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.
Large language model (LLM) outputs are expected to be reproducible under greedy decoding, yet in practice the same model, prompt, and software stack produce different outputs on different GPUs. The root cause is floating-point non-associativity combined with hardware-dependent kernel selection. Inference frameworks select different matrix-multiplication kernels on each architecture, with different parallel reduction orders and unspecified tensor-core arithmetic, and the resulting rounding differences can flip output tokens. Existing solutions have imperfect cross-architecture reproducibility and incur a significant performance penalty. We present a solution employing a set of fixed-configuration fused-upcast GEMM kernels that load 16-bit weights from memory, upcast them to FP32 in registers, and accumulate with IEEE-754 arithmetic in a reduction order that is a pure function of the problem shape and is therefore independent of the device, its SM count, or kernel scheduling. By fixing the floating-point reduction order as a function of problem shape alone, every GPU runs the same operation sequence, so cross-architecture reproducibility of the linear layers reduces to correct IEEE-754 arithmetic rather than to rounding differences staying below a tie-flip threshold. We confirm our solution's linear-layer outputs are bitwise identical across NVIDIA Ampere, Ada, and Hopper GPUs, while running 1.17 to 3.1× faster end-to-end than the state-of-the-art solution and cutting weight-memory traffic in half.
Greedy decoding from large language models is commonly treated as deterministic. We show it is not precision-invariant: the same model, prompt, and decoding algorithm produce different outputs in BF16 versus FP16 on identical hardware. Across our evaluations of six models (1.1B-7B parameters, four families; divergence additionally characterised at 12B) and three benchmarks, 49-100% of prompts diverge; a single token flip often cascades into trajectory-level divergence. We develop an empirical error-propagation analysis and find that 22 layers of accumulated body error do not distinguish flipping from non-flipping steps; the outcome depends primarily on the top-two logit margin at the LM head relative to the directional perturbation between the top-two candidates. The analysis makes five testable predictions about intervention outcomes, including that applying more FP32 compute (broader scope) makes agreement worse. The experiments match all five predictions. The best-performing low-overhead intervention we evaluate, selective FP32 LM head recomputation, triggered only when the margin falls below a threshold, delivers +22-36 pp exact agreement on A10G (+12-21 pp on L4 and A100) at less than 4% latency overhead in low-batch (batch size <=4) single-stream inference. We map the applicability boundary across six models and four batch sizes, and hypothesise that training-time precision stability is a determining factor. The method is a partial mitigation rather than a universal determinism guarantee: its benefit vanishes when body-originated error dominates, including at batch size >=8 and under end-to-end FP8 in our tests.
Large language models (LLMs) are increasingly integrated into high-performance computing (HPC) workflows, accelerating scientific discovery through diverse perspectives such as code generation and domain-specific decision-making. Yet, how soft errors propagate and affect LLM inference remains largely unexplored. To bridge this gap, we present a comprehensive study on error propagation in LLM inference, enabled by our proposed LLMFI, a configurable and deterministic fault-injection framework. Using LLMFI, we systematically inject faults across three open-weighted LLMs and thirteen representative tasks, covering reasoning, multilingual, mathematical, and coding domains. In addition, we conduct fine-grained case studies that reveal critical vulnerability patterns. Overall, our study yields 17 takeaways that advance the understanding of error propagation in LLM inference and introduces four low-overhead directions to improve reliability through software-only modification, offering practical guidance for future error detection and mitigation.