def backward_impl(self, inputs, outputs, prop_down, accum):
# inputs: [inputs_fwd_graph] + [inputs_bwd_graph] or
# [inputs_fwd_graph] + [outputs_fwd_graph] + [inputs_bwd_graph]
# Inputs
x0 = inputs[0].data
x1 = inputs[1].data
dy = inputs[2].data
# Outputs
dx0 = outputs[0].data
dx1 = outputs[1].data
# Grads of inputs
g_x0 = inputs[0].grad
g_x1 = inputs[1].grad
g_dy = inputs[2].grad
# Grads of outputs
g_dx0 = outputs[0].grad
g_dx1 = outputs[1].grad
# Computation
if prop_down[2]:
mask = F.less(x0, x1)
if accum[2]:
g_dy += g_dx0 * mask + g_dx1 * (1.0 - mask)
else:
g_dy.copy_from(g_dx0 * mask + g_dx1 * (1.0 - mask))
def minimum2_backward(inputs):
"""
Args:
inputs (list of nn.Variable): Incomming grads/inputs to/of the forward function.
kwargs (dict of arguments): Dictionary of the corresponding function arguments.
Return:
list of Variable: Return the gradients wrt inputs of the corresponding function.
"""
dy = inputs[0]
x0 = inputs[1]
x1 = inputs[2]
m0 = F.less(x0, x1)
m1 = 1 - m0
m0 = no_grad(m0)
m1 = no_grad(m1)
dx0 = dy * m0
dx1 = dy * m1
return dx0, dx1
def parametric_pow2_quantize(x,
sign=True,
with_zero=True,
n_init=8,
n_min=1,
n_max=16,
m_init=1,
m_min=-8,
m_max=8,
fix_parameters=False):
"""Parametric version of `pow2_quantize` where the
bitwidth `n` and dynamic range `m` are learnable parameters.
Args:
x(~nnabla.Variable): N-D array as input
sign (bool): keep sign information during quantization.
with_zero (bool): quantize small weights to zero.
n_init (:obj:`nnabla.initializer.BaseInitializer` or :obj:`numpy.ndarray`): Initializer for bitwidth parameter.
n_min (int): lower bound for bitwidth.
n_max (int): upper bound for bitwidth.
m_init (:obj:`nnabla.initializer.BaseInitializer` or :obj:`numpy.ndarray`): Initializer for dynamic range.
m_min (float): lower bound for dynamic range.
m_max (float): upper bound for dynamic range.
fix_parameters (bool): When set to `True`, the negative slope values
will not be updated.
Returns:
~nnabla.Variable: N-D array.
"""
def clip_scalar(v, min_value, max_value):
return F.minimum_scalar(F.maximum_scalar(v, min_value), max_value)
def broadcast_scalar(v, shape):
return F.broadcast(F.reshape(v, (1, ) * len(shape), inplace=False),
shape=shape)
def quantize_pow2(v):
return 2**F.round(F.log(F.abs(v)) / np.log(2.))
n = get_parameter_or_create("n", (),
ConstantInitializer(n_init),
need_grad=True,
as_need_grad=not fix_parameters)
m = get_parameter_or_create("m", (),
ConstantInitializer(m_init),
need_grad=True,
as_need_grad=not fix_parameters)
# ensure that bitwidth is in specified range and an integer
n_q = F.round(clip_scalar(n, n_min, n_max))
if sign:
n_q = n_q - 1
if with_zero:
n_q = n_q - 1
# ensure that dynamic range is in specified range and an integer
m_q = F.round(clip_scalar(m, m_min, m_max))
# compute min/max value that we can represent
x_max = 2**m_q
x_min = 2**(m_q - (2**n_q) + 1)
# broadcast variables to correct size
x_min = broadcast_scalar(x_min, shape=x.shape)
x_max = broadcast_scalar(x_max, shape=x.shape)
# if unsigned, then quantize all negative values to zero
if not sign:
x = F.relu(x)
# compute absolute value/sign of input
ax = F.abs(x)
sx = F.sign(x)
if with_zero:
# prune smallest elements (in magnitude) to zero if they are smaller
# than `x_min / \sqrt(2)`
x_threshold = x_min / np.sqrt(2)
idx1 = F.greater_equal(ax, x_threshold) * F.less(ax, x_min)
idx2 = F.greater_equal(ax, x_min) * F.less(ax, x_max)
idx3 = F.greater_equal(ax, x_max)
else:
idx1 = F.less(ax, x_min)
idx2 = F.greater_equal(ax, x_min) * F.less(ax, x_max)
idx3 = F.greater_equal(ax, x_max)
# do not backpropagate gradient through indices
idx1.need_grad = False
idx2.need_grad = False
idx3.need_grad = False
# do not backpropagate gradient through sign
sx.need_grad = False
# take care of values outside of dynamic range
return sx * (x_min * idx1 + quantize_pow2(ax) * idx2 + x_max * idx3)
def parametric_pow2_quantize_xmin_xmax(x,
sign=True,
with_zero=True,
xmin_init=2**-7,
xmin_min=2**-15,
xmin_max=256,
xmax_init=2**0,
xmax_min=2**-8,
xmax_max=256,
fix_parameters=False):
"""Parametric version of `pow2_quantize` where the
min value `xmin` and max value `xmax` are learnable parameters.
Returns:
~nnabla.Variable: N-D array.
"""
def clip_scalar(v, min_value, max_value):
return F.minimum_scalar(F.maximum_scalar(v, min_value), max_value)
def broadcast_scalar(v, shape):
return F.broadcast(F.reshape(v, (1, ) * len(shape), inplace=False),
shape=shape)
def quantize_pow2(v):
return 2.**F.round(F.log(F.abs(v)) / np.log(2.))
xmin = get_parameter_or_create("xmin", (),
ConstantInitializer(xmin_init),
need_grad=True,
as_need_grad=not fix_parameters)
xmax = get_parameter_or_create("xmax", (),
ConstantInitializer(xmax_init),
need_grad=True,
as_need_grad=not fix_parameters)
# ensure that minimum dynamic range is in specified range and a power-of-two
xmin = quantize_pow2(clip_scalar(xmin, xmin_min, xmin_max))
# ensure that minimum dynamic range is in specified range and a power-of-two
xmax = quantize_pow2(clip_scalar(xmax, xmax_min, xmax_max))
# broadcast variables to correct size
xmin = broadcast_scalar(xmin, shape=x.shape)
xmax = broadcast_scalar(xmax, shape=x.shape)
# if unsigned, then quantize all negative values to zero
if not sign:
x = F.relu(x)
# compute absolute value/sign of input
ax = F.abs(x)
sx = F.sign(x)
if with_zero:
# prune smallest elements (in magnitude) to zero if they are smaller
# than `x_min / \sqrt(2)`
x_threshold = xmin / np.sqrt(2)
idx1 = F.greater_equal(ax, x_threshold) * F.less(ax, xmin)
idx2 = F.greater_equal(ax, xmin) * F.less(ax, xmax)
idx3 = F.greater_equal(ax, xmax)
else:
idx1 = F.less(ax, xmin)
idx2 = F.greater_equal(ax, xmin) * F.less(ax, xmax)
idx3 = F.greater_equal(ax, xmax)
# do not backpropagate gradient through indices
idx1.need_grad = False
idx2.need_grad = False
idx3.need_grad = False
# do not backpropagate gradient through sign
sx.need_grad = False
# take care of values outside of dynamic range
return sx * (xmin * idx1 + quantize_pow2(ax) * idx2 + xmax * idx3)
def bidirectional_sphere_trace(self, camloc, raydir, t_start, t_finish):
t_f = F.identity(t_start)
x_f = camloc + t_f * raydir
s_f = self.sdf(x_f)
mask_hit_eps_f = 0 * F.identity(t_f)
t_b = F.identity(t_finish)
x_b = camloc + t_b * raydir
s_b = self.sdf(x_b)
mask_hit_eps_b = 0 * F.identity(t_b)
for i in range(self.sphere_trace_itr - 1):
# Forward direction
mask_hit_eps_f_i = F.less_equal_scalar(F.abs(s_f), self.eps)
mask_hit_eps_f += (1 - mask_hit_eps_f) * mask_hit_eps_f_i
t_f += (1 - mask_hit_eps_f) * s_f
x_f = camloc + t_f * raydir
s_f_prev = F.identity(s_f)
s_f = self.sdf(x_f)
mask_pos_f_prev = (1 - mask_hit_eps_f) * \
F.greater_scalar(s_f_prev, 0)
mask_neg_f = (1 - mask_hit_eps_f) * F.less_scalar(s_f, 0)
mask_revert_f = mask_pos_f_prev * mask_neg_f
t_f -= mask_revert_f * s_f_prev
s_f = mask_revert_f * s_f_prev + (1 - mask_revert_f) * s_f
# Backward direction
mask_hit_eps_b_i = F.less_equal_scalar(F.abs(s_b), self.eps)
mask_hit_eps_b += (1 - mask_hit_eps_b) * mask_hit_eps_b_i
t_b -= (1 - mask_hit_eps_b) * s_b
x_b = camloc + t_b * raydir
s_b_prev = F.identity(s_b)
s_b = self.sdf(x_b)
mask_pos_b_prev = (1 - mask_hit_eps_b) * \
F.greater_scalar(s_b_prev, 0)
mask_neg_b = (1 - mask_hit_eps_b) * F.less_scalar(s_b, 0)
mask_revert_b = mask_pos_b_prev * mask_neg_b
t_b += mask_revert_b * s_b_prev
s_b = mask_revert_b * s_b_prev + (1 - mask_revert_b) * s_b
## print("s_f neg", np.sum(s_f.data < 0))
## print("s_b neg", np.sum(s_b.data < 0))
# Fine grained start/finish points
t_f0 = t_f
t_f1 = t_f + mask_revert_f * s_f_prev
x_hit_st0 = camloc + t_f0 * raydir
## x0, x1 = self.post_method(x_hit_st0, camloc + t_f1 * raydir)
## t_f0 = F.norm((x0 - camloc), axis=(x0.ndim - 1), keepdims=True)
## t_f1 = F.norm((x1 - camloc), axis=(x1.ndim - 1), keepdims=True)
mask_hit_f1b = mask_revert_f * F.less(t_f1, t_b)
t_b = t_f1 * mask_hit_f1b + t_b * (1 - mask_hit_f1b)
# Reverse the opposite case
mask_fb = F.less(t_f, t_b)
t_f = t_f * mask_fb + t_start * (1 - mask_fb)
t_b = t_b * mask_fb + t_finish * (1 - mask_fb)
return x_hit_st0, t_f, t_b, mask_hit_eps_f