{
 "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"
 }
}