One challenge for theories of embedded agency over Cartesian theories is that the ‘true dynamics’ of optimization (where a function defined over a space points to a single global maximum, possibly achieved by multiple inputs) are replaced by the ‘approximate dynamics’. But this means that by default we get the hassles associated with numerical approximations, like when integrating differential equations. If you tell me that you’re doing Euler’s Method on a particular system, I need to know lots about the system and about the particular hyperparameters you’re using to know how well you’ll approximate the true solution. This is the toy version of trying to figure out how a human reasons through a complicated cognitive task; you would need to know lots of details about the ‘hyperparameters’ of their process to replicate their final result.
This makes getting guarantees hard. We might be able to establish what the ‘sensible’ solution range for a problem is, but establishing what algorithms can generate sensible solutions under what parameter settings seems much harder. Imagine trying to express what the set of deep neural network parameters are that will perform acceptably well on a particular task (first for a particular architecture, and then across all architectures!).
One challenge for theories of embedded agency over Cartesian theories is that the ‘true dynamics’ of optimization (where a function defined over a space points to a single global maximum, possibly achieved by multiple inputs) are replaced by the ‘approximate dynamics’. But this means that by default we get the hassles associated with numerical approximations, like when integrating differential equations. If you tell me that you’re doing Euler’s Method on a particular system, I need to know lots about the system and about the particular hyperparameters you’re using to know how well you’ll approximate the true solution. This is the toy version of trying to figure out how a human reasons through a complicated cognitive task; you would need to know lots of details about the ‘hyperparameters’ of their process to replicate their final result.
This makes getting guarantees hard. We might be able to establish what the ‘sensible’ solution range for a problem is, but establishing what algorithms can generate sensible solutions under what parameter settings seems much harder. Imagine trying to express what the set of deep neural network parameters are that will perform acceptably well on a particular task (first for a particular architecture, and then across all architectures!).