Sparsity-Specific Code Optimization using Expression Trees

Herholz, Philipp; Tang, Xuan; Schneider, Teseo; Kamil, Shoaib; Panozzo, Daniele; Sorkine‐Hornung, Olga

doi:10.1145/3520484

Cited by 6 publications

(3 citation statements)

References 36 publications

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“…As the connectivity of the intrinsic Laplacian depends on the geometry and may change as the geometry changes, factorizations would have to be recalculated. THe iARAP Laplacian allows for a fixed symbolic factorization or sparse optimizations techniques that assume a fixed sparsity pattern [HTS*22] even after geometry changes.…”

Section: Discussionmentioning

confidence: 99%

ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

Finnendahl

Schwartz

Alexa

2023

Computer Graphics Forum

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As‐rigid‐as‐possible (ARAP) surface modelling is widely used for interactive deformation of triangle meshes. We show that ARAP can be interpreted as minimizing a discretization of an elastic energy based on non‐conforming elements defined over dual orthogonal cells of the mesh. Using the intrinsic Voronoi cells rather than an orthogonal dual of the extrinsic mesh guarantees that the energy is non‐negative over each cell. We represent the intrinsic Delaunay edges extrinsically as polylines over the mesh, encoded in barycentric coordinates relative to the mesh vertices. This modification of the original ARAP energy, which we term iARAP, remedies problems stemming from non‐Delaunay edges in the original approach. Unlike the spokes‐and‐rims version of the ARAP approach it is less susceptible to the triangulation of the surface. We provide examples of deformations generated with iARAP and contrast them with other versions of ARAP. We also discuss the properties of the Laplace‐Beltrami operator implicitly introduced with the new discretization.

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Section: Discussionmentioning

confidence: 99%

ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

Finnendahl

Schwartz

Alexa

2023

Computer Graphics Forum

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“…Graphs, particularly DAGs (Cosnard et al, 2004), are regularly used to represent codes at various levels, and as schedulers in heterogeneous architectures (Bosilca et al, 2011) The source code can be modeled as a graph representing each function as a vertex and dependencies between the functions as edges. Moreover, compiler optimization and automatic code generation regularly use expression graphs in their algorithms (Herholz et al, 2022); Kramer et al, 1992) Comparing the DAGS for the different refactored codes is an orthogonal method to identify whether the code is replicable after various optimizations.…”

Section: Replicability Of Codementioning

confidence: 99%

A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing

Bhowmick

Bell

Taufer

2023

The International Journal of High Performance Computing Applica

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The convergence of extremely high levels of hardware concurrency and the effective overlap of computation and communication in asynchronous executions has resulted in increasing nondeterminism in High-Performance Computing (HPC) applications. Nondeterminism can manifest at multiple levels: from low-level communication primitives to libraries to application-level functions. No matter its source, nondeterminism can drastically increase the cost of result reproducibility, debugging workflows, testing parallel programs, or ensuring fault-tolerance. Nondeterministic executions of HPC applications can be modeled as event graphs, and the applications’ nondeterministic behavior can be understood and, in some cases, mitigated using graph comparison algorithms. However, a connection between graph comparison algorithms and approaches to understanding nondeterminism in HPC still needs to be established. This survey article moves the first steps toward establishing a connection between graph comparison algorithms and nondeterminism in HPC with its three contributions: it provides a survey of different graph comparison algorithms and a timeline for each category’s significant works; it discusses how existing graph comparison methods do not fully support properties needed to understand nondeterministic patterns in HPC applications; and it presents the open challenges that should be addressed to leverage the power of graph comparisons for the study of nondeterminism in HPC applications.

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“…ADOL‐C [WG12] supports automatic inference of sparsity patterns by solving a graph coloring problem at run time. A recently‐described code generator [HTS∗22] supports automatic detection of per‐element computations and offers sparse second‐order differentiation in backward mode. The authors report striking run time performance, at the cost of limited branching capabilities and a more involved compilation procedure.…”

Section: Background and Related Workmentioning

confidence: 99%

TinyAD: Automatic Differentiation in Geometry Processing Made Simple

Schmidt

Born

Bommes

et al. 2022

Computer Graphics Forum

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Non‐linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second‐order derivatives are required. Deriving and manually implementing gradients and Hessians is both time‐consuming and error‐prone. Automatic differentiation techniques address this problem, but can introduce a diverse set of obstacles themselves, e.g. limiting the set of supported language features, imposing restrictions on a program's control flow, incurring a significant run time overhead, or making it hard to exploit sparsity patterns common in geometry processing. We show that for many geometric problems, in particular on meshes, the simplest form of forward‐mode automatic differentiation is not only the most flexible, but also actually the most efficient choice. We introduce TinyAD: a lightweight C++ library that automatically computes gradients and Hessians, in particular of sparse problems, by differentiating small (tiny) sub‐problems. Its simplicity enables easy integration; no restrictions on, e.g., looping and branching are imposed. TinyAD provides the basic ingredients to quickly implement first and second order Newton‐style solvers, allowing for flexible adjustment of both problem formulations and solver details. By showcasing compact implementations of methods from parametrization, deformation, and direction field design, we demonstrate how TinyAD lowers the barrier to exploring non‐linear optimization techniques. This enables not only fast prototyping of new research ideas, but also improves replicability of existing algorithms in geometry processing. TinyAD is available to the community as an open source library.

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Sparsity-Specific Code Optimization using Expression Trees

Cited by 6 publications

References 36 publications

ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

ARAP Revisited Discretizing the Elastic Energy using Intrinsic Voronoi Cells

A Survey of Graph Comparison Methods with Applications to Nondeterminism in High-Performance Computing

TinyAD: Automatic Differentiation in Geometry Processing Made Simple

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