# Demystifying Numerical Instability in LLM Inference: Achieving Reproducible Inference for Mission-Critical Tasks with HEAL

arXiv: https://arxiv.org/abs/2606.21023 · HTML: https://mlsanity.com/paper/2606.21023/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Serving systems and request scheduling, one of 12 directions in Efficient LLM inference and serving.
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Placed in

- Efficient LLM inference and serving / [Serving systems and request scheduling](https://mlsanity.com/inference/serving-systems-and-request-scheduling/)

## Builds on (most cited first, 23 of 23)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)
- [FinQA: A Dataset of Numerical Reasoning over Financial Data](https://mlsanity.com/paper/2109.00122/) (2021)
- [FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision](https://mlsanity.com/paper/2407.08608/) (2024)
- [LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models](https://mlsanity.com/paper/2308.11462/) (2023)
- [Good Debt or Bad Debt: Detecting Semantic Orientations in Economic Texts](https://mlsanity.com/paper/1307.5336/) (2013)
- [LexGLUE: A Benchmark Dataset for Legal Language Understanding in English](https://mlsanity.com/paper/2110.00976/) (2021)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [When Does Pretraining Help? Assessing Self-Supervised Learning for Law and the CaseHOLD Dataset](https://mlsanity.com/paper/2104.08671/) (2021)
- [Defeating the Training-Inference Mismatch via FP16](https://mlsanity.com/paper/2510.26788/) (2025)
- [Understanding and Mitigating Numerical Sources of Nondeterminism in LLM Inference](https://mlsanity.com/paper/2506.09501/) (2025)
- [A Reasoning-Focused Legal Retrieval Benchmark](https://mlsanity.com/paper/2505.03970/) (2025)
- [Automatic Evaluation of Healthcare LLMs Beyond Question-Answering](https://mlsanity.com/paper/2502.06666/) (2025)
- [LLM-42: Enabling Determinism in LLM Inference with Verified Speculation](https://mlsanity.com/paper/2601.17768/) (2026)
- [Deterministic Inference across Tensor Parallel Sizes That Eliminates Training-Inference Mismatch](https://mlsanity.com/paper/2511.17826/) (2025)
- [The Anatomy of a Triton Attention Kernel](https://mlsanity.com/paper/2511.11581/) (2025)

## Built on by (most cited first, 2 of 2)

- [The Integer Alibi: Localizing Cross-Kernel Divergence in INT8-Quantized LLM Inference](https://mlsanity.com/paper/2608.13756/) (2026)
- [Stateful Worlds, Stateless Elasticity: Exact-State Serving for Interactive World Models](https://mlsanity.com/paper/2607.10389/) (2026)

## Abstract (arXiv)

As Large Language Models (LLMs) deploy into mission-critical domains (e.g., finance, medicine, and law), output reproducibility has become a strict system requirement. While practitioners use greedy decoding to eliminate algorithmic stochasticity, empirical deployments with 16-bit precisions still exhibit catastrophic output divergence across heterogeneous GPUs. Through SASS-level profiling, we reveal that this inconsistency is fundamentally driven by truncation errors introduced during downcasting at kernel boundaries. However, achieving reproducibility via a global FP32 pipeline incurs prohibitive system penalties: bypassing 16-bit hardware accelerators hurts compute efficiency, while upcasting the KV cache doubles memory overhead. To bridge this gap, we propose Hybrid Error ALleviation (HEAL), a targeted intervention that approximates FP32 precision while resolving hardware constraints through two targeted mechanisms. First, recognizing that floating-point formats underutilize their bit-width for Q, K, V tensors, HEAL applies INT16 quantization that preserves numerical stability without expanding the KV cache footprint. Second, HEAL synthesizes high-precision matrix multiplications via an algebraic error compensation strategy, executing entirely on high-throughput 16-bit Tensor Cores. To evaluate our approach practically, we introduce MCR-Bench, a benchmark targeting reproducibility in mission-critical tasks. HEAL achieves the same level of reproducibility on downstream tasks as the FP32 baseline while reducing the performance overhead by up to 7.1x.