Quaternion small language-model comparison
This is a compact Karpathy-style decoder experiment where only the Transformer projections change. The real, complex, and quaternion models otherwise use the same data, batches, optimizer, schedule, attention, and head.
Phase 2 measured a data-dependent crossover. Quaternion projections had lower validation loss through 2M training tokens, 5M was inconclusive, and real projections won from 10M through 50M.
Articles
- Why I ran this test
- Quaternion Transformers win early, then lose
- Short LinkedIn post
- Short Twitter/X post
source .venv/bin/activate python -m unittest qllm.tests.test_layers python -m qllm.compare # quick pipeline test python -m qllm.compare --token-budget 50000000 # minimum evidence run (slow)
The quick command compares a normal model with quaternion models at (1) equal width and (2) equal total
parameter count, then writes an honest table and plots to qllm/report/. It is deliberately labeled a smoke
test because a few thousand tokens and one seed cannot establish the hypothesis.
Full-size YAML configurations are in qllm/experiments/configs/; run one with:
python -m qllm.data.prepare --vocab-size 8192 --train-mb 64 --val-mb 8 python -m qllm.train qllm/experiments/configs/real-base.yaml
Run the fixed-budget, three-seed equal-parameter follow-up overnight with:
It trains only the two arms needed to answer the main hypothesis (300M total tokens), skips completed runs when
relaunched with the same output directory, and writes manifest.json, per-run results, summary.json, and
summary.md under qllm/runs/overnight-50m/.
Phase 2 (qbench)
Phase 1 commands and caches above remain unchanged. Phase 2 byte-copies the pinned Phase-1 tokenizer, training binary, and training text, then encodes a separate 8 MiB validation prefix with that tokenizer:
python -m qbench.data python -m unittest tests.test_models python -m qbench.verify --device auto # strict 2x200-step Stage A python -m qbench.benchmark # 50 warmups, 200 iterations python -m qbench.run --model real --tokens 500000 --seed 1 python -m qbench.analysis.analyze python -m qbench.generate # after final 50M checkpoints exist python -m qbench.run_crossover # full 635M-token sweep; long python -m qbench.run_ablations
qbench/all.sh prepares data, runs Phase-1/layer/model tests and strict real-data verification, benchmarks, runs
the crossover and ablations, generates samples, then builds the report. Do not invoke it merely as a quick test.
Runs use source/data/config digests and atomic resumable 5%-boundary checkpoints. Every final metric uses exactly
2M fixed sequential validation tokens at batch 64; every curve point uses the same preregistered 131,072-token
prefix. Generated caches, results, checkpoints, and plots are ignored, while
qbench/benchmarks/throughput.csv and qbench/REPORT.md are intended deliverables. The Stage-D width-100 real
control is deliberately omitted because introducing low-rank projections would not be a clean algebra-only control.