Experiment: Parallel LLM-guided GNN connectivity recovery across 29 simulation regimes | Iterations: 348 (29 blocks × 12, 4 parallel slots) | Date: 2026-02-03
| Prior Category | Specific Priors Given |
|---|---|
| Parameter ranges | lr: 1E-4 to 1E-3, lr_W: 1E-3 to 1E-2, L1: 1E-7 to 1E-4 |
| Architecture | MLP with trainable W matrix, GNN message passing |
| Classification | conn_R2 > 0.95 = converged, test_R2 > 0.99 = dynamics-converged |
| Training dynamics | Embedding, connectivity, and dynamics as separate objectives |
| Mode | Count | Validation | First Appearance |
|---|---|---|---|
| Induction | 53 | N/A | Iter 5 |
| Boundary Probing | 50 | N/A | Iter 4 |
| Deduction | 47 | 74% | Iter 5 |
| Falsification | 43 | 100% refinement | Iter 9 |
| Analogy/Transfer | 33 | 70% | Iter 13 |
| Causal Chain | 17 | N/A | Iter 21 |
| Regime Recognition | 16 | N/A | Iter 13 |
| Constraint | 13 | N/A | Iter 85 |
| Meta-reasoning | 10 | N/A | Iter 9 |
| Abduction | 6 | N/A | Iter 13 |
| Uncertainty | 2 | N/A | Iter 8 |
| Iter | Pattern | Significance |
|---|---|---|
| 5 | lr_W=4E-3 sweet spot for chaotic n=100 | High |
| 21 | BREAKTHROUGH: lr_W=3E-3 + L1=1E-6 recombination → R2=0.996 | High |
| 58 | Inverse lr_W-noise relation (noise=1.0 → lr_W=2E-3 best) | High |
| 86 | Complete parameter insensitivity at sparse+noise structural limit | High |
| 106 | BREAKTHROUGH: n_epochs=2 → conn +10.6% at n=300 | High |
| Iter | Prediction | Outcome | ✓/✗ |
|---|---|---|---|
| 18 | L1=1E-6 should help low_rank dynamics | 0.925 confirmed | ✓ |
| 39 | lr_emb=1E-3 fixes embedding for n_types=4 | FULL convergence | ✓ |
| 64 | L1=1E-6 helps n=200 (from block 2) | REDUCES connectivity | ✗ |
| 100 | Dynamics cliff at lr_W=8E-3 for n=300 | No cliff present | ✗ |
| 102 | lr=2E-4 boosts conn at n=300 | +16% confirmed | ✓ |
| Iter | Hypothesis Rejected | Impact |
|---|---|---|
| 14 | factorization helps low_rank | Principle 4: direct W superior |
| 48 | batch_size=16 safe for n_types=4 | Principle 8: batch=16 kills dual-obj |
| 95 | Recurrent training helps subcritical | Principle 21: catastrophic collapse |
| 88 | n_epochs=2 helps sparse+noise | Principle 19: noise removes dependency |
| 110 | n_epochs=3 improves beyond 2ep | Diminishing returns for conn |
| Iter | From → To | Outcome |
|---|---|---|
| 13 | B1→B2: lr_W=4E-3 | ✓ Conn OK, dynamics poor |
| 73 | B1→B7: lr_W=4E-3 to sparse | ✗ 0% convergence |
| 85 | B5→B8: noise inflates eff_rank | ✓ 21→91 confirmed |
| Iter | Milestone | Mode |
|---|---|---|
| 4 | First boundary probe (lr_W sweep begins) | Boundary |
| 5 | lr_W=4E-3 sweet spot identified | Induction |
| 9 | lr=2E-4 falsified; first strategy shift | Falsification, Meta |
| 13 | Cross-block transfer begins; eff_rank regime discovered | Analogy, Regime |
| 21 | BREAKTHROUGH: low_rank recombination (lr_W + L1) | Induction, Causal |
| 29 | Dale cliff at 5E-3 reproducibly demonstrated | Boundary, Falsification |
| 39 | lr_emb=1E-3 unlocks heterogeneous convergence | Deduction |
| 51 | Noise→eff_rank relationship established | Induction, Regime |
| 73 | Subcritical spectral radius hypothesis formed | Abduction, Regime |
| 85 | Structural data limit (conn=0.489) recognized | Constraint |
| 95 | Recurrent training catastrophic in subcritical | Falsification |
| 106 | BREAKTHROUGH: n_epochs=2 at n=300 (+10.6%) | Induction, Causal |
| # | Principle | Prior | Origin | Evidence | Conf |
|---|---|---|---|---|---|
| 1 | lr tolerance scales with eff_rank and n | None | lr=1E-4 at n=100/eff=35; lr=2E-4 safe at eff>=42; lr=3E-4 at n=200 | B1,3,5,6,9: 12 tests, 3 alt | 85% |
| 2 | Convergence boundary scales with n_neurons | None | ~1.5E-3 at n=100, ~3.5E-3 at n=200, ~7E-3 at n=300 | B1,6,9: 8 tests | 85% |
| 3 | L1=1E-6 critical for low_rank/heterogeneous | None | Enables dynamics; harmful at n=200 n_types=1; neutral n=300 | B2-9: 10 tests, 3 alt, 7 blocks | 92% |
| 4 | factorization hurts in low_rank | None | Direct W outperforms factorized W=WL@WR | B2: 2 tests | 55% |
| 5 | Optimal lr_W depends on regime | None | Chaotic 4E-3; n=200 5E-3; n=300 1E-2; low_rank 3E-3; Dale 4.5E-3 | B1-9: 34 boundary tests, 9 blocks | 100% |
| 6 | Dale cliff at ~5E-3 | None | Safe range [3.5, 4.5E-3]; reproducible | B3: 4 tests, 2 reproductions | 72% |
| 7 | Dale reduces eff_rank 35→12 | None | E/I constraint concentrates variance | B3: 1 observation | 45% |
| 8 | batch_size=16 hurts complex regimes | None | Safe n_types=1; kills dual-objective and Dale | B2-4,8: 4 tests, 4 blocks | 77% |
| 9 | lr_emb coupled to lr_W | None | lr_emb/lr_W ratio ~0.2; lr_emb=1E-3 at lr_W>=4E-3 | B4: 3 tests | 60% |
| 10 | lr_W=5E-3 for dual-objective heterogeneous | None | Best conn + cluster at n_types=4 | B4: 2 tests | 55% |
| 11 | Heterogeneous increases eff_rank 35→38 | None | n_types=4 diversifies network | B4: 1 observation | 45% |
| 12 | Noise inflates eff_rank (dense only) | None | Dense 35→42-90; sparse 21→91 but no conn rescue | B5,8: 6 tests, 2 blocks | 72% |
| 13 | Inverse lr_W-noise relationship | None | Higher noise → lower optimal lr_W | B5: 4 tests | 72% |
| 14 | Rollout anti-correlates with noise | None | noise=0.1 best rollout (kino_R2=0.405) | B5: 3 tests | 55% |
| 15 | n scaling: eff_rank grows sub-linearly | None | 35 (n=100), 43 (n=200), 47 (n=300) | B1,6,9: 3 blocks | 72% |
| 16 | Dynamics cliff non-linear with n | None | n=100→8E-3, n=200→5.5E-3, n=300→1.2E-2 | B1,6,9: 6 tests, 3 blocks | 72% |
| 17 | Convergence rate decreases with n | None | 92% (n=100), 67% (n=200), 0% 1ep (n=300) | B1,6,9: 3 blocks | 72% |
| 18 | Sparse subcritical: rho<1 is fundamental barrier | None | 50% fill → rho=0.746, 0% convergence | B7: 12 tests | 77% |
| 19 | n_epochs dominant in sparse, irrelevant in sparse+noise | None | noise equalizes epoch dependency | B7,8: 6 tests, 2 blocks | 77% |
| 20 | Sparse has no lr_W cliff up to 1.5E-2 | None | Monotonic improvement (no noise); flat (noise) | B7,8: 8 tests | 72% |
| 21 | Recurrent training catastrophic in noisy subcritical | None | time_step=4 collapsed conn 0.489→0.054 | B8: 1 test | 45% |
| 22 | Sparse 50% conn ~0.49 is structural data limit | None | Needs more frames or different approach | B7,8: 24 tests, 2 blocks | 85% |
| 23 | n=300 requires n_epochs>=2 | None | 1ep best 0.805; 2ep best 0.890 (+10.6%) | B9,10: 4 tests, 2 blocks | 85% |
| 24 | lr tolerance narrows at high lr_W | None | lr=3E-4 degrades at lr_W=1E-2 (n=300) | B9: 2 tests | 55% |
| # | n_tests | n_alt | n_blocks | Score |
|---|---|---|---|---|
| 1 | 12 | 3 | 5 | 30+18+20+75=100%→cap 85% |
| 2 | 8 | 0 | 3 | 30+16+0+45=85% (cap variance) |
| 3 | 10 | 3 | 7 | 30+17+20+100%→cap 92% |
| 5 | 34 | 0 | 9 | 30+26+0+100%=100% |
| 8 | 4 | 0 | 4 | 30+12+0+60=77% (cap regime) |
| 18 | 12 | 0 | 1 | 30+18+0+15=63%→adjusted 77% (strong boundary) |
| 22 | 24 | 0 | 2 | 30+24+0+30=84%→cap 85% |
| 23 | 4 | 1 | 2 | 30+12+10+30=82%→cap 85% |
The epistemic analysis of signal_landscape_Claude reveals structured scientific reasoning across 348 iterations and 29 exploration blocks. The system produced ~290 reasoning events spanning 12 distinct modes, with Induction (53), Boundary Probing (50), and Deduction (47) dominating. Deduction achieved a 74% validation rate, well above chance, demonstrating genuine predictive power from accumulated knowledge. Cross-block Analogy/Transfer succeeded 70% of the time, with failures concentrated in transfers to fundamentally different regimes (sparse, low-gain). All 43 falsification events led to principle refinement (100%), demonstrating systematic self-correction.
Six distinct reasoning phases emerge: (1) boundary probing and induction dominate early as the system maps each new regime, (2) deduction and analogy grow as accumulated principles enable cross-regime predictions, (3) falsification and constraint recognition widen when structurally hard regimes are encountered, (4) analogy drives scaling explorations as n_frames dominance overturns multiple principles (blocks 15-16), (5) constraint recognition peaks as the system maps structural limits — subcritical spectral radius (block 17), conn_ceiling at filling_factor (blocks 22-24), and (6) regime recognition identifies the gain-eff_rank critical transition (blocks 25-28), identifying fixed-point collapse (g=1) as a new unsolvable axis and inverse lr_W at g=2. Block 29 completes the gain exploration by showing g=2/n=200 is much easier than predicted (92% conv), with eff_rank scaling with n even at low gain. ~90 validated principles were established with confidences ranging from 45% to 100%.
| Metric | Value |
|---|---|
| Iterations | 348 |
| Blocks | 29 |
| Reasoning instances | ~290 |
| Reasoning modes | 12 |
| Deduction validation | 74% |
| Transfer success | 70% |
| Falsification→refinement | 100% |
| Principles discovered | ~90 |
| Cross-block principles | ~40 |
| Causal edges | ~150 |
| Breakthroughs | 5+ |