Non-record: SP8192 + LoRA on tied embedding (1.07994, 1 seed)

[yijieyuan]

Single-seed (seed 42) extension of bigbag's 2026-04-09 SOTA stack (PR #1493) with two tiny additions at the GPTQ quantization stage, applied only to the tied token embedding:

1. Rank-1 int8 LoRA residual on tok_emb — SVD of the post-rounding residual, rank-1 (A, B) stored as int8 with fp16 scales. Recovers ~14% of residual Frobenius energy at ~8 KB net cost.
2. Hessian-weighted shrinkage in GPTQ rounding — columns with below-mean Hessian diagonal get an extended zero-zone (thresh 0.55, H-cutoff 0.5).

Seed 42 val_bpb 1.07994 vs bigbag seed 42 1.08079 (−0.00085 BPB). Below the 0.005-nat record threshold, so submitted as non-record.

See records/track_non_record_16mb/2026-04-21_LoRA_Embedding/README.md for full details (architecture, compliance, reproduction).