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Stay tuned for our new results in our preprint, "What’s the Magic Word? A Control Theory of LLM Prompting": https://arxiv.org/abs/2310.04444 Follow twitter and https://aman-bhargava.com/ for further updates :) - Aman's twitter: / abhargava2000 - Cameron's twitter: / witkowski_cam - Looi's twitter: https://x.com/Sz_Looi Thank you to the Information, Geometry, and Physics Seminar run by Juan Pablo Vigneaux for the opportunity to present our work. For a full reference list, see our preprint. 0:00 Introduction 1:51 1: MOTIVATIONS 1:55 Zero-shot learning miracle (Motivations) 3:28 Background on LLMs? (Motivations) 4:22 Transformer Information Flow for Generative Inference (Motivations) 6:03 LLMs are increasingly used as systems (Motivations) 6:42 We do not understand LLMs as systems (Motivations) 9:23 Control theory is great for understanding systems (Motivations) 11:36 Prompt engineering = system control problem (Motivations) 14:12 LLM systems get complicated fast (Motivations) 15:16 Plan for LLM Control Theory (Motivations) 16:58 2: FRAMEWORK 17:01 LLM systems are unusual (Framework) 18:44 LLM system formalization (Framework) 21:43 Reachability (Framework) 23:43 Reachable Sets (Framework) 25:11 k-epsilon Controllability (Framework) 27:29 3: SELF-ATTENTION CONTROLLABILITY THEOREM 27:40 Background on self attention (Theorem) 31:23 Controllability for self-attention (Theorem) 32:20 Theorem (Theorem) 40:23 Connecting self-attention theorem with empirical results (Theorem) 41:13 EXPERIMENTAL RESULTS ON LLM CONTROLLABILITY 41:24 Measuring k-epsilon controllability via prompt optimization (Experiments) 42:58 Experimental design for k-epsilon controllability measurement (Experiments) 45:15 Results on k-epsilon controllability (Experiments) 48:36 OPEN QUESTIONS IN LLM CONTROL THEORY 49:57 Typical sequences, AEP 50:58 More next steps 52:21 Acknowledgements