LNN for Regression

February 15, 2026

Linear Neural Networks for Regression #

A linear neural network for regression is a model that predicts a continuous target by taking a weighted sum of input features and applying the identity activation (so the output can be any real number).

Single neuron for regression (predicting how much / how many)
Data + linear model (single neuron, no hidden layers) + squared loss
Training using batch gradient descent algorithm
Prediction (inference)
Eg: Auto MPG (UCI) style prediction with a single neuron (from-scratch code)

flowchart LR
  D["Data<br/>X, y"] --> M["Linear model<br/>w, b<br/>Single neuron"]
  M --> A["Activation<br/>Identity"]
  A --> L["Loss<br/>MSE (Squared error)"]
  L --> O["Optimiser<br/>Batch Gradient DescentBatch GD / Mini-batch GD"]
  O --> P["Parameters<br/>w, b"]
  P --> I["Inference<br/>Predict ŷ (number) for new x"]

  %% Pastel colour scheme
  style D fill:#E3F2FD,stroke:#1E88E5,stroke-width:1px
  style M fill:#E8F5E9,stroke:#43A047,stroke-width:1px
  style A fill:#FFF3E0,stroke:#FB8C00,stroke-width:1px
  style L fill:#FCE4EC,stroke:#D81B60,stroke-width:1px
  style O fill:#F3E5F5,stroke:#8E24AA,stroke-width:1px
  style P fill:#E0F7FA,stroke:#00838F,stroke-width:1px
  style I fill:#F1F8E9,stroke:#558B2F,stroke-width:1px

Regression #

Regression is a supervised learning task that predicts a continuous-valued output based on input features.