Filters








7,577 Hits in 3.4 sec

Simplification and optimization transformations of chains of recurrences

Eugene V. Zima
1995 Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95  
Optimizing transformations of Chains of Recurrences are proposed.  ...  The Chain of Recurrences technique to expedite computations is extended by rational simplifications and examined as a form of internal representation, oriented towards fast evaluation.  ...  (Most of the optimizing transformations assume the same. ) Components of CRS (as expressions) are constructed almost from the same set of constants, operation-signs and variables as initial expression  ... 
doi:10.1145/220346.220352 dblp:conf/issac/Zima95 fatcat:xvfqgcifzrgmdfl3xo2jldc7ka

On computational properties of chains of recurrences

Eugene V. Zima
2001 Proceedings of the 2001 international symposium on Symbolic and algebraic computation - ISSAC '01  
Backward and mixed chains of recurrences are introduced. A complete set of chains of recurrences manipulation tools is described.  ...  Applications of these tools, related to the safety and numeric stability of chained computations are given. and F(i) = ~(i), i = O, 1, . . . , n.  ...  Loop optimization tools and mixed chains The operators V, E and E -1 and the CR/BCR simplification rules form a toolkit for loop optimization [6, 13] .  ... 
doi:10.1145/384101.384148 dblp:conf/issac/Zima01 fatcat:q66g3iypzfdrpp45tklmuaua7e

Low-cost register-pressure prediction for scalar replacement using pseudo-schedules

Y. Ma, S. Carr, R. Ge
2004 International Conference on Parallel Processing, 2004. ICPP 2004.  
PRP uses three approximation algorithms: one for constructing a data dependence graph, one for computing the recurrence constraints of a software pipelined loop, and one for building a pseudo-schedule.  ...  takes into account the effects of both software pipelining and register allocation.  ...  Figure 1 . 1 DDG Simplification Transformations and the backward vector of the second edge to compute the RecII.  ... 
doi:10.1109/icpp.2004.1327911 dblp:conf/icpp/MaCG04 fatcat:rdkkhaeapjccpc4cyisx7n5qea

Automatic Validation of Code-Improving Transformations [chapter]

Robert van Engelen, David Whalley, Xin Yuan
2001 Lecture Notes in Computer Science  
The approach ensures the correctness of compiler and hand-specified optimizations at the machine instruction level.  ...  The method verifies the semantic equivalence of the program representation before and after a transformation to determine the validity of the transformation, i.e. whether the instance of the transformation  ...  The types of transformations in the vpo compiler that were validated using the system include algebraic simplification of expressions, basic block reordering, branch chaining, common subexpression elimination  ... 
doi:10.1007/3-540-45245-1_15 fatcat:hi6asfafqzcuzkoleounzpldgq

Automatic validation of code-improving transformations on low-level program representations

Robert van Engelen, David Whalley, Xin Yuan
2004 Science of Computer Programming  
The approach ensures the correctness of compiler and hand-specified optimizations at the machine instruction level.  ...  The method verifies the semantic equivalence of the program representation before and after a transformation to determine the validity of the transformation, i.e. whether the instance of the transformation  ...  The types of transformations in the vpo compiler that were validated using the system include algebraic simplification of expressions, basic block reordering, branch chaining, common subexpression elimination  ... 
doi:10.1016/j.scico.2004.03.008 fatcat:cdxqoqpjj5ddzm74uno6nzcy2e

Minimum Entropy Rate Simplification of Stochastic Processes

Gustav Eje Henter, W. Bastiaan Kleijn
2016 IEEE Transactions on Pattern Analysis and Machine Intelligence  
We propose minimum entropy rate simplification (MERS), an information-theoretic, parameterization-independent framework for simplifying generative models of stochastic processes.  ...  This leads to analytic solutions for stationary and ergodic Gaussian processes and Markov chains. The same formulas are also valid for maximum-entropy smoothing under the same divergence constraint.  ...  ACKNOWLEDGEMENTS The authors wish to thank Associate Professor Richard Heusdens at TU Delft for pointing out some inaccuracies in an earlier version of the article.  ... 
doi:10.1109/tpami.2016.2533382 pmid:26929031 fatcat:r5djqtwvo5gmjbn4aii5qsmkza

DLVM: A modern compiler infrastructure for deep learning systems [article]

Richard Wei, Lane Schwartz, Vikram Adve
2018 arXiv   pre-print
We present DLVM, a design and implementation of a compiler infrastructure with a linear algebra intermediate representation, algorithmic differentiation by adjoint code generation, domain-specific optimizations  ...  However, many of the existing deep learning frameworks are software libraries that act as an unsafe DSL in Python and a computation graph interpreter.  ...  and optimizations (transform passes).  ... 
arXiv:1711.03016v5 fatcat:6rh2hyxr6zh4bikxpqf4ar6vee

Chains of recurrences---a method to expedite the evaluation of closed-form functions

Olaf Bachmann, Paul S. Wang, Eugene V. Zima
1994 Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94  
We are especially grateful to one of the referees who suggested to use the "chain" feature for defining CR's and who pointed out the close relationship of factorial polynomials and CR'S.  ...  Acknowledgments We would like to thank all referees for their very helpful suggestions and comments.  ...  The Chains of Recurrences investigation here extends Zima's studies of Systems of Recurrence Relations [6]: b q q q * q New definitions and concepts (sections 2 and 3) for describing CR's are developed  ... 
doi:10.1145/190347.190423 dblp:conf/issac/BachmannWZ94 fatcat:u2n4x4ss5fayjf56bmv3zkow7q

Page 9232 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
Mitrofanov and E. Zima, Multidimensional chains of recurrences (199-206 (electronic)). E. D. Popova and C. P.  ...  Tupikova, Application of com- puter algebra methods to the construction of an asteroid motion theory based on Lie transforms (76-79 (electronic)); Martin Dun- stan, Tom Kelsey, Steve Linton and Ursula  ... 

Flow-Sensitive Loop-Variant Variable Classification in Linear Time [chapter]

Yixin Shou, Robert van Engelen, Johnnie Birch
2008 Lecture Notes in Computer Science  
The remaining flow-sensitive variables (those that have no closed forms) are bounded by tight bounding functions on their value sequences by bounds derived from our extensions of the Chains of Recurrences  ...  The classification algorithm has a linear worst-case execution time in the size of the SSA region of a loop nest.  ...  IV recognition plays a critical role in optimizing compilers as a prerequisite to loop analysis and transformation.  ... 
doi:10.1007/978-3-540-85261-2_22 fatcat:saxsqdovlnfepmmhcqbodw5uey

SHAQ: Single Headed Attention with Quasi-Recurrence [article]

Nashwin Bharwani, Warren Kushner, Sangeet Dandona, Ben Schreiber
2021 arXiv   pre-print
Although they achieve state of the art on many important language tasks, transformers often require expensive compute resources, and days spanning to weeks to train.  ...  We analyze Merity's model here through an exploratory model analysis over several units of the architecture considering both training time and overall quality in our assessment.  ...  This optimizer often works significantly better than standard SGD optimizers on transformer models, and in practice has been able to reduce the training time of BERT from 3 days to 76 minutes.  ... 
arXiv:2108.08207v1 fatcat:uvsjkhojg5fi3dmihvgy2vr2si

Hidden Markov Models with Multiple Observation Processes [article]

James Y. Zhao
2011 arXiv   pre-print
We consider a hidden Markov model with multiple observation processes, one of which is chosen at each point in time by a policy---a deterministic function of the information state---and attempt to determine  ...  Using this fomula, we find computationally that the optimal policy is always a threshold policy, allowing it to be easily found. We also find that the greedy policy is almost optimal.  ...  Acknowledgements My deepest and sincerest appreciation goes to my supervisors, Bill Moran and Peter Taylor, for their countless hours of guidance, both in relation to this thesis and in more general matters  ... 
arXiv:1010.1042v3 fatcat:il7ucsjnxbe5zbabblpsycg6yq

Tangent: Automatic Differentiation Using Source Code Transformation in Python [article]

Bart van Merriënboer, Alexander B. Wiltschko, Dan Moldovan
2017 arXiv   pre-print
It takes numeric functions written in a syntactic subset of Python and NumPy as input, and generates new Python functions which calculate a derivative.  ...  Tangent is a new library that performs AD using source code transformation (SCT) in Python.  ...  To improve readability of the final code and performance, we use Tangent's ability to perform dataflow analysis on Python code to perform several simplifications on the transformed AST (similar to an optimizing  ... 
arXiv:1711.02712v1 fatcat:4ewylp4uivcsfh6dmjrf2nze5y

Randomized modulation of power converters via Markov chains

A.M. Stankovic, G.C. Verghese, D.J. Perreault
1997 IEEE Transactions on Control Systems Technology  
ACKNOWLEDGMENT The authors wish to acknowledge suggestions and clarifications offered by the reviewers, and in particular by Associate Editor J. Chiasson.  ...  The state is recurrent (or essential) if the chain can eventually return to from every state that may be reached from every state in an irreducible chain is therefore recurrent.  ...  ) (20) where Step 2: Let be the Fourier transform of for and be the Fourier transform of the same autocorrelation for For any we have we define to be the Fourier transform of Given that our conditioning  ... 
doi:10.1109/87.553665 fatcat:py3pmkwjhzfeljhss5wxtrefle

An empirical evaluation of chains of recurrences for array dependence testing

J. Birch, R.A. van Engelen, K.A. Gallivan, Y. Shou
2006 Proceedings of the 15th international conference on Parallel architectures and compilation techniques - PACT '06  
This paper evaluates a new approach for fast and accurate nonlinear array dependence testing using Chains of Recurrences (CRs).  ...  Dependences between statement instances in the iteration space of a loop nest impose ordering constraints that must be preserved in order to produce valid optimized, vectorized, and parallelized loop nests  ...  Acknowledgments We would like to thank the anonymous reviewers for their comments and suggestions for improvements.  ... 
doi:10.1145/1152154.1152198 dblp:conf/IEEEpact/BirchEGS06 fatcat:wgpjwoyl7fcwlmbzzct76tsoii
« Previous Showing results 1 — 15 out of 7,577 results