~/writing/math-foundations-for-reasoning-models $ ls
Embeddings and Representation
Learned Embedding
A learned embedding is a representation whose values are adjusted during training to become useful for the model objective.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Learned Embedding
Definition
A learned embedding is an embedding whose values are adjusted during training.
Simple form:
initial values -> training updates -> useful representation
The model learns the embedding values from data and objective feedback.
A learned embedding is a trainable representation.
Why Learning Is Needed
If embeddings were assigned manually, they would depend on human design.
Learning lets the model discover useful representation patterns from the task.
Example:
prediction error -> update embedding values
Over many updates, embeddings become better suited to the model's objective.
Learned embeddings are shaped by what helps reduce loss.
Learned Does Not Mean Perfect
A learned embedding can be useful without being perfect.
It may capture:
common usage patterns
task-relevant relationships
statistical regularities
It may also capture noise, bias, or shallow patterns.
Learned representations reflect training pressure, not guaranteed truth.
Embeddings Are Parameters
In many models, embeddings are trainable parameters.
They are updated like other weights.
Simple view:
embedding table = parameters
training = parameter adjustment
This connects embeddings to optimization.
Learning embeddings is part of model training.
What The Model Learns
The model does not learn a dictionary definition directly.
It learns representation values that help downstream computation.
Example:
embedding useful for attention
embedding useful for prediction
embedding useful for classification
The embedding is learned for computational usefulness.
Final Summary
- A learned embedding is adjusted during training.
- It is shaped by data and objective feedback.
- It is a trainable parameter.
- It can capture useful patterns but not guaranteed truth.
- Learned embeddings support later attention and transformation layers.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Contextual Embedding