def alg2_VT(self, Qx, Qxprime, M): #K1, K2, K3
B = T.outer(Qx, Qxprime)
C = T.sqrt(B)# in R^{n*n}
D = M / C # this is lamblda in ReLU analyrucal formula
E = np.clip(D, -1, 1) # clipping E between -1 and 1 for numerical stability.
F = (1 / (2 * np.pi)) * (E * (np.pi - T.arccos(E)) + T.sqrt(1 - E ** 2)) * C
G = (np.pi - T.arccos(E)) / (2 * np.pi)
return F,G
def VT(self, M):
A = T.diag(M) # GP_old is in R^{n*n} having the output gp kernel
# of all pairs of data in the data set
B = A * A[:, None]
C = T.sqrt(B) # in R^{n*n}
D = M / C # this is lamblda in ReLU analyrucal formula
E = T.clip(D, -1, 1) # clipping E between -1 and 1 for numerical stability.
F = (1 / (2 * np.pi)) * (E * (np.pi - T.arccos(E)) + T.sqrt(1 - E ** 2)) * C
G = (np.pi - T.arccos(E)) / (2 * np.pi)
return F,G
def alg1_VT_dep(self, M): #here i will use M as the previous little q ////// NxN, same value for every row
A = T.diag(M) # GP_old is in R^{n*n} having the output gp kernel
# of all pairs of data in the data set
B = A * A[:, None]
C = T.sqrt(B) # in R^{n*n}
D = M / C # this is lambda in ReLU analyrucal formula (c in alg)
E = T.clip(D, -1, 1) # clipping E between -1 and 1 for numerical stability.
F = (1 / (2 * np.pi)) * (E * (np.pi - T.arccos(E)) + T.sqrt(1 - E ** 2)) * C
G = (np.pi - T.arccos(E)) / (2 * np.pi)
return F,G
def RNTK_relu(x, RNTK_old, GP_old, param, output):
sw = param["sigmaw"]
su = param["sigmau"]
sb = param["sigmab"]
sv = param["sigmav"]
a = T.diag(GP_old) # GP_old is in R^{n*n} having the output gp kernel
# of all pairs of data in the data set
B = a * a[:, None]
C = T.sqrt(B) # in R^{n*n}
D = GP_old / C # this is lamblda in ReLU analyrucal formula
# clipping E between -1 and 1 for numerical stability.
E = T.clip(D, -1, 1)
F = (1 / (2 * np.pi)) * (E * (np.pi - T.arccos(E)) + T.sqrt(1 - E**2)) * C
G = (np.pi - T.arccos(E)) / (2 * np.pi)
if output:
GP_new = sv**2 * F
RNTK_new = sv**2.0 * RNTK_old * G + GP_new
else:
X = x * x[:, None]
GP_new = sw**2 * F + (su**2 / m) * X + sb**2
RNTK_new = sw**2.0 * RNTK_old * G + GP_new
return RNTK_new, GP_new
def create_network(self, state):
state = T.stack([T.arccos(state[:, 0]), state[:, 2]], 1)
input = nn.relu(nn.layers.Dense(state, 32))
input = nn.relu(nn.layers.Dense(input, 32))
input = nn.layers.Dense(input, 1)
return input