对导数（梯度）传播的理解(下)

向前传播的是值，反向传播的是梯度

    // every Unit corresponds to a wire in the diagrams
var Unit = function(value, grad) {
  // value computed in the forward pass
  this.value = value; 
  // the derivative of circuit output w.r.t this unit, computed in backward pass
  this.grad = grad; 
}


var multiplyGate = function(){ };
multiplyGate.prototype = {
  forward: function(u0, u1) {
    // store pointers to input Units u0 and u1 and output unit utop
    this.u0 = u0; 
    this.u1 = u1; 
    this.utop = new Unit(u0.value * u1.value, 0.0);
    return this.utop;
  },
  backward: function() {
    // take the gradient in output unit and chain it with the
    // local gradients, which we derived for multiply gate before
    // then write those gradients to those Units.
    this.u0.grad += this.u1.value * this.utop.grad;
    this.u1.grad += this.u0.value * this.utop.grad;
  }
}

var addGate = function(){ };
addGate.prototype = {
  forward: function(u0, u1) {
    this.u0 = u0; 
    this.u1 = u1; // store pointers to input units
    this.utop = new Unit(u0.value + u1.value, 0.0);
    return this.utop;
  },
  backward: function() {
    // add gate. derivative wrt both inputs is 1
    this.u0.grad += 1 * this.utop.grad;
    this.u1.grad += 1 * this.utop.grad;
  }
}


var sigmoidGate = function() { 
  // helper function
  this.sig = function(x) { return 1 / (1 + Math.exp(-x)); };
};
sigmoidGate.prototype = {
  forward: function(u0) {
    this.u0 = u0;
    this.utop = new Unit(this.sig(this.u0.value), 0.0);
    return this.utop;
  },
  backward: function() {
    var s = this.sig(this.u0.value);
    this.u0.grad += (s * (1 - s)) * this.utop.grad;
  }
}

// create input units
var a = new Unit(1.0, 0.0);
var b = new Unit(2.0, 0.0);
var c = new Unit(-3.0, 0.0);
var x = new Unit(-1.0, 0.0);
var y = new Unit(3.0, 0.0);

// create the gates
var mulg0 = new multiplyGate();
var mulg1 = new multiplyGate();
var addg0 = new addGate();
var addg1 = new addGate();
var sg0 = new sigmoidGate();

// do the forward pass
var forwardNeuron = function() {
  ax = mulg0.forward(a, x); // a*x = -1
  by = mulg1.forward(b, y); // b*y = 6
  axpby = addg0.forward(ax, by); // a*x + b*y = 5
  axpbypc = addg1.forward(axpby, c); // a*x + b*y + c = 2
  s = sg0.forward(axpbypc); // sig(a*x + b*y + c) = 0.8808
};
forwardNeuron();

console.log('circuit output: ' + s.value); // prints 0.8808
s.grad = 1.0;
sg0.backward(); // writes gradient into axpbypc
console.log("sig节点输入的梯度 (也就是a*x + b*y + c函数输出节点)为"+sg0.u0.grad);
addg1.backward(); // writes gradients into axpby and c
console.log("c的梯度为"+c.grad);
//console.log("c节点的梯度为"+addg1.u1.grad);

console.log("a*x + b*y输出的梯度为"+addg1.u0.grad);
addg0.backward(); // writes gradients into ax and by
console.log("a*x输出节点的梯度为"+addg0.u0.grad);
console.log("b*y输出的梯度为"+addg0.u1.grad);
mulg1.backward(); // writes gradients into b and y
console.log("b的梯度为"+b.grad);
//console.log("b输出节点的梯度为"+mulg1.u0.grad);
console.log("y的梯度为"+y.grad);
//console.log("y输出的梯度为"+mulg1.u1.grad);
mulg0.backward(); // writes gradients into a and x
console.log("a的梯度为"+a.grad);
//console.log("a输出节点的梯度为"+mulg0.u0.grad);
console.log("x的梯度为"+x.grad);
//console.log("x输出的梯度为"+mulg0.u1.grad);








var step_size = 0.01;
a.value += step_size * a.grad; // a.grad is -0.105
b.value += step_size * b.grad; // b.grad is 0.315
c.value += step_size * c.grad; // c.grad is 0.105
x.value += step_size * x.grad; // x.grad is 0.105
y.value += step_size * y.grad; // y.grad is 0.210

forwardNeuron();
console.log('circuit output after one backprop: ' + s.value); // prints 0.8825