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 conv2d_inference_rule(n: Node, module_instance, symbols, constraints, counter): assert isinstance(n.args[0], Node) my_conv, counter = gen_tvar(counter) symbols[n] = my_conv input_var = symbols[n.args[0]] # dim vars [d1, d2, d3, d4], counter = gen_tensor_dims(MAX_TENSOR_RANK, counter) # c1 = Matching(input_var, TensorType([d1, d2, d3, d4])) c1 = BinConstraintT(input_var, TensorType([d1, d2, d3, d4]), op_matching) # c2 = DConsistency(module_instance.in_channels, d2) c2 = BinConstraintD(module_instance.in_channels, d2, op_consistency) c3 = CalcConv(my_conv, input_var, module_instance.out_channels, module_instance.kernel_size, module_instance.padding, module_instance.stride, module_instance.dilation, [d1, d2, d3, d4]) nat_constraints = gen_nat_constraints([d1, d2, d3, d4]) return [c1, c2, c3, *nat_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 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 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 expand_inference_rule(n: Node, symbols, constraints, counter): """ We generate the exact constraints as we do for tensor additions but we constraint the rank of this expression to be equal to len(n.args[1:]) so that only those cases get considered for the output """ assert isinstance(n.args[0], Node) # define the output for expand expand, counter = gen_tvar(counter) symbols[n] = expand # since we do not have two nodes here, we will construct an argument variable e1 = symbols[n.args[0]] e2, counter = gen_tvar(counter) e2_nat_constraints = [] for arg in n.args[1:]: assert isinstance(arg, Node) or isinstance(arg, int) if isinstance(arg, Node): assert isinstance(symbols[arg], DVar) e2_nat_constraints.append(BinConstraintD(0, symbols[arg], op_leq)) e2_constraint = BinConstraintT(e2, TensorType([arg if isinstance(arg, int) else symbols[arg] for arg in n.args[1:]]), op_eq) constraints, counter = gen_broadcasting_constraints(e1, e2, symbols, counter, expand) # constraint the output size dims, counter = gen_tensor_dims(len(n.args[1:]), counter) nat_constraints = gen_nat_constraints(dims) c = [BinConstraintT(expand, TensorType(dims), op_eq), *nat_constraints, e2_constraint, *e2_nat_constraints] constraints += c return constraints, counter
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 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 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 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_broadcasting_constraints(e1: TVar, e2: TVar, e11: TVar, e12: TVar, i: int, counter: int): """ Simulates broadcasting on e1 and e2 and returns the results respectively in e11 and e12. Because of gradual types, e1 and e2 may not be equal. Similarly, e11 and e12 may not be equal. e11 and e12 should be guaranteed to be consistent as they represent the shapes of the tensors to be added after broadcasting. Args: e1: TVar representing the type of input 1 e2: TVar representing the type of input 2 e11: TVar representing the representing broadcasted input 1 e12: TVar representing the representing broadcasted input 2 i: The rank of the resulting type of addition counter: for variable tracking Returns: Simplified broadcasting constraints """ dims, counter = gen_lists_of_dims(4, i, counter) [d1, d2, d3, d4] = dims nat_dims_i = gen_nat_constraints(list(itertools.chain(*dims))) initialize_tensors_constraints = create_equality_constraints_for_broadcasting( e1, e2, e11, e12, d1, d2, d3, d4) [e1_tensor, e11_tensor, e2_tensor, e12_tensor] = initialize_tensors_constraints # without padding, broadcast all possibilities for tensors of size i final_tensor_constraint_no_padding = Conj([ *initialize_tensors_constraints, generate_all_broadcasting_possibilities_no_padding(d1, d2, d3, d4) ]) # with padding, broadcast all possibilities for tensors of size i final_tensor_constraint_padding_arg1, counter = \ apply_padding(e1, e11_tensor, e2_tensor, e12_tensor, d2, d3, d4, counter) final_tensor_constraint_padding_arg2, counter = \ apply_padding(e2, e12_tensor, e1_tensor, e11_tensor, d1, d4, d3, counter) return final_tensor_constraint_no_padding, \ final_tensor_constraint_padding_arg1, \ final_tensor_constraint_padding_arg2, nat_dims_i, counter
def maxpool_inference_rule(n: Node, module_instance, symbols, constraints, counter): assert isinstance(n.args[0], Node) maxpool, counter = gen_tvar(counter) symbols[n] = maxpool input_var = symbols[n.args[0]] # dim vars [d1, d2, d3, d4], counter = gen_tensor_dims(MAX_TENSOR_RANK, counter) c1 = BinConstraintT(input_var, TensorType([d1, d2, d3, d4]), op_matching) c2 = CalcMaxPool(maxpool, input_var, module_instance.kernel_size, module_instance.padding, module_instance.stride, module_instance.dilation, [d1, d2, d3, d4]) nat_constraints = gen_nat_constraints([d1, d2, d3, d4]) return [c1, c2, *nat_constraints], counter
def adaptive_inference_rule(n: Node, module_instance, symbols, constraints, counter): assert isinstance(n.args[0], Node) avg_pool, counter = gen_tvar(counter) symbols[n] = avg_pool input_var = symbols[n.args[0]] # dim vars d1, counter = gen_dvar(counter) d2, counter = gen_dvar(counter) d3, counter = gen_dvar(counter) d4, counter = gen_dvar(counter) nat_constraints = gen_nat_constraints([d1, d2, d3, d4]) c1 = BinConstraintT(input_var, TensorType([d1, d2, d3, d4]), op_matching) c2 = BinConstraintT(avg_pool, TensorType([d1, d2, module_instance.output_size[0], module_instance.output_size[1]]), op_eq) return [c1, c2, *nat_constraints], counter
def batchnorm_inference_rule(n: Node, module_instance, symbols, constraints, counter): assert isinstance(n.args[0], Node) # generate the new variable batchnorm_output, counter = gen_tvar(counter) symbols[n] = batchnorm_output batchnorm_input = symbols[n.args[0]] # dim vars d1, counter = gen_dvar(counter) d2, counter = gen_dvar(counter) d3, counter = gen_dvar(counter) d4, counter = gen_dvar(counter) nat_constraints = gen_nat_constraints([d1, d2, d3, d4]) c1 = BinConstraintT(batchnorm_input, TensorType([d1, d2, d3, d4]), op_matching) c2 = BinConstraintT(batchnorm_input, batchnorm_output, op_eq) return [c1, c2, *nat_constraints], counter
def transform_transpose(constraint, counter): """ Similar to a sequence of two index-selects """ dims, counter = gen_tensor_dims(constraint.tensor_size, counter) is_valid_index1 = valid_index(constraint.index1, dims) is_valid_index2 = valid_index(constraint.index2, dims) new_dims = copy.deepcopy(dims) nat_constraints = gen_nat_constraints(dims) if is_valid_index1 == T() and is_valid_index2 == T(): new_dims[constraint.index1] = dims[constraint.index2] new_dims[constraint.index2] = dims[constraint.index1] transformed_constraint = Conj([ BinConstraintT(constraint.input_var, TensorType(dims), op_eq), *nat_constraints, is_valid_index1, is_valid_index2, BinConstraintT(constraint.output, TensorType(new_dims), op_eq) ]) return transformed_constraint, 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 gen_greatest_upper_bound(constraint: TGreatestUpperBound, counter: int): """ Args: constraint: Greatest upper bound on tensors counter: variable tracking Returns: A set of equality constraints and DGreatestUpperBound constraints """ all_constraints = [] for i in range(1, MAX_TENSOR_RANK + 1): c = [] dims1, counter = gen_tensor_dims(i, counter) c1tensor = TensorType(dims1) dims2, counter = gen_tensor_dims(i, counter) c2tensor = TensorType(dims2) dims3, counter = gen_tensor_dims(i, counter) c3tensor = TensorType(dims3) c += [BinConstraintT(constraint.rhs1, c1tensor, op_eq), BinConstraintT(constraint.rhs2, c2tensor, op_eq), BinConstraintT(constraint.res, c3tensor, op_eq)] + \ gen_nat_constraints(dims1 + dims2 + dims3) assert len(c3tensor.__args__) == len(c1tensor.__args__) == len( c2tensor.__args__) for i in range(len(c3tensor.__args__)): c.append( DGreatestUpperBound(c3tensor.__args__[i], c1tensor.__args__[i], c2tensor.__args__[i])) all_constraints.append(Conj(c)) return all_constraints, counter
def linear_constraints(n: Node, in_features, out_features, symbols, counter): 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, in_features, out_features) + nat_constraints) c2.append(c_tensor_i) return [Disj([c1, Disj(c2)])], counter
def transform_index_select(constraint, counter): """ The constraints consider the given tensor size, checks if the index is valid and if so, generates a constraint for replacing the input dimension with the required dimension """ dims, counter = gen_tensor_dims(constraint.tensor_size, counter) is_valid_index = valid_index(constraint.index, dims) nat_constraints = gen_nat_constraints(dims) # if the index is valid then replace the input dimension with the new dimension # otherwise the dimension will not be replaced and the clause will contain False if is_valid_index == T(): new_dims = copy.deepcopy((dims)) new_dims[constraint.index] = constraint.dim_replace transformed_constraint = Conj([ BinConstraintT(constraint.input_var, TensorType(dims), op_eq), *nat_constraints, is_valid_index, BinConstraintT(constraint.output, TensorType(new_dims), op_eq) ]) # print(constraints) return transformed_constraint, counter