XARK: an extensible framework for automatic recognition of computational kernels

This is a post-peer-review, pre-copyedit version of an article published in ACM Transactions on Programming Languages and Systems. The final authenticated version is available online at: http://dx.doi.org/10.1145/1391956.1391959[Abstract] The recognition of program constructs that are frequently used by software developers is a powerful mechanism for optimizing and parallelizing compilers to improve the performance of the object code. The development of techniques for automatic recognition of computational kernels such as inductions, reductions and array recurrences has been an intensive research area in the scope of compiler technology during the 90's. This article presents a new compiler framework that, unlike previous techniques that focus on specific and isolated kernels, recognizes a comprehensive collection of computational kernels that appear frequently in full-scale real applications. The XARK compiler operates on top of the Gated Single Assignment (GSA) form of a high-level intermediate representation (IR) of the source code. Recognition is carried out through a demand-driven analysis of this high-level IR at two different levels. First, the dependences between the statements that compose the strongly connected components (SCCs) of the data-dependence graph of the GSA form are analyzed. As a result of this intra-SCC analysis, the computational kernels corresponding to the execution of the statements of the SCCs are recognized. Second, the dependences between statements of different SCCs are examined in order to recognize more complex kernels that result from combining simpler kernels in the same code. Overall, the XARK compiler builds a hierarchical representation of the source code as kernels and dependence relationships between those kernels. This article describes in detail the collection of computational kernels recognized by the XARK compiler. Besides, the internals of the recognition algorithms are presented. The design of the algorithms enables to extend the recognition capabilities of XARK to cope with new kernels, and provides an advanced symbolic analysis framework to run other compiler techniques on demand. Finally, extensive experiments showing the effectiveness of XARK for a collection of benchmarks from different application domains are presented. In particular, the SparsKit-II library for the manipulation of sparse matrices, the Perfect benchmarks, the SPEC CPU2000 collection and the PLTMG package for solving elliptic partial differential equations are analyzed in detail.Ministeiro de Educación y Ciencia; TIN2004-07797-C02Ministeiro de Educación y Ciencia; TIN2007-67537-C03Xunta de Galicia; PGIDIT05PXIC10504PNXunta de Galicia; PGIDIT06PXIB105228P

Detecting event-related recurrences by symbolic analysis: Applications to human language processing

Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there is ample evidence that event-related potentials reflect such quasistationary states. In order to detect them from time series, several segmentation techniques have been proposed. In this study we elaborate a recent approach for detecting quasistationary states as recurrence domains by means of recurrence analysis and subsequent symbolisation methods. As a result, recurrence domains are obtained as partition cells that can be further aligned and unified for different realisations. We address two pertinent problems of contemporary recurrence analysis and present possible solutions for them.Comment: 24 pages, 6 figures. Draft version to appear in Proc Royal Soc

Parallelization of dynamic programming recurrences in computational biology

The rapid growth of biosequence databases over the last decade has led to a performance bottleneck in the applications analyzing them. In particular, over the last five years DNA sequencing capacity of next-generation sequencers has been doubling every six months as costs have plummeted. The data produced by these sequencers is overwhelming traditional compute systems. We believe that in the future compute performance, not sequencing, will become the bottleneck in advancing genome science. In this work, we investigate novel computing platforms to accelerate dynamic programming algorithms, which are popular in bioinformatics workloads. We study algorithm-specific hardware architectures that exploit fine-grained parallelism in dynamic programming kernels using field-programmable gate arrays: FPGAs). We advocate a high-level synthesis approach, using the recurrence equation abstraction to represent dynamic programming and polyhedral analysis to exploit parallelism. We suggest a novel technique within the polyhedral model to optimize for throughput by pipelining independent computations on an array. This design technique improves on the state of the art, which builds latency-optimal arrays. We also suggest a method to dynamically switch between a family of designs using FPGA reconfiguration to achieve a significant performance boost. We have used polyhedral methods to parallelize the Nussinov RNA folding algorithm to build a family of accelerators that can trade resources for parallelism and are between 15-130x faster than a modern dual core CPU implementation. A Zuker RNA folding accelerator we built on a single workstation with four Xilinx Virtex 4 FPGAs outperforms 198 3 GHz Intel Core 2 Duo processors. Furthermore, our design running on a single FPGA is an order of magnitude faster than competing implementations on similar-generation FPGAs and graphics processors. Our work is a step toward the goal of automated synthesis of hardware accelerators for dynamic programming algorithms

Some advances in the polyhedral model

Department Head: L. Darrell Whitley.2010 Summer.Includes bibliographical references.The polyhedral model is a mathematical formalism and a framework for the analysis and transformation of regular computations. It provides a unified approach to the optimization of computations from different application domains. It is now gaining wide use in optimizing compilers and automatic parallelization. In its purest form, it is based on a declarative model where computations are specified as equations over domains defined by "polyhedral sets". This dissertation presents two results. First is an analysis and optimization technique that enables us to simplify---reduce the asymptotic complexity---of such equations. The second is an extension of the model to richer domains called Ƶ-Polyhedra. Many equational specifications in the polyhedral model have reductions---application of an associative and commutative operator to collections of values to produce a collection of answers. Moreover, expressions in such equations may also exhibit reuse where intermediate values that are computed or used at different index points are identical. We develop various compiler transformations to automatically exploit this reuse and simplify the computational complexity of the specification. In general, there is an infinite set of applicable simplification transformations. Unfortunately, different choices may result in equivalent specifications with different asymptotic complexity. We present an algorithm for the optimal application of simplification transformations resulting in a final specification with minimum complexity. This dissertation also presents the Ƶ-Polyhedral model, an extension to the polyhedral model to more general sets, thereby providing a transformation framework for a larger set of regular computations. For this, we present a novel representation and interpretation of Ƶ-Polyhedra and prove a number of properties of the family of unions of Ƶ-Polyhedra that are required to extend the polyhedral model. Finally, we present value based dependence analysis and scheduling analysis for specifications in the Ƶ-Polyhedral model. These are direct extensions of the corresponding analyses of specifications in the polyhedral model. One of the benefits of our results in the Ƶ-Polyhedral model is that our abstraction allows the reuse of previously developed tools in the polyhedral model with straightforward pre- and post-processing

Laughing Hyena Distillery: Extracting Compact Recurrences From Convolutions

Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In particular, long convolution sequence models have achieved state-of-the-art performance in many domains, but incur a significant cost during auto-regressive inference workloads -- naively requiring a full pass (or caching of activations) over the input sequence for each generated token -- similarly to attention-based models. In this paper, we seek to enable $\mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture to reduce memory footprint and increase throughput during generation. Concretely, our methods consist in extracting low-dimensional linear state-space models from each convolution layer, building upon rational interpolation and model-order reduction techniques. We further introduce architectural improvements to convolution-based layers such as Hyena: by weight-tying the filters across channels into heads, we achieve higher pre-training quality and reduce the number of filters to be distilled. The resulting model achieves 10x higher throughput than Transformers and 1.5x higher than Hyena at 1.3B parameters, without any loss in quality after distillation

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Enhancing representation learning with tensor decompositions for knowledge graphs and high dimensional sequence modeling

The capability of processing and digesting raw data is one of the key features of a human-like artificial intelligence system. For instance, real-time machine translation should be able to process and understand spoken natural language, and autonomous driving relies on the comprehension of visual inputs. Representation learning is a class of machine learning techniques that autonomously learn to derive latent features from raw data. These new features are expected to represent the data instances in a vector space that facilitates the machine learning task. This thesis studies two specific data situations that require efficient representation learning: knowledge graph data and high dimensional sequences. In the first part of this thesis, we first review multiple relational learning models based on tensor decomposition for knowledge graphs. We point out that relational learning is in fact a means of learning representations through one-hot mapping of entities. Furthermore, we generalize this mapping function to consume a feature vector that encodes all known facts about each entity. It enables the relational model to derive the latent representation instantly for a new entity, without having to re-train the tensor decomposition. In the second part, we focus on learning representations from high dimensional sequential data. Sequential data often pose the challenge that they are of variable lengths. Electronic health records, for instance, could consist of clinical event data that have been collected at subsequent time steps. But each patient may have a medical history of variable length. We apply recurrent neural networks to produce fixed-size latent representations from the raw feature sequences of various lengths. By exposing a prediction model to these learned representations instead of the raw features, we can predict the therapy prescriptions more accurately as a means of clinical decision support. We further propose Tensor-Train recurrent neural networks. We give a detailed introduction to the technique of tensorizing and decomposing large weight matrices into a few smaller tensors. We demonstrate the specific algorithms to perform the forward-pass and the back-propagation in this setting. Then we apply this approach to the input-to-hidden weight matrix in recurrent neural networks. This novel architecture can process extremely high dimensional sequential features such as video data. The model also provides a promising solution to processing sequential features with high sparsity. This is, for instance, the case with electronic health records, since they are often of categorical nature and have to be binary-coded. We incorporate a statistical survival model with this representation learning model, which shows superior prediction quality