Rasul Tutunov_On a theory of hidden variables in chain of thoughts_watermark.pdf

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1、On a theory of hidden variables in chain of thoughtsOn a theory of hidden variables in chain of thoughtsRasul TutunovSenior Research Scientist Huawei R&D,Noahs Ark,London*Elena.Ospina(https:/ is a prompting technique for large language model(LLM)that allows to improve its performance by providing a

2、demonstrations of several intermediate reasoning steps as exemplars Pre-trained LLMexampleprompt questionChain-of-Thought(CoT)CoT prompting:CoT is a prompting technique for large language model(LLM)that allows to improve its performance by providing a demonstrations of several intermediate reasoning

3、 steps as exemplars Pre-trained LLMexample step-by-stepreasoningprompt questionmodel also constructsstep-by step solution Significantly improving“reasoning”ability CoT(beyond math questions)Few-shot examplars of triples for non-arithmetic tasks:Chain of thoughts are highlightedChain-of-Thought(CoT)C

4、oT is a prompting technique for large language model(LLM)that allows to improve its performance by providing a demonstrations of several intermediate reasoning steps as exemplars Pre-trained LLMCOT is computationally efficient,as it does notrequire to re-train/fine tune the model.But why does COT wo

5、rk?What does effect its performance?Statistical model for natural languageeach CoT sequence generation has the following steps:general task description describingthe final goal behind the message Examples:Arithmetic demonstration.contextC“Provide simple arithmetic problem”“Alice has 2 apples,Bob has

6、 5 apples.Alice ate 1 apple and Bob ate 2 apples and gave 1 apple to John.Home many apples Alice and Bob have”“Calculate Alices apples after she ate 1”“Alice has 2 apples,She ate 1.Now,she has 1 apple”“Calculate Bobs apples after ate 2 one and gave 1 apple to John”“Bob has 5 apples,He ate 2 apples a

7、nd gave 1 apple to John.Hence,he has 5-2-1=2 apples left.“Calculate total number of apples Bob and Alice have”“Alice has 1 apple left and Bob has 2 apples left.In total they have 2+1=3 apples.Answer is 3intention for the first message.Statistical model for natural languageCoT:“Alice has 2 apples,She

8、 ate 1.Now,she has 1 apple”“Bob has 5 apples,He ate 2 apples and gave 1 apple to John.Hence,he has 5-2-1=2 apples left.“Alice has 1 apple left and Bob has 2 apples left.In total they have 2+1=3 apples.Answer is 3“Alice has 2 apples,Bob has 5 apples.Alice ate 1 apple and Bob ate 2 apples and gave 1 a

9、pple to John.Home many apples Alice and Bob have”natural language model:Formally:Input messageIntermediatethoughtsOutputmessage-Message generated from intentions-Subsequent intentions,generated from previousintentions,previous messages and contextAmbiguity:LLM as universal density approximator such

10、statistical model for natural language allows us to define density for each message :language model,parametrized by weights approximates each factor in this product:CoT setupGiven a collection of exemplar CoTsand input message the LLM prediction:Natural language prediction:Arithmetic demonstration.W

11、e want to establish proximity:Main Result:Under ambiguity assumption for long enough exemplar CoTswe have:In other words,prediction of LLM and prediction of the natural language will be asymptotically the same.Moreover,starting from some lengths of the convergence is geometric:withSketch of the Proo

12、fUsing universal approximator property for optimal weight for any collection of messages :where:andusing independence of exemplar thoughtsusing assumption on ambiguity ()for long enough exemplar thoughts :for some:What is next?The ambiguity of exemplar thoughts is crucial for CoT“reasoning”how can we quantify this measure?4 Oct 2023this work is ongoing nowThank youTeam:Antoine Grosnit,Juliusz Ziomek,Jun Wang,Haitham Bou Ammar.