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9b7bd53 | 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 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 | {
"what": "item 3(b): layer 12's measured weight step per 1,000 steps against the step decoupled weight decay alone would take, at a NAMED DEFAULT decay",
"why_not_3a": "OpenCoder publishes eta = 3e-4 constant after a 2,000-step warm-up (arXiv:2411.04905v3 s3.2) and states neither the optimiser's weight decay nor any schedule, so no comparison can be made at OpenCoder's own setting. 3(b) names a default instead of assuming one.",
"definition": {
"eta": 0.0003,
"eta_source": "OpenCoder, arXiv:2411.04905v3 s3.2 -- 3e-4, constant after a 2,000-step warm-up",
"lambda": 0.1,
"lambda_source": "Megatron-LM's DEFAULT weight decay. NOT a published OpenCoder setting and not presented as one.",
"decay_step": "under AdamW the decay is decoupled, so with no gradient W -> (1 - eta*lambda)^N W over N steps and ||dW||/||W|| = 1 - (1 - eta*lambda)^N exactly -- the same quantity B16C stores as relative_step, which is what makes the ratio meaningful",
"measured": "B16C_WEIGHT_STEPS.json, layer 12, window 1000 (~1,000 steps of gap), relative_step on each construct's rows",
"ratio": "measured relative_step / decay shrink, taken PER ROW with that row's own gap and then pooled by median over constructs and start points"
},
"fixed_before_computing": true,
"layer": 12,
"window": "1000",
"decay_shrink_per_1000_steps": 0.02955490316059306,
"per_matrix": {
"gate_proj": {
"carriers": {
"n_rows": 3211,
"n_start_points": 19,
"median_relative_step": 0.24653545589847872,
"median_decay_shrink": 0.02955490316059306,
"median_ratio": 8.341609328200947,
"ratio_iqr": [
7.680082322219295,
9.119040697315409
],
"relative_step_at_first_start": 0.26728141506552633,
"relative_step_at_last_start": 0.217385583900947,
"ratio_at_first_start": 9.043555771886446,
"ratio_at_last_start": 7.355313692612514,
"first_start_iter": 1000,
"last_start_iter": 19000
},
"random": {
"n_rows": 3211,
"n_start_points": 19,
"median_relative_step": 0.2475323047440543,
"median_decay_shrink": 0.02955490316059306,
"median_ratio": 8.375338041171482,
"ratio_iqr": [
7.711843934817122,
9.144811597311957
],
"relative_step_at_first_start": 0.2664884701100206,
"relative_step_at_last_start": 0.21775522372292128,
"ratio_at_first_start": 9.016726215003883,
"ratio_at_last_start": 7.367820579201374,
"first_start_iter": 1000,
"last_start_iter": 19000
}
},
"up_proj": {
"carriers": {
"n_rows": 3211,
"n_start_points": 19,
"median_relative_step": 0.2262124531316158,
"median_decay_shrink": 0.02955490316059306,
"median_ratio": 7.653973755300119,
"ratio_iqr": [
6.979967229727786,
8.428032765270096
],
"relative_step_at_first_start": 0.2391428266948024,
"relative_step_at_last_start": 0.19686955938821657,
"ratio_at_first_start": 8.091477254903097,
"ratio_at_last_start": 6.661147164600154,
"first_start_iter": 1000,
"last_start_iter": 19000
},
"random": {
"n_rows": 3211,
"n_start_points": 19,
"median_relative_step": 0.22633307766555014,
"median_decay_shrink": 0.02955490316059306,
"median_ratio": 7.658055126613666,
"ratio_iqr": [
6.987296942974811,
8.433419804742915
],
"relative_step_at_first_start": 0.24092294067407613,
"relative_step_at_last_start": 0.19698965828966508,
"ratio_at_first_start": 8.151708004758751,
"ratio_at_last_start": 6.665210750963334,
"first_start_iter": 1000,
"last_start_iter": 19000
}
},
"down_proj": {
"carriers": {
"n_rows": 3211,
"n_start_points": 19,
"median_relative_step": 0.22194329676229782,
"median_decay_shrink": 0.02955490316059306,
"median_ratio": 7.509525426502674,
"ratio_iqr": [
6.83867605138081,
8.773473151831679
],
"relative_step_at_first_start": 0.26121256021204836,
"relative_step_at_last_start": 0.19289148543378487,
"ratio_at_first_start": 8.838214044982402,
"ratio_at_last_start": 6.526547706337138,
"first_start_iter": 1000,
"last_start_iter": 19000
},
"random": {
"n_rows": 3211,
"n_start_points": 19,
"median_relative_step": 0.2217999272472068,
"median_decay_shrink": 0.02955490316059306,
"median_ratio": 7.504674471170085,
"ratio_iqr": [
6.825834172216856,
8.775769976230254
],
"relative_step_at_first_start": 0.26124332931101085,
"relative_step_at_last_start": 0.19263285341382963,
"ratio_at_first_start": 8.839255127702089,
"ratio_at_last_start": 6.517796805731918,
"first_start_iter": 1000,
"last_start_iter": 19000
}
}
},
"carrier_ratio_range": [
7.509525426502674,
8.341609328200947
],
"summary": "at lambda = 0.1 and eta = 0.0003, decoupled decay alone would move a weight by 2.96% per 1,000 steps, while layer 12's carrier rows move by 22.2% to 24.7% over the same gap -- 7.5 to 8.3 times as much. The decay term is too small to be what the measured step is made of, at this default; accounting for even the smallest of them would need lambda = 0.75, 7.5x Megatron's default. The carrier rows and the random rows move alike, so this says nothing about the carriers in particular -- it bounds the decay term for the layer as a whole.",
"lambda_that_would_account_for_the_smallest": 0.7509525426502675,
"minutes": 0.001174465815226237,
"provenance": {
"inputs": [
"validation/paper2/B16C_WEIGHT_STEPS.json"
],
"reference": null,
"battery_prompt_hash": "570b42db13f8fe5772b8d1a9ad7d55d6fa1279dae5948ad94e8363789bcbc1ad",
"code_commit": "f7c2832",
"design": "9-Paper-1/2610-18Oct_PAPER-1-Design.md sha256 47f6a664\u2026"
}
} |