Crafting a Self-Attention-Driven VAE with Hyperdimensional Computing and Neuro-Symbolic AI for Noisy Sine Wave Data

Introduction

In this in-depth technical blog article, we explore a hybrid architecture I created that combines Variational Autoencoders (VAEs), self-attention mechanisms, hyperdimensional representations and neuro-symbolic constraints.

I apply these methods to learn structured representations of noisy sine wave data and observe how they help capture temporal dependencies, regularize latent spaces via KL annealing and optionally enforce symbolic constraints within the model’s high-dimensional feature space.

Below, I break down the mathematics behind each module, provide a detailed tour of the code (with subsections explaining key components), discuss potential use cases, highlight the benefits of this approach and analyse the final results.

1. Mathematical Breakdown

1.1 Variational Autoencoder (VAE)

1.2 Self-Attention