For HDMM, weconsiderworkloadsofkrandom 3-waymarginals, fork = 1, 2, 4, 8,..., 256, 455, runfivetrials, andreportrootmeansquarederror, theobjectivefunctionthat HDMMoptimizes. Figure 3ashowstheresults.

Here, we integrate these two approaches by trading off utility, informativeness, and complexity in EC.

LastLetters F 500 15.0 - CoinFlip Y 500 37.0 - A.2.2 Datasetcreation Regarding "Last Letter Concatenation" and "Coin Flip", datasets are not publicly available sowe created the datasets following Wei et al. [2022] with a minor rephrasing of the question template. Asfor Coin Flip, we use the following template. A.5 PromptsForAnswerExtraction Table 9 and Table 10 summarizes a list of answer extraction prompts used for the experiments at Table1. Number Pick up the first number encounteredinthetext. MultipleChoice Pick up the first large letter encountered in the text. YesorNo Pickupthefirst"yes" or "no" encountered in the text after removing unnecessaryletters. Table 13 lists example texts generated by Zero-shot-CoT for each reasoning extraction template(SeeTable4). Dataset Question Answer SingleEq Q: A spaceship traveled 0.5 of a light-year from Earth to Planet X and 0.1 of a lightyearfromPlanetXtoPlanetY. A: Let's think step by step. So the total distance the spaceship traveled is 0.5 + 0.1 + 0.1 = 0.7 light-years. Therefore, the answer (arabic numerals) is: 0.7 light-years Q:Whilemaking desserts for abakesale,Victorused0.625 of a scoop of brown sugar as well as 0.25 of a scoop of whitesugar.Howmuchmore brownsugardidVictoruse? A: Let's think step by step.

Notably,chainofthought(CoT)prompting, a recent technique for eliciting complex multi-step reasoning through step-bystep answer examples, achieved the state-of-the-art performances in arithmetics and symbolic reasoning, difficultsystem-2 tasks that do not follow the standard scaling laws for LLMs. While these successes are often attributed to LLMs' ability forfew-shot learning, weshowthatLLMs aredecentzero-shotreasoners by simply adding "Let's think step by step" before each answer.

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner.

Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner.