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bound_crown.py
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bound_crown.py
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## bound_crown.py
##
## Implementation of CROWN-adaptive and CROWN-general bounds
##
## Copyright (C) 2018, Huan Zhang <huan@huan-zhang.com> and contributors
##
## This program is licenced under the BSD 2-Clause License,
## contained in the LICENCE file in this directory.
## See CREDITS for a list of contributors.
##
from numba import jit, njit
import numpy as np
from activation_functions import *
from bound_interval import interval_bound
# for numba
linear_wrapper_constructed = False
leaky_wrapper = """
@njit
def get_leaky_relu_bounds_wrapper(UBs, LBs, neuron_states, bounds_ul, leaky_slope = {}): return get_leaky_relu_bounds(UBs, LBs, neuron_states, bounds_ul, leaky_slope)"""
sigmoid_family_ub_lb = """
@njit(cache=False)
def ub_pn(u, l):
return general_ub_pn(u, l, {0}, {1})
@njit(cache=False)
def lb_pn(u, l):
return general_lb_pn(u, l, {0}, {1})
@njit(cache=False)
def ub_p(u, l):
return general_ub_p (u, l, {0}, {1})
@njit(cache=False)
def lb_p(u, l):
return general_lb_p (u, l, {0}, {1})
@njit(cache=False)
def ub_n(u, l):
return general_ub_n (u, l, {0}, {1})
@njit(cache=False)
def lb_n(u, l):
return general_lb_n (u, l, {0}, {1})
"""
@jit(nopython=True,cache=False)
# def get_general_bounds(UBs, LBs, neuron_states, bounds_ul, ub_pn, lb_pn, ub_p, lb_p, ub_n, lb_n):
def get_general_bounds(UBs, LBs, neuron_states, bounds_ul):
# step 1: get indices of three classes of neurons
upper_k = bounds_ul[0]
upper_b = bounds_ul[1]
lower_k = bounds_ul[2]
lower_b = bounds_ul[3]
idx_p = np.nonzero(neuron_states == 1)[0]
idx_n = np.nonzero(neuron_states == -1)[0]
idx_pn = np.nonzero(neuron_states == 0)[0]
upper_k[idx_pn], upper_b[idx_pn] = ub_pn(UBs[idx_pn], LBs[idx_pn])
lower_k[idx_pn], lower_b[idx_pn] = lb_pn(UBs[idx_pn], LBs[idx_pn])
upper_k[idx_p], upper_b[idx_p] = ub_p(UBs[idx_p], LBs[idx_p])
lower_k[idx_p], lower_b[idx_p] = lb_p(UBs[idx_p], LBs[idx_p])
upper_k[idx_n], upper_b[idx_n] = ub_n(UBs[idx_n], LBs[idx_n])
lower_k[idx_n], lower_b[idx_n] = lb_n(UBs[idx_n], LBs[idx_n])
return upper_k, upper_b, lower_k, lower_b
# cannot unify the bounds calculation functions due to limitations of numba
@jit(nopython=True)
def get_relu_bounds(UBs, LBs, neuron_states, bounds_ul):
ub_pn = relu_ub_pn
lb_pn = relu_lb_pn
ub_p = relu_ub_p
lb_p = relu_lb_p
ub_n = relu_ub_n
lb_n = relu_lb_n
# step 1: get indices of three classes of neurons
upper_k = bounds_ul[0]
upper_b = bounds_ul[1]
lower_k = bounds_ul[2]
lower_b = bounds_ul[3]
idx_p = np.nonzero(neuron_states == 1)[0]
idx_n = np.nonzero(neuron_states == -1)[0]
idx_pn = np.nonzero(neuron_states == 0)[0]
upper_k[idx_pn], upper_b[idx_pn] = ub_pn(UBs[idx_pn], LBs[idx_pn])
lower_k[idx_pn], lower_b[idx_pn] = lb_pn(UBs[idx_pn], LBs[idx_pn])
upper_k[idx_p], upper_b[idx_p] = ub_p(UBs[idx_p], LBs[idx_p])
lower_k[idx_p], lower_b[idx_p] = lb_p(UBs[idx_p], LBs[idx_p])
upper_k[idx_n], upper_b[idx_n] = ub_n(UBs[idx_n], LBs[idx_n])
lower_k[idx_n], lower_b[idx_n] = lb_n(UBs[idx_n], LBs[idx_n])
return upper_k, upper_b, lower_k, lower_b
# cannot unify the bounds calculation functions due to limitations of numba
@jit(nopython=True)
def get_leaky_relu_bounds(UBs, LBs, neuron_states, bounds_ul, k):
ub_pn = lambda u, l: leaky_relu_ub_pn(u, l, k = k)
lb_pn = lambda u, l: leaky_relu_lb_pn(u, l, k = k)
ub_p = lambda u, l: leaky_relu_ub_p (u, l, k = k)
lb_p = lambda u, l: leaky_relu_lb_p (u, l, k = k)
ub_n = lambda u, l: leaky_relu_ub_n (u, l, k = k)
lb_n = lambda u, l: leaky_relu_lb_n (u, l, k = k)
# step 1: get indices of three classes of neurons
upper_k = bounds_ul[0]
upper_b = bounds_ul[1]
lower_k = bounds_ul[2]
lower_b = bounds_ul[3]
idx_p = np.nonzero(neuron_states == 1)[0]
idx_n = np.nonzero(neuron_states == -1)[0]
idx_pn = np.nonzero(neuron_states == 0)[0]
upper_k[idx_pn], upper_b[idx_pn] = ub_pn(UBs[idx_pn], LBs[idx_pn])
lower_k[idx_pn], lower_b[idx_pn] = lb_pn(UBs[idx_pn], LBs[idx_pn])
upper_k[idx_p], upper_b[idx_p] = ub_p(UBs[idx_p], LBs[idx_p])
lower_k[idx_p], lower_b[idx_p] = lb_p(UBs[idx_p], LBs[idx_p])
upper_k[idx_n], upper_b[idx_n] = ub_n(UBs[idx_n], LBs[idx_n])
lower_k[idx_n], lower_b[idx_n] = lb_n(UBs[idx_n], LBs[idx_n])
return upper_k, upper_b, lower_k, lower_b
def init_crown_bounds(Ws):
nlayer = len(Ws)
# preallocate all upper and lower bound slopes and intercepts
bounds_ul = [None] * nlayer
# first k is identity
bounds_ul[0] = np.ones((4,Ws[0].shape[1]), dtype=np.float32)
for i in range(1,nlayer):
bounds_ul[i] = np.empty((4,Ws[i].shape[1]), dtype=np.float32)
return bounds_ul
# we need to build this part of code dynamically due to the limit of numba
def compile_crown_bounds(activation, leaky_slope):
global linear_wrapper_constructed
if not linear_wrapper_constructed:
if activation == "relu":
exec("get_bounds = get_relu_bounds", globals())
if activation == "leaky":
code = compile(leaky_wrapper.format(leaky_slope), __file__, 'exec')
exec(code, globals())
exec("get_bounds = get_leaky_relu_bounds_wrapper", globals())
print("Leaky ReLU Slope: {:.3f}".format(leaky_slope))
elif activation == "tanh" or activation == "sigmoid" or activation == "arctan":
exec(sigmoid_family_ub_lb.format("act_" + activation, "act_" + activation + "_d"), globals())
exec("get_bounds = get_general_bounds", globals())
linear_wrapper_constructed = True
# adaptive matrix version of get_layer_bound_relax
# get_bounds should be defined somewhere else (as a numba function)
@jit(nopython=True)
def crown_general_bound(Ws,bs,UBs,LBs,neuron_state,nlayer,bounds_ul,x0,eps,p_n):
assert nlayer >= 2
assert nlayer == len(Ws) == len(bs) == len(UBs) == len(LBs) == (len(neuron_state) + 1) == len(bounds_ul)
assert p_n <= 2 or p_n == np.inf
# step 2: compute slopes and intercepts for upper and lower bounds
# only need to create upper/lower bounds' slope and intercept for this layer,
# slopes and intercepts for previous layers have been stored
# index: 0->slope for ub, 1->intercept for ub,
# 2->slope for lb, 3->intercept for lb
get_bounds(UBs[nlayer-1], LBs[nlayer-1], neuron_state[nlayer - 2], bounds_ul[nlayer-1])
# step 3: update matrix A (merged into one loop)
# step 4: adding all constants (merged into one loop)
constants_ub = np.copy(bs[-1]) # the last bias
constants_lb = np.copy(bs[-1]) # the last bias
# step 5: bounding l_n term for each layer
UB_final = np.zeros_like(constants_ub)
LB_final = np.zeros_like(constants_lb)
# first A is W_{nlayer} D_{nlayer}
# A_UB = Ws[nlayer-1] * diags[nlayer-1]
A_UB = np.copy(Ws[nlayer-1])
# A_LB = Ws[nlayer-1] * diags[nlayer-1]
A_LB = np.copy(Ws[nlayer-1])
for i in range(nlayer-1, 0, -1):
# create intercepts array for this layer
l_ub = np.empty_like(LBs[i])
l_lb = np.empty_like(LBs[i])
diags_ub = np.empty_like(bounds_ul[i][0,:])
diags_lb = np.empty_like(bounds_ul[i][0,:])
upper_k = bounds_ul[i][0]
upper_b = bounds_ul[i][1]
lower_k = bounds_ul[i][2]
lower_b = bounds_ul[i][3]
# bound the term A[i] * l_[i], for each element
for j in range(A_UB.shape[0]):
# index for positive entries in A for upper bound
idx_pos_ub = np.nonzero(A_UB[j] > 0)[0]
# index for negative entries in A for upper bound
idx_neg_ub = np.nonzero(A_UB[j] <= 0)[0]
# index for positive entries in A for lower bound
idx_pos_lb = np.nonzero(A_LB[j] > 0)[0]
# index for negative entries in A for lower bound
idx_neg_lb = np.nonzero(A_LB[j] <= 0)[0]
# for upper bound, set the neurons with positive entries in A to upper bound
diags_ub[idx_pos_ub] = upper_k[idx_pos_ub]
l_ub[idx_pos_ub] = upper_b[idx_pos_ub]
# for upper bound, set the neurons with negative entries in A to lower bound
diags_ub[idx_neg_ub] = lower_k[idx_neg_ub]
l_ub[idx_neg_ub] = lower_b[idx_neg_ub]
# for lower bound, set the neurons with negative entries in A to upper bound
diags_lb[idx_neg_lb] = upper_k[idx_neg_lb]
l_lb[idx_neg_lb] = upper_b[idx_neg_lb]
# for lower bound, set the neurons with positve entries in A to lower bound
diags_lb[idx_pos_lb] = lower_k[idx_pos_lb]
l_lb[idx_pos_lb] = lower_b[idx_pos_lb]
# compute the relavent terms
UB_final[j] += np.dot(A_UB[j], l_ub)
LB_final[j] += np.dot(A_LB[j], l_lb)
# update the j-th row of A with diagonal matrice
A_UB[j] = A_UB[j] * diags_ub
# update A with diagonal matrice
A_LB[j] = A_LB[j] * diags_lb
# constants of previous layers
constants_ub += np.dot(A_UB, bs[i-1])
constants_lb += np.dot(A_LB, bs[i-1])
# compute A for next loop
# diags matrices is multiplied above
A_UB = np.dot(A_UB, Ws[i-1])
A_LB = np.dot(A_LB, Ws[i-1])
# after the loop is done we get A0
# now we have obtained A_L x + b_L <= f(x) <= A_U x + b_U
# treat it as a one layer network and obtain bounds
UB_first, _ = interval_bound(A_UB, constants_ub, UBs[0], LBs[0], x0, eps, p_n)
_, LB_first = interval_bound(A_LB, constants_lb, UBs[0], LBs[0], x0, eps, p_n)
UB_final += UB_first
LB_final += LB_first
return UB_final, LB_final
# adaptive matrix version of get_layer_bound_relax
@jit(nopython=True)
def crown_adaptive_bound(Ws,bs,UBs,LBs,neuron_state,nlayer,diags,x0,eps,p_n,skip = False):
assert nlayer >= 2
assert nlayer == len(Ws) == len(bs) == len(UBs) == len(LBs) == (len(neuron_state) + 1) == len(diags)
# step 1: create auxillary arrays; we have only nlayer-1 layers of activations
# we only need to create for this new layer
idx_unsure = np.nonzero(neuron_state[nlayer - 2] == 0)[0]
# step 2: calculate all D matrices, there are nlayer such matrices
# only need to create diags for this layer
alpha = neuron_state[nlayer - 2].astype(np.float32)
np.maximum(alpha, 0, alpha)
# prefill diags with u/(u-l)
alpha[idx_unsure] = UBs[nlayer-1][idx_unsure]/(UBs[nlayer-1][idx_unsure] - LBs[nlayer-1][idx_unsure])
diags[nlayer-1][:] = alpha
# step 3: update matrix A (merged into one loop)
# step 4: adding all constants (merged into one loop)
constants_ub = np.copy(bs[-1]) # the last bias
constants_lb = np.copy(bs[-1]) # the last bias
# step 5: bounding l_n term for each layer
UB_final = np.zeros_like(constants_ub)
LB_final = np.zeros_like(constants_lb)
if skip:
return UB_final, LB_final
# first A is W_{nlayer} D_{nlayer}
# A_UB = Ws[nlayer-1] * diags[nlayer-1]
A_UB = np.copy(Ws[nlayer-1])
# A_LB = Ws[nlayer-1] * diags[nlayer-1]
A_LB = np.copy(Ws[nlayer-1])
for i in range(nlayer-1, 0, -1):
# unsure neurons of this layer
idx_unsure = np.nonzero(neuron_state[i-1] == 0)[0]
# create l array for this layer
l_ub = np.empty_like(LBs[i])
l_lb = np.empty_like(LBs[i])
# bound the term A[i] * l_[i], for each element
for j in range(A_UB.shape[0]):
l_ub[:] = 0.0
l_lb[:] = 0.0
diags_ub = np.copy(diags[i])
diags_lb = np.copy(diags[i])
# positive entries in j-th row, unsure neurons
pos_ub = np.nonzero(A_UB[j][idx_unsure] > 0)[0]
pos_lb = np.nonzero(A_LB[j][idx_unsure] > 0)[0]
# negative entries in j-th row, unsure neurons
neg_ub = np.nonzero(A_UB[j][idx_unsure] < 0)[0]
neg_lb = np.nonzero(A_LB[j][idx_unsure] < 0)[0]
# unsure neurons, corresponding to positive entries in the j-th row of A
idx_unsure_pos_ub = idx_unsure[pos_ub]
idx_unsure_pos_lb = idx_unsure[pos_lb]
# unsure neurons, corresponding to negative entries in the j-th row of A
idx_unsure_neg_ub = idx_unsure[neg_ub]
idx_unsure_neg_lb = idx_unsure[neg_lb]
# for upper bound, set the neurons with positive entries in A to upper bound
l_ub[idx_unsure_pos_ub] = LBs[i][idx_unsure_pos_ub]
# for upper bound, set the neurons with negative entries in A to lower bound, depending on the magnitude of LBs[i][idx_unsure_neg] and UBs[i][idx_unsure_neg]
mask = np.abs(LBs[i][idx_unsure_neg_ub]) > np.abs(UBs[i][idx_unsure_neg_ub])
# for |LB| > |UB|, use y = 0 as the lower bound, adjust A
diags_ub[idx_unsure_neg_ub[mask]] = 0.0
# for |LB| < |UB|, use y = x as the lower bound, adjust A
diags_ub[idx_unsure_neg_ub[np.logical_not(mask)]] = 1.0
# update the j-th row of A with diagonal matrice
A_UB[j] = A_UB[j] * diags_ub
# for lower bound, set the neurons with negative entries in A to upper bound
l_lb[idx_unsure_neg_lb] = LBs[i][idx_unsure_neg_lb]
# for upper bound, set the neurons with positive entries in A to lower bound, depending on the magnitude of LBs[i][idx_unsure_pos] and UBs[i][idx_unsure_pos]
mask = np.abs(LBs[i][idx_unsure_pos_lb]) > np.abs(UBs[i][idx_unsure_pos_lb])
# for |LB| > |UB|, use y = 0 as the lower bound, adjust A
diags_lb[idx_unsure_pos_lb[mask]] = 0.0
# for |LB| > |UB|, use y = x as the lower bound, adjust A
diags_lb[idx_unsure_pos_lb[np.logical_not(mask)]] = 1.0
# update A with diagonal matrice
A_LB[j] = A_LB[j] * diags_lb
# compute the relavent terms
UB_final[j] -= np.dot(A_UB[j], l_ub)
LB_final[j] -= np.dot(A_LB[j], l_lb)
# constants of previous layers
constants_ub += np.dot(A_UB, bs[i-1])
constants_lb += np.dot(A_LB, bs[i-1])
# compute A for next loop
A_UB = np.dot(A_UB, Ws[i-1])
A_LB = np.dot(A_LB, Ws[i-1])
# after the loop is done we get A0
# now we have obtained A_L x + b_L f(x) <= A_U x + b_U
# treat it as a one layer network and obtain bounds
UB_first, _ = interval_bound(A_UB, constants_ub, UBs[0], LBs[0], x0, eps, p_n)
_, LB_first = interval_bound(A_LB, constants_lb, UBs[0], LBs[0], x0, eps, p_n)
UB_final += UB_first
LB_final += LB_first
return UB_final, LB_final