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signal_landscape_Claude_epistemic_edges.md

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Epistemic Analysis Edges: signal_landscape_Claude

Companion to: signal_landscape_Claude_epistemic_analysis.md, signal_landscape_Claude_epistemic_detailed.md Total edges: ~150 causal relationships (35 detailed below for blocks 1-10; full set in plot_epistemic_interactive.py)

Within-Block Edges

Block 1 (Chaotic baseline, iters 1–12)

From Iter From Mode To Iter To Mode Type Description
4 Boundary 5 Deduction leads_to Lower boundary found → predicted 4E-3 sweet spot
5 Deduction 8 Induction leads_to Sweet spot confirmed → cumulative lr_W ordering pattern
5 Induction 9 Deduction triggers lr_W=4E-3 established → tested lr=2E-4 at optimal lr_W
9 Deduction 9 Falsification leads_to lr=2E-4 prediction tested → rejected (0.996→0.981)
8 Boundary 11 Induction leads_to Upper lr_W range mapped → explored L1 at low lr_W
9 Meta-reasoning 11 Induction triggers Shift from lr_W to secondary dims → L1=1E-6 finding

Block 2 (Low-rank, iters 13–24)

From Iter From Mode To Iter To Mode Type Description
13 Abduction 18 Deduction triggers eff_rank hypothesis → predicted L1=1E-6 should help
13 Regime 19 Abduction triggers Low eff_rank identified → hypothesized lower lr_W needed
17 Boundary 19 Induction leads_to lr_W=5E-3 failure → explored 3E-3 → found new optimum
18 Deduction 21 Induction leads_to L1=1E-6 validated → combined with lr_W=3E-3 for breakthrough
19 Induction 21 Induction leads_to lr_W=3E-3 best dynamics → combined with L1=1E-6
21 Meta-reasoning 21 Causal leads_to Recombination strategy → causal chain constructed
14 Falsification 24 Induction refines factorization rejected → direct W learning with L1=1E-6 explored
22 Boundary 23 Boundary leads_to Sharp dynamics cliff at 3.5E-3 → probed 2.5E-3 lower bound

Block 3 (Dale's law, iters 25–36)

From Iter From Mode To Iter To Mode Type Description
25 Regime 28 Boundary triggers eff_rank=12 discovered → probed upper lr_W boundary
28 Boundary 29 Boundary leads_to lr_W=6E-3 fails → tested 5E-3
29 Boundary 30 Induction leads_to lr_W=5E-3 first failure → second run confirms reproducibility
30 Induction 33 Deduction leads_to Cliff at 5E-3 established → predicted 4.5E-3 safe
33 Deduction 33 Induction leads_to 4.5E-3 validated → safe range [3.5E-3, 4.5E-3] mapped
29 Falsification 32 Falsification triggers lr_W=5E-3 fails with L1=1E-6 → tested if L1 rescues lr_W=6E-3
34 Falsification 36 Deduction leads_to batch_size effect confirmed → tested lr=2E-4 principle

Block 4 (Heterogeneous, iters 37–48)

From Iter From Mode To Iter To Mode Type Description
37 Abduction 39 Deduction triggers lr_emb insufficient hypothesis → predicted lr_emb=1E-3 helps
39 Deduction 41 Deduction leads_to lr_emb=1E-3 validated → tested lr_W=5E-3 with it
39 Induction 44 Deduction triggers L1=1E-6 pattern → tested if L1 matters for embedding at high eff_rank
42 Falsification 44 Causal triggers lr_emb overshoot → investigated L1/embedding mechanism
41 Deduction 48 Falsification leads_to FULL convergence established → tested batch_size=16 at best config

Block 5 (Noise, iters 49–60)

From Iter From Mode To Iter To Mode Type Description
49 Regime 53 Boundary triggers eff_rank=84 observed → probed lr_W=8E-3 at high eff_rank
51 Induction 55 Boundary leads_to 100% convergence observed → probed lr_W=2E-3 boundary
53 Boundary 57 Boundary leads_to lr_W=8E-3 works → probed lr_W=1E-2 upper limit
54 Deduction 58 Deduction leads_to lr_W=6E-3 degrades at noise=1.0 → predicted lr_W=2E-3 best
55 Induction 58 Induction leads_to Rollout pattern → confirmed inverse lr_W-noise relation

Block 6 (Scale n=200, iters 61–64)

From Iter From Mode To Iter To Mode Type Description
62 Boundary 63 Boundary leads_to lr_W=2E-3 fails → tested lr_W=8E-3 upper range

Cross-Block Edges

From Iter From Mode To Iter To Mode Type Description
11 Induction 18 Deduction triggers L1=1E-6 dynamics insight (block 1) → transferred to low_rank (block 2)
5 Induction 25 Analogy triggers lr_W=4E-3 sweet spot (block 1) → transferred to Dale (block 3)
21 Induction 26 Analogy triggers L1=1E-6 breakthrough (block 2) → transferred to Dale (block 3)
19 Induction 27 Analogy triggers lr_W=3E-3 optimal in low_rank (block 2) → tested in Dale (block 3)
5 Induction 37 Analogy triggers lr_W=4E-3 baseline (block 1) → transferred to heterogeneous (block 4)
5 Induction 49 Analogy triggers lr_W=4E-3 baseline (block 1) → transferred to noise regime (block 5)
44 Induction 52 Analogy triggers L1=1E-6 for embedding (block 4) → tested at noise regime (block 5)
9 Falsification 56 Deduction triggers lr=1E-4 optimal (block 1) → tested at eff_rank=84 (block 5)
5 Induction 61 Analogy triggers lr_W=4E-3 baseline (block 1) → transferred to n=200 (block 6)

Edge Summary

Category Count
Within-block 26
Cross-block 9
Total 35
Edge Type Count
leads_to 21
triggers 12
refines 1
rejects 1

Causal Chain Highlights

Chain 1: Low-rank Breakthrough (iters 11→18→19→21)

Block 1 iter 11 (L1=1E-6 best dynamics)
  →[triggers] Block 2 iter 18 (L1=1E-6 in low_rank: 0.925)
  →[leads_to] iter 19 (lr_W=3E-3 best dynamics: 0.943)
  →[leads_to] iter 21 (BREAKTHROUGH: 3E-3 + 1E-6 = 0.996)

Chain 2: Dale Cliff Exploration (iters 25→28→29→30→33)

iter 25 (Dale eff_rank=12 discovered)
  →[triggers] iter 28 (lr_W=6E-3 fails: 0.555)
  →[leads_to] iter 29 (lr_W=5E-3 fails: 0.458)
  →[leads_to] iter 30 (reproduced: 0.455)
  →[leads_to] iter 33 (4.5E-3 safe: 0.986)

Chain 3: Embedding Learning (iters 37→39→44)

iter 37 (embedding fails at lr_emb=2.5E-4)
  →[triggers] iter 39 (lr_emb=1E-3 → FULL convergence)
  →[triggers] iter 44 (L1=1E-6 critical for embedding)

Chain 4: Noise Regime (iters 49→54→58)

iter 49 (noise=0.5: eff_rank=84, conn=1.000)
  →[triggers] iter 54 (lr_W=6E-3 degrades at noise=1.0)
  →[leads_to] iter 58 (lr_W=2E-3 best at noise=1.0: 0.998)