Two Codes, Two Test Sets

Two autoencoders are trained on the same $60{,}000$ images of handwritten digits. Each image is $28 \times 28$ , so $784$ numbers go in and $784$ numbers come out. The two models are identical except for the middle layer:

Model P has a code of $784$ numbers, as wide as the input.
Model Q has a code of $16$ numbers.

After training, both are scored with the usual reconstruction loss (lower is better) on two test sets that neither model has seen: $1{,}000$ new handwritten digits, and $1{,}000$ images of random static, where every pixel is an independent random brightness and nothing looks like a digit.

	new digits	random static
Model P ( $784$ -number code)	$0.0004$	$0.0005$
Model Q ( $16$ -number code)	$0.0110$	$0.2600$

A teammate reads the table and backs model P: "It wins on digits, and it even copes with static it has never seen. Q falls apart the moment you show it something new."

What does the table actually tell you about the two models?

Two Codes, Two Test Sets

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