stepMnist.apple

-- x: 60000x784
-- targets: 60000x10
λx.λtargets.
λl1.λl2.
  {
    softmax ← λxs.
      { m ⟜ (⋉)/* _1 xs; a ⟜ [e:(x-m)]`{0} xs
      ; sum ← [(+)/x]
      ; n ⟜ sum`{1} (a::M float)
      ; ⍉([(%x)'y]`{0,1} n a)
      };
    dsoftmax ← λxs.
        { m ⟜ (⋉)/* _1 xs; a ⟜ [e:(x-m)]`{0} xs
        ; sum ← [(+)/x]
        ; n ⟜ sum`{1} (a::M float)
        ; ⍉([x*(1-x)]`{0} ([(%x)'y]`{0,1} n a))
        };
    dsigmoid ← ((λx.⸎x⟜ℯ(_x);x%(1+x)^2)`{0});
    -- fw
    xl1p ⟜ x%.l1;
    xSigmoid ← [1%(1+ℯ(_x))]`{0} xl1p;
    xl2p ⟜ xSigmoid%.l2;
    out ← softmax xl2p;
    -- bw
    error ⟜ (*)`{0,0} ({n⟜2%(ℝ(𝓉out)); [x*n]`{0} ((-)`{0,0} out targets)}) (dsoftmax xl2p);
    ul2 ← (⍉xSigmoid)%.error;
    ul1 ← (⍉x)%.((*)`{0,0} (⍉(l2%.(⍉error))) (dsigmoid xl1p));
    ((+)`{0,0} l1 ul1, (+)`{0,0} l2 ul2)
  }