[rachitj27]

Summary

• use the upper Cholesky factor of the inverse Hessian for the per-group GPTQ correction in quantize_hadamard, instead of reusing one global inverse for every 128-column block
• compute the inverse and factor in float64 and reject a non-finite factor, so ill-conditioned or NaN Hessians disable GPTQ cleanly instead of silently producing a wrong correction
• add tests covering the block update against an explicit per-step recompute, calibrated error reduction, and bad-Hessian fallbacks

Root cause

_gptq_correct_group sliced H^-1[B, B] and H^-1[B, rest] from a single inverse computed once per tensor. The OBS/GPTQ block update needs the inverse Hessian of the columns that are not yet quantized, which changes after every block (it becomes the Schur complement). Using the stale global inverse is only correct for the first block; every later block applies a miscalibrated correction to the remaining columns.

The standard GPTQ remedy is to factor H^-1 = U^T U with U upper triangular. Processing columns left to right, U[rest, rest] is exactly the factor of the correctly updated inverse at every step, so the block update becomes solve_triangular(U[B, B], U[B, rest]) with no refactorisation.

Impact

Conversion only. The weight file format, engine, and inference speed are unchanged; the stored indices and norms are closer to the original weights on calibration data.

Measured with hook-collected Hessians and diagonal-derived input scales (collect_text_hessians and _input_scale_from_diag) on a 1024→2048→1024 MLP block, evaluating output error on held-out activations. Values are error relative to plain Hadamard CQ with no GPTQ, lower is better.

layer	bits	old GPTQ	new GPTQ
up (1024 wide)	4	0.72	0.50
up (1024 wide)	3	0.73	0.51
up (1024 wide)	2	0.76	0.57
down (2048 wide)	4	0.63	0.33
down (2048 wide)	3	0.64	0.35
down (2048 wide)	2	0.66	0.40

The old correction plateaus at roughly 35–40% error reduction regardless of width, while the fixed version keeps improving as layers get wider.

Related: #767 and #790 cover calibration being silently skipped. This change only matters when GPTQ actually runs, so those fixes and this one compound.

Validation

• python -m pytest cactus/convert/tests -q (83 passed)
• new tests in cactus/convert/tests/test_cq.py:
  • test_gptq_cholesky_block_update_matches_explicit_obs: block update matches a reference that recomputes inv(H[start:, start:]) from scratch at every group
  • test_gptq_reduces_calibrated_error: GPTQ strictly lowers calibrated output error vs plain Hadamard CQ4
  • test_gptq_disabled_on_bad_hessian / test_gptq_disabled_on_nan_hessian: negative-definite and NaN Hessians fall back with gptq_used=False and indices identical to the no-GPTQ baseline
• git diff --check clean

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