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>Unless I see a mathematical proof that evolutionary algorithms are as efficient as RM AD, I see little future in it, and apparently neither did biology since i

>Unless I see a mathematical proof that evolutionary algorithms are as efficient as RM AD, I see little future in it, and apparently neither did biology since it decided to create brains. In the biological context the complexity is shifted away from the actual selection algorithm and onto the "scoring function." Although the filter of reproduction is relatively simple [1], the reason why the organism was fit and could ultimately reproduce is very complex. The brain's "topology" is the result of selection pressure favoring adaptations that improve fitness by dynamically adapting to relevant patterns found in the environment. The brain attempts to accurately model important aspects of the complex environment it's challenged with to increase fitness. [1] Nothing in biology is ever actually simple, even though individuals undergo fitness based scoring, the actual notion of individual is arbitrary. In the case of bees most of the individual bees in the colony are sterile, which is obviously bad for fitness of the "individual." However a few individuals reproduce, so all the sterile worker's fitness is shifted onto the queen/drones through the concept of inclusive fitness. This indirect selection also applies to humans, who undergo inclusive fitness through their siblings. This can even be generalized to your individual cells/organs which function as a colony supporting the gonads which actually undergo direct selective pressure.

DoctorOetker 7y ago
with efficiency I meant computational efficiency: consider the task of computing a gradient at a point p0 = <x1, x2, x3, ..., xN> in an N-dimensional space. the naive approach was for a long time: compute the value of the score at p0, then for each coordinate compute the score for the same point but shifted a delta in the direction of that coordinate, i.e. the i-th component is computed as: component_i = (score( <x1, x2, ..., xi+delta, ..., xN> ) - score (p0))/delta thats N+1 evaluations or trials of the score to compute the final gradient <component_1, ..., component_N> notice how reminescent this is of natural selection: the average of the last generation p0 is used to generate ~N trials, which then result in the average of the next generation shifting somewhat. compare reverse mode automatic differentiation to calculate a gradient: one forward pass of the computation with one backward pass... I am not complaining about the complexity of the fitness or scoring function, I am complaining about trial and error approaches, when we have discovered a rocket for differentiation!
- rectangletangle 7y ago
  Ah, in that sense it's almost certainly more efficient. Biological selection is undirected so progress toward the goal happens stochastically, so slow, but then sometimes fast.

DoctorOetker 7y ago

with efficiency I meant computational efficiency: consider the task of computing a gradient at a point p0 = <x1, x2, x3, ..., xN> in an N-dimensional space. the naive approach was for a long time: compute the value of the score at p0, then for each coordinate compute the score for the same point but shifted a delta in the direction of that coordinate, i.e. the i-th component is computed as: component_i = (score( <x1, x2, ..., xi+delta, ..., xN> ) - score (p0))/delta thats N+1 evaluations or trials of the score to compute the final gradient <component_1, ..., component_N> notice how reminescent this is of natural selection: the average of the last generation p0 is used to generate ~N trials, which then result in the average of the next generation shifting somewhat. compare reverse mode automatic differentiation to calculate a gradient: one forward pass of the computation with one backward pass... I am not complaining about the complexity of the fitness or scoring function, I am complaining about trial and error approaches, when we have discovered a rocket for differentiation!

rectangletangle 7y ago
Ah, in that sense it's almost certainly more efficient. Biological selection is undirected so progress toward the goal happens stochastically, so slow, but then sometimes fast.