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"gini_we_init": 0.03394181242552419, "gini_wl_init": 0.04096392429269691, "key_freqs": [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56 ] } }, "fmt": "json" }, "seeds.t1_ci": { "value": "1,576 [1,567, 1,586]", "fmt": "str" }, "seeds.t2_ci": { "value": "7,445 [5,874, 9,017]", "fmt": "str" }, "seeds.tgrok_ci": { "value": "8,455 [6,816, 10,093]", "fmt": "str" }, "seeds.nkey_ci": { "value": "4.364 [3.743, 4.985]", "fmt": "str" }, "seeds.neurons085_ci": { "value": "80.2 % [75.3 %, 85.2 %]", "fmt": "str" }, "seeds.logitfve_ci": { "value": "96.5 % [95.3 %, 97.7 %]", "fmt": "str" }, "seeds.patch_key_ci": { "value": "0.997 [0.995, 0.998]", "fmt": "str" }, "seeds.patch_random_ci": { "value": "0.058 [0.049, 0.067]", "fmt": "str" }, "hyp.summary": { "value": "**H1** supported (11/11 seeds; Holm-adjusted p = 0.002); **H2** supported (11/11 seeds; Holm-adjusted p = 0.002); **H3** supported (11/11 seeds; Holm-adjusted p = 0.002); **H4** not supported (6/11 seeds; Holm-adjusted p = 0.5); **H5** supported (11/11 weight-decay runs vs 0/5 without grokked; Holm-adjusted p = 0.0011).", "fmt": "str" }, "hyp.h4_key_ok": { "value": "9/11", "fmt": "str" }, "hyp.h4_nonkey_ok": { "value": "11/11", "fmt": "str" }, "hyp.h4_keep_ok": { "value": "8/11", "fmt": "str" }, "hyp.h4_key_min": { "value": 5.919525368096768, "fmt": ".1f" }, "hyp.h4_nonkey_max": { "value": 1.8375855871722213, "fmt": ".2f" }, "hyp.h4_keep_max": { "value": 2.7831531079973093, "fmt": ".2f" }, "controls.wd0": { "value": "final train accuracy 100 %, 100 %, 100 %, 100 %, 100 %, final test accuracy 6.0 %, 1.9 %, 8.1 %, 21.5 %, 16.2 %; Gini of the embedding spectrum 0.07, 0.07, 0.08, 0.07, 0.07 (initially \u2248 0.03)", "fmt": "str" }, "controls.rand": { "value": "final train accuracy 100 %, 100 %, 100 %, final test accuracy 0.9 %, 0.9 %, 0.8 %; Gini of the embedding spectrum 0.09, 0.09, 0.08 (initially \u2248 0.04)", "fmt": "str" }, "controls.split0": { "value": "final test accuracy 100.0 %, 100.0 %, 100.0 %; key frequencies split0_init100: [2, 14, 27, 30, 37, 52]; split0_init101: [9, 14, 15, 27]; split0_init102: [7, 38, 49, 53] (the paper's run: {14, 35, 41, 42, 52})", "fmt": "str" }, "seeds.same_init_diff": { "value": 2.9802322387695312e-08, "fmt": "sci" }, "seeds.same_init_cos40k": { "value": 0.7352586156787267, "fmt": ".2f" }, "seeds.same_init_keys": { "value": [ 14, 35, 41, 42, 52 ], "fmt": "g" }, "seeds.same_init_keys_equal": { "value": "the same", "fmt": "str" }, "seeds.same_init_loss_steps": { "value": 52, "fmt": "int" }, "seeds.spikes": { "value": "split0_init102 (6 spikes; test loss up to 0.64, test accuracy down to 87 %); wd1_s4 (4 spikes; test loss up to 0.25, test accuracy down to 93 %)", "fmt": "str" }, "seeds.spike_n": { "value": 2, "fmt": "int" }, "paper.neuron_linear_share": { "value": 0.7618141461388657, "fmt": "pct" }, "paper.logit_linear_share": { "value": 0.009948816856354528, "fmt": "pct" }, "paper.logit_key_product_share": { "value": 0.9696048452014524, "fmt": "pct" }, "seeds.adam_ratio_end_ci": { "value": "0.992 [0.972, 1.004]", "fmt": "str" }, "seeds.adam_cos_w_end_ci": { "value": "-0.991 [-1.000, -0.976]", "fmt": "str" }, "seeds.cos_gw_end_ci": { "value": "-0.814 [-0.965, -0.625]", "fmt": "str" }, "seeds.cos_tt_mid_ci": { "value": "-0.251 [-0.305, -0.199]", "fmt": "str" }, "seeds.cos_tt_neg_ci": { "value": "97.9 % [96.0 %, 99.6 %]", "fmt": "str" }, "seeds.dynamics_n": { "value": 11, "fmt": "int" }, "seeds.cos_gw_end_range": { "value": "-0.996 to -0.157", "fmt": "str" }, "seeds.adam_dip_ci": { "value": "0.906 [0.897, 0.914]", "fmt": "str" }, "seeds.adam_dip_near_grok": { "value": "10 of 11", "fmt": "str" } }