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Proceedings of the 36th Symposium on Implementation and Application of Functional Languages

作者： Marco T. Morazán Oliwia Kempinski Andrés M. Garced Seton Hall University South Orange New Jersey USA University of Maryland College Park Maryland USA

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Flexible Extensions to Structural Equation Models Using computation graphs

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STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL 2022年第2期29卷 233-247页

作者： van Kesteren, Erik-Jan Oberski, Daniel L. Univ Utrecht Utrecht Netherlands

Structural equation modeling (SEM) is being applied to ever more complex data types and questions, often requiring extensions such as regularization or novel fitting functions. To extend SEM, researchers currently need to completely reformulate SEM and its optimization algorithm - a challenging and time-consuming task. In this paper, we introduce the computation graph for SEM, and show that this approach can extend SEM without the need for bespoke software development. We show that both existing and novel SEM improvements follow naturally. To demonstrate, we introduce three SEM extensions: least absolute deviation estimation, Bayesian LASSO optimization, and sparse high-dimensional mediation analysis. We provide an implementation of SEM in PyTorch - popular software in the machine learning community - to accelerate development of structural equation models adequate for modern-day data and research questions.

关键词： Structural equation modeling computation graphs deep learning optimization regularization

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Static Prediction of Parallel computation graphs

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PROCEEDINGS OF THE ACM ON PROGRAMMING LANGUAGES-PACMPL 2022年第POPL期6卷 1–31页

作者： Muller, Stefan K. IIT Chicago IL 60616 USA

Many algorithms for analyzing parallel programs, for example to detect deadlocks or data races or to calculate the execution cost, are based on a model variously known as a cost graph, computation graph or dependency graph, which captures the parallel structure of threads in a program. In modern parallel programs, computation graphs are highly dynamic and depend greatly on the program inputs and execution details. As such, most analyses that use these graphs are either dynamic analyses or are specialized static analyses that gather a subset of dependency information for a specific purpose. This paper introduces graph types, which compactly represent all of the graphs that could arise from program execution. Graph types are inferred from a parallel program using a graph type system and inference algorithm, which we present drawing on ideas from Hindley-Milner type inference, affine logic and region type systems. We have implemented the inference algorithm over a subset of OCaml, extended with parallelism primitives, and we demonstrate how graph types can be used to accelerate the development of new graph-based static analyses by presenting proof-of-concept analyses for deadlock detection and cost analysis.

关键词： parallel programs graph types cost graphs computation graphs type systems type inference

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Using computation graphs to Explain Nondeterminism to Students

Using Computation Graphs to Explain Nondeterminism to Studen...

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ACM SIGPLAN International Symposium on SPLASH-E (SPLASH-E)

作者： Morazan, Marco T. Kempinski, Oliwia Seton Hall Univ S Orange NJ 07079 USA Univ Maryland College Pk MD 20742 USA

ISBN: (纸本)9798400712166

Students find their first course in Formal Languages and Automata Theory challenging. Most students struggle to understand nondeterministic computation models like non-deterministic finite-statemachines, pushdown automata, and Turing machines. Often, students find it difficult to understand why a nondeterministic machine accepts or rejects a word. Furthermore, they may feel uncomfortable with there being multiple computations on the same input and with a computation not consuming all of its input. This article presents a visualization tool developed to help students understand nondeterministic behavior. The tool is integrated into FSM-a domain-specific language for the Automata Theory classroom. The strategy is based on the automatic generation of computation graphs. Unlike previous visualization tools, the computation graphs generated reflect the structure of the given machine's transition diagram and not the structure of the computation tree. Empirical data collected from students at two universities suggests that the visualizations are well-received and useful.

关键词： State Machines Nondeterminism computation graphs Visualization

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Optimizing Tensor computation graphs with Equality Saturation and Monte Carlo Tree Search 24

Optimizing Tensor Computation Graphs with Equality Saturatio...

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International Conference on Parallel Architectures and Compilation Techniques (PACT)

作者： Hartmann, Jakob He, Guoliang Yoneki, Eiko Univ Cambridge Dept Comp Sci & Technol Cambridge England

ISBN: (数字)9798400706318

ISBN: (纸本)9798400706318

The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to sequentially rewrite the input computation graph into an equivalent but faster one by replacing individual subgraphs. This approach gives rise to the so-called phase-ordering problem in which the application of one rewrite rule can eliminate the possibility to apply an even better one later on. Recent work has shown that equality saturation, a technique from compiler optimization, can mitigate this issue by first building an intermediate representation (IR) that efficiently stores multiple optimized versions of the input program before extracting the best solution in a second step. In practice, however, memory constraints prevent the IR from capturing all optimized versions and thus reintroduce the phase-ordering problem in the construction phase. In this paper, we present a tensor graph rewriting approach that uses Monte Carlo tree search to build superior IRs by identifying the most promising rewrite rules. We also introduce a novel extraction algorithm that can provide fast and accurate runtime estimates of tensor programs represented in an IR. Our approach improves the inference speedup of neural networks by up to 11% compared to existing methods.

关键词： Deep Learning Tensor Programs computation graphs Equality Saturation Monte Carlo Tree Search Phase-Ordering Problem

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FRAMEWORK FOR FORMULATION AND ANALYSIS OF PARALLEL computation STRUCTURES

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PARALLEL COMPUTING 1986年第1期3卷 1-9页

作者： BROWNE, JC UNIV TEXAS CTR COMPUTATAUSTINTX 78712

This paper gives a systematic methodology for the formulation of parallel computation structures and algorithms. The fundamental definition of a computation structure is a graph where each node is the binding of an action to a data object and the arcs are the dependency relationships between the unit computations executed at the nodes. The structure of the graph is determined by the selection of elements for the model of computation in which the graph is expressed. An abstract machine is created by defining the resources including for example instruction sets for the processors, which realize the conceptual elements of the model of parallel computations. An algorithm is a mapping of the computation graph to the abstract machine and a program which traverses the mapped graph to execute the computation. The methodology proceeds by describing parallel computations on successively more fully specified abstract machines. A model of parallel computation is selected and an abstract machine implementing the model of computation is defined. Specification of increasingly resolved abstract machines is structured by both increasing the span of elements from the model of computation represented in the machine and be increasing the level of detail resolved for each element.

关键词： abstract machines computation graphs methodology of parallel computation Parallel algorithms

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STATIC SCHEDULING OF SYNCHRONOUS DATA FLOW PROGRAMS FOR DIGITAL SIGNAL-PROCESSING

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IEEE TRANSACTIONS ON COMPUTERS 1987年第1期36卷 24-35页

作者： LEE, EA MESSERSCHMITT, DG Department of Electrical Engineering and Computer Science University of California Berkeley CA 94720.

Large grain data flow (LGDF) programming is natural and convenient for describing digital signal processing (DSP) systems, but its runtime overhead is costly in real time or cost-sensitive applications. In some situations, designers are not willing to squander computing resources for the sake of programmer convenience. This is particularly true when the target machine is a programmable DSP chip. However, the runtime overhead inherent in most LGDF implementations is not required for most signal processing systems because such systems are mostly synchronous (in the DSP sense). Synchronous data flow (SDF) differs from traditional data flow in that the amount of data produced and consumed by a data flow node is specified a priori for each input and output. This is equivalent to specifying the relative sample rates in signal processing system. This means that the scheduling of SDF nodes need not be done at runtime, but can be done at compile time (statically), so the runtime overhead evaporates. The sample rates can all be different, which is not true of most current data-driven digital signal processing programming methodologies. Synchronous data flow is closely related to computation graphs, a special case of Petri nets. This self-contained paper develops the theory necessary to statically schedule SDF programs on single or multiple processors. A class of static (compile time) scheduling algorithms is proven valid, and specific algorithms are given for scheduling SDF systems onto single or multiple processors.

关键词： Block diagram Petri nets computation graphs data flow digital signal processing hard real-time systems multiprocessing static scheduling synchronous data flow

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Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2023年第6期42卷 356-370页

作者： Leung, Karen Arechiga, Nikos Pavone, Marco Stanford Univ 496 Lomita MallRm 261 Stanford CA 94305 USA Toyota Res Inst Los Altos CA USA

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, that is, how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

关键词： Signal Temporal Logic backpropagation computation graphs gradient-based methods

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Pipelines and Beyond: Graph Types for ADTs with Futures

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PROCEEDINGS OF THE ACM ON PROGRAMMING LANGUAGES-PACMPL 2024年第POPL期8卷 482-511页

作者： Rinaldi, Francis Wunder, June de Amorim, Arthur Azevedo Muller, Stefan K. IIT Chicago IL 60616 USA Boston Univ Boston MA USA

Parallel programs are frequently modeled as dependency or cost graphs, which can be used to detect various bugs, or simply to visualize the parallel structure of the code. However, such graphs reflect just one particular execution and are typically constructed in a post-hoc manner. Graph types, which were introduced recently to mitigate this problem, can be assigned statically to a program by a type system and compactly represent the family of all graphs that could result from the program. Unfortunately, prior work is restricted in its treatment of futures, an increasingly common and especially dynamic form of parallelism. In short, each instance of a future must be statically paired with a vertex name. Previously, this led to the restriction that futures could not be placed in collections or be used to construct data structures. Doing so is not a niche exercise: such structures form the basis of numerous algorithms that use forms of pipelining to achieve performance not attainable without futures. All but the most limited of these examples are out of reach of prior graph type systems. In this paper, we propose a graph type system that allows for almost arbitrary combinations of futures and recursive data types. We do so by indexing datatypes with a type-level vertex structure, a codata structure that supplies unique vertex names to the futures in a data structure. We prove the soundness of the system in a parallel core calculus annotated with vertex structures and associated operations. Although the calculus is annotated, this is merely for convenience in defining the type system. We prove that it is possible to annotate arbitrary recursive types with vertex structures, and show using a prototype inference engine that these annotations can be inferred from OCaml-like source code for several complex parallel algorithms.

关键词： parallel programs graph types cost graphs computation graphs futures pipelining affine type system

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OPTIMAL PREEMPTIVE SCHEDULING ON 2-PROCESSOR SYSTEMS

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IEEE TRANSACTIONS ON COMPUTERS 1969年第11期C 18卷 1014-&页

作者： MUNTZ, RR COFFMAN, EG IEEE

One of the important potentials of multiprocessor systems is the ability to speed the completion of a computation by concurrently processing independent portions of the job. In this paper we consider the static scheduling of computations for a system containing two indentical processors. The object is to complete the computation in the minimum amount of time. A computation is assumed to be specified as a partially ordered set of tasks and the execution time for each task. A solution for the two-machine case with preemptive scheduling is presented.

关键词： computation graphs multiprocessing parallel processing preemptive scheduling static scheduling.

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