arXiv subjects

Peichen Xie

Publications and source records attributed to Peichen Xie.

9 recordsLinked to original sources

arXiv2026

Evaluating Numerical Accuracy in Mixed-Precision Computing by Dual-Delta Testing

Mixed-precision computing has become increasingly important in modern high-performance computing and machine learning applications. When implementing custom mixed-precision functions -- such as fused operators, optimized GPU kernels, or quantized inference paths -- it is critical to verify their numerical accuracy. Traditional approaches typically compare the custom implementation against a reference using a single error metric. However, this single-delta approach provides limited insight into whether the observed errors are inherent to the precision level or specific to the implementation. This paper introduces \textit{Dual-Delta Testing}, a systematic methodology that evaluates two error distributions against a high-precision oracle, enabling rigorous comparison between a custom implementation and a baseline reference. We present the mathematical framework, algorithmic formulation, statistical analysis techniques, and practical examples demonstrating the methodology's effectiveness in evaluating numerical accuracy.

math.NA↗

arXiv2025

Bit-Accurate Modeling of GPU Matrix Multiply-Accumulate Units: Demystifying Numerical Discrepancy and Accuracy

Modern AI accelerators rely on matrix multiply-accumulate units (MMAUs), such as NVIDIA Tensor Cores and AMD Matrix Cores, to accelerate deep neural network workloads. MMAUs expose only instruction-level or API-level interfaces of matrix multiply-accumulate (MMA) operations, while leaving internal floating-point arithmetic behaviors undocumented. Consequently, MMAUs across vendors and architectural generations often produce numerical discrepancies for identical inputs, and sometimes exhibit reduced numerical accuracy that can cause training instability. Diagnosing and understanding the root causes of these effects is challenging without white-box models of their arithmetic behaviors. This paper proposes closed-loop feature probing (CLFP), a generic and systematic framework for constructing complete arithmetic behavior models of MMA operations. Based on this framework, we analyze all MMA instructions on ten GPU architectures spanning from NVIDIA Volta to RTX Blackwell and from AMD CDNA1 to CDNA3, and derive the first bit-accurate arithmetic models for these MMAUs. Our models explain previously observed cross-platform numerical discrepancies and accuracy issues, enable white-box numerical error analysis, reveal four precision bottleneck designs and one numerical asymmetry design that significantly affect numerical accuracy, and provide software workarounds as well as design guidance for future MMAUs. This work is open-source on https://github.com/microsoft/MMA-Sim .

cs.AR↗

arXiv2025

RepDL: Bit-level Reproducible Deep Learning Training and Inference

Non-determinism and non-reproducibility present significant challenges in deep learning, leading to inconsistent results across runs and platforms. These issues stem from two origins: random number generation and floating-point computation. While randomness can be controlled through deterministic configurations, floating-point inconsistencies remain largely unresolved. To address this, we introduce RepDL, an open-source library that ensures deterministic and bitwise-reproducible deep learning training and inference across diverse computing environments. RepDL achieves this by enforcing correct rounding and order invariance in floating-point computation. The source code is available at https://github.com/microsoft/RepDL .

cs.LG↗

arXiv2024

Revealing Floating-Point Accumulation Orders in Software/Hardware Implementations

Accumulation-based operations, such as summation and matrix multiplication, are fundamental to numerous computational domains. However, their accumulation orders are often undocumented in existing software and hardware implementations, making it difficult for developers to ensure consistent results across systems. To address this issue, we introduce FPRev, a diagnostic tool designed to reveal the accumulation order in the software and hardware implementations through numerical testing. With FPRev, developers can identify and compare accumulation orders, enabling developers to create reproducible software and verify implementation equivalence. FPRev is a testing-based tool that non-intrusively reveals the accumulation order by analyzing the outputs of the tested implementation for distinct specially designed inputs. Employing FPRev, we showcase the accumulation orders of popular libraries (such as NumPy and PyTorch) on CPUs and GPUs (including GPUs with specialized matrix accelerators such as Tensor Cores). We also validate the efficiency of FPRev through extensive experiments. FPRev exhibits a lower time complexity compared to the basic solution. FPRev is open-sourced at https://github.com/peichenxie/FPRev.

math.NA↗

arXiv2024

Hyb Error: A Hybrid Metric Combining Absolute and Relative Errors

Suppose $x$ is an approximation of $y$. This paper proposes using $\frac{|x-y|}{1+|y|}$, named Hyb Error, to measure the error. This metric equals half the harmonic mean of absolute error and relative error, effectively combining their advantages while mitigating their limitations. For example, Hyb Error approaches absolute error as $|y|$ approaches 0, thereby avoiding the exaggeration of relative error, and approaches relative error as $|y|$ approaches infinity, thereby avoiding the exaggeration of absolute error. The Hyb Error of $\epsilon$ is equivalent to $|x-y|=\epsilon+\epsilon |y|$, which implies $\mathrm{isclose}(x,y,\epsilon,\epsilon)=\mathrm{True}$, where ``isclose'' is a common floating-point equality check function in numerical libraries. For sequences, this property makes the Maximum Element-wise Hyb Error (MEHE) a pragmatic error metric that reflects the most significant error and equals the decision boundary of the ``isclose'' function.

math.NA↗

arXiv2022

Decentralized Verifiable Mail-in Ballot Counting for Postal Voting

As computer vision is prevalently used for mail-in ballot processing and counting, it becomes a point of centralized trust in postal voting. We propose DVote, a prototype system of postal voting that provides decentralized trust in computer vision. With blockchain and layer-2 technologies, DVote decentralizes the computation and model training of computer vision to a group of scrutineers that hold the AnyTrust assumption, i.e., at least one member is honest. Consequently, the computational integrity is anchored to the trustworthiness of a large public blockchain such as Ethereum.

cs.CR↗

arXiv2021

Agatha: Smart Contract for DNN Computation

Smart contract is one of the core features of Ethereum and has inspired many blockchain descendants. Since its advent, the verification paradigm of smart contract has been improving toward high scalability. It shifts from the expensive on-chain verification to the orchestration of off-chain VM (virtual machine) execution and on-chain arbitration with the pinpoint protocol. The representative projects are TrueBit, Arbitrum, YODA, ACE, and Optimism. Inspired by visionaries in academia and industry, we consider the DNN computation to be promising but on the next level of complexity for the verification paradigm of smart contract. Unfortunately, even for the state-of-the-art verification paradigm, off-chain VM execution of DNN computation has an orders-of-magnitude slowdown compared to the native off-chain execution. To enable the native off-chain execution of verifiable DNN computation, we present Agatha system, which solves the significant challenges of misalignment and inconsistency: (1) Native DNN computation has a graph-based computation paradigm misaligned with previous VM-based execution and arbitration; (2) Native DNN computation may be inconsistent cross platforms which invalidates the verification paradigm. In response, we propose the graph-based pinpoint protocol (GPP) which enables the pinpoint protocol on computational graphs, and bridges the native off-chain execution and the contract arbitration. We also develop a technique named Cross-evaluator Consistent Execution (XCE), which guarantees cross-platform consistency and forms the correctness foundation of GPP. We showcase Agatha for the DNN computation of popular models (MobileNet, ResNet50 and VGG16) on Ethereum. Agatha achieves a negligible on-chain overhead, and an off-chain execution overhead of 3.0%, which represents an off-chain latency reduction of at least 602x compared to the state-of-the-art verification paradigm.

cs.CR↗

arXiv2020

Customizing Trusted AI Accelerators for Efficient Privacy-Preserving Machine Learning

The use of trusted hardware has become a promising solution to enable privacy-preserving machine learning. In particular, users can upload their private data and models to a hardware-enforced trusted execution environment (e.g. an enclave in Intel SGX-enabled CPUs) and run machine learning tasks in it with confidentiality and integrity guaranteed. To improve performance, AI accelerators have been widely employed for modern machine learning tasks. However, how to protect privacy on an AI accelerator remains an open question. To address this question, we propose a solution for efficient privacy-preserving machine learning based on an unmodified trusted CPU and a customized trusted AI accelerator. We carefully leverage cryptographic primitives to establish trust and protect the channel between the CPU and the accelerator. As a case study, we demonstrate our solution based on the open-source versatile tensor accelerator. The result of evaluation shows that the proposed solution provides efficient privacy-preserving machine learning at a small design cost and moderate performance overhead.

cs.AR↗

arXiv2019

BAYHENN: Combining Bayesian Deep Learning and Homomorphic Encryption for Secure DNN Inference

Recently, deep learning as a service (DLaaS) has emerged as a promising way to facilitate the employment of deep neural networks (DNNs) for various purposes. However, using DLaaS also causes potential privacy leakage from both clients and cloud servers. This privacy issue has fueled the research interests on the privacy-preserving inference of DNN models in the cloud service. In this paper, we present a practical solution named BAYHENN for secure DNN inference. It can protect both the client's privacy and server's privacy at the same time. The key strategy of our solution is to combine homomorphic encryption and Bayesian neural networks. Specifically, we use homomorphic encryption to protect a client's raw data and use Bayesian neural networks to protect the DNN weights in a cloud server. To verify the effectiveness of our solution, we conduct experiments on MNIST and a real-life clinical dataset. Our solution achieves consistent latency decreases on both tasks. In particular, our method can outperform the best existing method (GAZELLE) by about 5x, in terms of end-to-end latency.

cs.CR↗