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"what": "Exactness of the symmetry action and of the fitted alignment map, on the real models used in the study.",
"pythia-1.4b (MHA, fused QKV)": {
"free_hidden_axes": 24, "axis_width": 8192,
"mlp_permutation_rel_logit_change": 1.057e-06,
"flat_head_permutation_rel_logit_change": 1.257,
"note": "mergeschool.core.alignment.apply_head_perms permutes q/o but not k/v; on this arch head_match finds no head-structured q tensor (QKV is fused) so it is never applied by that library -- but applying it directly destroys the model."
},
"Llama-3.1-8B (GQA, 32 heads / 8 KV groups)": {
"free_hidden_axes": 32, "axis_width": 14336,
"mlp_permutation_rel_logit_change": 1.057e-06,
"mlp_plus_GQA_group_respecting_head_permutation_rel_logit_change": 9.368e-07,
"mlp_plus_FLAT_head_permutation_rel_logit_change": 1.115,
"fit_g_recovery_on_fully_scrambled_model": {
"coord_share": 1.0, "hidden_layers_matched": 32, "head_sets_matched": 32,
"max_abs_weight_error_vs_original": 0.0,
"max_abs_logit_error_vs_original": 0.0,
"verdict": "the fitted map recovers the ground-truth group element BIT-EXACTLY"
}
},
"conclusion": "The MLP free-hidden-axis permutation is exact on both architectures. The flat head permutation in the shared library is NOT function-preserving for GQA (rel logit change 1.115 on Llama-3.1-8B); the group-respecting action implemented in gmap.py is exact (9.4e-07). With that fix, fit_g recovers a fully scrambled Llama-3.1-8B bit-exactly, so any failure of alignment to help downstream accuracy in this study is a fact about the models, not about the aligner."
}
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