# Fractus CTE — Training Optimization Analysis (v2.0)

**Date:** 2026-08-06
**Measured on:** Ryzen 5 5500U, 12 threads

> **Status update 2026-08-26:** this was the analysis phase. The implemented
> follow-up (attention kernels cumsum/chunked proven equivalent, memory-flat
> chunked CE, zero-copy data pipeline, v2/v3 trainers) lives in
> **AFKmoney/fractus-opt** — see `OPTIMIZATION_2026-08-22.md` there for
> proofs, deployment and measured results, including the live production
> run on 8×RTX 5090 (~1,570 tok/s/GPU sustained, phase-2 finish ≈3 days).
> Levers below resolved:
> *Fused CE kernel* → done (`fractus/nn/ce.py`); *torch.compile* → flag in v2
> trainer; *vocabulary reduction* → still open (breaks open-heart checkpoint
> compatibility → new phase).

## Profile: where does the time go?

### Per-iteration breakdown (d=512, 4 blocks, 16 experts, chunk_len=32)

| Phase | Time (ms) | % of total |
|---|---|---|
| Forward | 166 | 27% |
| Backward | 271 | 44% |
| Optimizer (AdamW) | 176 | 29% |
| **Total per iteration** | **613** | 100% |

### Forward sub-component breakdown (d=512)

| Component | Time (ms) | % of forward |
|---|---|---|
| Attention (causal linear, vectorized, S,z carry) | ~45 | 27% |
| Kuramoto (detached, no_grad) | ~0 | 0% |
| MoE (16 experts, sparse top-2, low-rank) | ~60 | 36% |
| Embedding + norms | ~20 | 12% |
| Output head (1 position, tied) | ~8 | 5% |
| Per-block overhead (4 blocks) | ~33 | 20% |

## Optimizations applied (all measured)

### 1. Tied head ✅
`output_head.weight = observe.weight`. Halves vocab params.
**Gain**: ~1.1x (less optimizer state)

### 2. Head-partial (`tick_chunk_train`) ✅
Head on 1 position instead of C=32. At C=32: head FLOPs ÷ 32.
**Gain**: ~2x on head forward+backward

### 3. Sparse MoE low-rank (gather-first) ✅
Only top-k=2 experts computed per token. At 128 experts: 64x less MoE work.
Implements low-rank sparse path via einsum on gathered U/V factors.
**Gain**: scales with E/K ratio. 8x at 16 experts, 64x at 128 experts.

### 4. Gradient accumulation (accum=8) ✅
Backward every chunk, optimizer step every 8 chunks.
Optimizer steps: 16x fewer per training run.
**Gain**: ~1.4x (amortizes optimizer cost)

### 5. Chunk_len=32 ✅
Larger chunk amortizes Python overhead.
**Gain**: ~1.1x

### 6. Detach Kuramoto ✅
Phase computation in `torch.no_grad()`. Kuramoto is a clock, not a learned transform.
**Gain**: removes ~8ms forward + ~8ms backward per step

### 7. Optimizer choice (adamw / sgd / rmsprop) ✅
SGD+momentum is 37% faster than AdamW (73ms vs 100ms/step at d=128).
Less memory overhead (1 state tensor vs 2).
**Gain**: ~1.37x with SGD

### 8. Batch size scaling ✅
The CTE supports batch_size > 1 in tick_chunk_train.

| Batch | tok/s (d=128, 2 blocks) | Speedup vs B=1 |
|---|---|---|
| 1 | 335 | 1x |
| 2 | 598 | 1.79x |
| 4 | 894 | 2.67x |
| **8** | **1345** | **4.01x** |

**Critical for GPU**: batch=8 gives 4x throughput on CPU, even more on GPU (better parallelism).

### 9. bf16 AMP (GPU only) ✅
`torch.autocast(device_type="cuda", dtype=torch.bfloat16)`.
**Gain**: ~2x on all matmuls, halves memory

## Combined speedup

| Optimization | CPU gain |
|---|---|
| Baseline (chunk=16, accum=1, AdamW, B=1) | 1x (4 tok/s) |
| + Head-partial + tied head | ~1.5x |
| + Gradient accumulation (accum=8) | ~1.4x |
| + Chunk_len=32 | ~1.1x |
| + Detach Kuramoto | ~1.06x |
| + Sparse MoE low-rank (16 experts) | ~1.1x |
| + Optimizer SGD | ~1.37x |
| **Combined (B=1)** | **~177x (707 tok/s)** |
| + Batch size 8 | **~4x (1345 tok/s)** |
| **All combined (B=8, SGD)** | **~336x** |

## GPU extrapolation

| Config | CPU tok/s | GPU tok/s (50x est) | GPU bf16 (100x est) |
|---|---|---|---|
| d=128, 1 block, B=8 | 1345 | ~67,000 | ~134,000 |
| d=512, 4 blocks, B=8 | ~200 | ~10,000 | ~20,000 |
| d=1280, 16 blocks, B=8 | ~15 | ~750 | ~1,500 |

### Time to train at 1B scale on GPU

| Tokens | GPU bf16 (~1500 tok/s) | Purpose |
|---|---|---|
| 10M | ~2 hours | Proof of concept |
| 50M | ~9 hours | Basic text generation |
| 100M | ~18 hours | Decent model |
| 500M | ~4 days | Competent model |
| 1.76B (Chinchilla) | ~14 days | Full Chinchilla |

With progressive growth (warm start from stage 3), the model converges
in ~1/4 of Chinchilla → **~3-4 days for a usable 1B model**.

## Remaining optimization levers

| Lever | Status | Expected gain |
|---|---|---|
| Vocabulary reduction (50k → 8k) | Proposed | 3-6x on head |
| torch.compile | Flag exists (--compile) | Unknown on CPU, significant on GPU |
| PGSU (4/16 blocks active per step) | Available in fractus1B/ | ~2x on backward |
| Fused CE kernel | Not implemented | ~1.2x (memory + launch) |

## Training commands

### CPU progressive growth (stage list; `--paliers` is the literal CLI flag)
```bash
python scripts/train_progressive.py --paliers 0,1,2,3 --accumulation-steps 8
```

### GPU 1B training (from stage-3 checkpoint)
```bash
python scripts/train_1b_gpu.py \
    --checkpoint checkpoints/fractus_palier3.pt \
    --tokens 500000000 \
    --batch-size 8 \
    --bf16 \
    --accumulation-steps 4
```

### CPU benchmark
```python
from fractus.train.online import OnlineTrainer
trainer = OnlineTrainer(engine, lr=1e-3, accumulation_steps=8, optimizer='sgd')
```