def __init__(
self,
sequence,
init_h,
units,
W=initializers.glorot_uniform,
H=initializers.orthogonal,
b=T.zeros,
trainable_W=True,
trainable_H=True,
trainable_b=True,
activation=nn.sigmoid,
only_last=False,
):
W = create_variable("W",
W, (sequence.shape[2], units),
trainable=trainable_W)
H = create_variable("H", H, (units, units), trainable=trainable_H)
b = create_variable("b", b, (units, ), trainable=trainable_b)
last, output = T.scan(
lambda h, x, W, H, b: RNN.gate(h, x, W, H, b, activation),
init=init_h,
sequences=[sequence.transpose((1, 0, 2))],
non_sequences=[W, H, b],
)
if only_last:
return last
else:
return output.transpose((1, 0, 2))
def forward(
self,
sequence,
init_h,
units,
W=initializers.he,
H=initializers.he,
b=T.zeros,
trainable_W=True,
trainable_H=True,
trainable_b=True,
activation=nn.sigmoid,
only_last=False,
):
self.create_variable("W",
W, (sequence.shape[2], units),
trainable=trainable_W)
self.create_variable("H", H, (units, units), trainable=trainable_H)
self.create_variable("b", b, (units), trainable=trainable_b)
last, output = T.scan(
lambda h, x, W, H, b: self.gate(h, x, W, H, b, activation),
init=init_h,
sequences=[sequence.transpose((1, 0, 2))],
non_sequences=[self.W, self.H, self.b],
)
if only_last:
return last
else:
return output.transpose((1, 0, 2))
def compute_kernels(self, final_ema):
diag_ends = self.get_ends_of_diags(final_ema)
S_init, D_init = self.VT(diag_ends[0][0])
init_Kappa = self.sv**2 * S_init
init_Theta = init_Kappa + self.sv**2 * diag_ends[0][1] * D_init
init_list = T.concatenate([
T.expand_dims(init_Kappa, axis=0),
T.expand_dims(init_Theta, axis=0)
])
def map_test(gp_rntk_sum, gp_rntk):
S, D = self.VT(gp_rntk[0])
ret1 = self.sv**2 * S
ret2 = ret1 + self.sv**2 * gp_rntk[1] * D
gp_rntk_sum = T.index_add(gp_rntk_sum, 0, ret1)
gp_rntk_sum = T.index_add(gp_rntk_sum, 1, ret2)
return gp_rntk_sum, gp_rntk_sum
final_K_T, inter_results = T.scan(map_test,
init=init_list,
sequences=[diag_ends[1:]])
return final_K_T
def RNTK_function(self):
print(f"N, {self.N}, length, {self.length}")
DATA = T.Placeholder((self.N, self.length), 'float32')
RNTK,GP = self.RNTK_first(DATA[:,0])
v, _ = T.scan(lambda a,b:self.RNTK_middle(a,b),sequences=[ T.transpose(DATA[:, 1:]) ], init=T.stack([RNTK,GP]))
RNTK_last,RNTK_avg = self.RNTK_output(v)
f = symjax.function(DATA, outputs= [RNTK_last,RNTK_avg])
return RNTK_last,RNTK_avg
def RNTK_function(N,length,param):
DATA = T.Placeholder((N, length), 'float32')
RNTK,GP = RNTK_first(DATA[:,0], param['sigmaw'],param['sigmau'],param['sigmab'],param['sigmah'],param['L'], param['Lf'],param['sigmav'])
v, _ = T.scan(lambda a,b:RNTK_middle(a,b,param['sigmaw'],param['sigmau'],param['sigmab'],param['L'], param['Lf'],param['sigmav']
),sequences=[ T.transpose(DATA[:, 1:]) ], init=T.stack([RNTK,GP]))
RNTK_last,RNTK_avg = RNTK_output(v, param['sigmav'],param['L'],param['Lf'],length)
f = symjax.function(DATA, outputs= [RNTK_last,RNTK_avg])
return f
def create_func_for_diag(self,
dim1idx,
dim2idx,
function=False,
jmode=False):
diag = self.make_inputs(dim1idx, dim2idx, jmode=jmode)
# print('test')
## prev_vals - (2,1) - previous phi and lambda values
## idx - where we are on the diagonal
## d1idx - y value of first dimension diag start
## d2idx - x value of second dimension diag start
## d1ph - max value of first dimension
## d2ph - max value of second dimension
bc = self.sh**2 * self.sw**2 * T.eye(
self.n, self.n) + (self.su**2) * self.X + self.sb**2
single_boundary_condition = T.expand_dims(bc, axis=0)
# single_boundary_condition = T.expand_dims(T.Variable((bc), "float32", "boundary_condition"), axis = 0)
boundary_condition = T.concatenate(
[single_boundary_condition,
single_boundary_condition]) #one for phi and lambda
def fn(prev_vals, idx, Xph):
## change - xph must now index the dataset instead of being passed in
# tiprime_iter = d1idx + idx
# ti_iter = d2idx + idx
prev_lambda = prev_vals[0]
prev_phi = prev_vals[1]
## not boundary condition
S, D = self.VT(prev_lambda)
new_lambda = self.sw**2 * S + self.su**2 * Xph + self.sb**2 ## took out an X
new_phi = new_lambda + self.sw**2 * prev_phi * D
lambda_expanded = T.expand_dims(new_lambda, axis=0)
phi_expanded = T.expand_dims(new_phi, axis=0)
to_return = T.concatenate([lambda_expanded, phi_expanded])
# jax.lax.cond(to_return.shape == (2,10,10), lambda _: print(f'{idx}, true'), lambda _: print(f'{idx}, false'), operand = None)
return to_return, to_return
last_ema, all_ema = T.scan(fn,
init=boundary_condition,
sequences=[diag],
non_sequences=[self.X])
expanded_ema = T.concatenate(
[T.expand_dims(boundary_condition, axis=0), all_ema])
print(expanded_ema)
if function:
f = symjax.function(diag, outputs=expanded_ema)
return f
else:
return expanded_ema
def create_func_for_diag(self):
# NEW_DATA = self.reorganize_data()
## change - bc should be a function that takes a passed in X?
bc = self.sh**2 * self.sw**2 * T.eye(self.n, self.n) + (
self.su**2) * self.X + self.sb**2 ## took out X ||
single_boundary_condition = T.expand_dims(bc, axis=0)
# single_boundary_condition = T.expand_dims(T.Variable((bc), "float32", "boundary_condition"), axis = 0)
boundary_condition = T.concatenate(
[single_boundary_condition, single_boundary_condition])
self.boundary_condition = boundary_condition
# self.save_vts = {}
## prev_vals - (2,1) - previous phi and lambda values
## idx - where we are on the diagonal
def fn(prev_vals, idx, Xph):
## change - xph must now index the dataset instead of being passed in
# x = Xph['indexed']
# X = x*x[:, None]
# tiprime_iter = d1idx + idx
# ti_iter = d2idx + idx
prev_lambda = prev_vals[0]
prev_phi = prev_vals[1]
## not boundary condition
S, D = self.VT(prev_lambda)
new_lambda = self.sw**2 * S + self.su**2 * Xph + self.sb**2 ## took out an X
new_phi = new_lambda + self.sw**2 * prev_phi * D
lambda_expanded = T.expand_dims(new_lambda, axis=0)
phi_expanded = T.expand_dims(new_phi, axis=0)
to_return = T.concatenate([lambda_expanded, phi_expanded])
if idx in self.ends_of_calced_diags:
# self.save_vts[idx] = [S,D]
return boundary_condition, to_return
return to_return, to_return
last_ema, all_ema = T.scan(
fn,
init=boundary_condition,
sequences=[jnp.arange(0,
sum(self.dim_lengths) - self.dim_num)],
non_sequences=[self.X])
# if fbool:
# return all_ema, f
return self.compute_kernels(all_ema)
def compute_q(self, DATA):
DATAT = T.transpose(DATA)
xz = DATAT[0]
# print(xz)
init = self.su * 2 * T.linalg.norm(T.expand_dims(xz, axis = 0), ord = 2, axis = 0) + self.sb**2 + self.sh**2
# print("init", init)
# init = self.su * 2 * T.linalg.norm(xz, ord = 2) + self.sb**2 + self.sh**2 #make this a vectorized function
def scan_func(prevq, MINIDATAT): #MINIDATAT shuold be a vector of lenght N
# print(MINIDATAT)
# the trick to this one is to use the original VT
S = self.alg1_VT(prevq) # -> M is K3
# S = prevq
# newq = self.su * 2 * T.linalg.norm(T.expand_dims(xz, axis = 0), ord = 2, axis = 0) + self.sb**2 + self.sh**2
newq = self.sw*2 * S + self.su * 2 * T.linalg.norm(T.expand_dims(MINIDATAT, axis = 0), ord = 2, axis = 0) + self.sb**2
# print("newq", newq)
return newq, newq
last_ema, all_ema = T.scan(scan_func, init = init, sequences = [DATAT[1:]])
return T.concatenate([T.expand_dims(init, axis = 0), all_ema])
# this function should output the new value of the carry as well as an
# additional output, in our case, the carry (EMA) is also what we want to
# output at each tiem step
def fn(at, xt, alpha):
# the function first input is the carry, then are the (ordered)
# values from sequences and non_sequences similar to Theano
EMA = at * alpha + (1 - alpha) * xt
return EMA, EMA
# the scan function will return the carry at each time steps (first arg.)
# as well as the last one, we also need to provide an init.
last_ema, all_ema = T.scan(
fn, init=signal[0], sequences=[signal[1:]], non_sequences=[alpha]
)
f = symjax.function(signal, alpha, outputs=all_ema)
# generate a signal
x = np.cos(np.linspace(-3, 3, 512)) + np.random.randn(512) * 0.2
fig, ax = plt.subplots(3, 1, figsize=(3, 9))
for k, alpha in enumerate([0.1, 0.5, 0.9]):
ax[k].plot(x, c="b")
ax[k].plot(f(x, alpha), c="r")
ax[k].set_title("EMA: {}".format(alpha))
ax[k].set_xticks([])
def __init__(
self,
sequence,
init_h,
units,
Wf=initializers.glorot_uniform,
Uf=initializers.orthogonal,
bf=T.zeros,
Wi=initializers.glorot_uniform,
Ui=initializers.orthogonal,
bi=T.zeros,
Wo=initializers.glorot_uniform,
Uo=initializers.orthogonal,
bo=T.zeros,
Wc=initializers.glorot_uniform,
Uc=initializers.orthogonal,
bc=T.zeros,
trainable_Wf=True,
trainable_Uf=True,
trainable_bf=True,
trainable_Wi=True,
trainable_Ui=True,
trainable_bi=True,
trainable_Wo=True,
trainable_Uo=True,
trainable_bo=True,
trainable_Wc=True,
trainable_Uc=True,
trainable_bc=True,
activation_g=nn.sigmoid,
activation_c=T.tanh,
activation_h=T.tanh,
only_last=False,
gate="minimal",
):
self.create_variable("Wf",
Wf, (sequence.shape[2], units),
trainable=trainable_Wf)
self.create_variable("Uf", Uf, (units, units), trainable=trainable_Uf)
self.create_variable("bf", bf, (units, ), trainable=trainable_bf)
self.create_variable("Wi",
Wi, (sequence.shape[2], units),
trainable=trainable_Wi)
self.create_variable("Ui", Ui, (units, units), trainable=trainable_Ui)
self.create_variable("bi", bi, (units, ), trainable=trainable_bi)
self.create_variable("Wo",
Wo, (sequence.shape[2], units),
trainable=trainable_Wo)
self.create_variable("Uo", Uo, (units, units), trainable=trainable_Uo)
self.create_variable("bo", bo, (units, ), trainable=trainable_bo)
self.create_variable("Wc",
Wc, (sequence.shape[2], units),
trainable=trainable_Wc)
self.create_variable("Uc", Uc, (units, units), trainable=trainable_Uc)
self.create_variable("bc", bc, (units, ), trainable=trainable_bc)
def fn(*args):
return self.gate(*args, activation_g, activation_c, activation_h)
init = T.stack((init_h, T.zeros(init_h.shape, init_h.dtype)))
last, output = T.scan(
fn,
init=init,
sequences=[sequence.transpose((1, 0, 2))],
non_sequences=[
self.Wf,
self.Uf,
self.bf,
self.Wi,
self.Ui,
self.bi,
self.Wo,
self.Uo,
self.bo,
self.Wc,
self.Uc,
self.bc,
],
)
if only_last:
return last
else:
return output.transpose((1, 0, 2))
def __init__(
self,
sequence,
init_h,
units,
Wh=initializers.glorot_uniform,
Uh=initializers.orthogonal,
bh=T.zeros,
Wz=initializers.glorot_uniform,
Uz=initializers.orthogonal,
bz=T.zeros,
Wr=initializers.glorot_uniform,
Ur=initializers.orthogonal,
br=T.zeros,
trainable_Wh=True,
trainable_Uh=True,
trainable_bh=True,
trainable_Wz=True,
trainable_Uz=True,
trainable_bz=True,
trainable_Wr=True,
trainable_Ur=True,
trainable_br=True,
activation=nn.sigmoid,
phi=T.tanh,
only_last=False,
gate="minimal",
):
Wh = create_variable("Wh",
Wh, (sequence.shape[2], units),
trainable=trainable_Wh)
Uh = create_variable("Uh", Uh, (units, units), trainable=trainable_Uh)
bh = create_variable("bh", bh, (units, ), trainable=trainable_bh)
Wz = create_variable("Wz",
Wz, (sequence.shape[2], units),
trainable=trainable_Wz)
Uz = create_variable("Uz", Uz, (units, units), trainable=trainable_Uz)
bz = create_variable("bz", bz, (units, ), trainable=trainable_bz)
if gate == "full":
Wr = create_variable("Wr",
Wr, (sequence.shape[2], units),
trainable=trainable_Wr)
Ur = create_variable("Ur",
Ur, (units, units),
trainable=trainable_Ur)
br = create_variable("br", br, (units, ), trainable=trainable_br)
if gate == "minimal":
def fn(*args):
return GRU.minimal_gate(*args, activation, phi)
last, output = T.scan(
fn,
init=init_h,
sequences=[sequence.transpose((1, 0, 2))],
non_sequences=[Wh, Uh, bh, Wz, Uz, bz],
)
elif gate == "full":
def fn(*args):
return GRU.full_gate(*args, activation, phi)
last, output = T.scan(
fn,
init=init_h,
sequences=[sequence.transpose((1, 0, 2))],
non_sequences=[Wh, Uh, bh, Wz, Uz, bz, Wr, Ur, br],
)
if only_last:
return last
else:
return output.transpose((1, 0, 2))
import numpy as np
import sys
sys.path.insert(0, "../")
import symjax
import symjax.tensor as T
# map
xx = T.ones(10)
a = T.map(lambda a: a * 2, xx)
g = symjax.gradients(a.sum(), xx)[0]
f = symjax.function(outputs=[a, g])
# scan
xx = T.ones(10) * 2
a = T.scan(lambda c, x: (c * x, c * x), T.ones(1), xx)
g = symjax.gradients(a[1][-1], xx)[0]
f = symjax.function(outputs=[a, g])
# scan with updates
xx = T.range(5)
uu = T.ones((10, 2))
vvar = T.Variable(T.zeros((10, 2)))
vv = T.index_add(vvar, 1, 1)
a = T.scan(lambda c, x, p: (T.index_update(c, x, p[x]), 1), vv, xx, [vv])
#a = T.scan(lambda c, x: (c*x,c*x), T.ones(1), xx)
#a = T.scan(lambda c, x: (T.square(c),c[0]), uu, xx)
#g = symjax.gradients(a[1][-1],xx)
f = symjax.function(outputs=a[0], updates={vvar: vvar + 1})
print(f(), f(), f())
asdf
def forward(
self,
sequence,
init_h,
units,
Wh=initializers.he,
Uh=initializers.he,
bh=T.zeros,
Wz=initializers.he,
Uz=initializers.he,
bz=T.zeros,
Wr=initializers.he,
Ur=initializers.he,
br=T.zeros,
trainable_Wh=True,
trainable_Uh=True,
trainable_bh=True,
trainable_Wz=True,
trainable_Uz=True,
trainable_bz=True,
trainable_Wr=True,
trainable_Ur=True,
trainable_br=True,
activation=nn.sigmoid,
phi=T.tanh,
only_last=False,
gate="minimal",
):
self.create_variable("Wh",
Wh, (sequence.shape[2], units),
trainable=trainable_Wh)
self.create_variable("Uh", Uh, (units, units), trainable=trainable_Uh)
self.create_variable("bh", bh, (units), trainable=trainable_bh)
self.create_variable("Wz",
Wz, (sequence.shape[2], units),
trainable=trainable_Wz)
self.create_variable("Uz", Uz, (units, units), trainable=trainable_Uz)
self.create_variable("bz", bz, (units), trainable=trainable_bz)
if gate == "full":
self.create_variable("Wr",
Wr, (sequence.shape[2], units),
trainable=trainable_Wr)
self.create_variable("Ur",
Ur, (units, units),
trainable=trainable_Ur)
self.create_variable("br", br, (units), trainable=trainable_br)
if gate == "minimal":
def fn(h, x, Wh, Uh, bh, Wz, Uz, bz):
return self.minimal_gate(h, x, Wh, Uh, bh, Wz, Uz, bz,
activation, phi)
elif gate == "full":
def fn(h, x, Wh, Uh, bh, Wz, Uz, bz):
return self.full_gate(h, x, Wh, Uh, bh, Wz, Uz, bz, Wr, Ur, br,
activation, phi)
last, output = T.scan(
fn,
init=init_h,
sequences=[sequence.transpose((1, 0, 2))],
non_sequences=[self.W, self.H, self.b],
)
if only_last:
return last
else:
return output.transpose((1, 0, 2))
def create_func_for_diag(self):
NEW_DATA = self.reorganize_data()
NEW_DATA_ATTACHED = jnp.array(list(zip(NEW_DATA[:-1], NEW_DATA[1:])))
# print(NEW_DATA_ATTACHED)
x = self.DATA[:,0]
X = x*x[:, None]
boundary_condition = self.make_boundary_condition(X)
# #lets create the inital kernels - should be starting with top right
temp_K, temp_theta = self.compute_kernels(self.qt, self.qtprime, 0, self.dim_1, boundary_condition, boundary_condition, T.empty((self.N, self.N)), T.empty((self.N, self.N)))
init_K, init_theta = self.compute_kernels(self.qt, self.qtprime, 0, self.dim_1 - 1, boundary_condition, boundary_condition, temp_K, temp_theta)
initial_conditions = create_T_list([boundary_condition, boundary_condition, init_K, init_theta])
# initial_conditions = create_T_list([T.empty((self.N, self.N)), T.empty((self.N, self.N)), T.empty((self.N, self.N)), T.empty((self.N, self.N)) + 2])
## prev_vals - (4,self.N,self.N) - previous phi, lambda, and the two kernel values
## idx - where we are on the diagonal
def fn(prev_vals, idx, data_idxs, DATAPH, DATAPRIMEPH, qtph, qtprimeph):
xTP = DATAPRIMEPH[data_idxs[0][0]] #N1
xT = DATAPH[data_idxs[0][1]] #N2
xINNER = T.inner(xT, xTP) #N1 x N2
prev_lambda = prev_vals[0]
prev_phi = prev_vals[1]
prev_K = prev_vals[2]
prev_theta = prev_vals[3]
## not boundary condition
# print(qtph[data_idxs[0][1] - 1])
# print(qtprimeph[data_idxs[0][0] - 1])
S, D = self.alg2_VT(qtph[data_idxs[0][1] - 1], qtprimeph[data_idxs[0][0] - 1] ,prev_lambda)
new_lambda = self.sw ** 2 * S + self.su ** 2 * xINNER + self.sb ** 2 ## took out an X
new_phi = new_lambda + self.sw ** 2 * prev_phi * D
# new_phi = prev_phi
# new_lambda = prev_lambda
#compute kernels
S_kernel, D_kernel = self.alg2_VT(qtph[data_idxs[0][1]], qtprimeph[data_idxs[0][0]], new_lambda)
new_K = prev_K + self.sv**2 * S_kernel#get current lamnda, get current qtph and qtprimeph
new_theta = prev_theta + self.sv**2 * S_kernel + self.sv**2 * D_kernel * new_phi #TODO
# ret_K = prev_K
# ret_theta = prev_theta
equal_check = lambda e: T.equal(idx, e)
equal_result = sum(np.vectorize(equal_check)(self.ends_of_calced_diags)) > 0
def true_f(k,t, qp, gph, dataph, dataprimeph, di):
xTP_NEXT = dataprimeph[di[1][0]]
xT_NEXT = dataph[di[1][1]]
xINNER_NEXT = T.inner(xT_NEXT, xTP_NEXT)
new_bc = self.make_boundary_condition(xINNER_NEXT)
ret_lambda = ret_phi = new_bc
S_bc_kernel, D_bc_kernel = self.alg2_VT(qp[di[1][1]], gph[di[1][0]], ret_lambda)
ret_K = k + self.sv**2 * S_bc_kernel#get current lamnda, get current qtph and qtprimeph
ret_theta = t + self.sv**2 * S_bc_kernel + self.sv**2 * D_bc_kernel * ret_phi #TODO
return ret_lambda, ret_phi, ret_K, ret_theta
false_f = lambda l,p,k,t: (l,p,k,t)
ret_lambda, ret_phi, ret_K, ret_theta = T.cond(equal_result, true_f, false_f, [new_K, new_theta, qtph, qtprimeph, DATAPH, DATAPRIMEPH, data_idxs], [new_lambda, new_phi, new_K, new_theta])
to_carry = create_T_list([ret_lambda, ret_phi, ret_K, ret_theta])
# print('got poast second create list')
return to_carry, np.array(())
carry_ema, _ = T.scan(
fn, init = initial_conditions, sequences=[jnp.arange(0, sum(self.dim_lengths) - self.dim_num), NEW_DATA_ATTACHED], non_sequences=[T.transpose(self.DATA), T.transpose(self.DATAPRIME), self.qt, self.qtprime]
)
return carry_ema[2:4] ## so here, the output will be the added up kernels except for the boundary conditions
import sys
sys.path.insert(0, "../")
import symjax as sj
import symjax.tensor as T
import numpy as np
__author__ = "Randall Balestriero"
# example of cumulative sum
def func(carry, x):
return carry + 1, 0
output, _ = T.scan(func, T.zeros(1), T.ones(10), length=10)
f = sj.function(outputs=output)
print(f())
# [10.]
# example of simple RNN
w = T.Placeholder((3, 10), 'float32')
h = T.random.randn((3, 3))
b = T.random.randn((3, ))
t_steps = 100
X = T.random.randn((t_steps, 10))
def rnn_cell(carry, x, w):
