The diminishing returns isn’t too surprising, because you are holding the model size fixed (whatever that is for Houdini 3), and the search sigmoids hard. Hence, diminishing returns as you jump well past the initial few searches with the largest gains, to large search budgets like 2k vs 4k (and higher).
This is not necessarily related to ‘approaching perfection’, because you can see the sigmoid of the search budget even with weak models very far from the known oracle performance (as well as stronger models); for example, NNs playing Hex: https://arxiv.org/pdf/2104.03113#page=5 Since it’s a sigmoid, at a certain point, your returns will steeply diminish and indeed start to look like a flat line and a mere 2x increase in search budget does little. This is why you cannot simply replace larger models with small models that you search the hell out of: because you hit that sigmoid where improvement basically stops happening.
At that point, you need a smarter model, which can make intrinsically better choices about where to explore, and isn’t trapped dumping endless searches into its own blind spots & errors. (At least, that’s how I think of it qualitatively: the sigmoiding happens because of ‘unknown unknowns’, where the model can’t see a key error it made somewhere along the way, and so almost all searches increasingly explore dead branches that a better model would’ve discarded immediately in favor of the true branch. Maybe you can think of very large search budgets applied to a weak model as the weak model ‘approaching perfection… of its errors’? In the spirit of the old Dijkstra quip, ‘a mistake carried through to perfection’. Remember, no matter how deeply you search, your opponent still gets to choose his move, and you don’t; and what you predict may not be what he will select.)
Fortunately, ‘when making an axe handle with an axe, the model is indeed near at hand’, and a weak model which has been ‘policy-improved’ by search is, for that one datapoint, equivalent to a somewhat larger better model—if only you can figure out how to keep that improvement around...
Thanks, I especially appreciate that NNs playing Hex paper; Figure 8 in particular amazes me in illustrating how much more quickly perf. vs test-time compute sigmoids than I anticipated even after reading your comment. I’m guessing https://www.gwern.net/ has papers with the analogue of Fig 8 for smarter models, in which case it’s time to go rummaging around…
The diminishing returns isn’t too surprising, because you are holding the model size fixed (whatever that is for Houdini 3), and the search sigmoids hard. Hence, diminishing returns as you jump well past the initial few searches with the largest gains, to large search budgets like 2k vs 4k (and higher).
This is not necessarily related to ‘approaching perfection’, because you can see the sigmoid of the search budget even with weak models very far from the known oracle performance (as well as stronger models); for example, NNs playing Hex: https://arxiv.org/pdf/2104.03113#page=5 Since it’s a sigmoid, at a certain point, your returns will steeply diminish and indeed start to look like a flat line and a mere 2x increase in search budget does little. This is why you cannot simply replace larger models with small models that you search the hell out of: because you hit that sigmoid where improvement basically stops happening.
At that point, you need a smarter model, which can make intrinsically better choices about where to explore, and isn’t trapped dumping endless searches into its own blind spots & errors. (At least, that’s how I think of it qualitatively: the sigmoiding happens because of ‘unknown unknowns’, where the model can’t see a key error it made somewhere along the way, and so almost all searches increasingly explore dead branches that a better model would’ve discarded immediately in favor of the true branch. Maybe you can think of very large search budgets applied to a weak model as the weak model ‘approaching perfection… of its errors’? In the spirit of the old Dijkstra quip, ‘a mistake carried through to perfection’. Remember, no matter how deeply you search, your opponent still gets to choose his move, and you don’t; and what you predict may not be what he will select.)
Fortunately, ‘when making an axe handle with an axe, the model is indeed near at hand’, and a weak model which has been ‘policy-improved’ by search is, for that one datapoint, equivalent to a somewhat larger better model—if only you can figure out how to keep that improvement around...
Thanks, I especially appreciate that NNs playing Hex paper; Figure 8 in particular amazes me in illustrating how much more quickly perf. vs test-time compute sigmoids than I anticipated even after reading your comment. I’m guessing https://www.gwern.net/ has papers with the analogue of Fig 8 for smarter models, in which case it’s time to go rummaging around…