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%20through%20the%20angle%20of%20time%20directionality%2C%20addressing%20a%20question%20first%20raised%20in%20(Shannon%2C%201951).%20For%20large%20enough%20models%2C%20we%20empirically%20find%20a%20time%20asymmetry%20in%20their%20ability%20to%20learn%20natural%20language:%20a%20difference%20in%20the%20average%20log-perplexity%20when%20trying%20to%20predict%20the%20next%20token%20versus%20when%20trying%20to%20predict%20the%20previous%20one.%20This%20difference%20is%20at%20the%20same%20time%20subtle%20and%20very%20consistent%20across%20various%20modalities%20(language%2C%20model%20size%2C%20training%20time%2C%20...).%20Theoretically%2C%20this%20is%20surprising:%20from%20an%20information-theoretic%20point%20of%20view%2C%20there%20should%20be%20no%20such%20difference.%20We%20provide%20a%20theoretical%20framework%20to%20explain%20how%20such%20an%20asymmetry%20can%20appear%20from%20sparsity%20and%20computational%20complexity%20considerations%2C%20and%20outline%20a%20number%20of%20perspectives%20opened%20by%20our%20results.)
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