User Manual

The User Manual explains why PyHDC works the way it does. It is understanding-oriented: you can read it without running any code, and it will deepen your intuition for HDC as a computational paradigm.

Contents

• HDC Theory and Mathematics
  • The vector space
  • Near-orthogonality and capacity
  • Bundling: algebraic requirements
  • Binding: algebraic requirements
  • Sequence and structure encoding
  • Similarity metrics: why they differ
  • Key references
• Encodings Overview
  • The Encoding base class
  • MAP family
  • HRR family
  • Matrix family
  • Binary family
  • Sparse Binary (BSDC) family
• Binding Operations
  • ElementMultiplication
  • CircularConvolution and CircularCorrelation
  • ExclusiveOr (XOR)
  • Shifting and Inverse Shifting
  • SegmentShifting and SegmentInverseShifting
  • AdditiveContextDependentThinning (CDT)
  • VectorDerivedTransformation (VTB)
  • MatrixMultiplication (MBAT)
  • ElementAngleAddition and ElementAngleSubtraction
• Bundling Operations
  • ElementAddition
  • ElementAdditionCut
  • ElementAdditionBits
  • ElementAdditionBinaryThreshold
  • ElementAdditionBipolarThreshold
  • ElementAdditionNormalized
  • ElementAdditionConstantNormalized
  • AnglesOfElementAddition
  • Disjunction (bitwise OR)
  • DisjunctionThinned
• Similarity Metrics
  • CosineSimilarity
  • HammingDistance
  • Overlap
  • AngleDistance
  • remap_to_unit
  • Batched calling conventions
  • Choosing the right metric
• Random Number Generators
  • The HDCGenerator interface
  • Generator output types and encoding compatibility
  • LCG: Linear Congruential Generator
  • LFSR: Linear Feedback Shift Register
  • DLFSR: Digit-Serial LFSR
  • LCA: Linear Cellular Automata
  • PCG: Permuted Congruential Generator
  • Xorshift family
  • ShiftedCounter family
  • When to use each family
• Dual Backend Architecture
  • Design rationale
  • The TORCH_AVAILABLE flag
  • The BackendManager
  • Backend selection
  • What changes between backends
  • PyTorch batching
  • Memory layout and data movement
  • Limitations
• The components Submodule
  • Submodule layout
  • The EncodingSpec wiring
  • elements submodule
  • thinning submodule
  • similarity submodule
  • input_formatting submodule

Overview

HDC Theory and Mathematics

The mathematics of hypervectors: near-orthogonality, capacity, and why the three primitives (bundle, bind, similarity) are sufficient for symbolic reasoning.

Encodings Overview

The Encoding base class and EncodingSpec design; a tour of all four encoding families (MAP, HRR/FHRR, Matrix, Binary/Sparse).

Binding Operations

Deep dive on every binding operation: element multiplication, circular convolution, XOR, shift, matrix transformation, and more.

Bundling Operations

Deep dive on every bundling operation: addition variants, normalisation, majority vote, bitwise OR, and thinned OR.

Similarity Metrics

Cosine, Hamming, Overlap, and Angle distance: formulas, output ranges, batched calling conventions, and remapping.

Random Number Generators

The seven generator families; LCG, LFSR, DLFSR, LCA, PCG, Xorshift, ShiftedCounter; with design rationale and a compatibility matrix.

Dual Backend Architecture

How PyHDC’s dual NumPy / PyTorch backend is implemented, when to use each, and how device placement works.

The components Submodule

The pyhdc.components submodule: building blocks for custom encodings and advanced post-processing pipelines.