Can LLMs even teach? Exploring the Teacher Axis

TLDRAs a passionate teacher, it has pained my heart to watch my students lose deeper critical thinking skills and independent reasoning. But attempting to build a constitutionally constrained AI using prompt engineering that acted more Socratically — asking follow-up questions rather than giving the answer directly — I was thoroughly frustrated that my AI kept caving. This led me to ask: does the model actually know how to be a good teacher internally, or does it not even have these capabilities in the first place? After extracting the Teacher Axis from Gemma-2-2B using MathDial conversations, I found that RLHF doesn't suppress pedagogical ability but rather optimizes in a direction orthogonal to it. I also ran further experiments regarding the sub-directions that compose the Teacher Axis, how steering at different layers affects pedagogical capabilities, and whether the Teacher Axis projection shrinks when student pressure is applied.Motivation and BackgroundI love teaching! I've spent a lot of my life teaching many different age ranges, experience levels, and backgrounds. From being a TA back at Berkeley for 5 semesters, to founding a computer science program for Chicago public high school students, I've had the absolute pleasure of getting to meet and be inspired by my students, watching their thought processes and problem solving skills evolve as they tackled more challenging problems.Well, that was before AI came around. At Berkeley, I had the absolute displeasure of being in my last semester of teaching when ChatGPT came out. Students just... stopped trying. I noticed this even more obviously with my high school students over the past 3 years. Before, you could see the passion and fearlessness in their eyes as I threw harder and harder questions at them — but now? They simply pipe whatever coding question I give them directly into ChatGPT, copy the answer, and paste it into their assignment. Students have started to heavily lose the ability to critically think