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

• URL: http://arxiv.org/abs/2606.21023v1
• Date: Fri, 19 Jun 2026 01:21:10 GMT
• Title: Demystifying Numerical Instability in LLM Inference: Achieving Reproducible Inference for Mission-Critical Tasks with HEAL
• Abstract summary: Large Language Models (LLMs) deploy into mission-critical domains (e.g. finance, medicine, law)<n>Experiments with 16-bit precisions still exhibit catastrophic output divergence across heterogeneous GPUs.<n>We propose Hybrid Error ALleviation (HEAL), a targeted intervention that approximates FP32 accelerators while resolving hardware constraints.
• Score: 18.134050827462005
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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