{ "rows": [ { "metric": "l2", "transformation": "identity_replay", "adjusted_rand": 1.0, "adjusted_rand_core_atoms_only": 1.0, "n_modules_original": 3, "n_modules_transformed": 3, "exact_set_recovery": 1.0, "mean_best_jaccard": 1.0, "median_best_jaccard": 1.0, "mean_best_jaccard_modules_le8": 1.0, "mean_best_jaccard_modules_gt8": null, "module_sizes": [ 2, 2, 2 ], "per_module_best_jaccard": [ 1.0, 1.0, 1.0 ], "note": "same data and rule, fresh run; upper bound on agreement achievable under any transformation" }, { "metric": "l2", "transformation": "positive_powers_of_two_scaling", "gram_max_relative_change": 0.0, "adjusted_rand": 1.0, "adjusted_rand_core_atoms_only": 1.0, "n_modules_original": 3, "n_modules_transformed": 3, "exact_set_recovery": 1.0, "mean_best_jaccard": 1.0, "median_best_jaccard": 1.0, "mean_best_jaccard_modules_le8": 1.0, "mean_best_jaccard_modules_gt8": null, "module_sizes": [ 2, 2, 2 ], "per_module_best_jaccard": [ 1.0, 1.0, 1.0 ], "note": "c_j -> a_j c_j, v_j -> v_j/a_j applied to the cached coefficients, output weights and (Fisher) score projections; z_j preserved" }, { "metric": "l2", "transformation": "positive_half_split_32_atoms", "cluster_count_mode": "free_C", "adjusted_rand": -0.0036128001617856094, "adjusted_rand_unsplit_atoms_only": -0.003494733857488641, "adjusted_rand_core_atoms_only": 0.0, "n_modules_original": 3, "n_modules_transformed": 43, "exact_set_recovery": 0.0, "mean_best_jaccard": 0.0, "median_best_jaccard": 0.0, "mean_best_jaccard_modules_le8": 0.0, "mean_best_jaccard_modules_gt8": null, "module_sizes": [ 2, 2, 2 ], "per_module_best_jaccard": [ 0.0, 0.0, 0.0 ], "reference_C_original": 3, "reference_C_transformed": 31, "split_copies_co_assigned": 0.96875, "split_copies_co_assigned_core_only": null, "n_split_atoms_in_a_core_module": 0, "split_atoms_in_a_core_module_originally": 0.0, "affinity_max_relative_change_on_unsplit_atoms": { "fcm": 0.0, "cosine": 0.0 }, "collinear_collapse": null, "note": "duplicate atoms with halved output weights; ARI lifts the original labels through the duplication index. 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Each split pair is a perfectly coupled 2-clique that adds a near-zero normalized-Laplacian eigenvalue, so the eigengap rule reacts to the duplicates; matched_C removes that reaction." }, { "metric": "fisher", "transformation": "positive_half_split_32_atoms", "cluster_count_mode": "matched_C_collinear_collapsed", "adjusted_rand": 1.0, "adjusted_rand_unsplit_atoms_only": 1.0, "adjusted_rand_core_atoms_only": null, "n_modules_original": 0, "n_modules_transformed": 0, "exact_set_recovery": 0.0, "mean_best_jaccard": null, "median_best_jaccard": null, "mean_best_jaccard_modules_le8": null, "mean_best_jaccard_modules_gt8": null, "module_sizes": [], "per_module_best_jaccard": [], "reference_C_original": 2, "reference_C_transformed": 2, "split_copies_co_assigned": 0.0, "split_copies_co_assigned_core_only": null, "n_split_atoms_in_a_core_module": 0, "split_atoms_in_a_core_module_originally": 0.0, "affinity_max_relative_change_on_unsplit_atoms": { "fcm": 0.0, "cosine": 0.0 }, "collinear_collapse": { "atoms": 3104, "merged_groups": 3072, "merged_gram_max_relative_difference_from_original": 0.0, "collinear_groups_in_original_layer": 3072, "original_width": 3072 }, "note": "duplicate atoms with halved output weights; ARI lifts the original labels through the duplication index. Each split pair is a perfectly coupled 2-clique that adds a near-zero normalized-Laplacian eigenvalue, so the eigengap rule reacts to the duplicates; matched_C removes that reaction." }, { "metric": "fisher", "transformation": "baseline_raw_covariance_affinity_under_scaling", "adjusted_rand": 0.8118744351996922, "n_modules_original": 3, "n_modules_transformed": 3, "note": "naive co-activation clustering on W=|E[c_i c_j]| (no mass normalization); the same function-preserving scaling changes this affinity" } ], "settings": { "root": "results/comparison/random_gpt2", "out": "results/modules/random_gpt2", "metrics": [ "l2", "fisher" ], "bootstraps": 12, "split_atoms": 32, "seed": 17, "affinity": "square", "knn": 0, "normalization": "fcm", "cluster_rule": "reference", "clusters": null, "min_clusters": 2, "max_clusters": 32, "threshold": 0.8, "min_size": 2, "max_module_fraction": 0.5, "restarts": 5 }, "seconds": 29.21317982673645, "scope": "partition identity only; semantic and causal changes under reparameterization are not remeasured here", "ari_convention": "the rest module is treated as one additional label, so ARI scores the whole assignment including which neurons are declared unstructured" }