~/writing/math-foundations-for-reasoning-models $ ls
Neural Network Foundations
Layer
A layer is a group of neurons that transform a set of input values into a new set of output values.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Layer
Definition
A layer is a group of neurons that operate at the same stage of a network.
It takes input values and produces output values.
Basic pattern:
input values -> layer -> output values
A layer transforms one representation into another.
Why Multiple Neurons
A single neuron produces one output.
A layer can produce multiple outputs.
Example:
input: [x1, x2, x3]
layer output: [a1, a2, a3, a4]
Each output may capture a different transformation of the input.
A layer can compute several signals in parallel.
Layer Parameters
Each neuron in a layer has its own weights and bias.
Example:
neuron 1 -> weights and bias
neuron 2 -> weights and bias
neuron 3 -> weights and bias
The whole layer therefore has many parameters.
Training adjusts these parameters to reduce loss.
A layer is a structured collection of trainable parameters.
Layer Output Becomes Next Input
The output of one layer can become the input to another layer.
layer 1 output -> layer 2 input
layer 2 output -> layer 3 input
This creates a sequence of transformations.
Layers compose transformations step by step.
Final Summary
- A layer is a group of neurons at one stage of a network.
- A layer maps input values to output values.
- Multiple neurons let the layer compute multiple signals.
- Each neuron has parameters.
- The output of one layer can become the input to the next.
- A neural network is built by composing layers.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Input Layer