LLM Control Theory Seminar (April 2024)

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