Very long baseline interferometry (VLBI) achieves the highest angular resolution in astronomy. VLBI measures corrupted Fourier components, known as visibilities. Reconstructing on-sky images from these visibilities is a challenging inverse problem, particularly for sparse arrays such as the Event Horizon Telescope (EHT) and the Very Long Baseline Array, where incomplete sampling and severe calibration errors introduce significant uncertainty in the image. To help guide convergence and control the uncertainty in image reconstructions, regularization on the space of images is utilized, such as enforcing smoothness or similarity to a fiducial image. Coupled with this regularization is the introduction of a new set of parameters that modulate its strength. We present a hierarchical Bayesian imaging approach (hierarchical interferometric Bayesian Imaging, HIBI) that enables the quantification of uncertainty for all parameters. Incorporating instrumental effects within HIBI is straightforward, allowing for simultaneous imaging and calibration of data. To showcase HIBI’s effectiveness and flexibility, we build a simple imaging model based on Markov random fields and demonstrate how different physical components can be included, e.g., black hole shadow size, and their uncertainties can be inferred. For example, while the original EHT publications were unable to constrain the ring width of M87*, HIBI measures a width of 9.3 ± 1.3 μ as. We apply HIBI to image and calibrate EHT synthetic data, real EHT observations of M87*, and multifrequency observations of OJ 287. Across these tests, HIBI accurately recovers a wide variety of image structures and quantifies their uncertainties. HIBI is publicly available in the Comrade VLBI software repository.

The proliferation of low-precision units in modern high-performance architectures increasingly burdens domain scientists. Historically, the choice in HPC was easy: can we get away with 32 bit floating-point operations and lower bandwidth requirements, or is FP64 necessary? Driven by Artificial Intelligence, vendors introduce novel low-precision units for vector and tensor operations, and FP64 capabilities stagnate or are reduced. This forces scientists to re-evaluate their codes, but a trivial search-and-replace approach to go from FP64 to FP16 will not suffice. We introduce RAPTOR: a numerical profiling tool to guide scientists in their search for code regions where precision lowering is feasible. Using LLVM, we transparently replace high-precision computations using low-precision units, or emulate a user-defined precision. RAPTOR is a novel, feature-rich approach-with focus on ease of use-to change, profile, and reason about numerical requirements and instabilities, which we demonstrate with four real-world multi-physics Flash-X applications.

To take full advantage of a specific hardware target, performance engineers need to gain control on compilers in order to leverage their domain knowledge about the program and hardware. Yet, modern compilers are poorly controlled, usually by configuring a sequence of coarse-grained monolithic black-box passes, or by means of predefined compiler annotations/pragmas. These can be effective, but often do not let users precisely optimize their varying compute loads. As a consequence, performance engineers have to resort to implementing custom passes for a specific optimization heuristic, requiring compiler engineering expert knowledge. In this paper, we present a technique that provides fine-grained control of general-purpose compilers by introducing the Transform dialect, a controllable IR-based transformation system implemented in MLIR. The Transform dialect empowers performance engineers to optimize their various compute loads by composing and reusing existing - but currently hidden - compiler features without the need to implement new passes or even rebuilding the compiler. We demonstrate in five case studies that the Transform dialect enables precise, safe composition of compiler transformations and allows for straightforward integration with state-of-the-art search methods.

Machine learning (ML) compilers rely on graph-level transformations to enhance the runtime performance of ML models. However, performing local transformations on individual operations can create effects far beyond the location of the rewrite. In particular, a local rewrite can change the profitability or legality of hard-to-predict downstream transformations, particularly regarding data layout, parallelization, fine-grained scheduling, and memory management. As a result, program transformations are often driven by manually-tuned compiler heuristics, which are quickly rendered obsolete by new hardware and model architectures. Instead of hand-written local heuristics, we propose the use of equality saturation. We replace such heuristics with a more robust global performance model, which accounts for downstream transformations. Equality saturation addresses the challenge of local optimizations inadvertently constraining or negating the benefits of subsequent transformations, thereby providing a solution that is inherently adaptable to newer workloads. While this approach still requires a global performance model to evaluate the profitability of transformations, it holds significant promise for increased automation and adaptability. This paper addresses challenges in applying equality saturation on real-world ML compute graphs and state-of-the-art hardware. By doing so, we present an improved method for discovering effective compositions of graph optimizations. We study different cost modeling approaches to deal with fusion and layout optimization, and tackle scalability issues that arise from considering a very wide range of algebraic optimizations. We design an equality saturation pass for the XLA compiler, with an implementation in C++ and Rust. We demonstrate an average speedup of 3.45% over XLA’s optimization flow across our benchmark suite on various CPU and GPU platforms, with a maximum speedup of 56.26% for NasRNN on CPU.

Computing derivatives is paramount for multiple domains ranging from training neural networks to precise climate simulations. While derivatives can be generated by AD (Automatic Differentiation) tools, they often require aggressive optimization to avoid compromising program performance. One of the central optimizations consists of identifying inactive operations that do not contribute to the partial derivatives of interest. Multiple tools provide activity analyses for a variety of input languages, though often with only informal correctness guarantees. This paper formally defines activity analysis for AD as an abstract interpretation, proves its soundness, and implements it within the MLIR compiler infrastructure. To account for MLIR's genericity, a subset of MLIR's internal representation amenable to AD is formalized for the first time. Furthermore, the paper proposes a sound intraprocedural approximation of the whole-program activity analysis via function summaries along with a mechanism to automatically derive these summaries from function definitions. The implementation is evaluated on a differentiation-specific benchmark suite. It achieves a 1.24x geometric mean speedup on CPU and a 1.7x geometric mean speedup on GPU in the runtime of generated programs, when compared to a baseline that does not use activity analysis. The evaluation also demonstrates that the intraprocedural analysis with function summaries proves inactive 100% of instructions proven inactive by the whole-program analysis.

The size and complexity of software applications is increasing at an accelerating pace. Source code repositories (along with their dependencies) require vast amounts of labor to keep them tested, maintained, and up to date. As the discipline now begins to also incorporate automatically generated programs, automation in testing and tuning is required to keep up with the pace - let alone reduce the present level of complexity. While machine learning has been used to understand and generate code in various contexts, machine learning models themselves are trained almost exclusively on static code without inputs, traces, or other execution time information. This lack of training data limits the ability of these models to understand real-world problems in software. In this work we show that inputs, like code, can be generated automatically at scale. Our generated inputs are stateful, and appear to faithfully reproduce the arbitrary data structures and system calls required to rerun a program function. By building our tool within the compiler, it both can be applied to arbitrary programming languages and architectures and can leverage static analysis and transformations for improved performance. Our approach is able to produce valid inputs, including initial memory states, for 90 dataset modules we explored, for a total of 21.4 million executable functions. Further, we find that a single generated input results in an average block coverage of 37

Code is increasingly becoming a core data modality of modern machine learning research impacting not only the way we write code with conversational agents like OpenAI's ChatGPT, Google's Bard, or Anthropic's Claude, the way we translate code from one language into another, but also the compiler infrastructure underlying the language. While modeling approaches may vary and representations differ, the targeted tasks often remain the same within the individual classes of models. Relying solely on the ability of modern models to extract information from unstructured code does not take advantage of 70 years of programming language and compiler development by not utilizing the structure inherent to programs in the data collection. This detracts from the performance of models working over a tokenized representation of input code and precludes the use of these models in the compiler itself. To work towards the first intermediate representation (IR) based models, we fully utilize the LLVM compiler infrastructure, shared by a number of languages, to generate a 182B token dataset of LLVM IR. We generated this dataset from programming languages built on the shared LLVM infrastructure, including Rust, Swift, Julia, and C/C++, by hooking into LLVM code generation either through the language's package manager or the compiler directly to extract the dataset of intermediate representations from production grade programs. Statistical analysis proves the utility of our dataset not only for large language model training, but also for the introspection into the code generation process itself with the dataset showing great promise for machine-learned compiler components.

In order to come close to peak performance, accelerators like GPUs require significant architecture-specific tuning that understand the availability of shared memory, parallelism, tensor cores, etc. Unfortunately, the pursuit of higher performance and lower costs have led to a significant diversification of architecture designs, even from the same vendor. This creates the need for performance portability across different GPUs, especially important for programs in a particular programming model with a certain architecture in mind. Even when the program can be seamlessly executed on a different architecture, it may suffer a performance penalty due to it not being sized appropriately to the available hardware resources such as fast memory and registers, let alone not using newer advanced features of the architecture. We propose a new approach to improving performance of (legacy) CUDA programs for modern machines by automatically adjusting the amount of work each parallel thread does, and the amount of memory and register resources it requires. By operating within the MLIR compiler infrastructure, we are able to also target AMD GPUs by performing automatic translation from CUDA and simultaneously adjust the program granularity to fit the size of target GPUs. Combined with autotuning assisted by the platform-specific compiler, our approach demonstrates 27% geomean speedup on the Rodinia benchmark suite over baseline CUDA implementation as well as performance parity between similar NVIDIA and AMD GPUs executing the same CUDA program.

AbstractAutomatic differentiation is a popular technique for computing derivatives of computer programs. While automatic differentiation has been successfully used in countless engineering, science, and machine learning applications, it can sometimes nevertheless produce surprising results. In this paper, we categorize problematic usages of automatic differentiation, and illustrate each category with examples such as chaos, time‐averages, discretizations, fixed‐point loops, lookup tables, linear solvers, and probabilistic programs, in the hope that readers may more easily avoid or detect such pitfalls. We also review debugging techniques and their effectiveness in these situations.This article is categorized under: Technologies > Machine Learning

Automatic differentiation (AutoDiff) in machine learning is largely restricted to expressions used for neural networks (NN), with the depth rarely exceeding a few tens of layers. Compared to NN, numerical simulations typically involve iterative algorithms like time steppers that lead to millions of iterations. Even for modest-sized models, this may yield infeasible memory requirements when applying the adjoint method, also called backpropagation, to time-dependent problems. In this situation, checkpointing algorithms provide a trade-off between recomputation and storage. This paper presents the package Checkpointing.jl that leverages expression transformations in the programming language Julia and the package ChainRules.jl to automatically and transparently transform loop iterations into differentiated loops. The user may choose between various checkpointing algorithm schemes and storage devices. We describe the unique design of Checkpointing.jl and demonstrate its features on an automatically differentiated MPI implementation of Burgers' equation on the Polaris cluster at the Argonne Leadership Computing Facility.

. Automatic differentiation (AutoDiff) in machine learning is largely restricted to expressions used for neural networks (NN), with the depth rarely exceeding a few tens of layers. Compared to NN, numerical simulations typically involve iterative algorithms like time steppers that lead to millions of iterations. Even for modest-sized models, this may yield infeasible memory requirements when applying the adjoint method, also called backpropagation, to time-dependent problems. In this situation, checkpointing algorithms provide a trade-off between recomputation and storage. This paper presents the package Checkpointing.jl that leverages expression transformations in the programming language Julia and the package ChainRules.jl to automatically and transparently transform loop iterations into differentiated loops. The user may choose between various checkpointing algorithm schemes and storage devices. We describe the unique design of Checkpointing.jl and demonstrate its features on an automatically differentiated MPI implementation of Burgers’ equation on the Polaris cluster at the Argonne Leadership Computing Facility.

Automatic differentiation, also known as backpropagation, AD, autodiff, or algorithmic differentiation, is a popular technique for computing derivatives of computer programs accurately and efficiently. Sometimes, however, the derivatives computed by AD could be interpreted as incorrect. These pitfalls occur systematically across tools and approaches. In this paper we broadly categorize problematic usages of AD and illustrate each category with examples such as chaos, time-averaged oscillations, discretizations, fixed-point loops, lookup tables, and linear solvers. We also review debugging techniques and their effectiveness in these situations. With this article we hope to help readers avoid unexpected behavior, detect problems more easily when they occur, and have more realistic expectations from AD tools.

Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper, we introduce a framework for answering this question both intuitively and quantitatively. The underlying structure of the framework is a race between quantum and classical computers, where their relative strengths determine when each wins. While classical computers operate faster, quantum computers can sometimes run more efficient algorithms. Whether the speed advantage or the algorithmic advantage dominates determines whether a problem will benefit from quantum computing or not. Our analysis reveals that many problems, particularly those of small to moderate size that can be important for typical businesses, will not benefit from quantum computing. Conversely, larger problems or those with particularly big algorithmic gains will benefit from near-term quantum computing. Since very large algorithmic gains are rare in practice and theorized to be rare even in principle, our analysis suggests that the benefits from quantum computing will flow either to users of these rare cases, or practitioners processing very large data.

While parallelism remains the main source of performance, architectural implementations and programming models change with each new hardware generation, often leading to costly application re-engineering. Most tools for performance portability require manual and costly application porting to yet another programming model. We propose an alternative approach that automatically translates programs written in one programming model (CUDA), into another (CPU threads) based on Polygeist/MLIR. Our approach includes a representation of parallel constructs that allows conventional compiler transformations to apply transparently and without modification and enables parallelism-specific optimizations. We evaluate our framework by transpiling and optimizing the CUDA Rodinia benchmark suite for a multi-core CPU and achieve a 58% geomean speedup over handwritten OpenMP code. Further, we show how CUDA kernels from PyTorch can efficiently run and scale on the CPU-only Supercomputer Fugaku without user intervention. Our PyTorch compatibility layer making use of transpiled CUDA PyTorch kernels outperforms the PyTorch CPU native backend by 2.7×.

Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that high-order methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs; these data structures also offer up to 2x benefit for linear elements. We demonstrate the reliability, efficiency, and scalability of matrix-free p-multigrid methods with algebraic multigrid coarse solvers through large deformation hyperelastic simulations of multiscale structures. We investigate accuracy, cost, and execution time on multi-node CPU and GPU systems for moderate to large models (millions to billions of degrees of freedom) using AMD MI250X (OLCF Crusher), NVIDIA A100 (NERSC Perlmutter), and V100 (LLNL Lassen and OLCF Summit), resulting in order of magnitude efficiency improvements over a broad range of model properties and scales. We discuss efficient matrix-free representation of Jacobians and demonstrate how automatic differentiation enables rapid development of nonlinear material models without impacting debuggability and workflows targeting GPUs. The methods are broadly applicable and amenable to common workflows, presented here via open source libraries that encapsulate all GPU-specific aspects and are accessible to both new and legacy code, allowing application code to be GPU-oblivious without compromising end-to-end performance on GPUs.

Derivatives are key to numerous science, engineering, and machine learning applications. While existing tools generate derivatives of programs in a single language, modern parallel applications combine a set of frameworks and languages to leverage available performance and function in an evolving hardware landscape. We propose a scheme for differentiating arbitrary DAG-based parallelism that preserves scalability and efficiency, implemented into the LLVM-based Enzyme automatic differentiation framework. By integrating with a full-fledged compiler backend, Enzyme can differentiate numerous parallel frameworks and directly control code generation. Combined with its ability to differentiate any LLVM-based language, this flexibility permits Enzyme to leverage the compiler tool chain for parallel and differentiation-specitic optimizations. We differentiate nine distinct versions of the LULESH and miniBUDE applications, written in different programming languages (C++, Julia) and parallel frameworks (OpenMP, MPI, RAJA, Julia tasks, MPI.jl), demonstrating similar scalability to the original program. On benchmarks with 64 threads or nodes, we find a differentiation overhead of 3.4–6.8× on C++ and 5.4–12.5× on Julia.

Unlike prior approaches to machine learning, Transformer models can first be trained on a large corpus of unlabeled data with a generic objective and then on a smaller task-specific dataset. This versatility has led to both larger models and datasets. Consequently, Transformers have led to breakthroughs in the field of natural language processing. Generic program optimization presently operates on low-level programs such as LLVM. Unlike the high-level languages (e.g. C, Python, Java), which have seen initial success in machine-learning analyses, lower-level languages tend to be more verbose and repetitive to precisely specify program behavior, provide more details about microarchitecture, and derive properties necessary for optimization, all of which makes it difficult for machine learning. In this work, we apply transfer learning to low-level (LLVM) programs and study how low-level programs can be made more amenable to Transformer models through various techniques, including preprocessing, infix/prefix operators, and information deduplication. We evaluate the effectiveness of these techniques through a series of ablation studies on the task of translating C to both unoptimized (-O0) and optimized (-01) LLVM IR. On the AnghaBench dataset, our model achieves a 49.57% verbatim match and BLEU score of 87.68 against Clang -O0 and 38.73% verbatim match and BLEU score of 77.03 against Clang -O1.

Recently, transformer networks have enabled breakthroughs in the field of natural language processing. This is partially due to the fact that transformer models can be first trained on a large corpus of unlabeled data prior to fine-tuning on a downstream task. Unlike natural language, which is somewhat tolerant of minor differences in word choices or ordering, the structured nature of programming languages means that program meaning can be completely redefined or be invalid if even one token is altered. In comparison to high-level languages, low-level languages are less expressive and more repetitive with more details from the computer microarchitecture. Whereas recent literature has examined how to effectively use transformer models on high-level programming semantics, this project explores the effectiveness of applying transformer models on low-level representations of programs that can shed light on better optimizing compilers. In this paper, we show that transformer models can translate C to LLVM-IR with high accuracy, by training on a parallel corpus of functions extract from 1 million compilable, open-sourced C programs (AnghaBench) and its corresponding LLVM-IR after compiling with Clang. We also present another case study that analyzes x86_64 basic blocks for estimating their throughput. We discuss various changes in data selection, program representation, network architecture, and other modifications that influence the effectiveness of transformer models on low-level programs.