參考
- 深度學習/01-MNIST
- https://cs.stanford.edu/people/karpathy/convnetjs/demo/mnist.html
卷積層的 JavaScript 實作
https://github.com/karpathy/convnetjs/blob/master/src/convnet_layers_dotproducts.js
var ConvLayer = function(opt) {
var opt = opt || {};
// required
this.out_depth = opt.filters;
this.sx = opt.sx; // filter size. Should be odd if possible, it's cleaner.
this.in_depth = opt.in_depth;
this.in_sx = opt.in_sx;
this.in_sy = opt.in_sy;
// optional
this.sy = typeof opt.sy !== 'undefined' ? opt.sy : this.sx;
this.stride = typeof opt.stride !== 'undefined' ? opt.stride : 1; // stride at which we apply filters to input volume
this.pad = typeof opt.pad !== 'undefined' ? opt.pad : 0; // amount of 0 padding to add around borders of input volume
this.l1_decay_mul = typeof opt.l1_decay_mul !== 'undefined' ? opt.l1_decay_mul : 0.0;
this.l2_decay_mul = typeof opt.l2_decay_mul !== 'undefined' ? opt.l2_decay_mul : 1.0;
// computed
// note we are doing floor, so if the strided convolution of the filter doesnt fit into the input
// volume exactly, the output volume will be trimmed and not contain the (incomplete) computed
// final application.
this.out_sx = Math.floor((this.in_sx + this.pad * 2 - this.sx) / this.stride + 1);
this.out_sy = Math.floor((this.in_sy + this.pad * 2 - this.sy) / this.stride + 1);
this.layer_type = 'conv';
// initializations
var bias = typeof opt.bias_pref !== 'undefined' ? opt.bias_pref : 0.0;
this.filters = [];
// 注意下列這行，決定了卷積層的參數數量
for(var i=0;i<this.out_depth;i++) { this.filters.push(new Vol(this.sx, this.sy, this.in_depth)); }
this.biases = new Vol(1, 1, this.out_depth, bias);
}
ConvLayer.prototype = {
forward: function(V, is_training) {
// optimized code by @mdda that achieves 2x speedup over previous version
this.in_act = V;
var A = new Vol(this.out_sx |0, this.out_sy |0, this.out_depth |0, 0.0);
var V_sx = V.sx |0;
var V_sy = V.sy |0;
var xy_stride = this.stride |0;
for(var d=0;d<this.out_depth;d++) {
var f = this.filters[d];
var x = -this.pad |0;
var y = -this.pad |0;
for(var ay=0; ay<this.out_sy; y+=xy_stride,ay++) { // xy_stride
x = -this.pad |0;
for(var ax=0; ax<this.out_sx; x+=xy_stride,ax++) { // xy_stride
// 遮罩累加迴圈開始
// convolve centered at this particular location
var a = 0.0;
for(var fy=0;fy<f.sy;fy++) {
var oy = y+fy; // coordinates in the original input array coordinates
for(var fx=0;fx<f.sx;fx++) {
var ox = x+fx;
if(oy>=0 && oy<V_sy && ox>=0 && ox<V_sx) {
for(var fd=0;fd<f.depth;fd++) {
// avoid function call overhead (x2) for efficiency, compromise modularity :(
a += f.w[((f.sx * fy)+fx)*f.depth+fd] * V.w[((V_sx * oy)+ox)*V.depth+fd];
}
}
}
}
// 遮罩累加迴圈結束
a += this.biases.w[d]; // 加上 bias
A.set(ax, ay, d, a); // 設定進結果格子中
}
}
}
this.out_act = A;
return this.out_act;
},
backward: function() {
var V = this.in_act;
V.dw = global.zeros(V.w.length); // zero out gradient wrt bottom data, we're about to fill it
var V_sx = V.sx |0;
var V_sy = V.sy |0;
var xy_stride = this.stride |0;
for(var d=0;d<this.out_depth;d++) {
var f = this.filters[d];
var x = -this.pad |0;
var y = -this.pad |0;
for(var ay=0; ay<this.out_sy; y+=xy_stride,ay++) { // xy_stride
x = -this.pad |0;
for(var ax=0; ax<this.out_sx; x+=xy_stride,ax++) { // xy_stride
// convolve centered at this particular location
var chain_grad = this.out_act.get_grad(ax,ay,d); // gradient from above, from chain rule
for(var fy=0;fy<f.sy;fy++) {
var oy = y+fy; // coordinates in the original input array coordinates
for(var fx=0;fx<f.sx;fx++) {
var ox = x+fx;
if(oy>=0 && oy<V_sy && ox>=0 && ox<V_sx) {
for(var fd=0;fd<f.depth;fd++) {
// avoid function call overhead (x2) for efficiency, compromise modularity :(
var ix1 = ((V_sx * oy)+ox)*V.depth+fd;
var ix2 = ((f.sx * fy)+fx)*f.depth+fd;
f.dw[ix2] += V.w[ix1]*chain_grad;
V.dw[ix1] += f.w[ix2]*chain_grad;
}
}
}
}
this.biases.dw[d] += chain_grad;
}
}
}
},
getParamsAndGrads: function() {
var response = [];
for(var i=0;i<this.out_depth;i++) {
response.push({params: this.filters[i].w, grads: this.filters[i].dw, l2_decay_mul: this.l2_decay_mul, l1_decay_mul: this.l1_decay_mul});
}
response.push({params: this.biases.w, grads: this.biases.dw, l1_decay_mul: 0.0, l2_decay_mul: 0.0});
return response;
},
toJSON: function() {
var json = {};
json.sx = this.sx; // filter size in x, y dims
json.sy = this.sy;
json.stride = this.stride;
json.in_depth = this.in_depth;
json.out_depth = this.out_depth;
json.out_sx = this.out_sx;
json.out_sy = this.out_sy;
json.layer_type = this.layer_type;
json.l1_decay_mul = this.l1_decay_mul;
json.l2_decay_mul = this.l2_decay_mul;
json.pad = this.pad;
json.filters = [];
for(var i=0;i<this.filters.length;i++) {
json.filters.push(this.filters[i].toJSON());
}
json.biases = this.biases.toJSON();
return json;
},
fromJSON: function(json) {
this.out_depth = json.out_depth;
this.out_sx = json.out_sx;
this.out_sy = json.out_sy;
this.layer_type = json.layer_type;
this.sx = json.sx; // filter size in x, y dims
this.sy = json.sy;
this.stride = json.stride;
this.in_depth = json.in_depth; // depth of input volume
this.filters = [];
this.l1_decay_mul = typeof json.l1_decay_mul !== 'undefined' ? json.l1_decay_mul : 1.0;
this.l2_decay_mul = typeof json.l2_decay_mul !== 'undefined' ? json.l2_decay_mul : 1.0;
this.pad = typeof json.pad !== 'undefined' ? json.pad : 0;
for(var i=0;i<json.filters.length;i++) {
var v = new Vol(0,0,0,0);
v.fromJSON(json.filters[i]);
this.filters.push(v);
}
this.biases = new Vol(0,0,0,0);
this.biases.fromJSON(json.biases);
}
}
參考
卷積層的 JavaScript 實作
https://github.com/karpathy/convnetjs/blob/master/src/convnet_layers_dotproducts.js