Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.

Gradient-based learning applied to document recognition

A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.

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Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.

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Graph-Based Algorithms for Boolean Function Manipulation

Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

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Principles of Model Checking

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don't care sets. Specifically given an incompletely specified function g and a fixed ordering of the variables, we propose an exact algorithm for selecting f such that f is a cover for g and the binary decision diagram for f is of minimum size. The approach described is the only known exact algorithm for this problem not based on the enumeration of the assignments to the points in the don't care set. We show also that our problem is NP-complete. We show that the BDD minimization problem can be formulated as a binate covering problem and solved using implicit enumeration techniques. In particular, we show that the minimum-sized binary decision diagram compatible with the specification can be found by solving a problem that is very similar to the problem of reducing incompletely specified finite state machines. We report experiments of an implicit implementation of our algorithm, by means of which a class of interesting examples was solved exactly. We compare it with existing heuristic algorithms to measure the quality of the latter.

Exact minimization of binary decision diagrams using implicit techniques

The authors present an algorithm for the synthesis of two-level threshold gate networks inspired by techniques used in classical two-level minimization of logic circuits. They specifically address a restricted version of the problem where the on and off set minterms are explicitly listed. Experimental results show that a simple branch and bound algorithm can be used to obtain solutions close to the absolute minimum in a set of standard problems, outperforming other minimizers even when restricted to using only classic logic gates as building blocks. The algorithm has a run time polynomial in the input size and its performance degrades slowly with the size of the problem. >

LSAT-an algorithm for the synthesis of two level threshold gate networks

Logic Verification Using BDDs in a Logic Synthesis Environ-ment

The authors present two methods that are capable of computing the steady-state response of a circuit directly: harmonic balance, which is a frequency-domain method, and the finite-difference method, which is based in the time domain. Both of these methods are suitable for use on nonlinear circuits that contain distributed devices and that exhibit either periodic or quasiperiodic steady-state solutions. >

Finding the steady-state response of analog and microwave circuits

PLATypus (PLA Test pattern generation and logic simulation tool) is an efficient tool for large PLA's which is interfaced with other existing PLA tools such as the folding program PLEASURE [12] and the logic minimizer ESPRESSO II-C [11] developed at the University of California at Berkeley. A new algorithm is proposed based on complementation and the tautology check of a logic cover, derived from the PLA personality matrix. Both complementation and tautology check are performed by advanced logic manipulation algorithms used in the logic minimization program ESPRESSO II-C [11]. The algorithm is exact, i.e., every testable crosspoint fault is tested, and maximum fault coverage is guaranteed. A quick preprocess, the biased random test generation, is used followed by the proposed algorithm to achieve the best balance between run time and test-set compactness. The program is refined at various stages by many powerful heuristics in the area of fault processing order, backend fault simulation, "don't-care" bit fixing, and on-the-fly test compaction. Both single stuck-at and crosspoint fault models are supported. PLATYPUS can also be used as a logic simulation tool and redundancy identifier. Test pattern generation has been performed by PLATYPUS on a large number of industrial PLA's.

Alberto Sangiovanni-Vincentelli

Papers

Exact minimization of binary decision diagrams using implicit techniques

LSAT-an algorithm for the synthesis of two level threshold gate networks

Logic Verification Using BDDs in a Logic Synthesis Environ-ment

Finding the steady-state response of analog and microwave circuits

PLATYPUS: A PLA Test Pattern Generation Tool