def gen_embedding_rules(n: Node, symbols, embedding_dim, counter):
embedding_output, counter = gen_tvar(counter)
symbols[n] = embedding_output
embedding_input = symbols[n.args[0]]
input_dyn = BinConstraintT(embedding_input, Dyn, op_eq)
output_dyn = BinConstraintT(embedding_output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
c2 = []
for i in range(1, MAX_TENSOR_RANK):
new_dims, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims)
# we consider all tensor sizes and append embedding_dim to the end of the output dimension in all cases
c_tensor_i = Conj([
BinConstraintT(embedding_input, TensorType(new_dims), op_eq),
BinConstraintT(embedding_output,
TensorType(new_dims + [embedding_dim]), op_eq)
] + nat_constraints)
c2.append(c_tensor_i)
return [Disj([c1, Disj(c2)])], counter
def index_select_inference_rule(n: Node, symbols, constraints, counter):
"""
We constrain the second argument to a vector or Dyn.
The output replaces the input with the shape of the vector
at the position given by the index (first argument)
"""
# print(n.args)
assert isinstance(n.args[0], Node)
assert isinstance(n.args[1], int)
assert isinstance(n.args[2], Node)
index_select, counter = gen_tvar(counter)
symbols[n] = index_select
dims, counter = gen_tensor_dims(1, counter)
# equality constraint
is_size_1 = BinConstraintT(symbols[n.args[2]], TensorType(dims), op_eq)
is_dyn = BinConstraintT(symbols[n.args[2]], Dyn, op_eq)
c2 = Conj([is_size_1, Disj([IndexSelect(i + 1, symbols[n.args[0]], dims[0], n.args[1], index_select)
for i in range(MAX_TENSOR_RANK)])])
c3 = Conj([is_dyn, Disj([IndexSelect(i + 1, symbols[n.args[0]], Dyn, n.args[1], index_select)
for i in range(MAX_TENSOR_RANK)])])
return [Disj([c2, c3])], counter
def linear_inference_rule(n: Node, module_instance, symbols, constraints, counter):
"""
Input and output sizes should be the same except for the last dimension
If the input is Dyn, then so should the output
"""
assert isinstance(n.args[0], Node)
linear_output, counter = gen_tvar(counter)
symbols[n] = linear_output
linear_input = symbols[n.args[0]]
input_dyn = BinConstraintT(linear_input, Dyn, op_eq)
output_dyn = BinConstraintT(linear_output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
c2 = []
for i in range(1, MAX_TENSOR_RANK + 1):
new_dims_rhs_1, counter = gen_tensor_dims(i, counter)
new_dims_rhs_2, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims_rhs_1 + new_dims_rhs_2)
c_tensor_i = Conj([BinConstraintT(linear_input, TensorType(new_dims_rhs_1), op_eq),
BinConstraintT(linear_output, TensorType(new_dims_rhs_2), op_eq)] +
add_linear_constraints(new_dims_rhs_1, new_dims_rhs_2, module_instance) +
nat_constraints)
c2.append(c_tensor_i)
return [Disj([c1, Disj(c2)])], counter
def layer_norm_inference_rule(n: Node, module_instance, symbols, constraints, counter):
"""
Input and output shapes should be equal.
Input should be consistent with the normalized_shape
"""
assert isinstance(n.args[0], Node)
output, counter = gen_tvar(counter)
symbols[n] = output
input = symbols[n.args[0]]
input_dyn = BinConstraintT(input, Dyn, op_eq)
output_dyn = BinConstraintT(output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
c2 = []
for i in range(1, MAX_TENSOR_RANK + 1):
new_dims_rhs, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims_rhs)
c_tensor_i = Conj([BinConstraintT(input, TensorType(new_dims_rhs), op_eq),
BinConstraintT(output, TensorType(new_dims_rhs), op_eq)] +
add_layer_norm_constraints(new_dims_rhs, list(module_instance.normalized_shape)) +
nat_constraints)
c2.append(c_tensor_i)
return [Disj([c1, Disj(c2)])], counter
def arange_inference_rule(n: Node, symbols, constraints, counter):
start = 0
step = 1
if len(n.args) == 1:
end = symbols[n.args[0]]
else:
raise NotImplementedError('Not yet implemented')
# int((end - start) / step)
d1, counter = gen_dvar(counter)
size_constraint = BinConstraintD(d1, BinConstraintD(BinConstraintD(end, start, op_sub), step, op_div), op_eq)
arange, counter = gen_tvar(counter)
symbols[n] = arange
# either the a parameter is a number or it is Dyn
c1 = Disj([BinConstraintD(end, Dyn, op_eq),
BinConstraintD(start, Dyn, op_eq),
BinConstraintD(step, Dyn, op_eq)])
c2 = BinConstraintD(d1, Dyn, op_eq)
both_dyn = Conj([c1, c2])
c11 = Conj([BinConstraintD(end, Dyn, op_neq),
BinConstraintD(start, Dyn, op_neq),
BinConstraintD(step, Dyn, op_neq)])
c22 = BinConstraintD(d1, Dyn, op_neq)
both_numbers = Conj([c11, c22, size_constraint])
return [BinConstraintT(arange, TensorType([d1]), op_eq), Disj([both_dyn, both_numbers])], counter
def generate_calc_conv(constraint, counter):
d, counter = gen_tensor_dims(4, counter)
conv_result = TensorType([d[0], d[1], d[2], d[3]])
# the convolution result is a tensor of size 4
c1 = BinConstraintT(constraint.conv_result, conv_result, op_eq)
# the second dimension of the output is equal to the output channels
c2 = Conj([
BinConstraintD(d[1], constraint.c_out, op_eq),
BinConstraintD(d[1], Dyn, op_neq)
])
# the input corresponds to the output in the first dimension of the convolution
c3 = BinConstraintD(constraint.matching_constraint[0], d[0], op_eq)
c4, c5 = calc_last_two_dims(constraint, d)
leq_constraints = Conj([
BinConstraintD(0, d[0], op_leq),
BinConstraintD(0, d[1], op_leq),
BinConstraintD(0, d[2], op_leq),
BinConstraintD(0, d[3], op_leq)
])
return Conj([c1, c2, c3, c4, c5, leq_constraints]), counter
def cumsum_inference_rule(n: Node, symbols, constraints, counter):
"""
Input and output shapes should be equal
We should verify that the index is valid
"""
assert isinstance(n.args[0], Node)
arg_1 = n.args[1] if len(n.args) > 1 else n.kwargs["dim"]
assert isinstance(arg_1, int)
output, counter = gen_tvar(counter)
symbols[n] = output
input = symbols[n.args[0]]
input_dyn = BinConstraintT(input, Dyn, op_eq)
output_dyn = BinConstraintT(output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
c2 = []
for i in range(1, MAX_TENSOR_RANK + 1):
new_dims, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims)
c_tensor_i = Conj([BinConstraintT(input, TensorType(new_dims), op_eq),
BinConstraintT(output, TensorType(new_dims), op_eq)] +
[range_check(arg_1, i)] + nat_constraints)
c2.append(c_tensor_i)
dyn_or_tensor = Disj([c1, Disj(c2)])
return [dyn_or_tensor], counter
def no_broadcast_dim_with_index(d1: List[DVar], d2: List[DVar], d3: List[DVar],
d4: List[DVar], i: int):
"""
Args:
d1: inpput 1
d2: inpput 2
d3: simulated broadcasting for input 1
d4: simulated broadcasting for input 2
i: the rank of the resulting tensor addition
Returns: Constraints for when no broadcasting occurs
"""
return Conj([
Disj([
Conj([
BinConstraintD(d1[i], 1, op_eq),
BinConstraintD(d2[i], 1, op_eq)
]),
Conj([
BinConstraintD(d1[i], 1, op_neq),
BinConstraintD(d2[i], 1, op_neq)
])
]),
BinConstraintD(d1[i], d3[i], op_eq),
BinConstraintD(d2[i], d4[i], op_eq)
])
def embedding_inference_rule(n: Node, module_instance, symbols, constraints, counter):
"""
The output shape differs from the input shape in the last dimension
"""
assert isinstance(n.args[0], Node)
embedding_dim = module_instance.embedding_dim # number
embedding_output, counter = gen_tvar(counter)
symbols[n] = embedding_output
embedding_input = symbols[n.args[0]]
input_dyn = BinConstraintT(embedding_input, Dyn, op_eq)
output_dyn = BinConstraintT(embedding_output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
c2 = []
for i in range(1, MAX_TENSOR_RANK):
new_dims, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims)
# we consider all tensor sizes and append embedding_dim to the end of the output dimension in all cases
c_tensor_i = Conj([BinConstraintT(embedding_input, TensorType(new_dims), op_eq),
BinConstraintT(embedding_output, TensorType(new_dims + [embedding_dim]), op_eq)] +
nat_constraints)
c2.append(c_tensor_i)
return [Disj([c1, Disj(c2)])], counter
def bmm_inference_rule(n: Node, symbols, constraints, counter):
"""
Constraints that match the input to a size 3 tensor
and switch the dimensions according to the rules
of batch multiplication
"""
assert isinstance(n.args[0], Node)
assert isinstance(n.args[1], Node)
bmm_output, counter = gen_tvar(counter)
symbols[n] = bmm_output
bmm_input1 = symbols[n.args[0]]
bmm_input2 = symbols[n.args[1]]
dims_input1, counter = gen_tensor_dims(3, counter)
dims_input2, counter = gen_tensor_dims(3, counter)
inputs_dyn = Conj([
BinConstraintT(bmm_input1, Dyn, op_eq),
BinConstraintT(bmm_input2, Dyn, op_eq),
BinConstraintT(bmm_output, Dyn, op_eq)
])
input1_dyn = Conj([
BinConstraintT(bmm_input1, Dyn, op_eq),
BinConstraintT(bmm_input2, TensorType(dims_input2), op_eq),
BinConstraintT(bmm_output,
TensorType([dims_input2[0], Dyn, dims_input2[2]]),
op_eq)
])
input2_dyn = Conj([
BinConstraintT(bmm_input2, Dyn, op_eq),
BinConstraintT(bmm_input1, TensorType(dims_input1), op_eq),
BinConstraintT(bmm_output,
TensorType([dims_input1[0], dims_input1[1], Dyn]),
op_eq)
])
consistency_constraints = [
BinConstraintD(dims_input1[0], dims_input2[0], op_consistency)
]
batch_size, counter = gen_dvar(counter)
inputs_are_tensors = Conj([
BinConstraintT(bmm_input1, TensorType(dims_input1), op_eq),
BinConstraintT(bmm_input2, TensorType(dims_input2), op_eq),
BinConstraintT(
bmm_output,
TensorType([batch_size, dims_input1[1], dims_input2[2]]), op_eq),
*consistency_constraints,
DGreatestUpperBound(batch_size, dims_input1[0], dims_input2[0])
])
return [Disj([inputs_dyn, input1_dyn, input2_dyn,
inputs_are_tensors])], counter
def broadcasting_inference_rule(n: Node, symbols, constraints, counter):
op_code = None
if n.target == operator.add or n.target == torch.add:
op_code = op_add
elif n.target == operator.mul:
op_code = op_mul
if isinstance(n.args[0], Node) and isinstance(n.args[1], Node):
if isinstance(symbols[n.args[0]], TVar) and isinstance(symbols[n.args[1]], TVar):
my_output, counter = gen_tvar(counter)
symbols[n] = my_output
e1 = symbols[n.args[0]]
e2 = symbols[n.args[1]]
return gen_broadcasting_constraints(e1, e2, symbols, counter, my_output)
else:
raise NotImplementedError('Method not yet implemented')
elif isinstance(n.args[0], Node) and (isinstance(n.args[1], int) or isinstance(n.args[1], float)):
if isinstance(symbols[n.args[0]], TVar):
my_output, counter = gen_tvar(counter)
symbols[n] = my_output
e1 = symbols[n.args[0]]
return [BinConstraintT(my_output, e1, op_eq)], counter
elif isinstance(symbols[n.args[0]], DVar):
my_output, counter = gen_dvar(counter)
symbols[n] = my_output
e1 = symbols[n.args[0]]
# we will propagate the runtime value here since this is regular addition
c = Conj([BinConstraintD(my_output, BinConstraintD(e1, n.args[1], op_code), op_eq),
BinConstraintD(0, my_output, op_leq)])
return [c], counter
elif isinstance(n.args[1], Node) and (isinstance(n.args[0], int) or isinstance(n.args[1], float)):
if isinstance(symbols[n.args[1]], TVar):
my_output, counter = gen_tvar(counter)
symbols[n] = my_output
e2 = symbols[n.args[1]]
return [BinConstraintT(my_output, e2, op_eq)], counter
elif isinstance(symbols[n.args[1]], DVar):
my_output, counter = gen_dvar(counter)
symbols[n] = my_output
e2 = symbols[n.args[1]]
# we will propagate the runtime value here since this is regular addition
c = Conj([BinConstraintD(my_output, BinConstraintD(e2, n.args[0], op_code), op_eq),
BinConstraintD(0, my_output, op_leq)])
return [c], counter
else:
raise NotImplementedError('Method not yet implemented')
else:
# TODO generate add constraints for scalar addition
raise NotImplementedError('Addition not yet implemented')
def generate_calc_product(constraint, counter):
"""
Transform flatten constraints
"""
start = constraint.start
end = constraint.end
dims = constraint.dims_to_flatten
flattened = constraint.flattened
n = len(constraint.dims_to_flatten)
# this will be evaluated right here
boundary_check = (0 <= start and start < end and end <= n)
c_boundary = T() if boundary_check else F()
lhs = dims[0:start]
rhs = dims[end:]
mid = dims[start:end]
all_possibilities = generate_all_int_dyn_dim_possibilities(mid)
all_constraints = []
for p in all_possibilities:
p = list(p)
# this tells us there is a dynamic variable
contains_dyn = not (all([constraint.op == op_neq for constraint in p]))
if contains_dyn:
mid_var = [Dyn]
total_constraints = lhs + mid_var + rhs
if len(total_constraints) > 4:
all_constraints.append(F())
else:
all_constraints.append(
Conj([
BinConstraintT(flattened,
TensorType(lhs + mid_var + rhs), op_eq)
] + p))
else:
new_var, counter = gen_dvar(counter)
mid_eq_prod = Conj([
BinConstraintD(new_var, Prod(mid), op_eq),
BinConstraintD(new_var, Dyn, op_neq)
])
mid_var = [new_var]
total_constraints = lhs + mid_var + rhs
if len(total_constraints) > 4:
all_constraints.append(F())
else:
all_constraints.append(
Conj([
BinConstraintT(flattened,
TensorType(lhs + mid_var +
rhs), op_eq), mid_eq_prod
] + p))
return Conj([Disj(all_constraints), c_boundary]), counter
def getitem_inference_rule(n: Node, symbols, constraints, counter):
assert isinstance(n.args[0], Node)
# dimension output case
if isinstance(n.args[1], int):
# create and store the new dimension variable
get_item_output, counter = gen_dvar(counter)
symbols[n] = get_item_output
# retreive arg variables
get_item_arg = symbols[n.args[0]]
assert isinstance(get_item_arg, TVar)
# if the input is dynamic, we accept any index and return
# a dynamic dimension as output
input_dyn = BinConstraintT(get_item_arg, Dyn, op_eq)
output_dyn = BinConstraintD(get_item_output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
# if the input is a tensor,
# generate a getItem constraint which will be expanded based on the
# tensor dimension.
c2 = [
GetItem(i + 1, n.args[1], get_item_output, get_item_arg)
for i in range(MAX_TENSOR_RANK)
]
# since the output is a dimension, we make sure it's a natural number
# added as a conjunction to the disjuction of c2
c3 = BinConstraintD(0, get_item_output, op_leq)
return [Disj([c1, Conj([Disj(c2), c3])])], counter
# tensor output case
elif isinstance(n.args[1], tuple):
# create and store the new tensor variable
get_item_output, counter = gen_tvar(counter)
symbols[n] = get_item_output
# retreive arg variables
get_item_arg = symbols[n.args[0]]
assert isinstance(get_item_arg, TVar)
input_dyn = BinConstraintT(get_item_arg, Dyn, op_eq)
output_dyn = BinConstraintT(get_item_output, Dyn,
op_eq) # type: ignore[assignment]
c1 = Conj([input_dyn, output_dyn])
c2 = [
GetItemTensor(i + 1, n.args[1], get_item_output, get_item_arg)
for i in range(MAX_TENSOR_RANK)
] # type: ignore[misc]
return [Disj([c1, *c2])], counter
else:
raise RuntimeError('Method not yet implemented')
def generate_broadcasting(constraint, counter):
"""
Transform broadcasting constraints
"""
e11, e12 = constraint.res1, constraint.res2
e1, e2 = constraint.input1, constraint.input2
e1_dyn = BinConstraintT(e1, Dyn, op_eq)
e2_dyn = BinConstraintT(e2, Dyn, op_eq)
# Introduce dimensions
e1_equal_e11 = BinConstraintT(e1, e11, op_eq)
e2_equal_e12 = BinConstraintT(e2, e12, op_eq)
# dyn possibility
e1_dyn_constraint = Conj([e1_dyn, e1_equal_e11, e2_equal_e12])
e2_dyn_constraint = Conj([e2_dyn, e1_equal_e11, e2_equal_e12])
# tensor possibility
# generate dimensions to create tensors of size 1
final_tensor_1_constraint, _, _, nat_dims_1, counter = \
gen_broadcasting_constraints(e1, e2, e11, e12, 1, counter)
# generate dimensions to create tensors of size 2
final_tensor_2_constraint_no_padding, final_tensor_2_constraint_padding_arg1, \
final_tensor_2_constraint_padding_arg2, nat_dims_2, counter = \
gen_broadcasting_constraints(e1, e2, e11, e12, 2, counter)
# generate dimensions to create tensors of size 3
final_tensor_3_constraint_no_padding, final_tensor_3_constraint_padding_arg1, \
final_tensor_3_constraint_padding_arg2, nat_dims_3, counter = \
gen_broadcasting_constraints(e1, e2, e11, e12, 3, counter)
# generate dimensions to create tensors of size 4
final_tensor_4_constraint_no_padding, final_tensor_4_constraint_padding_arg1, \
final_tensor_4_constraint_padding_arg2, nat_dims_4, counter = \
gen_broadcasting_constraints(e1, e2, e11, e12, 4, counter)
final_result = Disj([
e1_dyn_constraint, e2_dyn_constraint, final_tensor_1_constraint,
final_tensor_2_constraint_no_padding,
final_tensor_2_constraint_padding_arg1,
final_tensor_2_constraint_padding_arg2,
final_tensor_3_constraint_no_padding,
final_tensor_3_constraint_padding_arg1,
final_tensor_3_constraint_padding_arg2,
final_tensor_4_constraint_no_padding,
final_tensor_4_constraint_padding_arg1,
final_tensor_4_constraint_padding_arg2
])
return Conj(
[final_result, *nat_dims_1, *nat_dims_2, *nat_dims_3,
*nat_dims_4]), counter
def transpose_inference_rule(n: Node, symbols, constraints, counter):
"""
Can be considered as a sequence of two index selects, so we generate constraints accordingly
"""
assert isinstance(n.args[0], Node)
assert isinstance(n.args[1], int)
assert isinstance(n.args[2], int)
output, counter = gen_tvar(counter)
symbols[n] = output
from_arg = symbols[n.args[0]]
assert isinstance(from_arg, TVar)
# input and output are dyn
is_dyn = Conj([
BinConstraintT(from_arg, Dyn, op_eq),
BinConstraintT(output, Dyn, op_eq)
])
# or input is a tensor and we actually do the replacement
c3 = Disj([
Transpose(i + 1, from_arg, n.args[1], n.args[2], output)
for i in range(MAX_TENSOR_RANK)
])
return [Disj([is_dyn, c3])], counter
def flatten_inference_rule(n: Node, symbols, constraints, counter):
assert isinstance(n.args[0], Node)
# generate the new variable
flattened, counter = gen_tvar(counter)
symbols[n] = flattened
input = symbols[n.args[0]]
# set the default start and end dims
start_dim = 1
end_dim = -1
if len(n.args) > 1:
assert isinstance(n.args[1], int)
start_dim = n.args[1]
if len(n.args) > 2:
assert isinstance(n.args[2], int)
end_dim = n.args[2]
c1 = BinConstraintT(input, Dyn, op_eq)
c2 = BinConstraintT(flattened, Dyn, op_eq)
both_dyn = Conj([c1, c2])
const = []
for i in range(1, MAX_TENSOR_RANK + 1):
c, counter = generate_flatten_constraints(start_dim, end_dim, input, flattened, i, counter)
const.append(c)
return [Disj([both_dyn, *const])], counter
def generate_all_broadcasting_possibilities_no_padding(d1: List[DVar],
d2: List[DVar],
d11: List[DVar],
d12: List[DVar]):
"""
Generate broadcasting constraints assuming no padding. Broadcasting can happen at any dimension.
We look at all combinations for all dimendions in d1 and d2
Args:
d1: input1 dimensions
d2: input2 dimensions
d11: broadcasted input1 dimensions
d12: broadcasted input2 dimensions
Returns: broadcasting constraints relating the input dimensions to the broadcasted dimensions
"""
size = len(d1)
res2 = []
for i in range(size):
t1 = broadcast_dim(d1, d2, d11, d12, i)
t2 = broadcast_dim(d2, d1, d12, d11, i)
t3 = no_broadcast_dim_with_index(d1, d2, d11, d12, i)
res2.append(Disj([t1, t2, t3]))
return Conj(res2)
def gen_consistency_constraints(constraint: Constraint, counter: int):
"""
Args:
constraint: Consistency constraint on tensors
counter: for variable tracking
Returns: Equality and consistency constraints on dimensions
"""
all_constraints = []
for i in range(1, MAX_TENSOR_RANK + 1):
new_dims_rhs_1, counter = gen_tensor_dims(i, counter)
new_dims_rhs_2, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims_rhs_1 + new_dims_rhs_2)
c_tensor_i = Conj([
BinConstraintT(constraint.lhs, TensorType(new_dims_rhs_1), op_eq),
BinConstraintT(constraint.rhs, TensorType(new_dims_rhs_2), op_eq)
] + [
BinConstraintD(d1, d2, op_consistency)
for d1, d2 in zip(new_dims_rhs_1, new_dims_rhs_2)
] + nat_constraints)
all_constraints.append(c_tensor_i)
return all_constraints, counter
def transform_get_item(constraint, counter):
"""
generate an equality of the form:
t = [a1, ..., an]
then generate constraints that check if the given index is valid
given this particular tensor size.
If the index is valid, generate a constraint to get the item
Note that we already handled the Dyn input case in the previous
step.
Args:
constraint: GetItem which assumes we are getting an item from a tensor (not Dyn)
counter: variable tracking
Returns: simplified constraints for GetItem
"""
dims, counter = gen_tensor_dims(constraint.tensor_size, counter)
nat_constraints = gen_nat_constraints(dims)
is_valid_index = valid_index(constraint.index, dims)
all_constraints = [
BinConstraintT(constraint.input_var, TensorType(dims), op_eq),
*nat_constraints, is_valid_index
]
# if the index is valid, we generate a constraint for getting an item
# otherwise this clause will have been UNSAT due to the wrong index
if is_valid_index == T():
all_constraints.append(
BinConstraintD(constraint.res, dims[constraint.index], op_eq))
return Conj(all_constraints), counter
def transform_get_item_tensor(constraint, counter):
"""
When the index is a tuple, then the output will be a tensor
TODO: we have to check if this is the case for all HF models
The cases we are covrering here are a tuple with one of:
- slice with default argument
- None
None appends 1 to the input tensor dimensions
so each occurrence of 'None' increases the rank by 1
slice with default arguments does not change the rank
"""
assert isinstance(constraint.index_tuple, tuple)
# generate a result tensor of the expected size
dims, counter = gen_tensor_dims(constraint.tensor_size, counter)
nat_constraints = gen_nat_constraints(dims)
# generate a place-holder list of the right rank
# where "slice" does not contribute to the rank and "None" does
none_c = constraint.index_tuple.count(None)
resulting_tensor_dims = (none_c + len(dims)) * [None]
dim_index = 0
for i in range(len(constraint.index_tuple)):
# append 1 to the right location of the resulting tensor
if constraint.index_tuple[i] is None:
resulting_tensor_dims[i] = 1
elif constraint.index_tuple[i] == slice(None, None, None):
pass
else:
raise NotImplementedError('Method not yet implemented')
# append the remaining dimensions to the right location
dim_index = 0
for i in range(len(resulting_tensor_dims)):
if resulting_tensor_dims[i] is None:
resulting_tensor_dims[i] = dims[dim_index]
dim_index += 1
# check if the index is valid
is_valid_index = valid_index_tensor(constraint.index_tuple, dims)
# check if the resulting tensor is within bounds
if len(resulting_tensor_dims) > 4:
return F(), counter
else:
constraints = [
BinConstraintT(constraint.input_var, TensorType(dims), op_eq),
BinConstraintT(constraint.res, TensorType(resulting_tensor_dims),
op_eq), *nat_constraints, is_valid_index
]
return Conj(constraints), counter
def generate_flatten_constraints(start_dim, end_dim, input, flattened, n, counter):
d, counter = gen_tensor_dims(n, counter)
c1 = BinConstraintT(input, TensorType(d), op_eq)
start_dim = n if start_dim == -1 else abs(start_dim)
end_dim = n + end_dim + 1 if end_dim < 0 else end_dim + 1
c2 = CalcProduct(start_dim, end_dim, flattened, d)
nat_constraints = gen_nat_constraints(d)
return Conj([c1, c2, *nat_constraints]), counter
def generate_d_gub(constraint, counter):
"""
Transform greatest upper bound for dimensions into equality constraints
"""
c1 = Conj([
BinConstraintD(constraint.rhs1, Dyn, op_eq),
BinConstraintD(constraint.res, constraint.rhs2, op_eq)
])
c2 = Conj([
BinConstraintD(constraint.rhs2, Dyn, op_eq),
BinConstraintD(constraint.res, constraint.rhs1, op_eq)
])
c3 = Conj([
BinConstraintD(constraint.rhs2, constraint.rhs1, op_eq),
BinConstraintD(constraint.res, constraint.rhs1, op_eq)
])
return Disj([c1, c2, c3]), counter
def generate_conj(constraint, counter):
"""
Transform conjunctions
"""
new = []
for c in constraint.conjucts:
new_c, counter = transform_constraint(c, counter)
new.append(new_c)
return Conj(new), counter
def apply_padding(e1_var: TVar, e11: BinConstraintT, e2: BinConstraintT,
e12: BinConstraintT, d2: List[DVar], d11: List[DVar],
d12: List[DVar], counter: int):
"""
We are considering the possibility where one input has less dimensions than
another input, so we apply padding to the broadcasted results
Args:
e1_var: Variable representing the first input where padding will be
e11: constraint of the form e11 = Tensortype[d1, ..., dn]
e2: constraint of the form e2 = Tensortype[d1, ..., dn]
e12: constraint of the form e11 = Tensortype[d1, ..., dn]
d2: Tensor variables for the second input
d11: Tensor variables for the broadcasted first input
d12: Tensor variables for the broadcasted second input
counter: variable tracking
Returns: A new constraint whose goal is to apply padding to the broadcasted result
"""
res = []
# pad the shorter input with None so we can pass it to the broadcasting helper function
for i in range(1, len(d2)):
d1, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(d1 + d2 + d11 + d12)
e1 = BinConstraintT(e1_var, TensorType(d1), op_eq)
simulate_padding = [None] * (len(d2) - i)
assert len(simulate_padding + d1) == len(d2)
broadcast_padding = []
# for every padding size, we also consider broadcasting
for j in range((len(d2) - i)):
broadcast_padding.append(
broadcast_dim(simulate_padding, d2, d11, d12, j, True))
# we consider the possibilities for broadcasting for every dimension. Since we already
# padded d1, we do not consider it while broadcasting
all_broadcasting_possibilities = generate_all_broadcasting_possibilities_no_padding(
d1, d2[(len(d2) - i):], d11[(len(d2) - i):], d12[(len(d2) - i):])
# combine all constraints into a conjunction
c = Conj([
e1, e11, e2, e12, *broadcast_padding,
all_broadcasting_possibilities, *nat_constraints
])
res.append(c)
return Disj(res), counter
def gen_all_reshape_possibilities(list_of_dims, target):
"""
Consider all possibilities what the input dimensions could be (number or dynamic)
Then generate the appropriate constraints using multiplication or mod depending on the possibility
The possibilities we consider here are the cross product of being equal to dyn or not equal to dyn
for the input. Target is fixed because at most one dimension could be dyn.
We have different cases for this.
Args:
list_of_dims: The input list of dimensions
target: The tensor we want to reshape to
Returns: A disjuncition of transformed reshape constraints
"""
all_possibilities = generate_all_int_dyn_dim_possibilities(list_of_dims)
all_constraints = []
for p in all_possibilities:
to_multiply = []
p = list(p)
for constraint in p:
assert isinstance(constraint, BinConstraintD)
if constraint.op == op_neq:
to_multiply.append(constraint.lhs)
if not to_multiply:
all_constraints.append(Conj(p))
elif len(to_multiply) < len(list_of_dims):
all_constraints.append(
Conj(p + [is_target_div_by_dim(target, Prod(to_multiply))]))
else:
all_constraints.append(
Conj(
p +
[BinConstraintD(Prod(list_of_dims), Prod(target), op_eq)]))
return Disj(all_constraints)
def torch_dim_inference_rule(n: Node, symbols, constraints, counter):
assert isinstance(n.args[0], Node)
my_dim, counter = gen_dvar(counter)
symbols[n] = my_dim
input = symbols[n.args[0]]
input_dyn = BinConstraintT(input, Dyn, op_eq)
output_dyn = BinConstraintD(my_dim, Dyn, op_eq)
c1 = []
for i in range(1, MAX_TENSOR_RANK + 1):
new_dims_rhs_1, counter = gen_tensor_dims(i, counter)
c_tensor_i = Conj([
BinConstraintT(input, TensorType(new_dims_rhs_1), op_eq),
BinConstraintD(my_dim, i, op_eq)
])
c1.append(c_tensor_i)
return [Disj([Conj([input_dyn, output_dyn]), Disj(c1)])], counter
def gen_layer_norm_constraints(n: Node, normalized_shape, symbols, counter):
output, counter = gen_tvar(counter)
symbols[n] = output
input = symbols[n.args[0]]
input_dyn = BinConstraintT(input, Dyn, op_eq)
output_dyn = BinConstraintT(output, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
c2 = []
for i in range(1, MAX_TENSOR_RANK + 1):
new_dims_rhs, counter = gen_tensor_dims(i, counter)
nat_constraints = gen_nat_constraints(new_dims_rhs)
c_tensor_i = Conj([
BinConstraintT(input, TensorType(new_dims_rhs), op_eq),
BinConstraintT(output, TensorType(new_dims_rhs), op_eq)
] + add_layer_norm_constraints(new_dims_rhs, list(normalized_shape)) +
nat_constraints)
c2.append(c_tensor_i)
return [Disj([c1, Disj(c2)])], counter
def generate_constraints(self, counter=0):
"""
Iterate through every node and generate constraints
Effect: self.constraints will be populated with the final constraints
"""
graph = self.traced.graph
all_constraints = []
for n in graph.nodes:
(constraints, counter) = self.generate_constraints_node(n, counter)
all_constraints += constraints
return Conj(all_constraints), counter
def size_inference_rule(n: Node, symbols, constraints, counter):
"""
The constraint is just lhs = rhs.
Ex: size = input_ids.size()
"""
if len(n.args) == 1:
# generate the new variable
size, counter = gen_tvar(counter)
symbols[n] = size
input = symbols[n.args[0]]
c = BinConstraintT(input, size, op_eq)
return [c], counter
elif len(n.args) == 2:
# TODO: review this rule; should input = dyn; output = dyn be included here?
if isinstance(n.args[1], int):
# generate the new variable
size_index, counter = gen_dvar(counter)
symbols[n] = size_index
input = symbols[n.args[0]]
c2 = [
GetItem(i + 1, n.args[1], size_index, input)
for i in range(MAX_TENSOR_RANK)
]
c3 = BinConstraintD(0, size_index, op_leq)
input_dyn = BinConstraintT(input, Dyn, op_eq)
output_dyn = BinConstraintD(size_index, Dyn, op_eq)
c1 = Conj([input_dyn, output_dyn])
return [Disj([c1, Conj([Disj(c2), c3])])], counter
else:
raise NotImplementedError
else:
raise NotImplementedError
def generate_calc_maxpool(constraint, counter):
"""
Transform maxpool constraints
"""
d, counter = gen_tensor_dims(4, counter)
maxpool_result = TensorType([d[0], d[1], d[2], d[3]])
# the maxpool result is a tensor of size 4
c1 = BinConstraintT(constraint.maxpool_result, maxpool_result, op_eq)
# the input corresponds to the output in the first and second dimension of maxpool
c2 = BinConstraintD(constraint.matching_constraint[1], d[1], op_eq)
c3 = BinConstraintD(constraint.matching_constraint[0], d[0], op_eq)
c4, c5 = calc_last_two_dims(constraint, d)
leq_constraints = Conj([
BinConstraintD(0, d[0], op_leq),
BinConstraintD(0, d[1], op_leq),
BinConstraintD(0, d[2], op_leq),
BinConstraintD(0, d[3], op_leq)
])
return Conj([c1, c2, c3, c4, c5, leq_constraints]), counter
