VSAX Course: From Foundations to Research¶

Welcome to the VSAX comprehensive course! This progressive learning path will take you from zero VSA knowledge to advanced research capabilities.

What You'll Learn¶

This course teaches Vector Symbolic Architectures (VSAs), also known as Hyperdimensional Computing (HDC), through a unique combination of mathematical foundations and hands-on implementation.

By the end of this course, you will:

✅ Understand why high-dimensional vectors enable symbolic computation
✅ Master the three VSA models (FHRR, MAP, Binary) and when to use each
✅ Build encoders for any data type (images, graphs, sequences, continuous spaces)
✅ Implement advanced techniques (operators, resonators, spatial encoding)
✅ Debug common VSA issues and optimize performance
✅ Design research extensions and contribute to VSAX

Course Structure¶

The course consists of 5 modules, 20 lessons, and takes approximately 12-20 hours to complete.

Module Breakdown¶

Module	Topics	Level	Duration
Module 1	Foundations	Beginner	3-4 hours
Module 2	Core Operations	Beginner-Intermediate	4-5 hours
Module 3	Encoders & Applications	Intermediate	6-8 hours
Module 4	Advanced Techniques	Advanced	6-8 hours
Module 5	Research & Extensions	Research	3-4 hours

Detailed Module Overview¶

Module 1: Foundations¶

Why high dimensions work | Binding & bundling | Three VSA models | First program

Start here if you're new to VSA. Learn the mathematical intuitions behind hyperdimensional computing and write your first VSAX program.

Start Module 1 →

Module 2: Core Operations¶

FHRR mathematics | MAP & Binary operations | Similarity metrics | Model selection

Deep dive into the three VSA models. Understand the mathematical foundations, implementation details, and decision frameworks for choosing the right model.

Start Module 2 →

Module 3: Encoders & Applications¶

Scalar encoding | Dictionaries & sets | Image classification | Knowledge graphs | Analogies

Learn encoding strategies for different data types and build real-world applications: classifiers, knowledge bases, and analogical reasoning systems.

Start Module 3 →

Module 4: Advanced Techniques¶

Clifford operators | Spatial semantic pointers | Hierarchical structures | Multi-modal fusion

Master advanced VSA techniques for complex reasoning: exact transformations, continuous spatial encoding, tree structures, and neural-symbolic integration.

Start Module 4 →

Module 5: Research & Extensions¶

Vector function architecture | Custom encoders | Research frontiers

Prepare for VSA research. Learn VFA, design custom encoders, explore open problems, and contribute to VSAX development.

Start Module 5 →

Learning Paths¶

Choose a learning path based on your background and goals:

Path 1: Full Course (Beginners)¶

Recommended for: Complete beginners to VSA

Path: Module 1 → Module 2 → Module 3 → Module 4 → Module 5

Duration: ~20 hours

You'll learn: Complete VSA foundations, all three models, encoding strategies, advanced techniques, and research preparation

Start with Module 1 →

Path 2: Application-Focused (ML Engineers)¶

Recommended for: ML practitioners who want to build VSA applications

Path: Module 1 (skim 1.1-1.2) → Module 3 → Module 4 (selected topics)

Duration: ~10 hours

You'll learn: Practical encoding strategies, image classification, knowledge graphs, multi-modal systems

Skip: Deep mathematical foundations, model comparison details

Start with Module 1.3 →

Path 3: Research-Focused (PhD Students)¶

Recommended for: Researchers exploring VSA for their work

Path: Module 1 → Module 2 → Module 4 → Module 5

Duration: ~15 hours

You'll learn: Mathematical foundations, model selection, advanced techniques (operators, SSP, VFA), research frontiers

Skip: Basic application tutorials (can revisit as needed)

Start with Module 1 →

Path 4: Quick Start (Developers)¶

Recommended for: Developers who need to use VSAX immediately

Path: Getting Started → Module 3 → Tutorials (as needed)

Duration: ~6 hours

You'll learn: How to use VSAX API, encoding strategies, specific application recipes

Skip: Mathematical foundations (can revisit later)

Start with Getting Started →

Prerequisites¶

Required¶

Python proficiency: Comfortable with Python syntax, functions, classes
NumPy basics: Understand arrays, array operations, broadcasting
Basic linear algebra: Vectors, dot products, norms

Recommended (Not Required)¶

JAX familiarity: Helps but not necessary (we'll teach JAX patterns)
Machine learning basics: Helpful for understanding applications
Complex numbers: Useful for FHRR model (we'll review when needed)

Installation¶

Before starting, ensure VSAX is installed:

pip install vsax

Or for development:

git clone https://github.com/vasanthsarathy/vsax.git
cd vsax
pip install -e ".[dev]"

How to Use This Course¶

Progressive Learning¶

This course is designed for progressive learning. Each lesson builds on previous concepts. We recommend:

Follow in order within modules
Complete exercises before moving forward
Check self-assessments to ensure understanding
Build capstone projects at module end

Exercises and Assessments¶

Each lesson includes:

Self-Assessment Checklist: "I can..." statements to verify understanding
Quick Quiz: 3-5 conceptual questions
Hands-On Exercise: Coding problems with solutions

Each module includes:

Capstone Project: Larger application combining module concepts

Code Examples¶

All code examples are:

✅ Copy-paste ready (runnable as-is)
✅ Tested with latest VSAX version
✅ Commented with explanations
✅ Available in /exercises/ directories

Getting Help¶

Stuck on a concept?

Check Troubleshooting for common issues
Review previous lessons for foundations
Try the exercises (learning by doing!)
Ask questions on GitHub Discussions

Found an error?

Open an issue on GitHub
Or submit a pull request with fixes!

Course vs Tutorials vs User Guide¶

Confused about where to start? Here's how the documentation is organized:

Section	Purpose	When to Use
Course (you are here)	Progressive learning with theory + practice	Learning VSA from scratch
Tutorials	Cookbook recipes for specific tasks	Need to solve a specific problem
User Guide	Feature reference documentation	Looking up API details
Getting Started	Quick introduction	Want to try VSAX right now

Time Commitment¶

Full Course¶

Self-paced: 2-4 weeks at 1 hour/day
Intensive: 1 week full-time
Casual: 4-8 weeks at 2-3 hours/week

Individual Modules¶

Module 1: One weekend (3-4 hours)
Module 2: One weekend (4-5 hours)
Module 3: Two weekends (6-8 hours)
Module 4: Two weekends (6-8 hours)
Module 5: One weekend (3-4 hours)

What Makes This Course Unique?¶

1. Theory + Practice Together¶

Every mathematical concept is immediately followed by JAX/VSAX code. You'll understand both the "why" and the "how".

2. Multiple Learning Paths¶

Not everyone learns the same way. Choose a path that matches your background and goals.

3. Hands-On Throughout¶

No passive reading. Every lesson has exercises. Learning VSA requires building intuitions through coding.

4. Reuses Best Content¶

60% of content links to existing excellent tutorials and guides. 40% is new foundational material filling critical gaps.

5. Self-Paced with Scaffolding¶

Self-assessments help you know when you're ready to proceed. No instructor required.

6. Research-Ready¶

Module 5 prepares you for advanced VSA research and contributing to VSAX.

Ready to Start?¶

Beginners: Start with Module 1¶

Learn why high-dimensional vectors enable symbolic computation.

Module 1: Foundations →

Experienced ML practitioners: Jump to Module 3¶

Learn encoding strategies and build applications.

Module 3: Encoders & Applications →

Researchers: Start with Module 1, Focus on 2, 4, 5¶

Deep mathematical foundations and advanced techniques.

Module 1: Foundations →

Feedback and Contributions¶

This course is a living document. Help us improve it!

Found a typo? Submit a PR
Have a suggestion? Open an issue
Built something cool? Share in Discussions
Want to contribute a lesson? We welcome contributions!

Repository: github.com/vasanthsarathy/vsax

Course Completion¶

When you complete all 5 modules and capstone projects:

[ ] You can explain why high dimensions enable symbolic computation
[ ] You can choose the appropriate VSA model for any task
[ ] You can build encoders for custom data types
[ ] You can debug common VSA issues (low similarity, capacity limits)
[ ] You can implement advanced techniques (operators, resonators, SSP)
[ ] You can propose research extensions to VSAX

Congratulations! You're now a VSA expert ready to build advanced cognitive architectures.

Ready? Let's begin your VSA journey.

Start Module 1: Foundations →