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Module 4: Advanced Techniques

Duration: ~4 hours | Difficulty: Advanced

Overview

Module 4 introduces cutting-edge VSA techniques that enable sophisticated reasoning, spatial intelligence, and multi-modal AI systems. You'll learn how to build systems that combine continuous spatial representations, hierarchical structures, and heterogeneous data fusion.

What You'll Learn

  • Clifford Operators: Exact, invertible transformations for directional relations
  • Spatial Semantic Pointers: Encode continuous space without discretization
  • Hierarchical Structures: Recursive role-filler binding for trees and nested data
  • Resonator Networks: Convergent factorization for decoding complex bindings
  • Multi-Modal Integration: Fuse vision, language, and symbols in unified VSA space
  • Neural-Symbolic AI: Combine neural networks with symbolic VSA reasoning (HD-Glue)

Lessons

4.1: Clifford Operators

Time: 45 minutes

Learn how operators enable exact, invertible transformations for spatial and semantic relations where standard binding fails.

Key concepts: Operators vs hypervectors, phase-based transformations, exact inversion (>0.999 similarity)

4.2: Spatial Semantic Pointers

Time: 50 minutes

Encode continuous spatial coordinates using Fractional Power Encoding for smooth, queryable spatial representations.

Key concepts: SSP = \(X^x \otimes Y^y\), continuous spatial encoding, "what/where" queries

4.3: Hierarchical Structures & Resonators

Time: 60 minutes

Encode tree structures with recursive binding and decode using resonator networks for convergent factorization.

Key concepts: Recursive role-filler binding, resonator algorithm, parsing trees and nested data

4.4: Multi-Modal & Neural-Symbolic Integration

Time: 55 minutes

Fuse heterogeneous data (vision + language + symbols) and combine neural networks with VSA symbolically.

Key concepts: Cross-modal grounding, HD-Glue, ensemble learning, neuro-symbolic AI

Hands-On Exercises

Exercise 1: Spatial Reasoning System - Combine SSP + Clifford Operators for complete spatial reasoning - Build 2D scene encoder with locations and directional relations

Exercise 2: Tree Decoder - Encode/decode expression trees, JSON, family trees - Use resonators for factorization of complex bindings

Capstone: Multi-Modal Reasoning System - Integrate ALL Module 4 techniques - Build unified knowledge base with spatial, relational, hierarchical, and attribute representations

Prerequisites

✅ Module 1: Foundational concepts (binding, bundling, three models) ✅ Module 2: FHRR operations (exact unbinding needed for operators) ✅ Module 3: Encoders (FPE, DictEncoder used extensively)

Learning Outcomes

After Module 4, you will be able to:

  • [ ] Create Clifford Operators for exact relational encoding
  • [ ] Use SSP for continuous 2D/3D spatial reasoning
  • [ ] Encode hierarchical trees with recursive binding
  • [ ] Decode complex bindings using resonator networks
  • [ ] Fuse multiple modalities in unified VSA space
  • [ ] Integrate neural embeddings with symbolic VSA

Previous: Module 3: Encoders & Applications Next: Lesson 4.1: Clifford Operators or Module 5: Research & Extensions