~/tedtes/writing/math-foundations-for-reasoning-models

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Backpropagation and Training

Training Loop

The training loop repeatedly computes output, measures loss, computes gradients, and updates parameters.

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Training Loop

Definition

A training loop is the repeated process used to improve a neural network.

Basic pattern:

1. run the network
2. measure loss
3. compute gradients
4. update parameters
5. repeat

The training loop is how a network turns error into parameter change.


Why A Loop Is Needed

One update is usually not enough.

The network improves through repeated small changes.

Example:

start with current parameters
compute loss
update parameters
compute loss again
update again

Each loop uses the current state of the model.

Training is iterative, not one single correction.


The Main Parts

The training loop has four core stages.

forward pass:
compute output

loss computation:
measure error

backward pass:
compute gradients

parameter update:
change weights and biases

These stages connect neural network structure to optimization.

Forward computes behavior; backward computes how to improve it.


Parameters Change Across Loops

The input data may be the same, but parameters change over time.

Example:

loop 1: parameters A -> loss 5.0
loop 2: parameters B -> loss 3.2
loop 3: parameters C -> loss 2.4

The model is not just producing outputs.

It is being modified by the training process.

The loop changes the model itself.


Training Loop vs Forward Pass

A forward pass only computes output.

A training loop includes forward pass plus loss, gradients, and updates.

forward pass:
input -> output

training loop:
input -> output -> loss -> gradients -> updated parameters

A forward pass evaluates the current model; a training loop improves it.


Final Summary

  • A training loop repeatedly improves a neural network.
  • It includes forward pass, loss computation, backward pass, and parameter update.
  • Training is iterative.
  • Parameters change across loop iterations.
  • The forward pass computes output.
  • The full training loop uses loss to update the model.

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Continue the series.

Forward Pass