arXiv subjects

Tal Ben-Nun

Publications and source records attributed to Tal Ben-Nun.

At least 37 records · Page 2Linked to original sources

arXiv2023

VENOM: A Vectorized N:M Format for Unleashing the Power of Sparse Tensor Cores

The increasing success and scaling of Deep Learning models demands higher computational efficiency and power. Sparsification can lead to both smaller models as well as higher compute efficiency, and accelerated hardware is becoming available. However, exploiting it efficiently requires kernel implementations, pruning algorithms, and storage formats, to utilize hardware support of specialized sparse vector units. An example of those are the NVIDIA's Sparse Tensor Cores (SPTCs), which promise a 2x speedup. However, SPTCs only support the 2:4 format, limiting achievable sparsity ratios to 50%. We present the V:N:M format, which enables the execution of arbitrary N:M ratios on SPTCs. To efficiently exploit the resulting format, we propose Spatha, a high-performance sparse-library for DL routines. We show that Spatha achieves up to 37x speedup over cuBLAS. We also demonstrate a second-order pruning technique that enables sparsification to high sparsity ratios with V:N:M and little to no loss in accuracy in modern transformers.

cs.DC↗

arXiv2023

Cached Operator Reordering: A Unified View for Fast GNN Training

Graph Neural Networks (GNNs) are a powerful tool for handling structured graph data and addressing tasks such as node classification, graph classification, and clustering. However, the sparse nature of GNN computation poses new challenges for performance optimization compared to traditional deep neural networks. We address these challenges by providing a unified view of GNN computation, I/O, and memory. By analyzing the computational graphs of the Graph Convolutional Network (GCN) and Graph Attention (GAT) layers -- two widely used GNN layers -- we propose alternative computation strategies. We present adaptive operator reordering with caching, which achieves a speedup of up to 2.43x for GCN compared to the current state-of-the-art. Furthermore, an exploration of different caching schemes for GAT yields a speedup of up to 1.94x. The proposed optimizations save memory, are easily implemented across various hardware platforms, and have the potential to alleviate performance bottlenecks in training large-scale GNN models.

cs.LG↗

arXiv2023

Maximum Flows in Parametric Graph Templates

Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template representation allows us to reason about the execution graph of a parallel program at a cost that only depends on the program size. We develop structurally-parametric polynomial-time algorithm variants of maximum flows. When the graph models a parallel loop program, the maximum flow provides a bound on the data movement during an execution of the program. By reasoning about the structure of the repeating subgraphs, we avoid explicit construction of the instantiation (e.g., the execution graph), potentially saving an exponential amount of memory and computation. Hence, our approach enables graph-based dataflow analysis in previously intractable settings.

cs.DS↗

arXiv2023

FuzzyFlow: Leveraging Dataflow To Find and Squash Program Optimization Bugs

The current hardware landscape and application scale is driving performance engineers towards writing bespoke optimizations. Verifying such optimizations, and generating minimal failing cases, is important for robustness in the face of changing program conditions, such as inputs and sizes. However, isolation of minimal test-cases from existing applications and generating new configurations are often difficult due to side effects on the system state, mostly related to dataflow. This paper introduces FuzzyFlow: a fault localization and test case extraction framework designed to test program optimizations. We leverage dataflow program representations to capture a fully reproducible system state and area-of-effect for optimizations to enable fast checking for semantic equivalence. To reduce testing time, we design an algorithm for minimizing test inputs, trading off memory for recomputation. We demonstrate FuzzyFlow on example use cases in real-world applications where the approach provides up to 528 times faster optimization testing and debugging compared to traditional approaches.

cs.SE↗

arXiv2023

Bridging Control-Centric and Data-Centric Optimization

With the rise of specialized hardware and new programming languages, code optimization has shifted its focus towards promoting data locality. Most production-grade compilers adopt a control-centric mindset - instruction-driven optimization augmented with scalar-based dataflow - whereas other approaches provide domain-specific and general purpose data movement minimization, which can miss important control-flow optimizations. As the two representations are not commutable, users must choose one over the other. In this paper, we explore how both control- and data-centric approaches can work in tandem via the Multi-Level Intermediate Representation (MLIR) framework. Through a combination of an MLIR dialect and specialized passes, we recover parametric, symbolic dataflow that can be optimized within the DaCe framework. We combine the two views into a single pipeline, called DCIR, showing that it is strictly more powerful than either view. On several benchmarks and a real-world application in C, we show that our proposed pipeline consistently outperforms MLIR and automatically uncovers new optimization opportunities with no additional effort.

cs.PL↗

arXiv2023

On the Parallel I/O Optimality of Linear Algebra Kernels: Near-Optimal Matrix Factorizations

Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for Cholesky and LU factorizations that utilize an asymptotically communication-optimal 2.5D decomposition. We first establish a theoretical framework for deriving parallel I/O lower bounds for linear algebra kernels, and then utilize its insights to derive Cholesky and LU schedules, both communicating N^3/(P*sqrt(M)) elements per processor, where M is the local memory size. The empirical results match our theoretical analysis: our implementations communicate significantly less than Intel MKL, SLATE, and the asymptotically communication-optimal CANDMC and CAPITAL libraries. Our code outperforms these state-of-the-art libraries in almost all tested scenarios, with matrix sizes ranging from 2,048 to 262,144 on up to 512 CPU nodes of the Piz Daint supercomputer, decreasing the time-to-solution by up to three times. Our code is ScaLAPACK-compatible and available as an open-source library.

cs.DC↗

arXiv2023

STen: Productive and Efficient Sparsity in PyTorch

As deep learning models grow, sparsity is becoming an increasingly critical component of deep neural networks, enabling improved performance and reduced storage. However, existing frameworks offer poor support for sparsity. Specialized sparsity engines focus exclusively on sparse inference, while general frameworks primarily focus on sparse tensors in classical formats and neglect the broader sparsification pipeline necessary for using sparse models, especially during training. Further, existing frameworks are not easily extensible: adding a new sparse tensor format or operator is challenging and time-consuming. To address this, we propose STen, a sparsity programming model and interface for PyTorch, which incorporates sparsity layouts, operators, and sparsifiers, in an efficient, customizable, and extensible framework that supports virtually all sparsification methods. We demonstrate this by developing a high-performance grouped n:m sparsity layout for CPU inference at moderate sparsity. STen brings high performance and ease of use to the ML community, making sparsity easily accessible.

cs.LG↗

arXiv2023

Performance Embeddings: A Similarity-based Approach to Automatic Performance Optimization

Performance optimization is an increasingly challenging but often repetitive task. While each platform has its quirks, the underlying code transformations rely on data movement and computational characteristics that recur across applications. This paper proposes to leverage those similarities by constructing an embedding space for subprograms. The continuous space captures both static and dynamic properties of loop nests via symbolic code analysis and performance profiling, respectively. Performance embeddings enable direct knowledge transfer of performance tuning between applications, which can result from autotuning or tailored improvements. We demonstrate this transfer tuning approach on case studies in deep neural networks, dense and sparse linear algebra compositions, and numerical weather prediction stencils. Transfer tuning reduces the search complexity by up to four orders of magnitude and outperforms the MKL library in sparse-dense matrix multiplication. The results exhibit clear correspondences between program characteristics and optimizations, outperforming prior specialized state-of-the-art approaches and generalizing beyond their capabilities.

cs.SE↗

arXiv2023

The spatial computer: A model for energy-efficient parallel computation

We present a new parallel model of computation suitable for spatial architectures, for which the energy used for communication heavily depends on the distance of the communicating processors. In our model, processors have locations on a conceptual two-dimensional grid, and their distance therein determines their communication cost. In particular, we introduce the energy cost of a spatial computation, which measures the total distance traveled by all messages, and study the depth of communication, which measures the largest number of hops of a chain of messages. We show matching energy lower- and upper bounds for many foundational problems, including sorting, median selection, and matrix multiplication. Our model does not depend on any parameters other than the input shape and size, simplifying algorithm analysis. We also show how to simulate PRAM algorithms in our model and how to obtain results for a more complex model that introduces the size of the local memories of the processors as a parameter.

cs.DS↗

arXiv2023

A Theory of I/O-Efficient Sparse Neural Network Inference

As the accuracy of machine learning models increases at a fast rate, so does their demand for energy and compute resources. On a low level, the major part of these resources is consumed by data movement between different memory units. Modern hardware architectures contain a form of fast memory (e.g., cache, registers), which is small, and a slow memory (e.g., DRAM), which is larger but expensive to access. We can only process data that is stored in fast memory, which incurs data movement (input/output-operations, or I/Os) between the two units. In this paper, we provide a rigorous theoretical analysis of the I/Os needed in sparse feedforward neural network (FFNN) inference. We establish bounds that determine the optimal number of I/Os up to a factor of 2 and present a method that uses a number of I/Os within that range. Much of the I/O-complexity is determined by a few high-level properties of the FFNN (number of inputs, outputs, neurons, and connections), but if we want to get closer to the exact lower bound, the instance-specific sparsity patterns need to be considered. Departing from the 2-optimal computation strategy, we show how to reduce the number of I/Os further with simulated annealing. Complementing this result, we provide an algorithm that constructively generates networks with maximum I/O-efficiency for inference. We test the algorithms and empirically verify our theoretical and algorithmic contributions. In our experiments on real hardware we observe speedups of up to 45$\times$ relative to the standard way of performing inference.

cs.DC↗

arXiv2022

Python FPGA Programming with Data-Centric Multi-Level Design

Although high-level synthesis (HLS) tools have significantly improved programmer productivity over hardware description languages, developing for FPGAs remains tedious and error prone. Programmers must learn and implement a large set of vendor-specific syntax, patterns, and tricks to optimize (or even successfully compile) their applications, while dealing with ever-changing toolflows from the FPGA vendors. We propose a new way to develop, optimize, and compile FPGA programs. The Data-Centric parallel programming (DaCe) framework allows applications to be defined by their dataflow and control flow through the Stateful DataFlow multiGraph (SDFG) representation, capturing the abstract program characteristics, and exposing a plethora of optimization opportunities. In this work, we show how extending SDFGs with multi-level Library Nodes incorporates both domain-specific and platform-specific optimizations into the design flow, enabling knowledge transfer across application domains and FPGA vendors. We present the HLS-based FPGA code generation backend of DaCe, and show how SDFGs are code generated for either FPGA vendor, emitting efficient HLS code that is structured and annotated to implement the desired architecture.

cs.DC↗

arXiv2022

ENS-10: A Dataset For Post-Processing Ensemble Weather Forecasts

Post-processing ensemble prediction systems can improve the reliability of weather forecasting, especially for extreme event prediction. In recent years, different machine learning models have been developed to improve the quality of weather post-processing. However, these models require a comprehensive dataset of weather simulations to produce high-accuracy results, which comes at a high computational cost to generate. This paper introduces the ENS-10 dataset, consisting of ten ensemble members spanning 20 years (1998-2017). The ensemble members are generated by perturbing numerical weather simulations to capture the chaotic behavior of the Earth. To represent the three-dimensional state of the atmosphere, ENS-10 provides the most relevant atmospheric variables at 11 distinct pressure levels and the surface at 0.5-degree resolution for forecast lead times T=0, 24, and 48 hours (two data points per week). We propose the ENS-10 prediction correction task for improving the forecast quality at a 48-hour lead time through ensemble post-processing. We provide a set of baselines and compare their skill at correcting the predictions of three important atmospheric variables. Moreover, we measure the baselines' skill at improving predictions of extreme weather events using our dataset. The ENS-10 dataset is available under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

cs.LG↗

arXiv2022

Temporal Vectorization: A Compiler Approach to Automatic Multi-Pumping

The multi-pumping resource sharing technique can overcome the limitations commonly found in single-clocked FPGA designs by allowing hardware components to operate at a higher clock frequency than the surrounding system. However, this optimization cannot be expressed in high levels of abstraction, such as HLS, requiring the use of hand-optimized RTL. In this paper we show how to leverage multiple clock domains for computational subdomains on reconfigurable devices through data movement analysis on high-level programs. We offer a novel view on multi-pumping as a compiler optimization - a superclass of traditional vectorization. As multiple data elements are fed and consumed, the computations are packed temporally rather than spatially. The optimization is applied automatically using an intermediate representation that maps high-level code to HLS. Internally, the optimization injects modules into the generated designs, incorporating RTL for fine-grained control over the clock domains. We obtain a reduction of resource consumption by up to 50% on critical components and 23% on average. For scalable designs, this can enable further parallelism, increasing overall performance.

cs.DC↗

arXiv2022

A Data-Centric Optimization Framework for Machine Learning

Rapid progress in deep learning is leading to a diverse set of quickly changing models, with a dramatically growing demand for compute. However, as frameworks specialize performance optimization to patterns in popular networks, they implicitly constrain novel and diverse models that drive progress in research. We empower deep learning researchers by defining a flexible and user-customizable pipeline for optimizing training of arbitrary deep neural networks, based on data movement minimization. The pipeline begins with standard networks in PyTorch or ONNX and transforms computation through progressive lowering. We define four levels of general-purpose transformations, from local intra-operator optimizations to global data movement reduction. These operate on a data-centric graph intermediate representation that expresses computation and data movement at all levels of abstraction, including expanding basic operators such as convolutions to their underlying computations. Central to the design is the interactive and introspectable nature of the pipeline. Every part is extensible through a Python API, and can be tuned interactively using a GUI. We demonstrate competitive performance or speedups on ten different networks, with interactive optimizations discovering new opportunities in EfficientNet.

cs.LG↗

arXiv2022

Productive Performance Engineering for Weather and Climate Modeling with Python

Earth system models are developed with a tight coupling to target hardware, often containing specialized code predicated on processor characteristics. This coupling stems from using imperative languages that hard-code computation schedules and layout. We present a detailed account of optimizing the Finite Volume Cubed-Sphere Dynamical Core (FV3), improving productivity and performance. By using a declarative Python-embedded stencil domain-specific language and data-centric optimization, we abstract hardware-specific details and define a semi-automated workflow for analyzing and optimizing weather and climate applications. The workflow utilizes both local and full-program optimization, as well as user-guided fine-tuning. To prune the infeasible global optimization space, we automatically utilize repeating code motifs via a novel transfer tuning approach. On the Piz Daint supercomputer, we scale to 2,400 GPUs, achieving speedups of up to 3.92x over the tuned production implementation at a fraction of the original code.

cs.DC↗

arXiv2022

Boosting Performance Optimization with Interactive Data Movement Visualization

Optimizing application performance in today's hardware architecture landscape is an important, but increasingly complex task, often requiring detailed performance analyses. In particular, data movement and reuse play a crucial role in optimization and are often hard to improve without detailed program inspection. Performance visualizations can assist in the diagnosis of performance problems, but generally rely on data gathered through lengthy program executions. In this paper, we present a performance visualization geared towards analyzing data movement and reuse to inform impactful optimization decisions, without requiring program execution. We propose an approach that combines static dataflow analysis with parameterized program simulations to analyze both global data movement and fine-grained data access and reuse behavior, and visualize insights in-situ on the program representation. Case studies analyzing and optimizing real-world applications demonstrate our tool's effectiveness in guiding optimization decisions and making the performance tuning process more interactive.

cs.SE↗

arXiv2022

Deinsum: Practically I/O Optimal Multilinear Algebra

Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously hard problem. State-of-the-art libraries rely on heuristics and often fall back to suboptimal tensor folding and BLAS calls. We present Deinsum, an automated framework for distributed multilinear algebra computations expressed in Einstein notation, based on rigorous mathematical tools to address this problem. Our framework automatically derives data movement-optimal tiling and generates corresponding distributed schedules, further optimizing the performance of local computations by increasing their arithmetic intensity. To show the benefits of our approach, we test it on two important tensor kernel classes: Matricized Tensor Times Khatri-Rao Products and Tensor Times Matrix chains. We show performance results and scaling on the Piz Daint supercomputer, with up to 19x speedup over state-of-the-art solutions on 512 nodes.

cs.DC↗

arXiv2022

Lifting C Semantics for Dataflow Optimization

C is the lingua franca of programming and almost any device can be programmed using C. However, programming mod-ern heterogeneous architectures such as multi-core CPUs and GPUs requires explicitly expressing parallelism as well as device-specific properties such as memory hierarchies. The resulting code is often hard to understand, debug, and modify for different architectures. We propose to lift C programs to a parametric dataflow representation that lends itself to static data-centric analysis and enables automatic high-performance code generation. We separate writing code from optimizing for different hardware: simple, portable C source code is used to generate efficient specialized versions with a click of a button. Our approach can identify parallelism when no other compiler can, and outperforms a bespoke parallelized version of a scientific proxy application by up to 21%.

cs.PL↗