A Geometric Perspective on Large Language Models

Ever pondered over a geometric interpretation of Large Language Models (LLMs) without delving deep into the math? Here’s my personal perspective, simplifying these AI complexities into an intuitive, spatial understanding.

Understanding the High-Dimensional Space:

Imagine the workings of an LLM as operating within a vast, high-dimensional geometric space. Each dimension in this space can be thought of as representing different aspects of language — from basic grammar to complex contextual nuances.

Input Representation as a Vector:

When we input a sentence into an LLM, it gets converted into a series of vectors — points or directions in this high-dimensional space. The placement and orientation of these vectors are determined by the linguistic properties of the input text.

Transformation Through Layers:

As these vectors pass through the LLM’s layers, they undergo a series of transformations. Each layer of the neural network can be visualized as altering the vector’s position and trajectory in this space, based on the layer’s learned weights and biases.

Navigating the Geometric Landscape:

The journey of these vectors through the network is akin to a path traversing through the landscape of this high-dimensional space. This path is intricate, shaped by the complex and non-linear dynamics of the network’s architecture.

Arriving at a Prediction:

Eventually, the transformed vectors reach the final layer, which maps them to a new set of coordinates. These coordinates correspond to a probability distribution over possible next words or tokens. The proximity of the final vector to specific points in this layer’s space signifies the likelihood of different tokens being the next in the sequence.

Probability and Geometric Location:

In this geometric analogy, the probability of each token is represented by how closely the final vector lies to certain regions or points in this final space. The “closest” point or the densest region indicates the model’s prediction for the next word.

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