Free and Open Source Software

There's also the fact that GPL is ultimately about using copyright to reduce the harm that copyright can cause to people's rights.

If we look through the cases that could exist with AI law:

1. Training can legally use copyrighted materials without a licence, but models cannot be copyrighted: This probably is a net win for software freedom - people can train models on commercial software even and generate F/L/OSS software quickly. It would undermine AGPL style protection though - companies could benefit from F/L/OSS and use means other than copyright to undermine rights, but there would be nothing a licence could do to change that.
2. Training can legally use copyrighted materials without a licence, models can be copyrighted: This would allow companies to benefit heavily from F/L/OSS, but not share back. However, it would also allow F/L/OSS to benefit from commercial software where the source is available.
3. Training cannot legally use copyrighted materials without complying with licence, models cannot be copyrighted (or models can be copyrighted, outputs can't be copyrighted): This is probably the worst for F/L/OSS because proprietary software wouldn't be able to be used for training, but proprietary software could use a model trained on F/L/OSS by someone else.
4. Training cannot legally use copyrighted materials without complying with licence, models can be copyrighted, outputs can be copyrighted: In this case, GPLv2 and GPLv3 probably make the model and its outputs a derivative work, so it is more or less status quo.