# Deterministic LLM Inference Across GPU Kernels: Power-of-Two INT8 Quantization Scales and the Limits of Tolerance-Based Conformance

arXiv: https://arxiv.org/abs/2609.00363 · HTML: https://mlsanity.com/paper/2609.00363/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Integer Quantization for Deep Learning Inference: Principles and Empirical Evaluation](https://mlsanity.com/paper/2004.09602/) (2020)
- [Understanding and Mitigating Numerical Sources of Nondeterminism in LLM Inference](https://mlsanity.com/paper/2506.09501/) (2025)
- [RAPQ: Rescuing Accuracy for Power-of-Two Low-bit Post-training Quantization](https://mlsanity.com/paper/2204.12322/) (2022)
- [Deterministic Inference across Tensor Parallel Sizes That Eliminates Training-Inference Mismatch](https://mlsanity.com/paper/2511.17826/) (2025)
- [Pre-registration for Predictive Modeling](https://mlsanity.com/paper/2311.18807/) (2023)
- [A2Q: Accumulator-Aware Quantization with Guaranteed Overflow Avoidance](https://mlsanity.com/paper/2308.13504/) (2023)
- [Equivalence Checking of ML GPU Kernels](https://mlsanity.com/paper/2511.12638/) (2025)
- [An SMT Formalization of Mixed-Precision Matrix Multiplication: Modeling Three Generations of Tensor Cores](https://mlsanity.com/paper/2502.15999/) (2025)
- [DGEMM on Integer Matrix Multiplication Unit](https://mlsanity.com/paper/2306.11975/) (2023)
- [DiFR: Inference Verification Despite Nondeterminism](https://mlsanity.com/paper/2511.20621/) (2025)
- [The Integer Alibi: Localizing Cross-Kernel Divergence in INT8-Quantized LLM Inference](https://mlsanity.com/paper/2608.13756/) (2026)

## Built on by (most cited first, 1 of 1)

- [Is INT8 Portable? A Cross-Platform Measurement Study of Quantized Inference on Embedded and Automotive Accelerators](https://mlsanity.com/paper/2609.16085/) (2026)

## Abstract (arXiv)

Conformance suites for quantized GEMM kernels ask whether two implementations agree within a tolerance. We measure what such a suite can detect. Injecting nine faults into a reference INT8 pipeline over 8,232 layer--fault--regime cells of Qwen3-1.7B, we find that every one of five epilogue faults -- scale precision, double rounding, multiplication order, output truncation, fused ordering -- moves the output by at most a single bfloat16 spacing, and by exactly one whenever it moves it at all, across 5,880 cells. A tolerance of one spacing is therefore blind to the entire class by construction: four of the five faults are detected by no check in the suite, and the fifth only under power-of-two scales. Faults that violate the accumulator's exactness preconditions, or that break operand sharing, are detected without exception, and a null fault never fires. What a tolerance-based suite of this shape establishes is therefore narrower than interchangeability: that the preconditions hold, that operands are shared, and that differences stay within one spacing. The power-of-two constraint that exposes the one detected fault is also deployable. Requantizing every weight scale to its nearest power of two makes CUTLASS and Triton agree bitwise at every linear layer (196/196 and 252/252, against 8/196 and 10/252 under the checkpoints' own scales) and yields byte-identical generated token sequences at 1.7B, 8B and 14B (8/8 prompts, against 0/8 at all three). Observed perplexity point estimates are +0.32%, -0.28% and +0.48%; the 90% intervals cover zero at the two smaller sizes but not at 14B, reaching +0.71% and +0.76%. A previously reported +157% perplexity for this intervention was an artifact of a probe that rewrote scales without requantizing the weights; separating the effects attributes 99.8% of it to the resulting weight--scale mismatch rather than to the power-of-two constraint itself.