Periodic Polyhedra

Caches are crucial components of modern processors; they allow high-performance processors to access data fast and, due to their small sizes, they enable low-power processors to save energy - by circumventing memory accesses. We examine efficient utilization of data caches in an adaptive memory hierarchy. We exploit data reuse through the static analysis of cache-line size adaptivity. We present an approach that enables the quantification of data misses with respect to cache-line size at compile-time using (parametric) equations, which model interference. Our approach aims at the analysis of perfect loop nests in scientific applications; it is applied to direct mapped cache and it is an extension and generalization of the cache miss equation (CME) proposed by Ghosh et al. (1999). Part of this analysis is implemented in a software package, STAMINA. We present analytical results in comparison with simulation-based methods and we show evidence of both the expressiveness and the practicability of the analysis.

In this work, we present a minimalistic, energy efficient implementation of instruction buffer. We use loop detection and execution trace analysis to find most commonly executed loops in already scheduled application and tailor instruction buffer size to the size of most commonly executed loop(s). In addition to our previous work, we allow buffering of loops with limited control flow (early exit from the loop or early return to the beginning of the loop). We also show how analysis of loop nests can decrease the number of times loop body is copied from memory into the buffer. Our results show that in case of favorable loop nest, we can execute all but initial loop iterations from the instruction buffer, keeping instruction memory in the deselect mode.

The polyhedral model provides an expressive intermediate representation that is convenient for the analysis and subsequent transformation of affine loop nests. Several heuristics exist for achieving complex program transformations in this model. However, there is also considerable scope to utilize this model to tackle the problem of automatic memory footprint optimization. In this paper, we present a new automatic storage optimization technique which can be used to achieve both intra-array as well as inter-array storage reuse with a pre-determined schedule for the computation. Our approach works by finding statement-wise storage partitioning hyperplanes that partition a unified global array space so that values with overlapping live ranges are not mapped to the same partition. Our heuristic is driven by a fourfold objective function which not only minimizes the dimensionality and storage requirements of arrays required for each high-level statement, but also maximizes inter-statement storage reuse. The storage mappings obtained using our heuristic can be asymptotically better than those obtained by any existing technique. We implement our technique and demonstrate its practical impact by evaluating its effectiveness on several benchmarks chosen from the domains of image processing, stencil computations, and high-performance computing.

In this paper, we introduce a new topology of Fuzzy Polynomial Neural Networks (FPNN) that is based on a genetically optimized multilayer perceptron with fuzzy polynomial neurons (FPNs) and discuss its comprehensive design methodology involving mechanisms of genetic optimization, especially genetic algorithms (GAs). The proposed FPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional FPNNs. The structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. Through the consecutive process of such structural and parametric optimization, an optimized and flexible fuzzy neural network is generated in a dynamic fashion. The performance of the proposed gFPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling. These results reveal superiority of the proposed networks over the existing fuzzy and neural models.KeywordsRoot Mean Square ErrorMembership FunctionFuzzy RuleTriangular Membership FunctionElitist StrategyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Modern manufacturing systems have incorporated various “intelligent” decision support techniques and algorithms in the form of rules-based systems which have been promoted extensively because of the recent development in fuzzy inference, artificial neural network, machine learning and optimization algorithms, and etc. The basic elements of a modern manufacturing system include design automation (CAD and CAPP), production automation (CAM and MRP II), and shop floor automation (SFC and FMS), which must then be integrated into a coherent system through information automation (distributed DBMS and workflow automation) to form a fully automated factory. Therefore, considerable amount of rule-based systems have been developed and implemented fully or partially into each of the above areas of automation. To build a robust rule-based system requires a suitable modeling and analysis tool and a systematic design methodology. By incorporating neural network concept and associated learning algorithm, we present in this paper a Petri net based modeling methodology which can be used to design and implement adaptive rule-based systems for control and optimization in intelligent manufacturing systems. Demonstration is done on parametric design and optimization in manufacturing processes.

When solving systems of polynomial equations and inequalities, the task of computing their solutions with integer coordinates is a much harder problem than that of computing their real solutions or that of computing all their solutions. In fact, in the presence of non-linear constraints, this task may simply become an undecidable problem [12, 15]. However, studying the integer solutions of linear systems of equations and inequalities is of practical importance in various areas of scientific computing. Two such areas are combinatorial optimization (in particular, integer linear programming) and compiler optimization (in particular, the analysis, transformation, and scheduling of nested loops in computer programs), where a variety of algorithms solve questions related to the points with integer coordinates in a given polyhedron. Another area is at the crossroads of computer algebra and polyhedral geometry, with topics such as toric ideals and Hilbert bases, see [16], as well as the manipulation of Laurent series, see [1].

The elementary closure P′ of a polyhedron P is the intersection of P with all its Gomory-Chvátal cutting planes. P′ is a rational polyhedron provided that P is rational. The known bounds for the number of inequalities defining P′ are exponential, even in fixed dimension. We show that the number of inequalities needed to describe the elementary closure of a rational polyhedron is polynomially bounded in fixed dimension. If P is a simplicial cone, we construct a polytope Q, whose integral elements correspond to cutting planes of P. The vertices of the integer hull QI include the facets of P′. A polynomial upper bound on their number can be obtained by applying a result of Cook et al. (1992). Finally, we present a polynomial algorithm in varying dimension, which computes cutting planes for a simplicial cone that correspond to vertices of QI.

Improving data locality in programs which manipulate arrays has been the subject of a great deal of research. Much of the work on improving data locality examines individual loop nests; other work includes transformations such as loop fusion, which combines loops so that multiple loop nests can be transformed as a single loop nest. We propose a data-driven method to optimize locality across multiple loop nests. Our technique achieves loop fusion-like results even when normal loop fusion is illegal without enabling transformations. Given an array whose locality should be optimized, it also finds other calculations that can profitably be executed with the computation of that array.KeywordsTransitive ClosureArray ElementIteration SpaceLoop NestInnermost LoopThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Contributors

End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with few hundreds of nodes. While state-of-the-art learning-driven approaches for TSP perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances at practical scales. This work presents an end-to-end neural combinatorial optimization pipeline that unifies several recent papers in order to identify the inductive biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training. Our controlled experiments provide the first principled investigation into such zero-shot generalization, revealing that extrapolating beyond training data requires rethinking the neural combinatorial optimization pipeline, from network layers and learning paradigms to evaluation protocols. Additionally, we analyze recent advances in deep learning for routing problems through the lens of our pipeline and provide new directions to stimulate future research.

Journal Article The Random Neural Network: A Survey Get access Stelios Timotheou Stelios Timotheou * Intelligent Systems and Networks Group, Department of Electrical and Electronic Engineering, Imperial College, London SW7 2BT, UK *Corresponding author: stelios.timotheou05@imperial.ac.uk Search for other works by this author on: Oxford Academic Google Scholar The Computer Journal, Volume 53, Issue 3, March 2010, Pages 251–267, https://doi.org/10.1093/comjnl/bxp032 Published: 30 April 2009 Article history Received: 01 November 2008 Revision received: 17 February 2009 Published: 30 April 2009

Combinatorial Optimization (CO) problems have been intensively studied for decades with a wide range of applications. For some classic CO problems, e.g., the Traveling Salesman Problem (TSP), both traditional planning algorithms and the emerging reinforcement learning have made solid progress in recent years. However, for CO problems with nested sub-tasks, neither end-to-end reinforcement learning algorithms nor traditional evolutionary methods can obtain satisfactory strategies within a limited time and computational resources. In this paper, we propose an algorithmic framework for solving CO problems with nested sub-tasks, in which learning and planning algorithms can be combined in a modular way. We validate our framework in the Job-Shop Scheduling Problem (JSSP), and the experimental results show that our algorithm has good performance in both solution qualities and model generalizations.

High Performance Fortran is a dataparallel language that allows the user to specify the parallelism in his program. It is not always easy to extract the parallelism in a given program. To help the user, an automatic loop parallelizer has been developed: Bouclettes.Bouclettes has been written to validate some scheduling and mapping techniques that are mentioned in this paper. A Fortran 77 loop nest is rewritten into a HPF loop nest with explicit parallel loops (INDEPENDENT loops) and explicit data distribution (DISTRIBUTE and ALIGN directives).The different stages of parallelization (analysis, dependence analysis, scheduling, mapping and code generation) and their implementation issues are described here.KeywordsData DependenceLoop NestIteration DomainIndependent LoopAlign DirectiveThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Energy consumption has become a major constraint in providing increased functionality for devices with small form factors. Dynamic voltage and frequency scaling has been identified as an effective approach for reducing the energy consumption of embedded systems. Earlier works on dynamic voltage scaling focused mainly on performing voltage scaling when the CPU is waiting for memory subsystem or concentrated chiefly on loop nests and/or subroutine calls having sufficient number of dynamic instructions. This paper concentrates on coarser program regions and for the first time uses program phase behavior for performing dynamic voltage scaling. Program phases are annotated at compile time with mode switch instructions. Further, we relate the Dynamic Voltage Scaling Problem to the Multiple Choice Knapsack Problem, and use well known heuristics to solve it efficiently. Also, we develop a simple integer linear program formulation for this problem. Experimental evaluation on a set of media applications reveal that our heuristic method obtains a 38% reduction in energy consumption on an average, with a performance degradation of 1% and upto 45% reduction in energy with a performance degradation of 5%. Further, the energy consumed by the heuristic solution is within 1% of the optimal solution obtained from the ILP approach.KeywordsExecution TimeSupply VoltageKnapsack ProblemBasic BlockProgram RegionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Ensemble method has been deeply studied and widely used in the machine learning communities. Its basic idea can be represented as: A ‘weak’ learning algorithm that performs just slightly better than random guessing can be ‘boosted’ into an arbitrarily accurate ‘strong’ learning algorithm. Inspired from the fascinating idea, the paper used ensemble method to improve the performance of genetic algorithm and proposed an efficient hybrid optimization algorithm: GA ensemble. In GA ensemble, a collection of genetic algorithms are designed to solve the same problem and population of each algorithm is sampled from a solutions pool using bagging method. Experiments on combinatorial optimization problem and GA-deceptive problems show that ensemble method improves the performance of genetic algorithm greatly.