This makes a lot of sense to me, and makes me want to figure out exactly how to operationalize and rigorously quantify depth of search in LLMs! Quick thought is that it should have something to do with the spectrum of the transition matrix associated with the mixed state presentation (MSP) of the data generating process, as in Transformers Represent Belief State Geometry in their Residual Stream . The MSP describes synchronization to the hidden states of the data generating process, and that feels like a search process that has max-depth of the Markov order of the data generating process.
I really like the idea that memorization and this more lofty type of search are on a spectrum, and that placement on this spectrum has implications for capabilities like generalization. If we can figure out how to understand these things a more formally/​rigorously that would be great!
This makes a lot of sense to me, and makes me want to figure out exactly how to operationalize and rigorously quantify depth of search in LLMs! Quick thought is that it should have something to do with the spectrum of the transition matrix associated with the mixed state presentation (MSP) of the data generating process, as in Transformers Represent Belief State Geometry in their Residual Stream . The MSP describes synchronization to the hidden states of the data generating process, and that feels like a search process that has max-depth of the Markov order of the data generating process.
I really like the idea that memorization and this more lofty type of search are on a spectrum, and that placement on this spectrum has implications for capabilities like generalization. If we can figure out how to understand these things a more formally/​rigorously that would be great!