Discrete Neural Computation A Theoretical Foundation Kai-Yeung Siu, Vwani Roychowdhury, Thomas Kailath, (Foreword by Marvin Minsky)

Glossary: pp. 387 -388, Bibliography : pp. 389 - 399, Index : pp. 401 - 407. Ανα κεφάλαιο Περιέχει ασκήσεις και βιβλιογραφικές σημειώσεις.

Preface 1. Introduction 1.1 Aspects of neural Computation 1.1.1 Learning 1.1.2 Representation 1.2 Concepts in Discrete Neural Computation 1.2.1 Feedforward Model 1.2.2 Circuit as a model of Parallel Computation 1.2.3 Types of Fuctional Elements 1.2.4 Hopfield Model 1.3 Complexity Issues in Discrete Neural Computation 1.3.1 A Circuit Complexity Point of View 1.3.2 Complexity Measures for Feedforward Model 1.3.3 Continuous - Valued Elements vs. Binary Elements 1.3.4 Complexity Issues in Hopfield Model 1.4 Examples 1.4.1 The Parity Function 1.4.2 Multiplication and Other Arithmetic Functions 1.4.3 The Comparison Function 1.4.4 Symmetry Recognition/The Eguality Function 1.5 Analytical Techniques 1.5.1 Spectral / Polynomial Representation of Boolean Functions 1.5.2 Rational Approximation 1.5.3 Geometric and linear Algebraic Arguments 1.5.4 Communication Complexity Arguments 1.6 A Historical Perspective 1.7 An Overview of the Book 1.7.1 Linear Threshold Element (LTE) and its Properties 1.7.2 Computing Symmetric Functions 1.7.3 Depth -Efficient Arithmetic Circuits 1.7.4 Depth / Size Trade-offs and Optimization Issues 1.7.5 Computing with Small Weights 1.7.6 Rational Approximation and Optimal-Size Circuits 1.7.7 Spectral Analysis and Geometric Approach 1.7.8 Limitations of AND - OR Circuits 1.7.9 Lower Bounds for Unbounded Dept Circuits 1.7.10 The Hopfield Model 1.8 Notes on Terminology 2. Linear Threshold Element 2.1 Introduction 2.2 Linear Threshold Elements 2.3 perseptron Learning Algorithm 2.4 Analysis of Linearly Nonseparable Sets of input Vectors 2.4.1 Necessary and Sufficient Conditions for Linear Nonseparability 2.4.2 Structures Within Linearly Nonseparable Training Sets 2.5 Learning Problems for Linearly Nonseparable Sets 2.5.1 A Heuristic Algorithm 2.6 Learning Algorithm for Linearly Nonseparable Sets 2.6.1 A Dual Learning Problem 2.6.2 Determining Linearly Separable Subsets 2.7 Capacity of Linear Threshold Elements 2.7.1 Number of Binary Functions Implementable by an LTE 2.7.2 A Lower Bound on the Number of Linearly Separable Functions 2.7.3 Tighter Lower Bound on the Number of Linearly Separable Functions 2.7.4 Number of Weights in Universal Networks 2.8 Large Integer Weights are Sufficient Exercises Bibliographic Notes 3. Computing Symmetric Functions 3.1 Introduction 3.2 A Depth - 2 Construction 3.3 A Depth - 3 Construction 3.4 Generalized Symmetric Functions 3.5 Hyperplane Cuts of a Hypercube Exercises Bibliographic Notes 4. Depth - Efficient Arithmetic Circuits 4.1 Introduction 4.2 Depth - 2 Threshold Circuits for Comparison and Addition 4.2.1 Existence Proof via Harmonic Analysis 4.2.2 Explicit Constructions Based on Error - Correcting Codes 4.3 Multiple Sum and Multiplication 4.4 Division and Related Problems 4.4.1 Exponentiation and Powering Modulo a "Small" Number 4.4.2 Powering in Depth - 4 4.4.3 Multiple Product in Depth - 5 4.4.4 Division in Depth - 4 4.5 Sorting in Depth - 3 Threshold Circuits 4.6 Lower Bounds for Division and Sorting Exercises Bibliographic Notes 5. Depth / Size Trade - offs 5.1 Introduction 5.2 Trade - offs between Node Complexity and Circuit Depth 5.2.1 Parity 5.2.2 Multiple Sum 5.3 Trade - offs for Comparison and Addition 5.4 Addition and Parallel Prefix Circuits 5.4.1 Parallel prefix Circuits 5.4.2 Circuits for Addition 5.5 Trade - offs for Symmetric Functions and Multiplication 5.5.1 Computing the Sum of n Bits 5.5.2 Symmetric Functions and Multiplication Exercises Bibliographic Notes 6. Computing with Small Weights 6.1 Introduction 6.2 Necessity of Exponential Weights 6.3 Depth / Weight Trade - offs 6.3.1 Approximating Functions in LT1 6.3.2 Simulating LTd in LTd+1 6.4 Optimal - Depth Circuits for Multiplication and Division Exercises Bibliographic Notes 7. Rational Approximation and Optimal - Size Circuits 7.1 Introduction 7.2 Lower Bounds on Threshold Circuits 7.2.1 Approximating Parity with Threshold Circuits 7.3 Extensions to Threshold Circuits with Various Gates 7.4 Lower Bounds on Networks with Continuous - Valued Elements Exercises Bibliographic Notes 8. Geometric Framework and Spectral Analysis 8.1 Introduction 8.2 Geometric Concepts and Definitions 8.3 Uniqueness 8.4 Generalized Spectrum 8.4.1 Characterizations with Generalized L1 Spectral Norms 8.5 Spectral / Polynomial Representation 11 11.4 Combinatorial Optimization 11.4.1 Min - Cut and Related Problems 11.4.2 The Traveling - Salesman Problem Exercises Bibliographic Notes Glossary Bibliography Index