Ch6: AM and BAM 6.1 Introduction AM: Associative Memory BAM: Bidirectional Associative Memory 6.1 Introduction 。 Memory: store and deduce information Memory can be pre-stored or trained AM retrieves memory in one shot BAM retrieves memory through many iterations

。 Categories of memory LAM (Local Addressable Memory) -- give an address to access the content pointed by the address. CAM (Content Addressable Memory) -- give pieces of information (key) to find the address where stores the complete information, ex. hash table.

AM (Associative Memory) -- give a datum (i) to find or recover the original noise–free data (ii) to retrieve all the related data Matrix Representation

Example: Input vector: Fault tolerance Recall:

6.3 Types of AM Input vector: Output vector: Autoassociative memory － If e.g., color correction, color constancy Heteroassociative memory － If e.g., i, Space transforms: Fourier transforms ii, Dimensionality reduction: PCA

Interpolative associative memory － If e.g., Compute AM mapping is defined as output input Suppose are orthonormal vectors.

a. Continuous-valued input patterns i, Ideal pattern retrieval (noise-free) e.g., ii, Noisy input noise

b. Binary – valued input patterns: 0, 1 1. Memory matrix where i.e., W is formed from bipolar – valued patterns: -1, 1 2. Threshold vector i = 1, …, N (row sum) 3. Retrieval: where I : input vector, O : output vector

。 Example: Auto-association memory Two I/O pairs : ∵ Auto-AM i, Memory matrix ,

ii, Threshold vector 1. First test pattern

Output pattern: 2. Second test pattern Output pattern: nonlinear processing Output pattern: 2. Second test pattern Output pattern:

6.4 BAM Characteristics:

For autoassociative memory,

‧ Output

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Second trial:

6.4.2 Energy Function Dynamic system: a system whose state changes with time. State: a collection of adaptable quantitative and qualitative items that characterizing the system, e.g., weights, data flows …..

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