reasoning:
Let me analyze the current situation. We have one baseline result at 2e18 FLOPs with val_bpb=3.4738. The baseline uses depth=9, matrix_lr=0.03, warmup_ratio=0.0, warmdown_ratio=0.4.

Following the guidance to prioritize finding the optimal depth, I should explore different depth values. The suggested starting point is depth=9, but the compute-optimal depth for 2e18 FLOPs could be different.

At 2e18 FLOPs, let me think about what depth makes sense. At a previous scale (likely 2e17 or similar), the optimal depth might have been lower.

For this scale, a deeper model should perform better, so I'll test depth=12 while keeping the other hyperparameters fixed to see how increasing model depth affects the validation loss.

content: Looking at the situation: we have a single baseline at depth=9 with val_bpb=3.4738. The priority guidance is clear — locate the depth optimum first. At 2e18 FLOPs, the compute-optimal model is likely larger than the depth=9 baseline (more FLOPs favor deeper/wider models per Chinchilla-like scaling). I'll step depth up meaningfully to depth=13, keeping all other hyperparameters fixed at the baseline values so any change is cleanly attributable to depth alone.


reasoning:
Let me analyze the current state. We have one trial completed with the default configuration:

- depth=9, matrix_lr=0.03, warmup_ratio=0.0, warmdown_ratio=0.4 → val_bpb=3.4738

Since we only have one trial, I need to start exploring. The priority guidance says depth is most load-bearing, so let me explore different depths first.

At 2e18 FLOPs, deeper models are more parameter-efficient but see fewer tokens. Let me try depth=12 (a moderate increase) to see if going deeper helps.
I'll hold the other hyperparameters steady at their defaults and just vary depth to isolate its effect.

content:
## Analysis

Only one trial so far — the default config. The priority guidance is clear: **locate the depth optimum first**. With depth=9 as our baseline (val_bpb=3.4738), I need to probe both directions on depth to map the convex curve.

At 2e18 FLOPs, depth³ scaling means deeper models trade steps for parameters. A step up to depth=12 is a meaningful but not extreme jump — d_model goes from 576→768, which is a well-known GPT2-small size. I'll hold all other params at their defaults so the result is cleanly attributable to depth.


reasoning: The results so far show that increasing depth from 9 to 12 improved val_bpb (3.4738 → 3.4628). I should continue increasing depth to find the optimum. Let me try depth=16 to continue exploring in the same direction.

content:
## Analysis

- **depth=9**: val_bpb = 3.4739
- **depth=12**: val_bpb = 3.4628 ✅ improvement

The trend is clear: increasing depth is helping. At 2e18 FLOPs, we haven't hit the optimum yet. I'll continue moving depth upward — a moderate step to depth=16 — while keeping everything else fixed so the result stays fully attributable to depth.

At depth=16: d_model = round_up(16×64, 128) = 1024, which is a meaningful size jump. The depth³ FPT scaling means this is already ~2.4× costlier per token than depth=12, so the model will see fewer steps, but at 2e18 FLOPs this could still be in the compute-optimal zone. `matrix_lr` may need downward adjustment once we pin depth, but let's locate the depth optimum first.


reasoning:
Looking at the results so far:
- depth=9: 3.4738
- depth=12: 3.4628
- depth=16: 3.4590

The trend is consistently improving as depth increases, but the improvement is slowing down. Let me continue increasing depth to find the optimum. The improvement from 12→16 was smaller than 9→12, suggesting we might be approaching the optimum or it's still improving. Let me try depth=20 to see if the trend continues.

content:
## Analysis

| depth | val_bpb |
|-------|---------|
| 9 | 3.4739 |
| 12 | 3.4628 |
| 16 | 3.4590 |

The trend is **consistently improving** as depth increases, but the gains are shrinking:
- 9→12: −0.0111
- 12→16: −0.0038

This suggests we're still on the downward slope but approaching an optimum somewhere beyond depth=16. The diminishing returns could mean the convex minimum is in the 16–22 range. I'll make a **moderate jump to depth=20** to keep the trend moving while staying attributable — if it improves again (even slightly), we continue up; if it gets worse, we've bracketed the optimum between 16 and 20.

All other parameters stay fixed at their current best values so the depth signal remains clean.


reasoning:
Looking at the results so far:

- depth=9: 3.4738
- depth=12: 3.4628
- depth=16: 3.4590 ← best
- depth=20: 3.4605

The optimum appears to be around depth=16, with depth=20 slightly worse. The pattern suggests the optimum is bracketed between depth=12 and depth=20, with depth=16 being best. Let me try depth=14 to narrow down, or maybe try depth=18 to better bracket around 16.

Actually, depth=16 is best, depth=20 is slightly worse, depth=12 is slightly worse. Let me try depth=14 to bracket more tightly, or I could try depth=18.
The differences are quite small, so I should test depth=14 to see if the optimum lies between 12 and 16, or try depth=18 to check the region between 16 and 20 more carefully.

Actually, since 16 appears to be the best so far, let me pin that and start experimenting with matrix_lr instead—trying something like 0.01 or 0.05, since larger models typically benefit from smaller learning rates.

content:
## Analysis

Results so far:
| depth | val_bpb |
|-------|---------|
| 9 | 3.4739 |
| 12 | 3.4628 |
| **16** | **3.4590** ← best |
| 20 | 3.4605 |

The optimum is **bracketed around depth=16**: it improves from 9→12→16, then gets slightly worse at 20. The gap between 16 and 20 is small (~0.0015), suggesting the bowl is shallow but centered near depth=16. I should check **depth=14** to confirm whether the optimum is slightly left of 16, and also to tighten the bracket before moving on to tune `matrix_lr`.

**Rationale**: depth=12 (3.4628) < depth=16 (3.4590) < depth=20 (3.4605), so the minimum is somewhere between 12 and 20. Testing depth=14 will tell us if the true optimum is at 14 or 16 — both reasonable candidates. Keeping all other params fixed ensures the result is fully attributable to depth.


reasoning:
Let me analyze the results so far:

- depth=9: 3.4739
- depth=12: 3.4628
- depth=14: 3.4576 ← best
- depth=16: 3.4590
- depth=20: 3.4605

The optimum appears to be around depth=14, with depth=16 slightly worse. Let me try depth=13 to narrow down, or maybe try depth=15 to bracket more precisely between 14 and 16.

Actually, depth=14 is best, depth=16 is slightly worse, so the optimum is likely between 14-16.

Now testing depth=15 to see if it falls between these two.

content:
## Analysis

Results so far (sorted by val_bpb):

| depth | val_bpb |
|-------|---------|
| 9 | 3.4739 |
| 12 | 3.4628 |
| **14** | **3.4576** ← best |
| 16 | 3.4590 |
| 20 | 3.4605 |

The depth optimum is clearly bracketed between **12 and 16**, with depth=14 currently leading. The curve is quite flat but has a local minimum near 14–15. Depth=16 is slightly worse than 14 — we should try **depth=15** to check if the true minimum is between 14 and 16, or if 14 is genuinely the best. Once we nail down the optimal depth, we can tune `matrix_lr` and `warmdown_ratio`.


reasoning:
Let me analyze the results so far:

- depth=9: 3.4739
- depth=12: 3.4628
- depth=14: 3.4576 ← best
- depth=15: 3.4583
- depth=16: 3.4590
- depth=20: 3.4605

The optimum appears to be around depth=14. The values form a clear convex shape with minimum at depth=14. Now I should pin depth=14 and explore other hyperparameters.

The matrix_lr has been fixed at 0.03 throughout. Let me try a different value.

Since depth=14 gives a wider model than depth=9, the optimal learning rate might shift. I'll bracket it by testing matrix_lr=0.01 on the lower end and 0.05 on the higher end to see which direction helps. With depth=14 producing a model around 896 dimensions, the current 0.03 could be reasonable, but it's worth checking if a lower rate like 0.01 performs better.

content:
## Analysis

The depth sweep has revealed a clear convex minimum:
| depth | val_bpb |
|-------|---------|
| 9 | 3.4739 |
| 12 | 3.4628 |
| **14** | **3.4576** ← best |
| 15 | 3.4583 |
| 16 | 3.4590 |
| 20 | 3.4605 |

**Depth is well-bracketed at 14.** The pattern is clean: improving from 9→14, then slightly degrading at 15, 16, 20. I'm confident depth=14 is optimal (or very close — depth=13 could be checked later, but the gap 14→15 is small and 12→14 is larger, suggesting 14 is the true minimum).

**Next move**: Pin depth=14 and start exploring `matrix_lr`. The entire sweep used 0.03; we have no information about LR sensitivity. At depth=14 (d_model=896), Muon updates are moderately large — the optimal LR could be lower. I'll try **matrix_lr=0.01** (one step down on log scale) to test whether a smaller LR helps.


reasoning:
Let me analyze the results so far:

depth=9: 3.4739
depth=12: 3.4628
depth=14: 3.4576 (best)
depth=15: 3.4583
depth=16: 3.4590
depth=20: 3.4605

So depth=14 is the sweet spot. The optimum appears to be around depth=13-14.

For matrix_lr at depth=14:
- matrix_lr=0.03: 3.4576
- matrix_lr=0.01: 3.4583
- matrix_lr=0.05 or 0.06 might be worth testing

I should also explore warmdown_ratio variations at depth=14 since the default 0.4 might not be optimal—trying something like 0.6 could help. I could also narrow things down by testing depth=13 to bracket the optimum more precisely.

Looking at the results so far, depth=14 at 3.4576 is performing best, with depth=12 and depth=15 slightly worse. The gap between matrix_lr=0.03 and 0.01 is marginal, so I'll start with depth=13 to see if it lands between 14 and 12, keeping the other parameters at their current best values.

content:
## Analysis

**Depth sweep so far:**
| depth | val_bpb |
|-------|---------|
| 9 | 3.4739 |
| 12 | 3.4628 |
| **14** | **3.4576** ← best |
| 15 | 3.4583 |
| 16 | 3.4590 |
| 20 | 3.4605 |

The optimum is clearly near depth=14, but we jumped from 12→14 without testing 13. The valley might be at 13 or 14. Let me fill that gap to properly bracket the optimum.

For `matrix_lr` at depth=14: 0.03 (3.4576) vs 0.01 (3.4583) — 0.03 is very slightly better, but the gap is tiny. The LR question is secondary until we pin depth.

**Next step:** Test depth=13 with the current best other settings (matrix_lr=0.03, warmdown_ratio=0.4) to confirm whether the true minimum is 13 or 14.


reasoning:
Looking at the results so far, depth=13 gives the best val_bpb of 3.4575. The trend shows depth=13 > depth=14 > depth=15 > depth=12 > depth=16 > depth=20 > depth=9. So depth around 13 seems optimal.

Now I should explore matrix_lr at depth=13 to see if we can improve. We tried matrix_lr=0.03 at depth=14 and matrix_lr=0.01 at depth=14. At depth=14, matrix_lr=0.03 (3.4576) was slightly better than matrix_lr=0.01 (3.4583).

Since matrix_lr=0.03 performed well at depth=14, I'll test higher learning rates like 0.05 or 0.06 at depth=13 to see if we can push performance further, then potentially adjust warmdown_ratio if needed.

content:
## Analysis

The depth sweep is converging nicely:

| depth | val_bpb |
|-------|---------|
| 9 | 3.4739 |
| 12 | 3.4628 |
| 13 | **3.4575** ← best |
| 14 | 3.4576 |
| 15 | 3.4583 |
| 16 | 3.4590 |
| 20 | 3.4605 |

depth=13 is the clear winner, with depth=14 a very close second. The optimum is well-bracketed between 12 and 15, so **depth is pinned at 13**.

Now the priority shifts to `matrix_lr`. At depth=14 we saw that 0.03 beat 0.01, suggesting the optimum may be at or above 0.03. I should probe **above** 0.03 on the log scale — try `matrix_lr=0.06` — to check whether we're on the upward or downward slope. Keeping everything else at the best-known values (warmup=0.0, warmdown=0.4).


reasoning:
Let me analyze the results so far:

depth=9, matrix_lr=0.03: 3.4739
depth=12, matrix_lr=0.03: 3.4628
depth=16, matrix_lr=0.03: 3.4590
depth=20, matrix_lr=0.03: 3.4605 (worse than 16)
depth=14, matrix_lr=0.03: 3.4576
depth=15, matrix_lr=0.03: 3.4583
depth=14, matrix_lr=0.01: 3.4583
depth=13, matrix_lr=0.03: 3.4575
depth=13, matrix_lr=0.06: 3.4565 ← best

Depth 13 with matrix_lr=0.06 is looking like the best configuration so far. The pattern suggests that increasing the learning rate helps at this depth, so I'll test depth=13 with matrix_lr=0.1 to see if pushing it further improves things.

content:
## Analysis

Current best: `depth=13, matrix_lr=0.06` → 3.4565

Key observations:
- **depth** seems bracketed: 13 > 14 > 12 > 15 > 16, so depth=13 looks like the sweet spot
- **matrix_lr** trend at depth=13: 0.06 (3.4565) > 0.03 (3.4575) > 0.01 (3.4583 at depth 14, but consistent direction) — the learning rate is still improving as we increase it
- The matrix_lr optimum hasn't been found yet; 0.06 > 0.03, so we should push higher to 0.1

**Next step**: Keep `depth=13` pinned (consistent winner), push `matrix_lr` up to ~0.1 to follow the improving trend and find the optimum.


reasoning: Looking at the results, depth=13 with matrix_lr=0.06 is the best so far (3.4565). The matrix_lr sweet spot around 0.06 looks promising. Let me try warmdown_ratio tuning at depth=13, matrix_lr=0.06. The default warmdown_ratio=0.4 might not be optimal. Let me try a longer warmdown like 0.6.

content:
## Analysis

Current best: `depth=13, matrix_lr=0.06, warmup_ratio=0.0, warmdown_ratio=0.4` → val_bpb = **3.4565**

**What we know:**
- **Depth**: Convex optimum bracketed around depth=13 (13 < 14 < 15 on one side; 13 < 12 < 9 on the other). Depth=13 is the clear winner.
- **matrix_lr**: At depth=13, scanning 0.01 → 0.03 → 0.06 → 0.10 shows a peak at 0.06 — well localized.
- **warmdown_ratio**: Still at the default 0.4 throughout. This is a high-impact schedule knob and hasn't been touched. A longer warmdown (e.g., 0.6) could meaningfully improve final loss by spending more of the budget in decay, especially since there's no warmup consuming any budget.

**Next move:** Pin depth=13 and matrix_lr=0.06, and probe a longer warmdown_ratio=0.6. The plateau would shrink from 60% → 40% of steps, allowing the LR to ramp down more gently over a larger fraction of training.


reasoning:
Let me analyze the results so far:

Best result: depth=13, matrix_lr=0.06, warmup_ratio=0.0, warmdown_ratio=0.4, val_bpb=3.4565

The depth sweep shows depth=13 is optimal. matrix_lr=0.06 is better than 0.03 or 0.1 at depth=13. warmdown_ratio=0.6 was slightly worse than 0.4.

Now I should try a shorter warmdown_ratio (e.g., 0.2 or 0.3) to see if less warmdown helps, or try matrix_lr slightly higher like 0.08, or try warmdown_ratio around 0.3.
I'll test warmdown=0.2 to narrow down the optimal warmdown value, keeping depth=13 and matrix_lr=0.06 fixed since 0.4 outperformed 0.6.

content:
Looking at the results:

- **Depth** is pinned at **13** (best across the sweep)
- **matrix_lr=0.06** beats 0.03 and 0.1 at depth=13 (sweet spot bracketed)
- **warmdown_ratio**: 0.4 (3.4565) beat 0.6 (3.4570) — the optimum is at 0.4 or below

The warmdown direction is clear: 0.6 is worse, 0.4 is better. I should now test a **shorter warmdown** (e.g., 0.2) to bracket the optimum from below. Keep depth=13 and matrix_lr=0.06 fixed to keep results attributable.


reasoning:
Let me analyze the results so far:

Best result: depth=13, matrix_lr=0.06, warmup_ratio=0.0, warmdown_ratio=0.4 → 3.4565

The warmdown_ratio exploration at depth=13, matrix_lr=0.06:
- warmdown_ratio=0.2: 3.4584
- warmdown_ratio=0.4: 3.4565 (best)
- warmdown_ratio=0.6: 3.4570

So 0.4 is best for warmdown_ratio. Let me try to refine matrix_lr a bit more.

Looking at the matrix_lr values, 0.06 seems to be the optimal point with nearby values like 0.03 and 0.1 performing slightly worse. I should verify whether depth=13 is truly the best or if depth=12 might be competitive, then fine-tune matrix_lr around 0.06 to see if there's any marginal improvement.

content:
## Analysis

**Depth optimum**: The search has converged around depth=13 (best: 3.4565). Depth 12 hasn't been tested with the better matrix_lr=0.06 yet — worth checking to fully bracket the optimum.

**matrix_lr**: At depth=13, the trajectory 0.03→0.06→0.10 shows a clear peak at 0.06. The optimum seems well-located.

**warmdown_ratio**: At depth=13, matrix_lr=0.06: 0.2→3.4584, 0.4→3.4565 (best), 0.6→3.4570. The 0.4 default is winning; the optimum is near there.

**Next move**: Test depth=12 with matrix_lr=0.06 to confirm depth=13 is truly better than depth=12 at the improved matrix_lr (previously depth=12 was only tested at matrix_lr=0.03). This conclusively brackets the depth optimum before doing finer LR/schedule tuning.


reasoning:
Let me analyze the results so far:

Best result: depth=13, matrix_lr=0.06, warmup_ratio=0.0, warmdown_ratio=0.4 → 3.4565

Key findings:
1. Depth sweet spot is around 13 (3.4565 best)
2. matrix_lr=0.06 is better than 0.03 or 0.1 at depth=13
3. warmdown_ratio=0.4 seems better than 0.6 or 0.2 at depth=13

The best config is depth=13, matrix_lr=0.06, warmdown_ratio=0.4. Let me think about what to explore next.
I'm noticing that 0.4 outperforms both 0.2 and 0.6 for warmdown_ratio, so I could try values closer to that like 0.5, and similarly for matrix_lr I might test 0.05 or 0.07 to narrow in on the optimal range. The gains are modest though, so I should also consider whether a small warmup_ratio might help. I'll test depth=13 with matrix_lr=0.06 and warmdown_ratio=0.5 to narrow in on the warmdown parameter while keeping the other settings stable.

content:
## Analysis

**Current best**: depth=13, matrix_lr=0.06, warmup_ratio=0.0, warmdown_ratio=0.4 → val_bpb=3.4565

Key takeaways so far:
- **Depth**: Clearly convex around 13, with 13 > 14 > 12 at comparable LRs. Pin depth=13.
- **matrix_lr**: 0.06 > 0.03 > 0.1 at depth=13. Sweet spot is near 0.06.
- **warmdown_ratio**: 0.4 (3.4565) > 0.6 (3.4570) > 0.2 (3.4584). The optimum appears to be at or near 0.4, but the 0.6 result is very close — the optimum might sit just above 0.4. Worth probing 0.5 to confirm.

**Next move**: Hold depth=13, matrix_lr=0.06 (current best combination) and try warmdown_ratio=0.5 — this is the one unexplored point between the tested values of 0.4 and 0.6, and the slight edge of 0.4 over 0.6 suggests the optimum may be exactly around 0.4–0.5 rather than clearly at 0.4.