~/writing/math-foundations-for-reasoning-models $ ls
Generalization and Learning Theory
Training Data
Training data is the set of examples used to adjust a model's parameters during learning.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Training Data
Definition
Training data is the data used to fit a model.
Simple form:
training examples -> parameter updates
The model uses training data to change its internal parameters.
Training data is what the model learns from directly.
What Training Data Contains
Training data can contain inputs alone or input-output pairs.
Examples:
input only:
text sequences
input-output pair:
image -> label
question -> answer
features -> target value
The exact structure depends on the learning setup.
Training data supplies the examples that drive learning.
Training Data Shapes The Model
The model is not learning in the abstract.
It learns from the examples it receives.
If the training data contains certain patterns, the model may learn them.
If important patterns are missing, the model may not learn them.
Training data defines much of the model's experience.
Training Data Is Not The Whole World
Training data is only a sample.
It may not cover every situation the model will face later.
Example:
training data:
examples already collected
future use:
new examples from the real environment
The gap between these matters for generalization.
A model learns from a sample, then gets judged on cases outside that sample.
Quality Matters
Training data quality affects what the model can learn.
Problems include:
incorrect labels
missing cases
biased sampling
duplicate examples
irrelevant noise
Bad training data can make a model learn bad patterns.
The model can only learn from the signal available in its training data.
Final Summary
- Training data is used to adjust model parameters.
- It can contain inputs or input-output pairs.
- It shapes what the model learns.
- It is only a sample of possible cases.
- Data quality strongly affects learned behavior.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Test Data