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Kinda yes. The benchmarks become part of the validation set, which means the models get slightly overfit to them if they are used as criteria for stopping the training. But a lot less compared to using them in the training data.

I'd guess everybody uses at least some benchmarks as stopping criteria, which is kinda sensible, but it also does induce some benchmaxxing, and explains partly why the newest models always tend to eke out in benchmarks.

https://en.wikipedia.org/wiki/Training,_validation,_and_test...

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Correct. If just stopping criteria, that is less contaminated. The question gets muddier once you also use it to determine hyperparameters during small-scale runs.
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They are using it to evaluate checkpoints during the training, they are probably not using the benchmarks for training the models. It's a common practice for big reinforcement learning runs.
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They exist to detect degradation. Datasets are not perfect and if a batch contains too much bad data it can ruin a run, also an opportunity to find bad data and improve the dataset filtering.
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You gotta have something to aim at. And, presumably, the benchmark is not part of the training data, it is the test against which the model is tested at each stage; is behavior moving in the right direction?
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Not if you don't train against them.
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It's implicitly trained against. There is like information leakage with researchers messing with the training parameters and checkpoints used.

It's not the direct feedback loop of RL but its not far.

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