# Parameters and output gradient

> ML Prep screening item.

- Stable ID: `ml-screen-neural-networks-advanced-softmax`
- Collection: screening
- Area: Machine Learning
- Topic: Neural Networks
- Origin: original
- Difficulty: hard
- Expected time: 10 minutes
- Skills: neural-network-chain-rule, backpropagation, neural-network-losses, dense-network-parameter-count
- Item JSON: https://mlprep.iwase.dev/item/ml-screen-neural-networks-advanced-softmax.json

## Problem

A dense classifier has $4$ inputs, $3$ hidden units with biases, and $2$ softmax outputs with biases. Count the trainable scalars. For $h=(1,2,0)$, $p=(0.25,0.75)$, and one-hot $y=(1,0)$, compute the cross-entropy gradients for the output logits, output bias, and output weight matrix.


## Answer policy

The human page contains a collapsed answer. 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 `ml-screen-neural-networks-advanced-softmax`, and record a real attempt with `recorded_by: "agent"` and `agent_session_id` when available using https://mlprep.iwase.dev/schema/attempt-record.json.