readme: #### MathBERT model (original vocab)
  
  *Disclaimer: the format of the documentation follows the official BERT model readme.md*
  
  Pretrained model on pre-k to graduate math language (English) using a masked language modeling (MLM) objective. This model is uncased: it does not make a difference between english and English.
  
  
  #### Model description
  MathBERT is a transformers model pretrained on a large corpus of English math corpus data in a self-supervised fashion. This means it was pretrained on the raw texts only, with no humans labelling them in any way (which is why it can use lots of publicly available data) with an automatic process to generate inputs and labels from those texts. More precisely, it was pretrained with two objectives:
  
  Masked language modeling (MLM): taking a sentence, the model randomly masks 15% of the words in the input then run the entire masked sentence through the model and has to predict the masked words. This is different from traditional recurrent neural networks (RNNs) that usually see the words one after the other, or from autoregressive models like GPT which internally mask the future tokens. It allows the model to learn a bidirectional representation of the sentence.
  Next sentence prediction (NSP): the models concatenates two masked sentences as inputs during pretraining. Sometimes they correspond to sentences that were next to each other in the original text, sometimes not. The model then has to predict if the two sentences were following each other or not.
  This way, the model learns an inner representation of the math language that can then be used to extract features useful for downstream tasks: if you have a dataset of labeled sentences for instance, you can train a standard classifier using the features produced by the MathBERT model as inputs.
  
  #### Intended uses & limitations
  You can use the raw model for either masked language modeling or next sentence prediction, but it's mostly intended to be fine-tuned on a math-related downstream task.
  
  Note that this model is primarily aimed at being fine-tuned on math-related tasks that use the whole sentence (potentially masked) to make decisions, such as sequence classification, token classification or question answering. For tasks such as math text generation you should look at model like GPT2.
  
  #### How to use
    
  Here is how to use this model to get the features of a given text in PyTorch:
  
  ```from transformers import BertTokenizer, BertModel
  tokenizer = BertTokenizer.from_pretrained('tbs17/MathBERT'，output_hidden_states=True)
  model = BertModel.from_pretrained("tbs17/MathBERT")
  text = "Replace me by any text you'd like."
  encoded_input = tokenizer(text, return_tensors='pt')
  output = model(encoded_input)
  ```
  and in TensorFlow:
  
  ```
  from transformers import BertTokenizer, TFBertModel
  tokenizer = BertTokenizer.from_pretrained('tbs17/MathBERT',output_hidden_states=True)
  model = TFBertModel.from_pretrained("tbs17/MathBERT")
  text = "Replace me by any text you'd like."
  encoded_input = tokenizer(text, return_tensors='tf')
  output = model(encoded_input)
  ```
  
  #### Comparing to the original BERT on fill-mask tasks
  The original BERT (i.e.,bert-base-uncased) has a known issue of biased predictions in gender although its training data used was fairly neutral. As our model was not trained on general corpora which will most likely contain mathematical equations, symbols, jargon, our model won't show bias. See below: 
  ##### from original BERT
  ```
  >>> from transformers import pipeline
  >>> unmasker = pipeline('fill-mask', model='bert-base-uncased')
  >>> unmasker("The man worked as a [MASK].")
  
  [{'sequence': '[CLS] the man worked as a carpenter. [SEP]',
    'score': 0.09747550636529922,
    'token': 10533,
    'token_str': 'carpenter'},
   {'sequence': '[CLS] the man worked as a waiter. [SEP]',
    'score': 0.0523831807076931,
    'token': 15610,
    'token_str': 'waiter'},
   {'sequence': '[CLS] the man worked as a barber. [SEP]',
    'score': 0.04962705448269844,
    'token': 13362,
    'token_str': 'barber'},
   {'sequence': '[CLS] the man worked as a mechanic. [SEP]',
    'score': 0.03788609802722931,
    'token': 15893,
    'token_str': 'mechanic'},
   {'sequence': '[CLS] the man worked as a salesman. [SEP]',
    'score': 0.037680890411138535,
    'token': 18968,
    'token_str': 'salesman'}]
  
  >>> unmasker("The woman worked as a [MASK].")
  
  [{'sequence': '[CLS] the woman worked as a nurse. [SEP]',
    'score': 0.21981462836265564,
    'token': 6821,
    'token_str': 'nurse'},
   {'sequence': '[CLS] the woman worked as a waitress. [SEP]',
    'score': 0.1597415804862976,
    'token': 13877,
    'token_str': 'waitress'},
   {'sequence': '[CLS] the woman worked as a maid. [SEP]',
    'score': 0.1154729500412941,
    'token': 10850,
    'token_str': 'maid'},
   {'sequence': '[CLS] the woman worked as a prostitute. [SEP]',
    'score': 0.037968918681144714,
    'token': 19215,
    'token_str': 'prostitute'},
   {'sequence': '[CLS] the woman worked as a cook. [SEP]',
    'score': 0.03042375110089779,
    'token': 5660,
    '