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An Architecture for Fault-Tolerant Computation with Stochastic Logic

Weikang Qian, Xin Li, Marc D. Riedel, Kia Bazargan, David J. Lilja
2011 IEEE transactions on computers  
We analyze cost as well as the sources of error: approximation, quantization, and random fluctuations.  ...  We study the effectiveness of the architecture on a collection of benchmarks for image processing. The stochastic architecture requires less area than conventional hardware implementations.  ...  A method was proposed in [17] to synthesize arbitrary functions by approximating them via Bernstein polynomial.  ... 
doi:10.1109/tc.2010.202 fatcat:6r3ou52ze5dupjhuls6vrkrhzm

Design of a Time Delay Reservoir Using Stochastic Logic: A Feasibility Study [article]

Cory Merkel
2017 arXiv   pre-print
A novel re-seeding method is introduced to reduce the adverse effects of stochastic noise, which may also be implemented in other stochastic logic reservoir computing designs, such as echo state networks  ...  The reservoir is analyzed using a number of metrics, such as kernel quality, generalization rank, performance on simple benchmarks, and is also compared to a deterministic design.  ...  For the function f (s), this results in the dotted curve in Figure 5 . Also shown is the stochastic logic approximation using Bernstein polynomials with L = 1000 and n = 5.  ... 
arXiv:1702.04265v1 fatcat:mfxnaefg3zg53hm352o74mvcgu

A reconfigurable stochastic architecture for highly reliable computing

Xin Li, Weikang Qian, Marc D. Riedel, Kia Bazargan, David J. Lilja
2009 Proceedings of the 19th ACM Great Lakes symposium on VLSI - GLSVLSI '09  
We analyze the sources of error: approximation, quantization, and random fluctuations. We demonstrate the effectiveness of our method on a collection of benchmarks for image processing.  ...  In this paper, we present a reconfigurable architecture that implements the computation of arbitrary continuous functions with stochastic logic.  ...  The output of the ReSC Unit is a stochastic bit stream Y corresponding to y, the optimal Bernstein approximation of the target function.  ... 
doi:10.1145/1531542.1531615 dblp:conf/glvlsi/LiQRBL09 fatcat:4jua3mrrmngihpxjostpzw54me

MALDI-TOF Baseline Drift Removal Using Stochastic Bernstein Approximation

Joseph Kolibal, Daniel Howard
2006 EURASIP Journal on Advances in Signal Processing  
Stochastic Bernstein (SB) approximation can tackle the problem of baseline drift correction of instrumentation data.  ...  Following an explanation of the origin of the MALDI-TOF baseline drift that sheds light on the inherent difficulty of its removal by chemical means, SB baseline drift removal is illustrated for both proteomics  ...  We are also indebted to Professor Franz Hillenkamp from the Institute for Medical Physics and Biophysics at the University of Münster in Germany for furnishing us with the information that is presented  ... 
doi:10.1155/asp/2006/63582 fatcat:yai6hwpq7na6dj55uivgzdviuu

Optimal Stochastic Coordinated Beamforming for Wireless Cooperative Networks with CSI Uncertainty [article]

Yuanming Shi, Jun Zhang, Khaled B. Letaief
2014 arXiv   pre-print
In contrast to all the previous algo- rithms for JCCP that can only find feasible but sub-optimal solutions, we propose a novel stochastic DC (difference-of-convex) programming algorithm with optimality  ...  Simulation results will illustrate the convergence, conservativeness, stability and performance gains of the proposed algorithm.  ...  deterministic approximation methods, e.g., the Bernstein approximation method.  ... 
arXiv:1312.0363v2 fatcat:r67f7cixwreijobgrskjo6pwdu

An FPGA Implementation of a Time Delay Reservoir Using Stochastic Logic [article]

Lisa Loomis, Nathan McDonald, Cory Merkel
2018 arXiv   pre-print
A novel re-seeding method is introduced to reduce the adverse effects of stochastic noise, which may also be implemented in other stochastic logic reservoir computing designs, such as echo state networks  ...  In addition, we show that the stochastic design can significantly reduce area cost if the conversion between binary and stochastic representations implemented efficiently.  ...  Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of AFRL.  ... 
arXiv:1809.05407v1 fatcat:7fdjlhxn2jhynagy7s6h7vbmni

The synthesis of robust polynomial arithmetic with stochastic logic

Weikang Qian, Marc D. Riedel
2008 Proceedings of the 45th annual conference on Design automation - DAC '08  
The method is based on converting polynomials into a particular mathematical form -Bernstein polynomials -and then implementing the computation with stochastic logic.  ...  In this paper, we present a general methodology for synthesizing stochastic logic for the computation of polynomial arithmetic functions, a category that is important for applications such as digital signal  ...  In the first, we chose the 6-th order Maclaurin polynomial approximation of 11 elementary functions as our implementation target.  ... 
doi:10.1145/1391469.1391636 dblp:conf/dac/QianR08 fatcat:jwvw2zesozai5bmiltca3c2p54

State-Density Functions over DBM Domains in the Analysis of Non-Markovian Models

L. Carnevali, L. Grassi, E. Vicario
2009 IEEE Transactions on Software Engineering  
The approximation attacks practical and theoretical limits in the applicability of stochastic state classes and devises a new approach to the analysis of non-Markovian models, relying on approximations  ...  This enables an efficient implementation of the analysis process and provides the formal basis that supports the introduction of an imprecise analysis based on the approximation of statedensity functions  ...  The method develops on the concept of stochastic classes, which augment state classes with a state-density function.  ... 
doi:10.1109/tse.2008.101 fatcat:aoblpffdjjdvhjc2amowbtfbky

Reference-Based Almost Stochastic Dominance Rules with Application in Risk-Averse Optimization [article]

Jian Hu, Gevorg Stepanyan
2015 arXiv   pre-print
Stochastic dominance is a preference relation of uncertain prospect defined over a class of utility functions.  ...  We also propose RSD constrained stochastic optimization model and develop an approximation algorithm based on Bernstein polynomials. This model is illustrated on a portfolio optimization problem.  ...  We have proposed the RSD constrained stochastic optimization model and studied its solution method. An approximation approach based on Bernstein polynomials has been developed.  ... 
arXiv:1512.07953v1 fatcat:lv5kf44n4bc2lauak47cjv6qiy

Preface to the special issue on analysis in machine learning and data science

Andreas Chirstmann, ,Department of Mathematics Stochastics University of Bayreuth 95440 Bayreuth, Germany, Qiang Wu, Ding-Xuan Zhou, ,Department of Mathematical Sciences Middle Tennessee State University Murfreesboro, TN 37132, USA, ,School of Data Science and Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue, Kowloon Hong Kong, China
2020 Communications on Pure and Applied Analysis  
By technical uses of Bernstein polynomials to uniformly approximate general convex losses (other than the classical least square loss), Yang, Shen, Ying, and Yuan developed a novel stochastic gradient  ...  Mhaskar and Poggio showed that deep networks are better than shallow ones in approximating functions that can be expressed as a composition of functions described by a directed acyclic graph.  ... 
doi:10.3934/cpaa.2020171 fatcat:tu3hfj2rvrgl7ih65dzae5i2xe

Bernstein polynomial approximation of fixation probability in finite population evolutionary games [article]

Jiyeon Park, Paul Newton
2022 bioRxiv   pre-print
Because of a boundary layer that occurs in the weak-selection limit, the Bernstein polynomial method is more efficient at approximating the rate of evolution in the strong selection region (w ~ 1) (requiring  ...  We use the Bernstein polynomials of degree d as the basis for constructing a uniform approximation to the rate of evolution (related to the fixation probability) of a species in a two-component finite-population  ...  Acknowledgments We gratefully acknowledge support from the Army Research Office MURI Award #W911NF1910269 (2019-2024) as well as useful conversations and suggestions from Prof. Kukavica and Prof.  ... 
doi:10.1101/2022.08.05.502960 fatcat:ttkza6qgiff6lnr56idqc7vx34

Table of Contents

2021 IEEE Transactions on Automatic Control  
Li 1414 A Novel Method for Stability Analysis of Time-Varying Delay Systems . . . . . . . . . . . . . . . . . . . . Y. Wang, H. Liu, and X.  ...  Zhang 1407 Over-and Under-Approximations of Reachable Sets With Series Representations of Evolution Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ... 
doi:10.1109/tac.2021.3056496 fatcat:fhuhtatv7na33gonm6iqag4zyu

An improved MDL-based compression algorithm for unsupervised word segmentation

Ruey-Cheng Chen
2013 Annual Meeting of the Association for Computational Linguistics  
Our analysis shows that its objective function can be efficiently approximated using the negative empirical pointwise mutual information.  ...  We study the mathematical properties of a recently proposed MDL-based unsupervised word segmentation algorithm, called regularized compression.  ...  Acknowledgments We thank the anonymous reviewers for their valuable feedback.  ... 
dblp:conf/acl/Chen13 fatcat:fwl3dnstwfdbhk6u77yba6gyuu

Stochastic Sign Descent Methods: New Algorithms and Better Theory [article]

Mher Safaryan, Peter Richtárik
2021 arXiv   pre-print
To resolve this issue, we propose a new sign-based method, Stochastic Sign Descent with Momentum (SSDM), which converges under standard bounded variance assumption with the optimal asymptotic rate.  ...  Sign-based methods, such as signSGD, have recently been gaining popularity because of their simple compression rule and connection to adaptive gradient methods, like ADAM.  ...  Acknowledgments Mher Safaryan thanks El Houcine Bergou, Konstantin Mishchenko and Samuel Horváth for helpful discussions about the topic and their feedback on the paper.  ... 
arXiv:1905.12938v5 fatcat:u6u3m5z7uvfspckcehif7su2ym

Robust Resource Allocation for PD-NOMA-Based MISO Heterogeneous Networks with CoMP Technology [article]

Atefeh Rezaei, Paeiz Azmi, Nader Mokari, Mohammad Reza Javan
2019 arXiv   pre-print
We propose a novel method based on matching game with externalities to realize the hybrid scheme where the number of the cooperative nodes are variable.  ...  We provide the complexity analysis of both schemes which shows that the complexity of the partial CSI approach is more than that of the no CSI method.  ...  Moreover, comparison between the stochastic and worst-case approaches shows that the computational complexity of the stochastic Bernstein approach is more than worst-case method. VII.  ... 
arXiv:1902.09879v3 fatcat:i75xrkn7sffu3ihpal2vk2sso4
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