115
          ]
        ],
        "singular_values": [
          63.81763885310002,
          0.9113674488715964
        ],
        "variance_share": [
          0.9997961001058875,
          0.00020389989411243232
        ],
        "pc_feature_correlations": [
          [
            -0.8586222561496307,
            -0.4999026543238828,
            0.1364566898150378
          ],
          [
            -0.4021968471540417,
            0.5114374374009978,
            -0.7760352665703307
          ]
        ],
        "probe": [
          [
            4.81626861869756,
            -6.626636211462742,
            10.708280809936769
          ],
          [
            -19.40596498828815,
            22.200831881823422,
            -37.686276871112625
          ],
          [
            -0.0030029282936532287,
            0.007274407036872543,
            0.00634275225235037
          ]
        ],
        "probe_r2": [
          0.9137945845987286,
          0.49908019631431677,
          0.6152871078876067
        ],
        "population_linear_probe_r2": [
          0.9117352216452554,
          0.4820441916785713,
          0.6062205866761713
        ]
      },
      "basis_change_max_prediction_error": 1.7763568394002505e-15
    },
    {
      "seed": 11,
      "width": 2,
      "steps": 145,
      "train_mse": 8.374694815828345e-21,
      "test_mse": 8.77016991479531e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.013677106901273668,
          0.5438990161239847,
          0.489888431434373
        ],
        [
          -0.204122830715067,
          -0.11918780444257884,
          -0.2109536772133701
        ],
        [
          0.22789054302878406,
          -0.02242577561824704,
          0.29875424650261756
        ]
      ],
      "W1": [
        [
          0.8996203596042108,
          0.6462497660980661,
          -0.00874166632069051
        ],
        [
          -0.7794477254915718,
          -0.14840610362780907,
          0.1597068485891519
        ],
        [
          0.15961025317704738,
          -0.050210293632690695,
          0.3108632840508303
        ]
      ],
      "W2": [
        [
          -0.9382780015002188,
          0.8698529424922637,
          -0.016763039555551425
        ],
        [
          0.6201538347754239,
          -0.4178759200567484,
          -0.08718848829631436
        ]
      ],
      "W3": [
        [
          -0.880189675760268,
          0.7564790451435224
        ]
      ],
      "B": [
        [
          -1.5247744436435715,
          -0.7346117477906781,
          0.14191257185968678
        ],
        [
          0.8696992745854288,
          0.4671673673626926,
          -0.09926252398787871
        ]
      ],
      "effective_weights": [
        1.9999999999585776,
        1.0000000000823035,
        -0.1999999999763699
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.003689415066555404,
          0.004884484976492886,
          0.006112136240800505
        ],
        "pca": [
          [
            0.8175134002986197,
            -0.5698964653316644,
            0.0830051753486725
          ],
          [
            0.08440061486541468,
            0.2611298508405908,
            0.961606851686442
          ],
          [
            0.569691474872609,
            0.7791207992361943,
            -0.26157676436378174
          ]
        ],
        "singular_values": [
          62.37457795599482,
          15.60067861868741,
          13.112314416672579
        ],
        "variance_share": [
          0.9035477424442983,
          0.05652269300900344,
          0.03992956454669833
        ],
        "pc_feature_correlations": [
          [
            0.8889400167680312,
            0.46505033582114824,
            -0.03838733439689948
          ],
          [
            0.10048608428186569,
            -0.11207979448903758,
            0.9927131111542935
          ],
          [
            -0.441766372605067,
            0.8829466371419257,
            0.09894139611579102
          ]
        ],
        "probe": [
          [
            -0.27575148851713843,
            1.9374008113843417,
            0.4545092192260518
          ],
          [
            -1.4502435801140432,
            2.033345114747675,
            1.0730395558837544
          ],
          [
            0.7373122402230536,
            -0.9901556238388458,
            2.678352332906298
          ],
          [
            1.48318857196017e-16,
            -9.8879238130678e-17,
            1.438085761584773e-15
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000002,
          0.9999999999999996,
          0.9999999999999998
        ]
      },
      "h2": {
        "rank": 2,
        "mean": [
          0.0076080226431405554,
          -0.004862021474254373
        ],
        "pca": [
          [
            0.8636180216672317,
            -0.5041467173864933
          ],
          [
            0.5041467173864933,
            0.8636180216672317
          ]
        ],
        "singular_values": [
          91.3572008692665,
          1.7694966021291343
        ],
        "variance_share": [
          0.9996249829626872,
          0.0003750170373127635
        ],
        "pc_feature_correlations": [
          [
            -0.8916179273892958,
            -0.4544960047895168,
            0.07179215869485986
          ],
          [
            -0.43567460245784795,
            0.8240218408532939,
            -0.37711899753841344
          ]
        ],
        "probe": [
          [
            -5.917964439141482,
            9.971512375710525,
            -4.921134129313209
          ],
          [
            -9.238419802924959,
            17.536021234762533,
            -8.486487073027554
          ],
          [
            -0.0014531664344183196,
            0.006129021724669073,
            0.016113444283889344
          ]
        ],
        "probe_r2": [
          0.9930370423371616,
          0.877348252459036,
          0.143600468828046
        ],
        "population_linear_probe_r2": [
          0.9929450257363303,
          0.8744990424170495,
          0.13255593184661926
        ]
      },
      "history": [
        [
          0,
          5.51960849213393
        ],
        [
          25,
          0.09542295984748989
        ],
        [
          50,
          8.473816361917882e-06
        ],
        [
          75,
          8.643483666355072e-10
        ],
        [
          100,
          9.780166380386199e-14
        ],
        [
          125,
          1.1519988941098911e-17
        ],
        [
          145,
          8.374694815828345e-21
        ]
      ],
      "null_direction": [
        -0.08399389420469622,
        0.3542611432022281,
        0.9313667742374004
      ],
      "intervention_delta": 0.25,
      "intervention_effects": [
        0.4999999999896444,
        0.2500000000205759,
        -0.049999999994092464
      ],
      "basis_transform": [
        [
          1.0,
          2.0
        ],
        [
          0.0,
          0.3
        ]
      ],
      "transformed": {
        "rank": 2,
        "mean": [
          -0.0021160203053682686,
          -0.0014586064422763172
        ],
        "pca": [
          [
            0.7062981742762748,
            0.7079144644757592
          ],
          [
            0.7079144644757592,
            -0.7062981742762748
          ]
        ],
        "singular_values": [
          19.368514491530533,
          2.5039027632534996
        ],
        "variance_share": [
          0.9835621839634092,
          0.01643781603659087
        ],
        "pc_feature_correlations": [
          [
            0.8033591669487807,
            0.5866896824331715,
            -0.13450152126661932
          ],
          [
            -0.5672467979094183,
            0.746395092275068,
            -0.3623644509580533
          ]
        ],
        "probe": [
          [
            -5.917964439141496,
            9.971512375710542,
            -4.921134129313223
          ],
          [
            8.658363584526738,
            -8.02334505552849,
            4.519270618662931
          ],
          [
            -0.0014531664344183126,
            0.0061290217246691425,
            0.016113444283889333
          ]
        ],
        "probe_r2": [
          0.9930370423371616,
          0.8773482524590362,
          0.1436004688280469
        ],
        "population_linear_probe_r2": [
          0.9929450257363311,
          0.8744990424170498,
          0.13255593184661937
        ]
      },
      "basis_change_max_prediction_error": 1.7763568394002505e-15
    },
    {
      "seed": 23,
      "width": 2,
      "steps": 208,
      "train_mse": 8.386957550922857e-21,
      "test_mse": 8.44414948484258e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.2213042355554955,
          0.08704024368778956,
          -0.023195995146610474
        ],
        [
          -0.9275744378886263,
          0.1725976670835402,
          -0.8505119137803527
        ],
        [
          0.3639684868090537,
          0.24238622920256547,
          0.3320226594313664
        ]
      ],
      "W1": [
        [
          0.29411092519542076,
          0.22806039888160404,
          -0.2494500889570904
        ],
        [
          -1.3964455416893768,
          -0.43988775283174214,
          -0.037514590891929274
        ],
        [
          0.6042823524158379,
          0.5953077912294003,
          -0.17005487143104547
        ]
      ],
      "W2": [
        [
          0.2579981460120012,
          0.1961175051420555,
          -0.3119466097770347
        ],
        [
          -0.4505130518475545,
          0.9088111391790192,
          -0.6634944839511845
        ]
      ],
      "W3": [
        [
          -0.2020760197471671,
          -1.0662149245477808
        ]
      ],
      "B": [
        [
          -0.38649117346478584,
          -0.21313477578556128,
          -0.018666887826623995
        ],
        [
          -1.8025440816126361,
          -0.8975025118015069,
          0.1911173119389002
        ]
      ],
      "effective_weights": [
        1.9999999999718414,
        1.0000000000623384,
        -0.1999999999356381
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.006176793151336857,
          0.0028678511102556946,
          -0.00627802573956301
        ],
        "pca": [
          [
            -0.21813367907764258,
            0.8530235186069622,
            -0.47409764263857057
          ],
          [
            0.49484814251551934,
            0.5153914307939244,
            0.6996406141106526
          ],
          [
            0.8411557607845244,
            -0.08199115664258524,
            -0.5345413326688768
          ]
        ],
        "singular_values": [
          78.990597869827,
          19.128768023200756,
          6.738820445616189
        ],
        "variance_share": [
          0.9381549227925938,
          0.05501710838226986,
          0.006827968825136296
        ],
        "pc_feature_correlations": [
          [
            -0.9066551224208981,
            -0.42792213700753057,
            0.04390432965090276
          ],
          [
            -0.35729884399970163,
            0.7086559576849466,
            -0.6258407297068499
          ],
          [
            0.23188377712320624,
            -0.5885690429840881,
            -0.7549551783415657
          ]
        ],
        "probe": [
          [
            0.880629818281631,
            -2.358388192672617,
            -5.126685288731569
          ],
          [
            -0.9946684171563102,
            0.9131352420691515,
            -0.3379147357524739
          ],
          [
            -1.0723515664755368,
            3.2580322148958025,
            1.7143221593355893
          ],
          [
            -1.0148132334464322e-16,
            -7.676151381197371e-17,
            -1.5612511283791264e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000002,
          0.9999999999999996,
          0.9999999999999997
        ]
      },
      "h2": {
        "rank": 2,
        "mean": [
          0.0009272434690673328,
          0.009554496416050851
        ],
        "pca": [
          [
            0.21242693331334145,
            0.9771769532705369
          ],
          [
            0.9771769532705369,
            -0.21242693331334145
          ]
        ],
        "singular_values": [
          96.13421559526782,
          2.7833402635702362
        ],
        "variance_share": [
          0.9991624461626705,
          0.0008375538373295583
        ],
        "pc_feature_correlations": [
          [
            -0.8899037425481513,
            -0.45779070152704104,
            0.07245553611122103
          ],
          [
            0.05673071837070769,
            -0.27086558660916105,
            -0.9537412525307782
          ]
        ],
        "probe": [
          [
            0.5229762966790179,
            -4.302584758654233,
            -15.272780734074795
          ],
          [
            -0.5538145050019919,
            0.711033173072279,
            3.348095439457423
          ],
          [
            0.0032467139289168306,
            -0.006072018437207122,
            0.0021070471014612477
          ]
        ],
        "probe_r2": [
          0.7938645640357083,
          0.28606421475123756,
          0.9131540211693712
        ],
        "population_linear_probe_r2": [
          0.7966999168977053,
          0.2889245727259591,
          0.9143755103763359
        ]
      },
      "history": [
        [
          0,
          4.600936399200175
        ],
        [
          25,
          0.06904201014442918
        ],
        [
          50,
          0.000132869175252247
        ],
        [
          75,
          2.465318455288049e-07
        ],
        [
          100,
          5.067607062669307e-10
        ],
        [
          125,
          1.2348408910443699e-12
        ],
        [
          150,
          3.669008847666305e-15
        ],
        [
          175,
          1.2802343010846088e-17
        ],
        [
          200,
          4.9160843951818124e-20
        ],
        [
          208,
          8.386957550922857e-21
        ]
      ],
      "null_direction": [
        -0.4508881048578399,
        0.8432528845334839,
        -0.29261662567883
      ],
      "intervention_delta": 0.25,
      "intervention_effects": [
        0.4999999999929603,
        0.25000000001558464,
        -0.04999999998390947
      ],
      "basis_transform": [
        [
          1.0,
          2.0
        ],
        [
          0.0,
          0.3
        ]
      ],
      "transformed": {
        "rank": 2,
        "mean": [
          0.020036236301168877,
          0.0028663489248152577
        ],
        "pca": [
          [
            0.9909732242834656,
            0.13405994462639587
          ],
          [
            -0.13405994462639587,
            0.9909732242834656
          ]
        ],
        "singular_values": [
          210.20491544555642,
          0.38187627402417185
        ],
        "variance_share": [
          0.9999966996637857,
          3.3003362142936666e-06
        ],
        "pc_feature_correlations": [
          [
            -0.8895551064588892,
            -0.4597890074353115,
            0.06553875253753501
          ],
          [
            -0.06296480068771858,
            0.26762303677907323,
            0.9541363183534833
          ]
        ],
        "probe": [
          [
            0.5229762966789941,
            -4.302584758654186,
            -15.272780734074797
          ],
          [
            -5.332556994533259,
            31.054008967935513,
            112.97885635869021
          ],
          [
            0.0032467139289361555,
            -0.00607201843732047,
            0.002107047101049031
          ]
        ],
        "probe_r2": [
          0.7938645640357078,
          0.2860642147512348,
          0.913154021169376
        ],
        "population_linear_probe_r2": [
          0.7966999168977056,
          0.2889245727259552,
          0.9143755103763389
        ]
      },
      "basis_change_max_prediction_error": 1.7763568394002505e-15
    },
    {
      "seed": 42,
      "width": 2,
      "steps": 135,
      "train_mse": 7.03572478499512e-21,
      "test_mse": 6.952897196418711e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.12188683190177255,
          -0.41599364249619825,
          0.30018047832258293
        ],
        [
          0.3762258865564856,
          -0.7804140754615346,
          -0.5208718027449273
        ],
        [
          0.05113616126691415,
          -0.1264970369374329,
          -0.006720463001715519
        ]
      ],
      "W1": [
        [
          0.9124377084031259,
          -0.12557983983982912,
          0.004105973471322408
        ],
        [
          -0.21804736657553175,
          -0.9955651203596739,
          -0.3002105055040922
        ],
        [
          -0.7535212130389036,
          -0.40864503942439806,
          0.3239216147258282
        ]
      ],
      "W2": [
        [
          -0.819681386786861,
          0.47463537941128936,
          0.9539839003062431
        ],
        [
          0.022704826156015403,
          0.43866564722145973,
          0.16807818243681555
        ]
      ],
      "W3": [
        [
          -1.2634581507747848,
          -0.07965418001637621
        ]
      ],
      "B": [
        [
          -1.5702483065230546,
          -0.7594357599090625,
          0.1631598881973684
        ],
        [
          -0.20158362555146786,
          -0.508255801794224,
          -0.07715465403065098
        ]
      ],
      "effective_weights": [
        2.0000000000148863,
        0.9999999999774325,
        -0.19999999992120904
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.0009309540916406352,
          -0.0023910338780754547,
          0.008968098641886278
        ],
        "pca": [
          [
            -0.5165746254908596,
            0.5615038819134428,
            0.6464240457278124
          ],
          [
            0.6047312744634291,
            0.7737223243868321,
            -0.18882227207423063
          ],
          [
            0.6061771539614595,
            -0.29337204253570703,
            0.7392442780797241
          ]
        ],
        "singular_values": [
          61.44954479910593,
          42.46289514176715,
          15.784487574012186
        ],
        "variance_share": [
          0.6478819551798581,
          0.30936967881882393,
          0.042748366001317886
        ],
        "pc_feature_correlations": [
          [
            -0.8186433707189007,
            -0.5829303674210617,
            0.017883722322326295
          ],
          [
            0.5268802616397337,
            -0.7887039027985958,
            -0.2723216900268365
          ],
          [
            0.19417129568343836,
            -0.2630420343852622,
            0.9539691453921932
          ]
        ],
        "probe": [
          [
            0.9977307131337718,
            -0.6653081029509188,
            1.4816436429943254
          ],
          [
            -0.08740954856444472,
            -0.6693580522088547,
            -1.047768291062198
          ],
          [
            -0.09365821612659517,
            -0.6119276170059106,
            2.097314076345275
          ],
          [
            3.7947076036992655e-17,
            8.174884380540703e-17,
            3.0249240612345574e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000007,
          1.0000000000000002,
          0.9999999999999998
        ]
      },
      "h2": {
        "rank": 2,
        "mean": [
          0.008183638189683113,
          0.00043734014517799407
        ],
        "pca": [
          [
            0.9727044656803376,
            0.232047457313216
          ],
          [
            -0.232047457313216,
            0.9727044656803376
          ]
        ],
        "singular_values": [
          83.5516440844207,
          16.424461358814032
        ],
        "variance_share": [
          0.9627946050322153,
          0.037205394967784786
        ],
        "pc_feature_correlations": [
          [
            -0.8748974882626166,
            -0.4880197540136984,
            0.06341748241421424
          ],
          [
            0.43234977782454576,
            -0.8446634465672742,
            -0.2745367835158582
          ]
        ],
        "probe": [
          [
            -0.7408703926967554,
            0.26123864751884307,
            0.21478006450057782
          ],
          [
            1.0048673395750582,
            -2.2466776946730604,
            -0.7864441775143713
          ],
          [
            0.004063767992395464,
            -0.004423318374265659,
            0.018521088060723986
          ]
        ],
        "probe_r2": [
          0.9555246504715674,
          0.9478221309915981,
          0.07587403850367191
        ],
        "population_linear_probe_r2": [
          0.9564396043278899,
          0.9483904105788964,
          0.09516998509321362
        ]
      },
      "history": [
        [
          0,
          5.369225658751574
        ],
        [
          25,
          2.7470875300423545
        ],
        [
          50,
          3.916406871936448e-05
        ],
        [
          75,
          8.896972320642639e-10
        ],
        [
          100,
          2.105133107398694e-14
        ],
        [
          125,
          4.984079312670249e-19
        ],
        [
          135,
          7.03572478499512e-21
        ]
      ],
      "null_direction": [
        0.2087112734667445,
        -0.22717744038769216,
        0.9512255331448932
      ],
      "intervention_delta": 0.25,
      "intervention_effects": [
        0.5000000000037217,
        0.24999999999435807,
        -0.049999999980302245
      ],
      "basis_transform": [
        [
          1.0,
          2.0
        ],
        [
          0.0,
          0.3
        ]
      ],
      "transformed": {
        "rank": 2,
        "mean": [
          0.009058318480039098,
          0.00013120204355339288
        ],
        "pca": [
          [
            0.9984997371151161,
            0.054756506289610166
          ],
          [
            -0.054756506289610166,
            0.9984997371151161
          ]
        ],
        "singular_values": [
          123.48633690378125,
          3.333868630662887
        ],
        "variance_share": [
          0.99927164565725,
          0.0007283543427500027
        ],
        "pc_feature_correlations": [
          [
            -0.7440847500296706,
            -0.6765817097528797,
            -0.004640425222329536
          ],
          [
            0.6138152323733341,
            -0.7181415184022013,
            -0.28202385119698864
          ]
        ],
        "probe": [
          [
            -0.7408703926967557,
            0.2612386475188433,
            0.2147800645005777
          ],
          [
            8.28869374989523,
            -9.230516632369165,
            -4.053347688385091
          ],
          [
            0.0040637679923953285,
            -0.004423318374265517,
            0.018521088060724028
          ]
        ],
        "probe_r2": [
          0.9555246504715674,
          0.9478221309915981,
          0.0758740385036718
        ],
        "population_linear_probe_r2": [
          0.9564396043278903,
          0.9483904105788964,
          0.09516998509321367
        ]
      },
      "basis_change_max_prediction_error": 1.7763568394002505e-15
    },
    {
      "seed": 101,
      "width": 2,
      "steps": 145,
      "train_mse": 9.451973794573892e-21,
      "test_mse": 9.576124651574373e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          -0.31606099998520587,
          -0.8138501927327492,
          0.2413206987699059
        ],
        [
          0.29771781195196473,
          -0.12387471994650855,
          0.1469285491782161
        ],
        [
          0.684157716591058,
          0.42431913602632554,
          0.2830556083224302
        ]
      ],
      "W1": [
        [
          -0.9442888283308016,
          -0.8021422643850008,
          0.28577130846036247
        ],
        [
          0.7365040805738351,
          -0.11150516467500277,
          0.11671876377655448
        ],
        [
          0.6086754480762705,
          0.3491794353884705,
          0.28042543772295997
        ]
      ],
      "W2": [
        [
          0.8802091572493962,
          -0.7566702153107256,
          -0.20340088369239
        ],
        [
          -0.7337656350670825,
          -0.06189520310442048,
          -0.10950356733502697
        ]
      ],
      "W3": [
        [
          -1.2119389489133887,
          0.2879954392581433
        ]
      ],
      "B": [
        [
          -1.5122674990306813,
          -0.6927037352907764,
          0.10618212862567035
        ],
        [
          0.5806484892389523,
          0.5572496690402908,
          -0.24762108302856625
        ]
      ],
      "effective_weights": [
        1.9999999999640723,
        1.0000000000683953,
        -0.19999999993637027
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.009791082307470245,
          0.0015423838406275442,
          0.003499715950896062
        ],
        "pca": [
          [
            0.8019191686031322,
            -0.3819172738447175,
            -0.45941793931656716
          ],
          [
            0.5508124171837755,
            0.7704415033711557,
            0.32097596632670294
          ],
          [
            0.23136838181356592,
            -0.5104498857108437,
            0.8281965866113907
          ]
        ],
        "singular_values": [
          70.8813487236068,
          26.24675402975229,
          13.376297352457637
        ],
        "variance_share": [
          0.8527121642575242,
          0.11692024471121895,
          0.030367591031256896
        ],
        "pc_feature_correlations": [
          [
            -0.8652947621600231,
            -0.5098476330999836,
            0.02257404406227288
          ],
          [
            0.41472140102920957,
            -0.7073809195569869,
            0.5902314587973716
          ],
          [
            -0.2763738889201454,
            0.524783786600004,
            0.7855258469750144
          ]
        ],
        "probe": [
          [
            -0.2671709976779283,
            -0.502593963213174,
            1.2057247936368063
          ],
          [
            1.2045527030214194,
            -1.627495388485524,
            -0.5880127592320414
          ],
          [
            -0.2290951111031303,
            1.189571769938149,
            2.5820431138527553
          ],
          [
            -4.683753385137379e-17,
            5.377642775528102e-17,
            -3.729655473350135e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999999,
          0.9999999999999999,
          1.0
        ]
      },
      "h2": {
        "rank": 2,
        "mean": [
          0.006739279076553888,
          -0.007663057269697997
        ],
        "pca": [
          [
            0.9026571554249124,
            -0.43036038358590306
          ],
          [
            0.43036038358590306,
            0.9026571554249124
          ]
        ],
        "singular_values": [
          85.57979462437781,
          13.391154158373217
        ],
        "variance_share": [
          0.9761005397765329,
          0.0238994602234671
        ],
        "pc_feature_correlations": [
          [
            -0.8749809856458481,
            -0.4816818127965835,
            0.09466428126120632
          ],
          [
            -0.4255165499646462,
            0.6847337364864522,
            -0.6096243639690011
          ]
        ],
        "probe": [
          [
            -1.0437135309110341,
            0.701934134009922,
            -0.8677698943423305
          ],
          [
            -1.0833025894738342,
            2.0709765812303558,
            -1.9181201845847091
          ],
          [
            -0.0028273114414743413,
            0.007871483972753964,
            0.01108430545575327
          ]
        ],
        "probe_r2": [
          0.9594321316288887,
          0.6886301924605188,
          0.37628171458220994
        ],
        "population_linear_probe_r2": [
          0.9585423449436037,
          0.6786556536882892,
          0.36280200136810675
        ]
      },
      "history": [
        [
          0,
          5.543150396635458
        ],
        [
          25,
          0.0013449499562668125
        ],
        [
          50,
          3.2647451215447196e-07
        ],
        [
          75,
          8.806164072379857e-11
        ],
        [
          100,
          2.418631962287878e-14
        ],
        [
          125,
          6.660015136447064e-18
        ],
        [
          145,
          9.451973794573892e-21
        ]
      ],
      "null_direction": [
        -0.20361152977274266,
        0.5668724250761457,
        0.7982468281376964
      ],
      "intervention_delta": 0.25,
      "intervention_effects": [
        0.49999999999101796,
        0.25000000001709877,
        -0.049999999984092616
      ],
      "basis_transform": [
        [
          1.0,
          2.0
        ],
        [
          0.0,
          0.3
        ]
      ],
      "transformed": {
        "rank": 2,
        "mean": [
          -0.00858683546284222,
          -0.002298917180909402
        ],
        "pca": [
          [
            0.9961204548187906,
            0.08800022438383706
          ],
          [
            -0.08800022438383706,
            0.9961204548187906
          ]
        ],
        "singular_values": [
          30.2533917664767,
          11.364136274401213
        ],
        "variance_share": [
          0.8763479555973538,
          0.12365204440264621
        ],
        "pc_feature_correlations": [
          [
            -0.4966770765476662,
            0.6437288087798525,
            -0.6006193833139253
          ],
          [
            0.8318395874848765,
            0.5405633626239662,
            -0.14895112516296632
          ]
        ],
        "probe": [
          [
            -1.0437135309110346,
            0.7019341340099227,
            -0.8677698943423312
          ],
          [
            3.3470815744941165,
            2.2236943773683726,
            -0.6086013196668245
          ],
          [
            -0.0028273114414744116,
            0.007871483972753945,
            0.011084305455753257
          ]
        ],
        "probe_r2": [
          0.9594321316288887,
          0.6886301924605188,
          0.3762817145822096
        ],
        "population_linear_probe_r2": [
          0.9585423449436037,
          0.6786556536882897,
          0.3628020013681067
        ]
      },
      "basis_change_max_prediction_error": 1.7763568394002505e-15
    },
    {
      "seed": 7,
      "width": 3,
      "steps": 134,
      "train_mse": 7.400410852836707e-21,
      "test_mse": 7.766606163295743e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.0004920613429930297,
          0.11949821500338796,
          -0.10965514214488703
        ],
        [
          -0.3562367355029097,
          -0.18186831406868903,
          -0.396658621998585
        ],
        [
          0.024057441038975395,
          0.5360860982218134,
          -0.19688260742053187
        ]
      ],
      "W1": [
        [
          0.1434815924868137,
          0.11811148679124842,
          -0.1109080201327348
        ],
        [
          -0.3221309167404397,
          -0.05773153243891553,
          -0.3957089652085548
        ],
        [
          1.073834949287198,
          0.5572005216262719,
          -0.20452981273765955
        ]
      ],
      "W2": [
        [
          -0.3528671795592079,
          0.6062838089832764,
          -0.6200165356928417
        ],
        [
          -0.01507096418955049,
          -0.1404565948591388,
          -0.42288249897389907
        ],
        [
          0.19062209537173094,
          -0.18764505045965463,
          -0.8168215572357507
        ]
      ],
      "W3": [
        [
          -1.139754994960449,
          -0.5596558690546899,
          -0.925870938502886
        ]
      ],
      "B": [
        [
          -0.9117281292151008,
          -0.42215289770804515,
          -0.07396427248123012
        ],
        [
          -0.411023001118094,
          -0.2293016285403134,
          0.1437435029333465
        ],
        [
          -0.7893345015574585,
          -0.42178570235011215,
          0.22017566969417648
        ]
      ],
      "effective_weights": [
        1.9999999999607825,
        1.000000000078154,
        -0.19999999998127832
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.0028207197826511264,
          -0.007197270286771025,
          -0.007573141243490484
        ],
        "pca": [
          [
            0.14862666125302829,
            -0.2258927517205942,
            0.9627474125048974
          ],
          [
            0.21892597286357318,
            0.9569191493330265,
            0.19072797394586594
          ],
          [
            0.9643555018614843,
            -0.18242315192939393,
            -0.1916774886877164
          ]
        ],
        "singular_values": [
          58.910906618623905,
          20.73033052994398,
          0.877473351279132
        ],
        "variance_share": [
          0.8896397600082971,
          0.1101628656733345,
          0.00019737431836832928
        ],
        "pc_feature_correlations": [
          [
            0.8881344871999658,
            0.4593378281256674,
            -0.08192230115263326
          ],
          [
            -0.18120889047669048,
            0.18462016475589996,
            -0.9733085918884713
          ],
          [
            -0.418448004740762,
            0.8759770120898539,
            0.1939365612259053
          ]
        ],
        "probe": [
          [
            -20.010564040303567,
            42.2795482164907,
            10.121474572410467
          ],
          [
            3.2424489628269613,
            -7.7313118714169695,
            -4.038707017762827
          ],
          [
            4.577650089713156,
            -7.968479228722117,
            -2.5639300395929636
          ],
          [
            -9.367506770274758e-17,
            1.4072944198861848e-16,
            3.8163916471489756e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999938,
          1.000000000000003,
          1.0000000000000004
        ]
      },
      "h2": {
        "rank": 3,
        "mean": [
          0.0013272237883868764,
          0.0042559639377233735,
          0.006998745654381685
        ],
        "pca": [
          [
            0.6972245787569534,
            0.33450077650170285,
            0.6340245399800757
          ],
          [
            0.7128692702208048,
            -0.4166455535795608,
            -0.5641133629486523
          ],
          [
            0.07546714750171395,
            0.8452903129707208,
            -0.5289508450185283
          ]
        ],
        "singular_values": [
          66.47046913469649,
          11.012491988914437,
          0.12761613024955373
        ],
        "variance_share": [
          0.9732815936662167,
          0.026714818831676514,
          3.5875021067692166e-06
        ],
        "pc_feature_correlations": [
          [
            -0.8889079217438752,
            -0.4583808725174524,
            0.07924058297665841
          ],
          [
            -0.1620365928138782,
            0.15077181118486693,
            -0.9815161808206739
          ],
          [
            0.4240242104990891,
            -0.8816635907637326,
            -0.15711477272046429
          ]
        ],
        "probe": [
          [
            10.022328777257751,
            -22.69276702735787,
            -7.541772400948459
          ],
          [
            122.67620692823066,
            -256.05741941804405,
            -50.726748591503174
          ],
          [
            -76.72334312563316,
            159.5459501236039,
            35.125674134880335
          ],
          [
            -1.1879386363489175e-14,
            1.5681900222830336e-14,
            -8.194833700514437e-15
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000073,
          0.9999999999999843,
          1.0000000000000022
        ]
      },
      "history": [
        [
          0,
          6.125605242233615
        ],
        [
          25,
          0.010091918010755922
        ],
        [
          50,
          6.885405493628909e-07
        ],
        [
          75,
          4.789586910668776e-11
        ],
        [
          100,
          3.3347808638489486e-15
        ],
        [
          125,
          2.3219491490674174e-19
        ],
        [
          134,
          7.400410852836707e-21
        ]
      ]
    },
    {
      "seed": 11,
      "width": 3,
      "steps": 123,
      "train_mse": 6.89736866840617e-21,
      "test_mse": 7.195043862405161e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.013677106901273668,
          0.5438990161239847,
          0.489888431434373
        ],
        [
          -0.204122830715067,
          -0.11918780444257884,
          -0.2109536772133701
        ],
        [
          0.22789054302878406,
          -0.02242577561824704,
          0.29875424650261756
        ]
      ],
      "W1": [
        [
          0.5643962163901695,
          0.6561592047950079,
          0.15972779938805948
        ],
        [
          -0.9927101863753626,
          -0.28089895171332396,
          0.2595182767454561
        ],
        [
          0.2993021182355155,
          -0.012797787471529053,
          0.24731752815534763
        ]
      ],
      "W2": [
        [
          -0.8490477493793739,
          0.9716454176487703,
          -0.08840571787994203
        ],
        [
          0.3852556704433181,
          -0.32154115039136805,
          -0.09017076600444861
        ],
        [
          0.04212796666971765,
          0.6745060278939786,
          -0.15851194867046908
        ]
      ],
      "W3": [
        [
          -0.8768003756485215,
          0.48213260894306403,
          -0.6710261148826001
        ]
      ],
      "B": [
        [
          -1.4702216595547835,
          -0.8289132777316601,
          0.09467893219120951
        ],
        [
          0.5096457168053797,
          0.3442636127379567,
          -0.044210575770731175
        ],
        [
          -0.693255101672048,
          -0.15979678081932153,
          0.14257286609404762
        ]
      ],
      "effective_weights": [
        1.9999999999617988,
        1.0000000000726184,
        -0.199999999973237
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.00015948590812337295,
          0.007639837074837129,
          0.004505210246554696
        ],
        "pca": [
          [
            -0.6108754762281842,
            0.7676178738296595,
            -0.19389159940601444
          ],
          [
            0.75256366621295,
            0.6390463085538362,
            0.15895830843286984
          ],
          [
            -0.24592494960681138,
            0.04881204053252697,
            0.9680590394495256
          ]
        ],
        "singular_values": [
          61.31620301651861,
          21.113201566015547,
          13.561337083825768
        ],
        "variance_share": [
          0.8565444576230242,
          0.1015564684246444,
          0.04189907395233136
        ],
        "pc_feature_correlations": [
          [
            -0.8836000901545666,
            -0.4766058685166302,
            0.025593425639702613
          ],
          [
            -0.31733363737553405,
            0.6482365174929597,
            0.667883608619078
          ],
          [
            0.34670399926641055,
            -0.6250823612585746,
            0.7161591522844317
          ]
        ],
        "probe": [
          [
            -0.3478158004905902,
            1.6993240154725326,
            0.5088583667181393
          ],
          [
            -0.8640128212681184,
            0.4825687569162015,
            1.0705940737580502
          ],
          [
            1.1312702862309871,
            -1.603868114821369,
            2.5913345024448318
          ],
          [
            9.443400922348744e-17,
            2.17653586126465e-17,
            -3.344763702117781e-17
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999996,
          1.0000000000000002,
          0.9999999999999996
        ]
      },
      "h2": {
        "rank": 3,
        "mean": [
          0.0068895151879520625,
          -0.002801317410328356,
          0.004445705320775711
        ],
        "pca": [
          [
            0.8771445682628092,
            -0.3181878882676131,
            0.35968579917317706
          ],
          [
            -0.2745019341829927,
            0.28236088783167107,
            0.9191958535332427
          ],
          [
            0.394038189135071,
            0.905002097667573,
            -0.16032812828835286
          ]
        ],
        "singular_values": [
          89.58335505569296,
          9.586277046743499,
          1.2969209859425603
        ],
        "variance_share": [
          0.9884737625830764,
          0.011319062327624408,
          0.00020717508929924203
        ],
        "pc_feature_correlations": [
          [
            -0.8817873618190671,
            -0.47548558358115234,
            0.06168675505202962
          ],
          [
            -0.3925175376465783,
            0.8105699085820441,
            0.40034149612393016
          ],
          [
            -0.26016080162338856,
            0.38115682992286526,
            -0.8993790958530934
          ]
        ],
        "probe": [
          [
            -3.482534649613957,
            3.4820788862493917,
            -13.030950186464247
          ],
          [
            -8.541094403775574,
            11.933119130395028,
            -28.15601142829942
          ],
          [
            -0.3358566091191868,
            1.3879959220943583,
            6.9365440951892445
          ],
          [
            -7.494005416219807e-16,
            1.1102230246251565e-15,
            1.942890293094024e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0000000000000002,
          1.0000000000000007,
          1.000000000000001
        ]
      },
      "history": [
        [
          0,
          5.088889618141541
        ],
        [
          25,
          0.0054269736270186626
        ],
        [
          50,
          1.2226666971879728e-07
        ],
        [
          75,
          3.0023316733444997e-12
        ],
        [
          100,
          8.708989498999322e-17
        ],
        [
          123,
          6.89736866840617e-21
        ]
      ]
    },
    {
      "seed": 23,
      "width": 3,
      "steps": 214,
      "train_mse": 9.809870179900682e-21,
      "test_mse": 9.942736927868586e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.2213042355554955,
          0.08704024368778956,
          -0.023195995146610474
        ],
        [
          -0.9275744378886263,
          0.1725976670835402,
          -0.8505119137803527
        ],
        [
          0.3639684868090537,
          0.24238622920256547,
          0.3320226594313664
        ]
      ],
      "W1": [
        [
          0.22356666427289215,
          0.13418414320602903,
          -0.13600027390668187
        ],
        [
          -1.3802002850339237,
          -0.36788494733941934,
          -0.09668589872327754
        ],
        [
          0.6975998107591194,
          0.6551488841194639,
          -0.26877969885714026
        ]
      ],
      "W2": [
        [
          0.19960366316584707,
          0.3224179282141115,
          -0.5007698870725777
        ],
        [
          -0.3260152788600485,
          0.8428624425489776,
          -0.6909974826056828
        ],
        [
          -0.13355834547692846,
          -0.21469371734922318,
          -0.2958220131082453
        ]
      ],
      "W3": [
        [
          -0.4893628982396077,
          -0.956528761315292,
          -0.17359992250010778
        ]
      ],
      "B": [
        [
          -0.7497135697262213,
          -0.4199078887358684,
          0.07627735942688076
        ],
        [
          -1.718244844947978,
          -0.806528715815887,
          0.14857134975058253
        ],
        [
          0.060095755733613414,
          -0.13274628704055366,
          0.11843277817808366
        ]
      ],
      "effective_weights": [
        1.9999999999673204,
        1.00000000007246,
        -0.1999999999362561
      ],
      "h1": {
        "rank": 3,
        "mean": [
          -0.0034983698934372607,
          0.001427637301856623,
          -0.008587203212524793
        ],
        "pca": [
          [
            -0.1541732517548368,
            0.8295639103064678,
            -0.5367069285563422
          ],
          [
            0.21624996306890304,
            0.5583625221213893,
            0.8009165046138952
          ],
          [
            0.9640884616652342,
            0.007417048421308581,
            -0.265477730660555
          ]
        ],
        "singular_values": [
          78.89709189907008,
          21.77691940810173,
          3.5198223393237456
        ],
        "variance_share": [
          0.927492740901579,
          0.07066126624846304,
          0.0018459928499580814
        ],
        "pc_feature_correlations": [
          [
            -0.9149927236146649,
            -0.4108620382262798,
            0.03288776972586818
          ],
          [
            -0.3394225469390017,
            0.7164762003003831,
            -0.6267799836816945
          ],
          [
            0.22930596947089088,
            -0.5901187941604801,
            -0.7546001258180541
          ]
        ],
        "probe": [
          [
            2.4762101922459894,
            -6.692086715669574,
            -9.885082072746828
          ],
          [
            -0.8095271213749367,
            0.53094267927083,
            -0.8069041811640791
          ],
          [
            -0.9617370963063744,
            3.1951481450202177,
            1.5715105241170906
          ],
          [
            -4.683753385137379e-17,
            -6.852157730108388e-17,
            1.734723475976807e-18
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999981,
          0.9999999999999958,
          1.0000000000000058
        ]
      },
      "h2": {
        "rank": 3,
        "mean": [
          0.0040622211982719115,
          0.008277559702159465,
          0.002701015476770428
        ],
        "pca": [
          [
            0.41223051952350726,
            0.911064780435593,
            0.005192747175076466
          ],
          [
            0.22670605388774095,
            -0.10809489776824523,
            0.9679462062568981
          ],
          [
            0.882423007351932,
            -0.3978397402551907,
            -0.25110391707349855
          ]
        ],
        "singular_values": [
          97.08300342126194,
          8.65828036384434,
          1.2384880702390746
        ],
        "variance_share": [
          0.9919487668089981,
          0.007889802357147733,
          0.00016143083385419156
        ],
        "pc_feature_correlations": [
          [
            -0.8961105711095307,
            -0.4468734183649327,
            0.06392800591230421
          ],
          [
            0.3844622157446382,
            -0.7054555959418276,
            0.6130789286870503
          ],
          [
            0.22414587809259096,
            -0.5791981974965181,
            -0.7647408803889154
          ]
        ],
        "probe": [
          [
            6.721057875367919,
            -18.83607763525685,
            -24.52299494714553
          ],
          [
            -3.5118693593080055,
            8.27968076458797,
            11.062354043535649
          ],
          [
            0.07682521436858053,
            1.744811870980711,
            10.360311115011532
          ],
          [
            -6.765421556309548e-17,
            1.942890293094024e-16,
            5.93275428784068e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.000000000000005,
          0.9999999999999984,
          1.0000000000000002
        ]
      },
      "history": [
        [
          0,
          5.584587645555462
        ],
        [
          25,
          0.17031700388600987
        ],
        [
          50,
          0.0002742959747726826
        ],
        [
          75,
          4.890388718214581e-07
        ],
        [
          100,
          1.25744817565148e-09
        ],
        [
          125,
          4.1555587337902975e-12
        ],
        [
          150,
          1.523451479948253e-14
        ],
        [
          175,
          5.775064714010783e-17
        ],
        [
          200,
          2.210872054401712e-19
        ],
        [
          214,
          9.809870179900682e-21
        ]
      ]
    },
    {
      "seed": 42,
      "width": 3,
      "steps": 129,
      "train_mse": 9.448862670940954e-21,
      "test_mse": 9.311037468359937e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          0.12188683190177255,
          -0.41599364249619825,
          0.30018047832258293
        ],
        [
          0.3762258865564856,
          -0.7804140754615346,
          -0.5208718027449273
        ],
        [
          0.05113616126691415,
          -0.1264970369374329,
          -0.006720463001715519
        ]
      ],
      "W1": [
        [
          -0.55311138471807,
          -0.8700338721207793,
          0.08007829451302065
        ],
        [
          0.952824155505303,
          -0.40169055986230773,
          -0.3634812801566296
        ],
        [
          0.6521126612746765,
          0.27041791337914595,
          0.16973681274327637
        ]
      ],
      "W2": [
        [
          -0.9472844649217396,
          0.5187899047903444,
          0.7544143048565219
        ],
        [
          -0.040308273717736286,
          0.46725206176443,
          0.2421800682998264
        ],
        [
          -0.33748527284777396,
          0.14561234549939345,
          -0.38300125858742967
        ]
      ],
      "W3": [
        [
          1.2373691958220925,
          0.2065782457625795,
          0.027548482884201114
        ]
      ],
      "B": [
        [
          1.5102324950749875,
          0.8197837058522545,
          -0.1363754635008621
        ],
        [
          0.6254327050970996,
          -0.08713135009416705,
          -0.13195832247687841
        ],
        [
          0.07564993670939457,
          0.13156211296417195,
          -0.14496201973093387
        ]
      ],
      "effective_weights": [
        1.9999999999834628,
        1.0000000000222835,
        -0.20000000009239002
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.005302347217003973,
          -0.00741940690836157,
          0.00148279746508166
        ],
        "pca": [
          [
            0.6284870695802475,
            -0.5817822072628693,
            -0.516268793055301
          ],
          [
            0.6303071131081164,
            0.7698488933533303,
            -0.10022786323156585
          ],
          [
            0.45575974650658424,
            -0.26241597648580184,
            0.8505415385207578
          ]
        ],
        "singular_values": [
          61.605015754974964,
          42.44810455971026,
          13.127783861760223
        ],
        "variance_share": [
          0.6578163112372593,
          0.3123123059374936,
          0.029871382825247043
        ],
        "pc_feature_correlations": [
          [
            -0.9299223507302616,
            -0.35444094737476645,
            0.11216167729794556
          ],
          [
            0.3131934864338549,
            -0.9112507240129206,
            -0.22934584981878434
          ],
          [
            0.20396507614757914,
            -0.22691562976927784,
            0.9608993334996748
          ]
        ],
        "probe": [
          [
            0.08096530484271923,
            -1.0722532343964737,
            1.3972100572333155
          ],
          [
            0.455326725965834,
            -0.39286750774245666,
            -1.1234210673514533
          ],
          [
            0.9368573331088171,
            -0.3354356278372397,
            2.8265599316403343
          ],
          [
            3.122502256758253e-17,
            -4.7704895589362195e-17,
            1.491862189340054e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999997,
          1.0000000000000009,
          0.9999999999999999
        ]
      },
      "h2": {
        "rank": 3,
        "mean": [
          -0.007753300931015946,
          -0.0033213576466024244,
          -0.0034377346347616846
        ],
        "pca": [
          [
            0.9526140484545782,
            0.2949075059739112,
            0.07453883288076336
          ],
          [
            -0.27899618339544574,
            0.9447326983896517,
            -0.17216636792411774
          ],
          [
            -0.1211924268993472,
            0.1432120508674305,
            0.9822437091417744
          ]
        ],
        "singular_values": [
          83.96064390116304,
          16.275431542833857,
          6.70900334864973
        ],
        "variance_share": [
          0.9578899061329933,
          0.035993916194270614,
          0.006116177672736151
        ],
        "pc_feature_correlations": [
          [
            0.899596106186211,
            0.43568123581344126,
            -0.08278361936195651
          ],
          [
            0.4060931633213924,
            -0.8939582848506011,
            -0.13826924672221944
          ],
          [
            -0.15422238414260026,
            0.13451608123422534,
            -0.9846882436602787
          ]
        ],
        "probe": [
          [
            0.3019831401954647,
            0.8123783758901211,
            0.8948773019469438
          ],
          [
            1.0159157113605735,
            -2.100484124847476,
            -1.3761547391268611
          ],
          [
            -1.2088795678200184,
            1.1478032953937127,
            -6.48752161242787
          ],
          [
            -1.9081958235744878e-16,
            3.469446951953614e-16,
            -7.667477763817487e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          1.0,
          1.0000000000000004,
          1.0000000000000002
        ]
      },
      "history": [
        [
          0,
          5.279762299134211
        ],
        [
          25,
          0.07919699667875085
        ],
        [
          50,
          1.5565676305346906e-06
        ],
        [
          75,
          4.907647688480211e-11
        ],
        [
          100,
          1.5593159170466572e-15
        ],
        [
          125,
          4.954982857796924e-20
        ],
        [
          129,
          9.448862670940954e-21
        ]
      ]
    },
    {
      "seed": 101,
      "width": 3,
      "steps": 168,
      "train_mse": 7.68232246396871e-21,
      "test_mse": 7.707966464162172e-21,
      "price_r2": 1.0,
      "initial_W1": [
        [
          -0.31606099998520587,
          -0.8138501927327492,
          0.2413206987699059
        ],
        [
          0.29771781195196473,
          -0.12387471994650855,
          0.1469285491782161
        ],
        [
          0.684157716591058,
          0.42431913602632554,
          0.2830556083224302
        ]
      ],
      "W1": [
        [
          -0.5047821290878268,
          -0.7254484135021987,
          0.37475105008639303
        ],
        [
          0.4266694219031143,
          -0.11458419781792757,
          0.09559615208517615
        ],
        [
          1.1737917057802092,
          0.3796129368105004,
          0.04371081662542786
        ]
      ],
      "W2": [
        [
          0.3488527439376341,
          -0.38046449978551883,
          0.27884003241202376
        ],
        [
          -0.4114894948781065,
          -0.2524429885127724,
          -0.5357109452321007
        ],
        [
          -0.8962178155622331,
          0.10183782147327686,
          1.0233155545503856
        ]
      ],
      "W3": [
        [
          -0.13090102021277758,
          -0.5021443352051431,
          1.0212134084510134
        ]
      ],
      "B": [
        [
          -0.011127081716396094,
          -0.10362816652505918,
          0.10655031545623135
        ],
        [
          -0.5288102248595099,
          0.1240775733645529,
          -0.20175506151906822
        ],
        [
          1.6970051318089387,
          1.0269546103177252,
          -0.2813933050635979
        ]
      ],
      "effective_weights": [
        1.9999999999738955,
        1.0000000000569456,
        -0.1999999999357413
      ],
      "h1": {
        "rank": 3,
        "mean": [
          0.010628709617209997,
          0.0016146439238263158,
          -0.002200061788116859
        ],
        "pca": [
          [
            -0.5414393897256368,
            0.21375585717705203,
            0.8131124281278904
          ],
          [
            0.7819233192132765,
            0.4834075571321481,
            0.3935899599558172
          ],
          [
            -0.30893253328845555,
            0.848896676415942,
            -0.42887658206755064
          ]
        ],
        "singular_values": [
          69.18901805018153,
          29.09346087529754,
          2.938380067414153
        ],
        "variance_share": [
          0.848451667082988,
          0.15001806063504147,
          0.0015302722819706715
        ],
        "pc_feature_correlations": [
          [
            0.8842752023783323,
            0.46666134725065217,
            -0.08301324561914002
          ],
          [
            0.42018654700090147,
            -0.7249591266104773,
            0.5635791232169454
          ],
          [
            0.1979147752694459,
            -0.5371589582310488,
            -0.8027871456035719
          ]
        ],
        "probe": [
          [
            -0.6445269529370053,
            1.4601609060960703,
            4.626873560000872
          ],
          [
            2.7151013519067124,
            -7.209421172273285,
            -10.298913130998166
          ],
          [
            -0.41216547143929416,
            3.248534366057191,
            5.733380433113179
          ],
          [
            7.632783294297951e-17,
            -1.6653345369377348e-16,
            -2.8449465006019636e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999998,
          0.999999999999999,
          1.0
        ]
      },
      "h2": {
        "rank": 3,
        "mean": [
          0.002480074521362744,
          -0.003602610709025403,
          -0.01161256454447563
        ],
        "pca": [
          [
            -0.03415242050946016,
            -0.18701890850596847,
            0.9817624661976956
          ],
          [
            -0.2736480354651334,
            0.9465448942431511,
            0.17079085417051798
          ],
          [
            0.961223368868765,
            0.26282444909760233,
            0.0835041561667664
          ]
        ],
        "singular_values": [
          94.58920333617037,
          20.876497881905664,
          1.4638996404640483
        ],
        "variance_share": [
          0.9533332942504907,
          0.04643836457349588,
          0.00022834117601333971
        ],
        "pc_feature_correlations": [
          [
            0.8650359806106706,
            0.49747852701800643,
            -0.10418763905629011
          ],
          [
            -0.44622299826106404,
            0.6875785924887347,
            -0.5908809433345779
          ],
          [
            -0.21740613190477806,
            0.5624782978927436,
            0.7793186638630055
          ]
        ],
        "probe": [
          [
            -5.501391245312318,
            15.684992711536365,
            24.06555621853876
          ],
          [
            -2.56301588162105,
            5.674042412704342,
            5.250774926974059
          ],
          [
            -0.24546975540076188,
            1.8709547662725559,
            1.7940092362412479
          ],
          [
            4.163336342344337e-17,
            -9.71445146547012e-17,
            -1.1102230246251565e-16
          ]
        ],
        "probe_r2": [
          1.0,
          1.0,
          1.0
        ],
        "population_linear_probe_r2": [
          0.9999999999999964,
          0.9999999999999987,
          1.0000000000000022
        ]
      },
      "history": [
        [
          0,
          6.214279731075238
        ],
        [
          25,
          0.003053889681207317
        ],
        [
          50,
          2.552994336233709e-06
        ],
        [
          75,
          2.139525959694471e-09
        ],
        [
          100,
          1.7936704290027458e-12
        ],
        [
          125,
          1.5037630812279713e-15
        ],
        [
          150,
          1.2607152093050107e-18
        ],
        [
          168,
          7.68232246396871e-21
        ]
      ]
    }
  ]
}