Neural Networks as Ordinary Differential Equations

Re:Neural Networks as Ordinary Differential Equations by SubiculumCode on Monday December 17, 2018 @11:52PM (#18704609)

Simulation has a number meanings, depending on the field. I tend to loosely think of a simulation as a model with an acceptable level of error, but I am not a mathmatician.

[ Parent | on HN ]

Re:Neural Networks as Ordinary Differential Equations by gnulinux on Tuesday December 18, 2018 @08:35AM (#18706275)

This is true, thanks. As the other answer said, in this field we say given any machine M, "M2 simulates M" if M2 computes the same function as M i.e. given any input i, iff M(i) halts then M2(i) halts and M(i) == M2(i) otherwise they both loop. This can also be called "compiling" informaly: given any Turing machine, you can "compile" it to C (i.e. constructing a C program that simulates M) which means C is Turing-complete.

Note that this is a very handwavy definition. The "types" of input, output, and what it means to "compute" will depend on your language, semantics and encoding. (E.g. for lambda calcus "compute" means appying reduction rules until the machine halts, if ever)

[ Parent | on HN ]

Re:Neural Networks as Ordinary Differential Equations by SubiculumCode on Tuesday December 18, 2018 @11:47AM (#18707998)

I appreciate the explanation. Clearly in this context simulation does not equal approximation !!

[ Parent | on HN ]

Re:Neural Networks as Ordinary Differential Equations by 0-_-0 on Tuesday December 18, 2018 @05:31AM (#18705624)

To simplify, in algorithm theory _simulating a Turing machine_ means the ability to execute any program "written" for a Turing machine.

Turing machines, neural networks, cellular automata, computer programs and (apparently) ODEs can execute each other's "programs" (among any others).

[ Parent | on HN ]