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effects-examples/algorithmic_differentiation.ml

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@patricoferris
patricoferris Effect.eff -> Effect.t
Latest commit 242e2dc Feb 28, 2022 History
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@patricoferris @kayceesrk
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 (* Reverse-mode Algorithmic differentiation using effect handlers.
 Adapted from https://twitter.com/tiarkrompf/status/
 963314799521222656.
 See https://openreview.net/forum?id=SJxJtYkPG for more information. 
 *)
 open Effect
 open Effect.Deep
 module F : sig
 type t
 val mk : float -> t
 val (+.) : t -> t -> t
 val ( *. ) : t -> t -> t
 val grad : (t -> t) -> float -> float
 val grad2 : (t * t -> t) -> float * float -> float * float
 end = struct
 type t = { v : float; mutable d : float }
 let mk v = {v; d = 0.0}
 type _ Effect.t += Add : t * t -> t Effect.t
 type _ Effect.t += Mult : t * t -> t Effect.t
 let run f =
 ignore (match_with f () {
 retc = (fun r -> r.d <- 1.0; r);
 exnc = raise;
 effc = fun (type a) (e : a Effect.t) ->
 match e with
 | Add (a, b) -> Some (fun (k : (a, _) continuation) ->
 let x = {v = a.v +. b.v; d = 0.0} in
 ignore (continue k x);
 a.d <- a.d +. x.d;
 b.d <- b.d +. x.d;
 x)
 | Mult(a,b) -> Some (fun k ->
 let x = {v = a.v *. b.v; d = 0.0} in
 ignore (continue k x);
 a.d <- a.d +. (b.v *. x.d);
 b.d <- b.d +. (a.v *. x.d);
 x)
 | _ -> None
 })
 let grad f x =
 let x = mk x in
 run (fun () -> f x);
 x.d
 let grad2 f (x, y) =
 let x,y = mk x, mk y in
 run (fun () -> f (x,y));
 x.d, y.d
 let (+.) a b = perform (Add(a,b))
 let ( *. ) a b = perform (Mult(a,b))
 end;;
 (* f = x + x^3 =>
 df/dx = 1 + 3 * x^2 *)
 for x = 0 to 10 do
 let x = float_of_int x in
 assert (F.(grad (fun x -> x +. x *. x *. x) x) =
 1.0 +. 3.0 *. x *. x)
 done;;
 (* f = x^2 + x^3 =>
 df/dx = 2*x + 3 * x^2 *)
 for x = 0 to 10 do
 let x = float_of_int x in
 assert (F.(grad (fun x -> x *. x +. x *. x *. x) x) =
 2.0 *. x +. 3.0 *. x *. x)
 done;;
 (* f = x^2 * y^4 =>
 df/dx = 2 * x * y^4
 df/dy = 4 * x^2 * y^3 *)
 for x = 0 to 10 do
 for y = 0 to 10 do
 let x = float_of_int x in
 let y = float_of_int y in
 assert (F.(grad2 (fun (x,y) -> x *. x *. y *. y *. y *. y) (x,y)) =
 (2.0 *. x *. y *. y *. y *. y,
 4.0 *. x *. x *. y *. y *. y))
 done
 done;;

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