Latent spaces, health trajectories and Manifolds

https://aistudio.google.com/prompts/14InwG9qYnHYOo4iLcC7C2Vv9vKdfkPuX 

To explain logits and embeddings as tools, it is best to visualize them as the two ends of a bridge. Together, they create, shape, and navigate the "embedding space"—the mathematical map where a model stores the meaning of words or data.

Here is an explanation of how these two tools function to generate and maintain that space.

The Concepts: The Map and The Scoreboard

Embeddings (The Map):

What they are: Embeddings are the model's internal dictionary. They act as coordinates. Just as "Paris" is at specific latitude/longitude coordinates on a map, the word "King" is stored as a specific vector (a list of numbers) in the embedding space.

The Goal: To place related concepts close together. In a well-generated space, the point for "Dog" is mathematically closer to "Cat" than it is to "Sandwich."

Logits (The Scoreboard):

What they are: Logits are the raw, unnormalized prediction scores the model outputs at the very end of its thinking process, right before it makes a final decision.

The Goal: To measure confidence. If the model is predicting the next word in "The sky is ___", the logit for "blue" will be a high number (e.g., 15.2), while the logit for "bicycle" will be low or negative (e.g., -4.1).

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Both define Latent spaces

A (numeric) vectorized multidimentional space designed to find and study patterns. In computational statistics this is referred to as "Multivariate statistics" (google it ...). 

Examples: