"""A single training/test example for simple sequence classification.

def __init__(self,

qas_id,

question_text,

doc_tokens,

orig_answer_text=None,

start_position=None,

end_position=None,

is_impossible=False):

self.qas_id = qas_id

self.question_text = question_text

self.doc_tokens = doc_tokens

self.orig_answer_text = orig_answer_text

self.start_position = start_position

self.end_position = end_position

self.is_impossible = is_impossible

def __str__(self):

return self.__repr__()

def __repr__(self):

s = ""

s += "qas_id: %s" % (tokenization.printable_text(self.qas_id))

s += ", question_text: %s" % (

tokenization.printable_text(self.question_text))

s += ", doc_tokens: [%s]" % (" ".join(self.doc_tokens))

if self.start_position:

s += ", start_position: %d" % (self.start_position)

if self.start_position:

s += ", end_position: %d" % (self.end_position)

if self.start_position:

s += ", is_impossible: %r" % (self.is_impossible)

"""A single set of features of data."""

def __init__(self,

unique_id,

example_index,

doc_span_index,

tokens,

token_to_orig_map,

token_is_max_context,

input_ids,

input_mask,

segment_ids,

start_position=None,

end_position=None,

is_impossible=None):

self.unique_id = unique_id

self.example_index = example_index

self.doc_span_index = doc_span_index

self.tokens = tokens

self.token_to_orig_map = token_to_orig_map

self.token_is_max_context = token_is_max_context

self.input_ids = input_ids

self.input_mask = input_mask

self.segment_ids = segment_ids

self.start_position = start_position

self.end_position = end_position

"""Read a SQuAD json file into a list of SquadExample."""

with open(input_file, "r") as reader:

input_data = json.load(reader)["data"]

def is_whitespace(c):

if c == " " or c == "\t" or c == "\r" or c == "\n" or ord(c) == 0x202F:

return True

return False

examples = []

for entry in input_data:

for paragraph in entry["paragraphs"]:

paragraph_text = paragraph["context"]

doc_tokens = []

char_to_word_offset = []

prev_is_whitespace = True

for c in paragraph_text:

if is_whitespace(c):

prev_is_whitespace = True

else:

if prev_is_whitespace:

doc_tokens.append(c)

else:

doc_tokens[-1] += c

prev_is_whitespace = False

char_to_word_offset.append(len(doc_tokens) - 1)

for qa in paragraph["qas"]:

qas_id = qa["id"]

question_text = qa["question"]

start_position = None

end_position = None

orig_answer_text = None

is_impossible = False

if is_training:

if version_2_with_negative:

is_impossible = qa["is_impossible"]

if (len(qa["answers"]) != 1) and (not is_impossible):

raise ValueError(

"For training, each question should have exactly 1 answer."

)

if not is_impossible:

answer = qa["answers"][0]

orig_answer_text = answer["text"]

answer_offset = answer["answer_start"]

answer_length = len(orig_answer_text)

start_position = char_to_word_offset[answer_offset]

end_position = char_to_word_offset[answer_offset +

answer_length - 1]

# Only add answers where the text can be exactly recovered from the

# document. If this CAN'T happen it's likely due to weird Unicode

# stuff so we will just skip the example.

#

# Note that this means for training mode, every example is NOT

# guaranteed to be preserved.

actual_text = " ".join(doc_tokens[start_position:(

end_position + 1)])

cleaned_answer_text = " ".join(

tokenization.whitespace_tokenize(orig_answer_text))

if actual_text.find(cleaned_answer_text) == -1:

print("Could not find answer: '%s' vs. '%s'",

actual_text, cleaned_answer_text)

continue

else:

start_position = -1

end_position = -1

orig_answer_text = ""

example = SquadExample(

qas_id=qas_id,

question_text=question_text,

doc_tokens=doc_tokens,

orig_answer_text=orig_answer_text,

start_position=start_position,

end_position=end_position,

is_impossible=is_impossible)

examples.append(example)

examples,

tokenizer,

max_seq_length,

doc_stride,

max_query_length,

is_training,

#output_fn

):

"""Loads a data file into a list of `InputBatch`s."""

unique_id = 1000000000

for (example_index, example) in enumerate(examples):

query_tokens = tokenizer.tokenize(example.question_text)

if len(query_tokens) > max_query_length:

query_tokens = query_tokens[0:max_query_length]

tok_to_orig_index = []

orig_to_tok_index = []

all_doc_tokens = []

for (i, token) in enumerate(example.doc_tokens):

orig_to_tok_index.append(len(all_doc_tokens))

sub_tokens = tokenizer.tokenize(token)

for sub_token in sub_tokens:

tok_to_orig_index.append(i)

all_doc_tokens.append(sub_token)

tok_start_position = None

tok_end_position = None

if is_training and example.is_impossible:

tok_start_position = -1

tok_end_position = -1

if is_training and not example.is_impossible:

tok_start_position = orig_to_tok_index[example.start_position]

if example.end_position < len(example.doc_tokens) - 1:

tok_end_position = orig_to_tok_index[example.end_position +

1] - 1

else:

tok_end_position = len(all_doc_tokens) - 1

(tok_start_position, tok_end_position) = _improve_answer_span(

all_doc_tokens, tok_start_position, tok_end_position, tokenizer,

example.orig_answer_text)

# The -3 accounts for [CLS], [SEP] and [SEP]

max_tokens_for_doc = max_seq_length - len(query_tokens) - 3

# We can have documents that are longer than the maximum sequence length.

# To deal with this we do a sliding window approach, where we take chunks

# of the up to our max length with a stride of `doc_stride`.

_DocSpan = collections.namedtuple( # pylint: disable=invalid-name

"DocSpan", ["start", "length"])

doc_spans = []

start_offset = 0

while start_offset < len(all_doc_tokens):

length = len(all_doc_tokens) - start_offset

if length > max_tokens_for_doc:

length = max_tokens_for_doc

doc_spans.append(_DocSpan(start=start_offset, length=length))

if start_offset + length == len(all_doc_tokens):

break

start_offset += min(length, doc_stride)

for (doc_span_index, doc_span) in enumerate(doc_spans):

tokens = []

token_to_orig_map = {}

token_is_max_context = {}

segment_ids = []

tokens.append("[CLS]")

segment_ids.append(0)

for token in query_tokens:

tokens.append(token)

segment_ids.append(0)

tokens.append("[SEP]")

segment_ids.append(0)

for i in range(doc_span.length):

split_token_index = doc_span.start + i

token_to_orig_map[len(tokens)] = tok_to_orig_index[

split_token_index]

is_max_context = _check_is_max_context(

doc_spans, doc_span_index, split_token_index)

token_is_max_context[len(tokens)] = is_max_context

tokens.append(all_doc_tokens[split_token_index])

segment_ids.append(1)

tokens.append("[SEP]")

segment_ids.append(1)

input_ids = tokenizer.convert_tokens_to_ids(tokens)

# The mask has 1 for real tokens and 0 for padding tokens. Only real

# tokens are attended to.

input_mask = [1] * len(input_ids)

# Zero-pad up to the sequence length.

#while len(input_ids) < max_seq_length:

# input_ids.append(0)

# input_mask.append(0)

# segment_ids.append(0)

#assert len(input_ids) == max_seq_length

#assert len(input_mask) == max_seq_length

#assert len(segment_ids) == max_seq_length

start_position = None

end_position = None

if is_training and not example.is_impossible:

# For training, if our document chunk does not contain an annotation

# we throw it out, since there is nothing to predict.

doc_start = doc_span.start

doc_end = doc_span.start + doc_span.length - 1

out_of_span = False

if not (tok_start_position >= doc_start and

tok_end_position <= doc_end):

out_of_span = True

if out_of_span:

start_position = 0

end_position = 0

else:

doc_offset = len(query_tokens) + 2

start_position = tok_start_position - doc_start + doc_offset

end_position = tok_end_position - doc_start + doc_offset

if is_training and example.is_impossible:

start_position = 0

end_position = 0

if example_index < 3:

print("*** Example ***")

print("unique_id: %s" % (unique_id))

print("example_index: %s" % (example_index))

print("doc_span_index: %s" % (doc_span_index))

print("tokens: %s" % " ".join(

[tokenization.printable_text(x) for x in tokens]))

print("token_to_orig_map: %s" % " ".join([

"%d:%d" % (x, y)

for (x, y) in six.iteritems(token_to_orig_map)

]))

print("token_is_max_context: %s" % " ".join([

"%d:%s" % (x, y)

for (x, y) in six.iteritems(token_is_max_context)

]))

print("input_ids: %s" % " ".join([str(x) for x in input_ids]))

print("input_mask: %s" % " ".join([str(x) for x in input_mask]))

print("segment_ids: %s" %

" ".join([str(x) for x in segment_ids]))

if is_training and example.is_impossible:

print("impossible example")

if is_training and not example.is_impossible:

answer_text = " ".join(tokens[start_position:(end_position +

1)])

print("start_position: %d" % (start_position))

print("end_position: %d" % (end_position))

print("answer: %s" %

(tokenization.printable_text(answer_text)))

feature = InputFeatures(

unique_id=unique_id,

example_index=example_index,

doc_span_index=doc_span_index,

tokens=tokens,

token_to_orig_map=token_to_orig_map,

token_is_max_context=token_is_max_context,

input_ids=input_ids,

input_mask=input_mask,

segment_ids=segment_ids,

start_position=start_position,

end_position=end_position,

is_impossible=example.is_impossible)

unique_id += 1

orig_answer_text):

"""Returns tokenized answer spans that better match the annotated answer."""

# The SQuAD annotations are character based. We first project them to

# whitespace-tokenized words. But then after WordPiece tokenization, we can

# often find a "better match". For example:

#

# Question: What year was John Smith born?

# Context: The leader was John Smith (1895-1943).

# Answer: 1895

#

# The original whitespace-tokenized answer will be "(1895-1943).". However

# after tokenization, our tokens will be "( 1895 - 1943 ) .". So we can match

# the exact answer, 1895.

#

# However, this is not always possible. Consider the following:

#

# Question: What country is the top exporter of electornics?

# Context: The Japanese electronics industry is the lagest in the world.

# Answer: Japan

#

# In this case, the annotator chose "Japan" as a character sub-span of

# the word "Japanese". Since our WordPiece tokenizer does not split

# "Japanese", we just use "Japanese" as the annotation. This is fairly rare

# in SQuAD, but does happen.

tok_answer_text = " ".join(tokenizer.tokenize(orig_answer_text))

for new_start in range(input_start, input_end + 1):

for new_end in range(input_end, new_start - 1, -1):

text_span = " ".join(doc_tokens[new_start:(new_end + 1)])

if text_span == tok_answer_text:

return (new_start, new_end)

"""Check if this is the 'max context' doc span for the token."""

# Because of the sliding window approach taken to scoring documents, a single

# token can appear in multiple documents. E.g.

# Doc: the man went to the store and bought a gallon of milk

# Span A: the man went to the

# Span B: to the store and bought

# Span C: and bought a gallon of

# ...

#

# Now the word 'bought' will have two scores from spans B and C. We only

# want to consider the score with "maximum context", which we define as

# the *minimum* of its left and right context (the *sum* of left and

# right context will always be the same, of course).

#

# In the example the maximum context for 'bought' would be span C since

# it has 1 left context and 3 right context, while span B has 4 left context

# and 0 right context.

best_score = None

best_span_index = None

for (span_index, doc_span) in enumerate(doc_spans):

end = doc_span.start + doc_span.length - 1

if position < doc_span.start:

continue

if position > end:

continue

num_left_context = position - doc_span.start

num_right_context = end - position

score = min(num_left_context,

num_right_context) + 0.01 * doc_span.length

if best_score is None or score > best_score:

best_score = score

best_span_index = span_index

def __init__(self, vocab_path, do_lower_case, max_seq_length, in_tokens,

doc_stride, max_query_length):

self._tokenizer = tokenization.FullTokenizer(

vocab_file=vocab_path, do_lower_case=do_lower_case)

self._max_seq_length = max_seq_length

self._doc_stride = doc_stride

self._max_query_length = max_query_length

self._in_tokens = in_tokens

self.vocab = self._tokenizer.vocab

self.vocab_size = len(self.vocab)

self.pad_id = self.vocab["[PAD]"]

self.cls_id = self.vocab["[CLS]"]

self.sep_id = self.vocab["[SEP]"]

self.mask_id = self.vocab["[MASK]"]

self.current_train_example = -1

self.num_train_examples = -1

self.current_train_epoch = -1

self.train_examples = None

self.predict_examples = None

self.num_examples = {'train': -1, 'predict': -1}

def get_train_progress(self):

"""Gets progress for training phase."""

return self.current_train_example, self.current_train_epoch

def get_examples(self,

data_path,

is_training,

version_2_with_negative=False):

examples = read_squad_examples(

input_file=data_path,

is_training=is_training,

version_2_with_negative=version_2_with_negative)

return examples

def get_num_examples(self, phase):

if phase not in ['train', 'predict']:

raise ValueError(

"Unknown phase, which should be in ['train', 'predict'].")

return self.num_examples[phase]

def get_features(self, examples, is_training):

features = convert_examples_to_features(

examples=examples,

tokenizer=self._tokenizer,

max_seq_length=self._max_seq_length,

doc_stride=self._doc_stride,

max_query_length=self._max_query_length,

is_training=is_training)

return features

def data_generator(self,

data_path,

batch_size,

phase='train',

shuffle=False,

version_2_with_negative=False,

epoch=1):

if phase == 'train':

self.train_examples = self.get_examples(

data_path,

is_training=True,

version_2_with_negative=version_2_with_negative)

examples = self.train_examples

self.num_examples['train'] = len(self.train_examples)

elif phase == 'predict':

self.predict_examples = self.get_examples(

data_path,

is_training=False,

version_2_with_negative=version_2_with_negative)

examples = self.predict_examples

self.num_examples['predict'] = len(self.predict_examples)

else:

raise ValueError(

"Unknown phase, which should be in ['train', 'predict'].")

def batch_reader(features, batch_size, in_tokens):

batch, total_token_num, max_len = [], 0, 0

for (index, feature) in enumerate(features):

if phase == 'train':

self.current_train_example = index + 1

seq_len = len(feature.input_ids)

labels = [feature.unique_id

] if feature.start_position is None else [

feature.start_position, feature.end_position

]

example = [

feature.input_ids, feature.segment_ids, range(seq_len)

] + labels

max_len = max(max_len, seq_len)

#max_len = max(max_len, len(token_ids))

if in_tokens:

to_append = (len(batch) + 1) * max_len <= batch_size

else:

to_append = len(batch) < batch_size

if to_append:

batch.append(example)

total_token_num += seq_len

else:

yield batch, total_token_num

batch, total_token_num, max_len = [example

], seq_len, seq_len

if len(batch) > 0:

yield batch, total_token_num

def wrapper():

for epoch_index in range(epoch):

if shuffle:

random.shuffle(examples)

if phase == 'train':

self.current_train_epoch = epoch_index

features = self.get_features(examples, is_training=True)

else:

features = self.get_features(examples, is_training=False)

for batch_data, total_token_num in batch_reader(

features, batch_size, self._in_tokens):

yield prepare_batch_data(

batch_data,

total_token_num,

voc_size=-1,

pad_id=self.pad_id,

cls_id=self.cls_id,

sep_id=self.sep_id,

mask_id=-1,

return_attn_bias=True,

return_max_len=False,

return_num_token=False)

max_answer_length, do_lower_case, output_prediction_file,

output_nbest_file, output_null_log_odds_file,

version_2_with_negative, null_score_diff_threshold,

verbose):

"""Write final predictions to the json file and log-odds of null if needed."""

print("Writing predictions to: %s" % (output_prediction_file))

print("Writing nbest to: %s" % (output_nbest_file))

example_index_to_features = collections.defaultdict(list)

for feature in all_features:

example_index_to_features[feature.example_index].append(feature)

unique_id_to_result = {}

for result in all_results:

unique_id_to_result[result.unique_id] = result

_PrelimPrediction = collections.namedtuple( # pylint: disable=invalid-name

"PrelimPrediction", [

"feature_index", "start_index", "end_index", "start_logit",

"end_logit"

])

all_predictions = collections.OrderedDict()

all_nbest_json = collections.OrderedDict()

scores_diff_json = collections.OrderedDict()

for (example_index, example) in enumerate(all_examples):

features = example_index_to_features[example_index]

prelim_predictions = []

# keep track of the minimum score of null start+end of position 0

score_null = 1000000 # large and positive

min_null_feature_index = 0 # the paragraph slice with min mull score

null_start_logit = 0 # the start logit at the slice with min null score

null_end_logit = 0 # the end logit at the slice with min null score

for (feature_index, feature) in enumerate(features):

result = unique_id_to_result[feature.unique_id]

start_indexes = _get_best_indexes(result.start_logits, n_best_size)

end_indexes = _get_best_indexes(result.end_logits, n_best_size)

# if we could have irrelevant answers, get the min score of irrelevant

if version_2_with_negative:

feature_null_score = result.start_logits[0] + result.end_logits[

0]

if feature_null_score < score_null:

score_null = feature_null_score

min_null_feature_index = feature_index

null_start_logit = result.start_logits[0]

null_end_logit = result.end_logits[0]

for start_index in start_indexes:

for end_index in end_indexes:

# We could hypothetically create invalid predictions, e.g., predict

# that the start of the span is in the question. We throw out all

# invalid predictions.

if start_index >= len(feature.tokens):

continue

if end_index >= len(feature.tokens):

continue

if start_index not in feature.token_to_orig_map:

continue

if end_index not in feature.token_to_orig_map:

continue

if not feature.token_is_max_context.get(start_index, False):

continue

if end_index < start_index:

continue

length = end_index - start_index + 1

if length > max_answer_length:

continue

prelim_predictions.append(

_PrelimPrediction(

feature_index=feature_index,

start_index=start_index,

end_index=end_index,

start_logit=result.start_logits[start_index],

end_logit=result.end_logits[end_index]))

if version_2_with_negative:

prelim_predictions.append(

_PrelimPrediction(

feature_index=min_null_feature_index,

start_index=0,

end_index=0,

start_logit=null_start_logit,

end_logit=null_end_logit))

prelim_predictions = sorted(

prelim_predictions,

key=lambda x: (x.start_logit + x.end_logit),

reverse=True)

_NbestPrediction = collections.namedtuple( # pylint: disable=invalid-name

"NbestPrediction", ["text", "start_logit", "end_logit"])

seen_predictions = {}

nbest = []

for pred in prelim_predictions:

if len(nbest) >= n_best_size:

break

feature = features[pred.feature_index]

if pred.start_index > 0: # this is a non-null prediction

tok_tokens = feature.tokens[pred.start_index:(pred.end_index + 1

)]

orig_doc_start = feature.token_to_orig_map[pred.start_index]

orig_doc_end = feature.token_to_orig_map[pred.end_index]

orig_tokens = example.doc_tokens[orig_doc_start:(orig_doc_end +

1)]

tok_text = " ".join(tok_tokens)

# De-tokenize WordPieces that have been split off.

tok_text = tok_text.replace(" ##", "")

tok_text = tok_text.replace("##", "")

# Clean whitespace

tok_text = tok_text.strip()

tok_text = " ".join(tok_text.split())

orig_text = " ".join(orig_tokens)

final_text = get_final_text(tok_text, orig_text, do_lower_case,

verbose)

if final_text in seen_predictions:

continue

seen_predictions[final_text] = True

else:

final_text = ""

seen_predictions[final_text] = True

nbest.append(

_NbestPrediction(

text=final_text,

start_logit=pred.start_logit,

end_logit=pred.end_logit))

# if we didn't inlude the empty option in the n-best, inlcude it

if version_2_with_negative:

if "" not in seen_predictions:

nbest.append(

_NbestPrediction(

text="",

start_logit=null_start_logit,

end_logit=null_end_logit))

# In very rare edge cases we could have no valid predictions. So we

# just create a nonce prediction in this case to avoid failure.

if not nbest:

nbest.append(

_NbestPrediction(

text="empty", start_logit=0.0, end_logit=0.0))

assert len(nbest) >= 1

total_scores = []

best_non_null_entry = None

for entry in nbest:

total_scores.append(entry.start_logit + entry.end_logit)

if not best_non_null_entry:

if entry.text:

best_non_null_entry = entry

# debug

if best_non_null_entry is None:

print("Emmm..., sth wrong")

probs = _compute_softmax(total_scores)

nbest_json = []

for (i, entry) in enumerate(nbest):

output = collections.OrderedDict()

output["text"] = entry.text

output["probability"] = probs[i]

output["start_logit"] = entry.start_logit

output["end_logit"] = entry.end_logit

nbest_json.append(output)

assert len(nbest_json) >= 1

if not version_2_with_negative:

all_predictions[example.qas_id] = nbest_json[0]["text"]

else:

# predict "" iff the null score - the score of best non-null > threshold

score_diff = score_null - best_non_null_entry.start_logit - (

best_non_null_entry.end_logit)

scores_diff_json[example.qas_id] = score_diff

if score_diff > null_score_diff_threshold:

all_predictions[example.qas_id] = ""

else:

all_predictions[example.qas_id] = best_non_null_entry.text

all_nbest_json[example.qas_id] = nbest_json

with open(output_prediction_file, "w") as writer:

writer.write(json.dumps(all_predictions, indent=4) + "\n")

with open(output_nbest_file, "w") as writer:

writer.write(json.dumps(all_nbest_json, indent=4) + "\n")

if version_2_with_negative:

with open(output_null_log_odds_file, "w") as writer:

"""Project the tokenized prediction back to the original text."""

# When we created the data, we kept track of the alignment between original

# (whitespace tokenized) tokens and our WordPiece tokenized tokens. So

# now `orig_text` contains the span of our original text corresponding to the

# span that we predicted.

#

# However, `orig_text` may contain extra characters that we don't want in

# our prediction.

#

# For example, let's say:

# pred_text = steve smith

# orig_text = Steve Smith's

#

# We don't want to return `orig_text` because it contains the extra "'s".

#

# We don't want to return `pred_text` because it's already been normalized

# (the SQuAD eval script also does punctuation stripping/lower casing but

# our tokenizer does additional normalization like stripping accent

# characters).

#

# What we really want to return is "Steve Smith".

#

# Therefore, we have to apply a semi-complicated alignment heruistic between

# `pred_text` and `orig_text` to get a character-to-charcter alignment. This

# can fail in certain cases in which case we just return `orig_text`.

def _strip_spaces(text):

ns_chars = []

ns_to_s_map = collections.OrderedDict()

for (i, c) in enumerate(text):

if c == " ":

continue

ns_to_s_map[len(ns_chars)] = i

ns_chars.append(c)

ns_text = "".join(ns_chars)

return (ns_text, ns_to_s_map)

# We first tokenize `orig_text`, strip whitespace from the result

# and `pred_text`, and check if they are the same length. If they are

# NOT the same length, the heuristic has failed. If they are the same

# length, we assume the characters are one-to-one aligned.

tokenizer = tokenization.BasicTokenizer(do_lower_case=do_lower_case)

tok_text = " ".join(tokenizer.tokenize(orig_text))

start_position = tok_text.find(pred_text)

if start_position == -1:

if verbose:

print("Unable to find text: '%s' in '%s'" % (pred_text, orig_text))

return orig_text

end_position = start_position + len(pred_text) - 1

(orig_ns_text, orig_ns_to_s_map) = _strip_spaces(orig_text)

(tok_ns_text, tok_ns_to_s_map) = _strip_spaces(tok_text)

if len(orig_ns_text) != len(tok_ns_text):

if verbose:

print("Length not equal after stripping spaces: '%s' vs '%s'",

orig_ns_text, tok_ns_text)

return orig_text

# We then project the characters in `pred_text` back to `orig_text` using

# the character-to-character alignment.

tok_s_to_ns_map = {}

for (i, tok_index) in six.iteritems(tok_ns_to_s_map):

tok_s_to_ns_map[tok_index] = i

orig_start_position = None

if start_position in tok_s_to_ns_map:

ns_start_position = tok_s_to_ns_map[start_position]

if ns_start_position in orig_ns_to_s_map:

orig_start_position = orig_ns_to_s_map[ns_start_position]

if orig_start_position is None:

if verbose:

print("Couldn't map start position")

return orig_text

orig_end_position = None

if end_position in tok_s_to_ns_map:

ns_end_position = tok_s_to_ns_map[end_position]

if ns_end_position in orig_ns_to_s_map:

orig_end_position = orig_ns_to_s_map[ns_end_position]

if orig_end_position is None:

if verbose:

print("Couldn't map end position")

return orig_text

output_text = orig_text[orig_start_position:(orig_end_position + 1)]

"""Get the n-best logits from a list."""

index_and_score = sorted(

enumerate(logits), key=lambda x: x[1], reverse=True)

best_indexes = []

for i in range(len(index_and_score)):

if i >= n_best_size:

break

best_indexes.append(index_and_score[i][0])

"""Compute softmax probability over raw logits."""

if not scores:

return []

max_score = None

for score in scores:

if max_score is None or score > max_score:

max_score = score

exp_scores = []

total_sum = 0.0

for score in scores:

x = math.exp(score - max_score)

exp_scores.append(x)

total_sum += x

probs = []

for score in exp_scores:

probs.append(score / total_sum)