a neural network with petalisp

nn.lisp

(ql:quickload :petalisp)
(use-package :petalisp)

(defvar x (as-matrix #2a((5.1 3.5 1.4 0.2)
			 (4.9 3.0 1.4 0.2)
			 (6.2 3.4 5.4 2.3)
			 (5.9 3.0 5.1 1.9))))
(defvar y (as-matrix #(0 0 1 1)))
(defvar w (as-matrix #(0.5 0.5 0.5 0.5)))

(defun as-matrix (x)
  (ecase (dimension x)
    (0 (reshape x (τ () (0 0))))
    (1 (reshape x (τ (i) (i 0))))
    (2 x)))

(defun sigmoid-derivative (n)
  (* n (- 1.0 n)))

(defun sigmoid (n)
  (/ 1.0 (+ 1.0 (exp (- n)))))

(defun transpose (x)
  (reshape
   (as-matrix x)
   (τ (m n) (n m))))

(defun matmul (a b)
  (β #'+
     (α #'*
        (reshape (as-matrix a) (τ (m n) (n m 0)))
        (reshape (as-matrix b) (τ (n k) (n 0 k))))))

(defun dot (x y)
  (reshape
   (matmul
    (transpose x)
    (as-matrix y))
   (τ (0 0) ())))

(defun predict (x w)
  (α #'sigmoid (matmul x w)))

(defun train (x y w)
  (let* ((prediction (predict x w))
	 (prediction-error (α #'- y prediction))
	 (prediction-delta (α #'* prediction-error
			      (α #'sigmoid-derivative prediction))))
    (compute (α #'+ (matmul (transpose x) prediction-delta) w))))
     
(defun train* (x y first-w &optional (steps 50))
  (loop for w = first-w then (train x y w)
     for step below steps
     finally (return w)))

#|

CL-USER> (compute (predict x (train* x y w 1000)))
#2A((0.0048913625) (0.00955967) (0.99563795) (0.9923453))

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