Integrating Hyperdimensional Computing and Neuro Symbolic AI with LSTM Networks for Time-Series Prediction

Introduction

In the forever evolving field of artificial intelligence, the fusion of different computational paradigms often leads to breakthroughs in performance and efficiency. This article dives into the integration of Hyperdimensional Computing (HDC) and Neuro Symbolic AI (NSAI) with Long Short-Term Memory (LSTM) networks for time-series prediction tasks.

We’ll explore the mathematical foundations, dissect the code implementation, discuss potential use cases, compare benefits over traditional approaches and analyse the results obtained from our experiments.

Mathematical Foundations

1. Hyperdimensional Computing (HDC)

Hyperdimensional Computing is inspired by the way the human brain processes information using patterns of neural activity that are high-dimensional, distributed, and holographic. HDC represents data as hypervectors in high-dimensional spaces (typically in the thousands or tens of thousands of dimensions).

Encoding and Manipulation

• Hypervectors: Random vectors with elements typically chosen from {-1, +1}.
• Superposition (Addition): Combines multiple hypervectors into one by element-wise addition.
• Binding (Multiplication): Combines hypervectors by element-wise multiplication, creating a new hypervector orthogonal to the originals.
• Similarity: Measured using cosine similarity or Hamming distance.

Mathematically, for hypervectors A and B:

2. Long Short-Term Memory (LSTM) Networks

LSTMs are a type of Recurrent Neural Network (RNN) capable of learning long-term dependencies.

LSTM Cell Mechanics

An LSTM cell consists of: