tvm学习笔记（八）：卷积操作

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对于卷积神经网络中，卷积操作可能是最常见操作，具体原理可以去学习一下Andred NG的课程，建议搞计算机视觉方向的都去刷一波，具体过程如图1所示：

图1 'VALID'方式卷积操作过程

其实就是卷积核与图像待操作区域进行乘加操作，常见的卷积操作有两种形式，第一种是'VALID'的方式，如图1所示，第二种是'SAME'的方式，区别在于'SAME'方式会对输入进行填充，以保证卷积操作之后，输出的size和输入的size一致。

图2 'SAME'方式卷积操作过程

1、padding

先说一下填充padding，padding就是在原始图像四周填充0，对应于图2中虚线部分，使用tvm实现，代码如下：

def padding(X, ph, pw):assert len(X.shape) >= 2nh, nw = X.shape[-2], X.shape[-1]return tvm.compute((*X.shape[0:-2], nh + ph * 2, nw + pw * 2),lambda *i: tvm.if_then_else(tvm.any(i[-2] < ph, i[-2] >= nh + ph, i[-1] < pw, i[-1] >= nw + pw),0, X[i[:-2] + (i[-2] - ph, i[-1] - pw)]), name = 'PaddedX')

2、输出feature map尺寸计算

对于输入size为n，卷积核size为k，填充size为p，卷积操作步长size为s，输出大小为：

$o=floor(\frac{n-k+2*p}{s})+1$

对应代码如下：

def conv_out_size(n, k, p, s):return (n - k + 2 * p) // s + 1

3、卷积操作

就是将卷积核与要操作的图像块进行乘加操作，对应于tvm代码为：

def conv(oc, ic, nh, nw, kh, kw, ph=0, pw=0, sh=1, sw=1):# reduction axesric = tvm.reduce_axis((0, ic), name='ric')rkh = tvm.reduce_axis((0, kh), name='rkh')rkw = tvm.reduce_axis((0, kw), name='rkw')# output height and widthoh = conv_out_size(nh, kh, ph, sh)ow = conv_out_size(nw, kw, pw, sw)# pad x and then conpute yX = tvm.placeholder((ic, nh, nw), name='x')K = tvm.placeholder((oc, ic, kh, kw), name='k')# 对输入填充PaddedX = padding(X, ph, pw) if ph * pw != 0 else XY = tvm.compute((oc, oh, ow),lambda c, i, j: tvm.sum(PaddedX[ric, i * sh + rkh, j * sw + rkw] * K[c, ric, rkh, rkw],axis=[ric, rkh, rkw]), name='Y')return X, K, Y, PaddedX

最后，看一下实际生成的伪代码：

import tvm
import numpy as np
import mxnet as mxdef padding(X, ph, pw):assert len(X.shape) >= 2nh, nw = X.shape[-2], X.shape[-1]return tvm.compute((*X.shape[0:-2], nh + ph * 2, nw + pw * 2),lambda *i: tvm.if_then_else(tvm.any(i[-2] < ph, i[-2] >= nh + ph, i[-1] < pw, i[-1] >= nw + pw),0, X[i[:-2] + (i[-2] - ph, i[-1] - pw)]), name = 'PaddedX')# 输入size：n
# 卷积核size：k
# 填充size：p
# 步长size：s
def conv_out_size(n, k, p, s):return (n - k + 2 * p) // s + 1def conv(oc, ic, nh, nw, kh, kw, ph=0, pw=0, sh=1, sw=1):# reduction axesric = tvm.reduce_axis((0, ic), name='ric')rkh = tvm.reduce_axis((0, kh), name='rkh')rkw = tvm.reduce_axis((0, kw), name='rkw')# output height and widthoh = conv_out_size(nh, kh, ph, sh)ow = conv_out_size(nw, kw, pw, sw)# pad x and then conpute yX = tvm.placeholder((ic, nh, nw), name='x')K = tvm.placeholder((oc, ic, kh, kw), name='k')# 对输入填充PaddedX = padding(X, ph, pw) if ph * pw != 0 else XY = tvm.compute((oc, oh, ow),lambda c, i, j: tvm.sum(PaddedX[ric, i * sh + rkh, j * sw + rkw] * K[c, ric, rkh, rkw],axis=[ric, rkh, rkw]), name='Y')return X, K, Y, PaddedXdef get_conv_data(oc, ic, n, k, p=0, s=1, constructor=None):np.random.seed(0)data = np.random.normal(size=(ic, n, n)).astype('float32')weight = np.random.normal(size=(oc, ic, k, k)).astype('float32')on = conv_out_size(n, k, p, s)out = np.empty((oc, on, on), dtype='float32')if constructor:data, weight, out = (constructor(x) for x in [data, weight, out])return data, weight, outoc, ic, n, k, p, s = 4, 6, 12, 3, 1, 1
X, K, Y, _ = conv(oc, ic, n, n, k, k, p, p, s, s)
sch = tvm.create_schedule(Y.op)
mod = tvm.build(sch, [X, K, Y])
print(tvm.lower(sch, [X, K, Y], simple_mode=True))data, weight, out = get_conv_data(oc, ic, n, k, p, s, tvm.nd.array)
mod(data, weight, out)def get_conv_data_mxnet(oc, ic, n, k, p, s, ctx='cpu'):ctx = getattr(mx, ctx)()data, weight, out = get_conv_data(oc, ic, n, k, p, s,lambda x: mx.nd.array(x, ctx=ctx))data, out = data.expand_dims(axis=0), out.expand_dims(axis=0)bias = mx.nd.zeros(out.shape[1], ctx=ctx)return data, weight, bias, outdef conv_mxnet(data, weight, bias, out, k, p, s):mx.nd.Convolution(data, weight, bias, kernel=(k, k), stride=(s, s),pad=(p, p), num_filter=out.shape[1], out=out)data, weight, bias, out_mx = get_conv_data_mxnet(oc, ic, n, k, p, s)
conv_mxnet(data, weight, bias, out_mx, k, p, s)
np.testing.assert_allclose(out_mx[0].asnumpy(), out.asnumpy(), atol=1e-5)

输出为：

// attr [PaddedX] storage_scope = "global"
allocate PaddedX[float32 * 1176]
produce PaddedX {for (i0, 0, 6) {for (i1, 0, 14) {for (i2, 0, 14) {PaddedX[(((i0*196) + (i1*14)) + i2)] = tvm_if_then_else(((((i1 < 1) |
| (13 <= i1)) || (i2 < 1)) || (13 <= i2)), 0f, x[((((i0*144) + (i1*12)) + i2) - 13)])      }}}
}
produce Y {for (c, 0, 4) {for (i, 0, 12) {for (j, 0, 12) {Y[(((c*144) + (i*12)) + j)] = 0ffor (ric, 0, 6) {for (rkh, 0, 3) {for (rkw, 0, 3) {Y[(((c*144) + (i*12)) + j)] = (Y[(((c*144) + (i*12)) + j)] + (P
addedX[(((((ric*196) + (i*14)) + (rkh*14)) + j) + rkw)]*k[((((c*54) + (ric*9)) + (rkh*3)) + rkw)]))            }}}}}}
}