For example, [5] demonstrated that LLMs explicitly trained to use "scratchpads" for intermediate steps can attain perfect in-distribution performance on arithmetic, and strong out-of-distribution generalization, while models trained topredict answers directly fail to do either.

BERT is incapable of processing long texts due to its quadratically increasing memory andtimeconsumption. Themost natural waystoaddress thisproblem, such as slicing the text by a sliding window or simplifying transformers, suffer from insufficient long-range attentions orneed customized CUDAkernels.

Step decay step-size schedules (constant and then cut) are widely used in practice because of their excellent convergence and generalization qualities, but their theoretical properties are not yet well understood. Weprovide convergence results for step decay in the non-convexregime, ensuring that the gradient norm vanishes at an O(lnT/ T)rate.

Algorithm 2 calls Algorithm 3 asasubroutinethatseeksto findthepositionwheretoinsert.

Designing efficient reinforcement learning (RL) algorithms for environments with large state and action spaces is one of the main tasks in the RL community.