Er, no, that's not how it works at all.
Let me try to explain how neural networks work. Those are mostly used to make decisions based on a given input. And the rules to make that decision are automatically generated during a training session.
Those are the two steps of using neural networks, training and decision. Training is the heavy task, and can take minutes, hours, weeks depending on the complexity of your problem. But you only need to do it once to get a functional AI : when it's done, it will have learnt the rules to apply to make the "right" decision from any input.
The decision is only the task of applying those rules. You can use the same set of rules for all your races onward, they're supposed to cover all possible situations (of course if it doesn't, your AI will have a silly behaviour). And they don't require any heavy computing.
What Turn10 claim they're doing with Forza is :
- do the training sessions on servers rather than on the console itself to generate the Drivatar
- update the Drivatar with new player data by launching new training sessions
Ok, let's try with a fake example of an AI of "how to approach a curve" (I'll just mention that I'm bad at driving games and driving in general, so it's purely theoretical).
Step 0 : the default AI says "brake 20 meters before the curve, then turn". That AI is applied to your Drivatar any time it is used in a game, and is run by the console on its own.
Step 1 : You play the game with your own, more aggressive style. All your gaming history is uploaded at the end of each game to MS servers ("the cloud").
Step 2 : On the server, a training session is applied on your data, and updates your Drivatar with a new behavior : "brake 10 meters before the curve, then turn". It does the same thing for other players, like your friend who generated his own Drivatar style "don't brake, drift !". In the meantime both you and your friends keep playing against Step0 AIs.
Step 3 : Some time after you uploaded your latest data (maybe 5 secs, maybe 2 days, who cares ?), your updated drivatar is available for all to download, so is your friend's. You now have different possible opponent AIs to face, the original, yours and your friend's.
Step 4 : you or your friends can race the updated avatars. Their AIs are still run by the console, since the rules aren't harder to apply than the default one, only different. If the console goes offline, either you can still play the drivatars you've downloaded, or are back to step 0.
Step 5 : go back to step 1 to keep updating your drivatar, and maybe generate improved behaviour ("brake 10 m before a curve, or 30m if there's a car in front of you").
So in the end, "the cloud" is not interacting with your game while you're playing. It's only collecting your data when you're done, do its thing in the background, and updates your game when it's finished.
In that case, being offline shouldn't have any impact on the resources available during your gaming session, since it's not at that moment that the hard work is done.
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