Four Houses, One Batch

A house-price network trains on batches of four houses. Prices are in thousands of dollars. Here is one batch, straight out of the forward pass. House 1 is the house from the lesson, guessed at 420 and sold for 500.

house	prediction	sold for
1	$420$	$500$
2	$310$	$300$
3	$640$	$600$
4	$250$	$250$

The loss for the batch is the MSE of the four predictions:

$L = \frac{1}{4}\sum_{i=1}^{4}\big(\text{prediction}_i - \text{sold}_i\big)^2$

The backward pass starts where the error was born, at the output. The first thing it works out is one number per house: that prediction's gradient,

$\frac{\partial L}{\partial\, \text{prediction}_i}$

which says how much $L$ changes per unit nudge of that one prediction, with the other three held still. Every weight's gradient in the network is later built from these four numbers.

What are the four numbers, for houses 1 to 4 in order?

Four Houses, One Batch

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