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Exploring Neural Manifolds, Memory Consolidation, and t-SNE Visualization for Latent Space Representations
Introduction
In modern machine learning, latent space representations provide a powerful way to capture the essential structure of high-dimensional data, projecting it into lower-dimensional manifolds. In this article, we take a deep dive into the mathematics and implementation behind neural networks that exploit this principle, using autoencoders and memory consolidation to model and strengthen learned representations over time. We explore how these concepts are rooted in both statistical learning and neuroscience and demonstrate their effectiveness on the MNIST digits dataset.
We’ll walk through the mathematics of neural manifolds and latent spaces, the code implementation, and the historical background, before delving into specific use cases. Finally, we will analyse the results and conclude with an assessment of the techniques.
Mathematics of Neural Manifolds and Latent Spaces
Manifold Learning
The goal of manifold learning is to find a mapping:
