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added ReLU #1

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merged 4 commits into from
Dec 17, 2018
Merged

added ReLU #1

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35cb2b4
added ReLU
twhughes Dec 6, 2018
2b11191
added mod_RELU
twhughes Dec 6, 2018
e3ee66c
added other complex ReLUs
twhughes Dec 6, 2018
bc75fae
rename ReLU to bpReLU (backprop ReLU) to avoid confusion
twhughes Dec 6, 2018
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added other complex ReLUs
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@twhughes
twhughes committed Dec 6, 2018
commit e3ee66cc0a7db82f9bc925342fea79667b0b12a5
62 changes: 52 additions & 10 deletions neuroptica/nonlinearities.py
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Expand Up @@ -297,45 +297,87 @@ def df_dZ(self, Z: np.ndarray):
class ReLU(ComplexNonlinearity):
'''
Discontinuous (but holomorphic and backpropable) ReLU
f(x_i) = alpha * x_i if |x_i| < cutoff
f(x_i) = x_i if |x_i| >= cutoff
f(x_i) = alpha * x_i if |x_i| < cutoff
f(x_i) = x_i if |x_i| >= cutoff

Arguments:
----------
cutoff: value of input |x_i| above which to fully transmit, below which to attentuate
alpha: attenuation factor f(x_i) = f
'''
def __init__(self, N, cutoff=1, alpha=0):
super().__init__(N, holomorphic=True)
self.cutoff = cutoff
self.alpha = alpha
super().__init__(N, holomorphic=True)

def forward_pass(self, X: np.ndarray):
return (np.abs(X) > self.cutoff) * X + (np.abs(X) <= self.cutoff) * self.alpha * X
return (np.abs(X) >= self.cutoff) * X + (np.abs(X) < self.cutoff) * self.alpha * X

def df_dZ(self, Z: np.ndarray):
return (np.abs(Z) > self.cutoff) * 1 + (np.abs(Z) <= self.cutoff) * self.alpha * 1
return (np.abs(Z) >= self.cutoff) * 1 + (np.abs(Z) < self.cutoff) * self.alpha * 1


class modReLU(ComplexNonlinearity):
'''
Contintous, but non-holomorphic and non-simply backpropabable ReLU of the form
f(z) = (|z| - cutoff) * z / |z| if |z| > cutoff (else 0)
f(z) = (|z| - cutoff) * z / |z| if |z| >= cutoff (else 0)
see: https://arxiv.org/pdf/1705.09792.pdf (note, cutoff subtracted in this definition)

Arguments:
----------
cutoff: value of input |x_i| above which to
'''
def __init__(self, N, cutoff=1):
self.cutoff = cutoff
super().__init__(N, holomorphic=False, mode="polar")
self.cutoff = cutoff

def forward_pass(self, X: np.ndarray):
return (np.abs(X) > self.cutoff) * ( np.abs(X) - self.cutoff ) * X / np.abs(X)
return (np.abs(X) >= self.cutoff) * ( np.abs(X) - self.cutoff ) * X / np.abs(X)

def df_dr(self, r: np.ndarray, phi: np.ndarray):
return (r > self.cutoff) * np.exp(1j * phi)
return (r >= self.cutoff) * np.exp(1j * phi)

def df_dphi(self, r: np.ndarray, phi: np.ndarray):
return (r > self.cutoff) * 1j * (r - self.cutoff) * np.exp(1j * phi)
return (r >= self.cutoff) * 1j * (r - self.cutoff) * np.exp(1j * phi)


class cReLU(ComplexNonlinearity):
'''
Contintous, but non-holomorphic and non-simply backpropabable ReLU of the form
f(z) = ReLU(Re{z}) + 1j * ReLU(Im{z})
see: https://arxiv.org/pdf/1705.09792.pdf
'''
def __init__(self, N):
super().__init__(N, holomorphic=False, mode="condensed")

def forward_pass(self, X: np.ndarray):
X_re = np.real(X)
X_im = np.imag(X)
return (X_re > 0) * X_re + 1j * (X_im > 0) * X_im

def df_dRe(self, a: np.ndarray, b: np.ndarray) -> np.ndarray:
return (a > 0)

def df_dIm(self, a: np.ndarray, b: np.ndarray) -> np.ndarray:
return 1j * (b > 0)


class zReLU(ComplexNonlinearity):
'''
Contintous, but non-holomorphic and non-simply backpropabable ReLU of the form
f(z) = z if Re{z} > 0 and Im{z} > 0, else 0
see: https://arxiv.org/pdf/1705.09792.pdf
'''
def __init__(self, N):
super().__init__(N, holomorphic=False, mode="condensed")

def forward_pass(self, X: np.ndarray):
X_re = np.real(X)
X_im = np.imag(X)
return (X_re > 0) * (X_im > 0) * X

def df_dRe(self, a: np.ndarray, b: np.ndarray) -> np.ndarray:
return (a > 0) * (b > 0)

def df_dIm(self, a: np.ndarray, b: np.ndarray) -> np.ndarray:
return (a > 0) * (b > 0) * 1j
4 changes: 3 additions & 1 deletion tests/test_nonlinearities.py
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Expand Up @@ -46,7 +46,9 @@ def test_OpticalMesh_adjoint_optimize(self):
SPMActivation(N, 1),
LinearMask(N, mask=np.random.rand(N)),
ReLU(N, cutoff=0.5, alpha=0.1),
modReLU(N, cutoff=0.5)]
modReLU(N, cutoff=0.5),
cReLU(N),
zReLU(N)]
for nonlinearity in nonlinearities:

print("Testing nonlinearity {}".format(nonlinearity))
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