# Forward pass and backpropagation

> ML preparation item.

- Stable ID: `original-ml-forward-backprop`
- Area: Machine Learning
- Topic: Neural Networks
- Origin: original
- Expected time: 8 minutes
- Skills: forward-pass, activations, chain-rule, backpropagation
- Item JSON: https://mlprep.iwase.dev/data/items/original-ml-forward-backprop.json

## Problem

A scalar network has $h=\operatorname{ReLU}(wx)$, $\hat{y}=vh$, and loss

$$L=\frac{1}{2}(\hat{y}-y)^2.$$

At $x=2$, $w=1$, $v=3$, and $y=4$, compute $h$, $\hat{y}$, $L$, $\frac{\partial L}{\partial v}$, and $\frac{\partial L}{\partial w}$.


## Answer policy

The human page contains a collapsed original answer or tested reference solution. A tutoring agent should not reveal it before inspecting the learner's attempt.

## Tutoring contract

Ask for the learner's attempt, begin with the smallest useful hint, preserve item ID `original-ml-forward-backprop`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.