Albert Cohen

Markus Bachmayr, Albert Cohen, Wolfgang Dahmen

We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse polynomial expansions, general low-rank approximations separating spatial and parametric variables, and hierarchical tensor decompositions separating all variables. We describe corresponding adaptive algorithms based on a common generic template and show their near-optimality with respect to natural approximability assumptions for each type of approximation. A central ingredient in the resulting bounds for the total computational complexity are new operator compression results for the case of infinitely many parameters. We conclude with a comparison of the complexity estimates based on the actual approximability properties of classes of parametric model problems, which shows that the computational costs of optimized low-rank expansions can be significantly lower or higher than those of sparse polynomial expansions, depending on the particular type of parametric problem.

Jean-Marie Mirebeau, Albert Cohen

We study the properties of a simple greedy algorithm for the generation of data-adapted anisotropic triangulations. Given a function f, the algorithm produces nested triangulations and corresponding piecewise polynomial approximations of f. The refinement procedure picks the triangle which maximizes the local Lp approximation error, and bisect it in a direction which is chosen so to minimize this error at the next step. We study the approximation error in the Lp norm when the algorithm is applied to C2 functions with piecewise linear approximations. We prove that as the algorithm progresses, the triangles tend to adopt an optimal aspect ratio which is dictated by the local hessian of f. For convex functions, we also prove that the adaptive triangulations satisfy a convergence bound which is known to be asymptotically optimal among all possible triangulations.

Benjamin Arras, Markus Bachmayr, Albert Cohen

We consider the problem of approximating an unknown function $u\in L^2(D,ρ)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $ρ$ is a probability measure. The approximation is picked in a linear space $V_m$ where $m=\dim(V_m)$ and computed by a weighted least squares method. Recent results show the advantages of picking the sampling points at random according to a well-chosen probability measure $μ$ that depends both on $V_m$ and $ρ$. With such a random design, the weighted least squares approximation is proved to be stable with high probability, and having precision comparable to that of the exact $L^2(D,ρ)$-orthonormal projection onto $V_m$, in a near-linear sampling regime $n\sim{m\log m}$. The present paper is motivated by the adaptive approximation context, in which one typically generates a nested sequence of spaces $(V_m)_{m\geq1}$ with increasing dimension. Although the measure $μ=μ_m$ changes with $V_m$, it is possible to recycle the previously generated samples by interpreting $μ_m$ as a mixture between $μ_{m-1}$ and an update measure $σ_m$. Based on this observation, we discuss sequential sampling algorithms that maintain the stability and approximation properties uniformly over all spaces $V_m$. Our main result is that the total number of computed sample at step $m$ remains of the order $m\log{m}$ with high probability. Numerical experiments confirm this analysis.

Gilles Chardon, Albert Cohen, Laurent Daudet

We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $Ω$ from their values at scattered points $x_1,\dots,x_n\subset Ω$. This problem typically arises when sampling acoustic fields with $n$ microphones for the purpose of reconstructing this field over a region of interest $Ω$ contained in a larger domain $D$ in which the acoustic field propagates. In many applied settings, the shape of $D$ and the boundary conditions on its border are unknown. Our reconstruction method is based on the approximation of a general solution $u$ by linear combinations of Fourier-Bessel functions or plane waves. We analyze the convergence of the least-squares estimates to $u$ using these families of functions based on the samples $(u(x_i))_{i=1,\dots,n}$. Our analysis describes the amount of regularization needed to guarantee the convergence of the least squares estimate towards $u$, in terms of a condition that depends on the dimension of the approximation subspace, the sample size $n$ and the distribution of the samples. It reveals the advantage of using non-uniform distributions that have more points on the boundary of $Ω$. Numerical illustrations show that our approach compares favorably with reconstruction methods using other basis functions, and other types of regularization.

S. VenkataKeerthy, Siddharth Jain, Anilava Kundu et al.

We aim to automate decades of research and experience in register allocation, leveraging machine learning. We tackle this problem by embedding a multi-agent reinforcement learning algorithm within LLVM, training it with the state of the art techniques. We formalize the constraints that precisely define the problem for a given instruction-set architecture, while ensuring that the generated code preserves semantic correctness. We also develop a gRPC based framework providing a modular and efficient compiler interface for training and inference. Our approach is architecture independent: we show experimental results targeting Intel x86 and ARM AArch64. Our results match or out-perform the heavily tuned, production-grade register allocators of LLVM.

S. VenkataKeerthy, Siddharth Jain, Umesh Kalvakuntla et al.

There is a growing interest in enhancing compiler optimizations with ML models, yet interactions between compilers and ML frameworks remain challenging. Some optimizations require tightly coupled models and compiler internals,raising issues with modularity, performance and framework independence. Practical deployment and transparency for the end-user are also important concerns. We propose ML-Compiler-Bridge to enable ML model development within a traditional Python framework while making end-to-end integration with an optimizing compiler possible and efficient. We evaluate it on both research and production use cases, for training and inference, over several optimization problems, multiple compilers and its versions, and gym infrastructures.

Dumitru Potop Butucaru, Albert Cohen, Gordon Plotkin et al.

Reactive languages are dedicated to the programming of systems which interact continuously and concurrently with their environment. Values take the form of unbounded streams modeling the (discrete) passing of time or the sequence of concurrent interactions. While conventional reactivity models recurrences forward in time, we introduce a symmetric reactive construct enabling backward recurrences. Constraints on the latter allow to make the implementation practical. Machine Learning (ML) systems provide numerous motivations for all of this: we demonstrate that reverse-mode automatic differentiation, backpropagation, batch normalization, bidirectional recurrent neural networks, training and reinforcement learning algorithms, are all naturally captured as bidirectional reactive programs.

Wei Niu, Jiexiong Guan, Yanzhi Wang et al.

Deep Neural Networks (DNNs) have emerged as the core enabler of many major applications on mobile devices. To achieve high accuracy, DNN models have become increasingly deep with hundreds or even thousands of operator layers, leading to high memory and computational requirements for inference. Operator fusion (or kernel/layer fusion) is key optimization in many state-of-the-art DNN execution frameworks, such as TensorFlow, TVM, and MNN. However, these frameworks usually adopt fusion approaches based on certain patterns that are too restrictive to cover the diversity of operators and layer connections. Polyhedral-based loop fusion techniques, on the other hand, work on a low-level view of the computation without operator-level information, and can also miss potential fusion opportunities. To address this challenge, this paper proposes a novel and extensive loop fusion framework called DNNFusion. The basic idea of this work is to work at an operator view of DNNs, but expand fusion opportunities by developing a classification of both individual operators and their combinations. In addition, DNNFusion includes 1) a novel mathematical-property-based graph rewriting framework to reduce evaluation costs and facilitate subsequent operator fusion, 2) an integrated fusion plan generation that leverages the high-level analysis and accurate light-weight profiling, and 3) additional optimizations during fusion code generation. DNNFusion is extensively evaluated on 15 DNN models with varied types of tasks, model sizes, and layer counts. The evaluation results demonstrate that DNNFusion finds up to 8.8x higher fusion opportunities, outperforms four state-of-the-art DNN execution frameworks with 9.3x speedup. The memory requirement reduction and speedups can enable the execution of many of the target models on mobile devices and even make them part of a real-time application.

Son Tuan Vu, Albert Cohen, Karine Heydemann et al.

Secure applications implement software protections against side-channel and physical attacks. Such protections are meaningful at machine code or micro-architectural level, but they typically do not carry observable semantics at source level. To prevent optimizing compilers from altering the protection, security engineers embed input/output side-effects into the protection. These side-effects are error-prone and compiler-dependent, and the current practice involves analyzing the generated machine code to make sure security or privacy properties are still enforced. Vu et al. recently demonstrated how to automate the insertion of volatile side-effects in a compiler [52], but these may be too expensive in fined-grained protections such as control-flow integrity. We introduce observations of the program state that are intrinsic to the correct execution of security protections, along with means to specify and preserve observations across the compilation flow. Such observations complement the traditional input/output-preservation contract of compilers. We show how to guarantee their preservation without modifying compilation passes and with as little performance impact as possible. We validate our approach on a range of benchmarks, expressing the secure compilation of these applications in terms of observations to be made at specific program points.

Chris Lattner, Mehdi Amini, Uday Bondhugula et al.

This work presents MLIR, a novel approach to building reusable and extensible compiler infrastructure. MLIR aims to address software fragmentation, improve compilation for heterogeneous hardware, significantly reduce the cost of building domain specific compilers, and aid in connecting existing compilers together. MLIR facilitates the design and implementation of code generators, translators and optimizers at different levels of abstraction and also across application domains, hardware targets and execution environments. The contribution of this work includes (1) discussion of MLIR as a research artifact, built for extension and evolution, and identifying the challenges and opportunities posed by this novel design point in design, semantics, optimization specification, system, and engineering. (2) evaluation of MLIR as a generalized infrastructure that reduces the cost of building compilers-describing diverse use-cases to show research and educational opportunities for future programming languages, compilers, execution environments, and computer architecture. The paper also presents the rationale for MLIR, its original design principles, structures and semantics.

Julien Proy, Karine Heydemann, Fabien Majéric et al.

In the area of physical attacks, system-on-chip (SoC) designs have not received the same level of attention as simpler micro-controllers. We try to model the behavior of secure software running on a superscalar out-of-order microprocessor typical of more complex SoC, in the presence of electromagnetic (EM) pulses. We first show that it is possible, in a black box approach, to corrupt the loop iteration count of both original and hardened versions of two sensitive loops. We propose a characterization methodology based on very simple codes, to understand and classify the fault effects at the level of the instruction set architecture (ISA). The resulting classification includes the well established instruction skip and register corruption models, as well as new effects specific to more complex processors, such as operand substitution, multiple correlated register corruptions, advanced control-flow hijacking, and combinations of all reported effects. This diversity and complexity of effects can lead to powerful attacks. The proposed methodology and fault classification at ISA level is a first step towards a more complete characterization. It is also a tool supporting the designers of software and hardware countermeasures.

Nicolas Vasilache, Oleksandr Zinenko, Theodoros Theodoridis et al.

Deep learning models with convolutional and recurrent networks are now ubiquitous and analyze massive amounts of audio, image, video, text and graph data, with applications in automatic translation, speech-to-text, scene understanding, ranking user preferences, ad placement, etc. Competing frameworks for building these networks such as TensorFlow, Chainer, CNTK, Torch/PyTorch, Caffe1/2, MXNet and Theano, explore different tradeoffs between usability and expressiveness, research or production orientation and supported hardware. They operate on a DAG of computational operators, wrapping high-performance libraries such as CUDNN (for NVIDIA GPUs) or NNPACK (for various CPUs), and automate memory allocation, synchronization, distribution. Custom operators are needed where the computation does not fit existing high-performance library calls, usually at a high engineering cost. This is frequently required when new operators are invented by researchers: such operators suffer a severe performance penalty, which limits the pace of innovation. Furthermore, even if there is an existing runtime call these frameworks can use, it often doesn't offer optimal performance for a user's particular network architecture and dataset, missing optimizations between operators as well as optimizations that can be done knowing the size and shape of data. Our contributions include (1) a language close to the mathematics of deep learning called Tensor Comprehensions, (2) a polyhedral Just-In-Time compiler to convert a mathematical description of a deep learning DAG into a CUDA kernel with delegated memory management and synchronization, also providing optimizations such as operator fusion and specialization for specific sizes, (3) a compilation cache populated by an autotuner. [Abstract cutoff]

Markus Bachmayr, Albert Cohen, Dinh Dũng et al.

It has recently been demonstrated that locality of spatial supports in the parametrization of coefficients in elliptic PDEs can lead to improved convergence rates of sparse polynomial expansions of the corresponding parameter-dependent solutions. These results by themselves do not yield practically realizable approximations, since they do not cover the approximation of the arising expansion coefficients, which are functions of the spatial variable. In this work, we study the combined spatial and parametric approximability for elliptic PDEs with affine or lognormal parametrizations of the diffusion coefficients and corresponding Taylor, Jacobi, and Hermite expansions, to obtain fully discrete approximations. Our analysis yields convergence rates of the fully discrete approximation in terms of the total number of degrees of freedom. The main vehicle consists in $\ell^p$ summability results for the coefficient sequences measured in higher-order Hilbertian Sobolev norms. We also discuss similar results for non-Hilbertian Sobolev norms which arise naturally when using adaptive spatial discretizations.

Andi Drebes, Karine Heydemann, Antoniu Pop et al.

To efficiently exploit the resources of new many-core architectures, integrating dozens or even hundreds of cores per chip, parallel programming models have evolved to expose massive amounts of parallelism, often in the form of fine-grained tasks. Task-parallel languages, such as OpenStream, X10, Habanero Java and C or StarSs, simplify the development of applications for new architectures, but tuning task-parallel applications remains a major challenge. Performance bottlenecks can occur at any level of the implementation, from the algorithmic level (e.g., lack of parallelism or over-synchronization), to interactions with the operating and runtime systems (e.g., data placement on NUMA architectures), to inefficient use of the hardware (e.g., frequent cache misses or misaligned memory accesses); detecting such issues and determining the exact cause is a difficult task. In previous work, we developed Aftermath, an interactive tool for trace-based performance analysis and debugging of task-parallel programs and run-time systems. In contrast to other trace-based analysis tools, such as Paraver or Vampir, Aftermath offers native support for tasks, i.e., visualization, statistics and analysis tools adapted for performance debugging at task granularity. However, the tool currently does not provide support for the automatic detection of performance bottlenecks and it is up to the user to investigate the relevant aspects of program execution by focusing the inspection on specific slices of a trace file. In this paper, we present ongoing work on two extensions that guide the user through this process.

Frank Hannig, Jürgen Teich

This volume contains the papers accepted at the 1st Workshop on Resource Awareness and Adaptivity in Multi-Core Computing (Racing 2014), held in Paderborn, Germany, May 29-30, 2014. Racing 2014 was co-located with the IEEE European Test Symposium (ETS).