Theory & Foundations

Theoretical foundations of hyperdimensional computing and vector symbolic architectures.

This section provides mathematical foundations, algorithm descriptions, and theoretical analysis of HDC/VSA systems.

Contents

VSA Models

Theory Guide: Hyperdimensional Computing & Vector Symbolic Architectures provides comprehensive mathematical descriptions of all 7 VSA models implemented in HoloVec:

  • MAP (Multiply-Add-Permute)

  • FHRR (Fourier Holographic Reduced Representations)

  • HRR (Holographic Reduced Representations)

  • BSC (Binary Spatter Codes)

  • BSDC (Block-Structured Distributed Codes)

  • GHRR (Generalized HRR)

  • VTB (Vector-derived Transformation Binding)

Each model includes:

  • Mathematical definition

  • Binding and unbinding operations

  • Bundling semantics

  • Theoretical properties

  • Computational complexity

Encoders

Encoder Theory: From Scalars to Sequences covers the theory and algorithms for all encoder types:

Scalar Encoders:

  • Fractional Power Encoder (FPE) - Smooth similarity via complex exponentials

  • Thermometer Encoder - Ordinal encoding with monotonic similarity

  • Level Encoder - Discrete bin encoding

Sequence Encoders:

  • Position Binding - Order-sensitive sequence encoding

  • N-gram - Overlapping subsequence patterns

  • Trajectory - Continuous motion path encoding

Spatial Encoders:

  • Image Encoder - 2D spatial data encoding

  • Vector Encoder - Multivariate feature vectors

Each encoder includes:

  • Algorithm description

  • Mathematical formulation

  • Similarity properties

  • Reversibility analysis

  • Use case guidance

Additional Topics

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Core concepts and mathematical foundations of HDC/VSA

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Detailed analysis of model properties and trade-offs

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Information capacity, bundling limits, and dimensionality analysis

See Also