forked from tinygrad/tinygrad
287 lines
8.0 KiB
Python
287 lines
8.0 KiB
Python
import sys
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import warnings
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import numpy as np
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from .tensor import Function, register
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# ************* basic ops *************
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def unbroadcast(out, in_sh):
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# adjoint operation to broadcast is sum. Need to sum all axis with 1 = in_sh[i] < out.shape[i]
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sum_axis = [i for i in range(len(in_sh)) if in_sh[i]==1 and out.shape[i]>1]
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return out.sum(axis=tuple(sum_axis)).reshape(in_sh)
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class Add(Function):
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@staticmethod
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def forward(ctx, x, y):
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ctx.save_for_backward(x.shape, y.shape)
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return x+y
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@staticmethod
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def backward(ctx, grad_output):
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shape_x, shape_y = ctx.saved_tensors
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return unbroadcast(grad_output, shape_x), unbroadcast(grad_output, shape_y)
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register('add', Add)
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class Sub(Function):
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@staticmethod
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def forward(ctx, x, y):
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ctx.save_for_backward(x.shape, y.shape)
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return x-y
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@staticmethod
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def backward(ctx, grad_output):
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shape_x, shape_y = ctx.saved_tensors
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return unbroadcast(grad_output, shape_x), unbroadcast(-grad_output, shape_y)
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register('sub', Sub)
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class Mul(Function):
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@staticmethod
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def forward(ctx, x, y):
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ctx.save_for_backward(x, y)
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return x*y
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@staticmethod
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def backward(ctx, grad_output):
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x,y = ctx.saved_tensors
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return unbroadcast(y*grad_output, x.shape), unbroadcast(x*grad_output, y.shape)
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register('mul', Mul)
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class Pow(Function):
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@staticmethod
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def forward(ctx, x, y):
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ctx.save_for_backward(x, y)
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return x ** y
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@staticmethod
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def backward(ctx, grad_output):
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x,y = ctx.saved_tensors
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return unbroadcast(y * (x**(y-1.0)) * grad_output, x.shape), \
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unbroadcast((x**y) * np.log(x) * grad_output, y.shape)
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register('pow', Pow)
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class Sum(Function):
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@staticmethod
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def forward(ctx, input):
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ctx.save_for_backward(input)
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return np.array([input.sum()])
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@staticmethod
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def backward(ctx, grad_output):
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input, = ctx.saved_tensors
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return grad_output * np.ones_like(input)
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register('sum', Sum)
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# ************* GEMM *************
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class Dot(Function):
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@staticmethod
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def forward(ctx, input, weight):
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ctx.save_for_backward(input, weight)
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return input.dot(weight)
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@staticmethod
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def backward(ctx, grad_output):
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input, weight = ctx.saved_tensors
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grad_input = grad_output.dot(weight.T)
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grad_weight = input.T.dot(grad_output)
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return grad_input, grad_weight
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register('dot', Dot)
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register('matmul', Dot)
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# ************* simple ops *************
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class Pad2D(Function):
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@staticmethod
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def forward(ctx, x, padding=None):
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ctx.save_for_backward(padding)
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return np.pad(x,
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((0,0), (0,0),
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(padding[2], padding[3]), (padding[0], padding[1])))
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@staticmethod
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def backward(ctx, grad_output):
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padding, = ctx.saved_tensors
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return grad_output[..., padding[2]:-padding[3], padding[0]:-padding[1]]
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register('pad2d', Pad2D)
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class Reshape(Function):
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@staticmethod
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def forward(ctx, x, shape):
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ctx.save_for_backward(x.shape)
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return x.reshape(shape)
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@staticmethod
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def backward(ctx, grad_output):
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in_shape, = ctx.saved_tensors
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return grad_output.reshape(in_shape)
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register('reshape', Reshape)
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# ************* activation ops *************
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class ReLU(Function):
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@staticmethod
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def forward(ctx, input):
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ctx.save_for_backward(input)
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return np.maximum(input, 0)
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@staticmethod
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def backward(ctx, grad_output):
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input, = ctx.saved_tensors
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grad_input = grad_output * (input >= 0)
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return grad_input
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register('relu', ReLU)
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class Sigmoid(Function):
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@staticmethod
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def forward(ctx, input):
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with np.warnings.catch_warnings():
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np.warnings.filterwarnings('ignore')
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ret = np.where(input >= 0,
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1/(1 + np.exp(-input)),
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np.exp(input)/(1 + np.exp(input))
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)
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ctx.save_for_backward(ret)
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return ret
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@staticmethod
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def backward(ctx, grad_output):
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ret, = ctx.saved_tensors
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grad_input = grad_output * (ret * (1 - ret))
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return grad_input
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register('sigmoid', Sigmoid)
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class LogSoftmax(Function):
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@staticmethod
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def forward(ctx, input):
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def logsumexp(x):
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#return np.log(np.exp(x).sum(axis=1))
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c = x.max(axis=1)
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return c + np.log(np.exp(x-c.reshape((-1, 1))).sum(axis=1))
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output = input - logsumexp(input).reshape((-1, 1))
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ctx.save_for_backward(output)
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return output
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@staticmethod
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def backward(ctx, grad_output):
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output, = ctx.saved_tensors
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return grad_output - np.exp(output)*(grad_output.sum(axis=1).reshape((-1, 1)))
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register('logsoftmax', LogSoftmax)
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# ************* conv ops *************
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class Conv2D(Function):
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@staticmethod
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def forward(ctx, x, w, stride=1, groups=1):
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if type(ctx.stride) == int:
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ctx.stride = (ctx.stride, ctx.stride)
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cout,cin,H,W = w.shape
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ys,xs = ctx.stride
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bs,cin_ = x.shape[0], x.shape[1]
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oy,ox = (x.shape[2]-(H-ys))//ys, (x.shape[3]-(W-xs))//xs
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assert cin*ctx.groups == cin_
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assert cout % ctx.groups == 0
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rcout = cout//ctx.groups
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gx = x.reshape(bs,ctx.groups,cin,x.shape[2],x.shape[3])
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tx = np.lib.stride_tricks.as_strided(gx,
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shape=(bs, ctx.groups, cin, oy, ox, H, W),
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strides=(gx.strides[0], gx.strides[1], gx.strides[2],
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gx.strides[3]*ys, gx.strides[4]*xs,
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gx.strides[3], gx.strides[4]),
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writeable=False,
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)
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tw = w.reshape(ctx.groups, rcout, cin, H, W)
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ctx.save_for_backward(tx, tw, x.shape)
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ret = np.zeros((bs,ctx.groups,oy,ox,rcout),dtype=x.dtype)
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for g in range(ctx.groups):
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#ijYXyx,kjyx -> iYXk ->ikYX
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ret[:,g] += np.tensordot(tx[:,g], tw[g], ((1,4,5),(1,2,3)))
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return np.moveaxis(ret,4,2).reshape(bs, cout, oy, ox)
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@staticmethod
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def backward(ctx, grad_output):
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bs,_,oy,ox = grad_output.shape
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tx, tw, x_shape = ctx.saved_tensors
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_,rcout,cin,H,W = tw.shape
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ys,xs = ctx.stride
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OY,OX = x_shape[2:4]
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ggg = grad_output.reshape(bs,ctx.groups,rcout,oy,ox)
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gdw = np.zeros((ctx.groups,rcout,cin,H,W), dtype=tx.dtype)
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for g in range(ctx.groups):
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#'ikYX,ijYXyx -> kjyx'
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gdw[g] += np.tensordot(ggg[:,g], tx[:,g], ((0,2,3),(0,2,3)))
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# needs to be optimized
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gdx = np.zeros((bs,ctx.groups,cin,OY,OX), dtype=tx.dtype)
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for Y in range(grad_output.shape[2]):
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for X in range(grad_output.shape[3]):
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iY,iX = Y*ys, X*xs
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#gdx[:,:,: , iY:iY+H, iX:iX+W] += np.einsum('igk,gkjyx->igjyx', ggg[:,:,:,Y,X], tw)
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for g in range(ctx.groups):
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tg = np.dot(ggg[:,g,:,Y,X].reshape(bs, -1), tw[g].reshape(rcout, -1))
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gdx[:, g, :, iY:iY+H, iX:iX+W] += tg.reshape((bs, cin, H, W))
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return gdx.reshape((bs, ctx.groups*cin, OY, OX)), gdw.reshape((ctx.groups*rcout, cin, H, W))
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register('conv2d', Conv2D)
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# ************* pooling ops *************
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def stack_for_pool(x, py, px):
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my, mx = (x.shape[2]//py)*py, (x.shape[3]//px)*px
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stack = []
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xup = x[:, :, :my, :mx]
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for Y in range(py):
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for X in range(px):
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stack.append(xup[:, :, Y::py, X::px][None])
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return np.concatenate(stack, axis=0)
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def unstack_for_pool(fxn, s, py, px):
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my, mx = (s[2]//py)*py, (s[3]//px)*px
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for Y in range(py):
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for X in range(px):
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ll = fxn(Y*px+X)
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if X == 0 and Y == 0:
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ret = np.zeros(s, dtype=ll.dtype)
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ret[:, :, Y:my:py, X:mx:px] = ll
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return ret
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class MaxPool2D(Function):
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@staticmethod
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def forward(ctx, x, kernel_size=(2, 2)):
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stack = stack_for_pool(x, *kernel_size)
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idxs = np.argmax(stack, axis=0)
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ctx.save_for_backward(idxs, x.shape)
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return np.max(stack, axis=0)
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@staticmethod
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def backward(ctx, grad_output):
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idxs,s = ctx.saved_tensors
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return unstack_for_pool(
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lambda idx: grad_output * (idxs == idx),
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s, *ctx.kernel_size)
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register('max_pool2d', MaxPool2D)
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class AvgPool2D(Function):
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@staticmethod
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def forward(ctx, x, kernel_size=(2, 2)):
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stack = stack_for_pool(x, *kernel_size)
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ctx.save_for_backward(x.shape)
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return np.mean(stack, axis=0)
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@staticmethod
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def backward(ctx, grad_output):
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s, = ctx.saved_tensors
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py, px = ctx.kernel_size
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return unstack_for_pool(
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lambda idx: grad_output/py/px,
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s, py, px)
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register('avg_pool2d', AvgPool2D)
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