ALBERT for ARQMath 3
This repository contains our best model for ARQMath 3, the math_10 model. It was initialised from ALBERT-base-v2 and further pre-trained on Math StackExchange in three different stages. We also added more LaTeX tokens to the tokenizer to enable a better tokenization of mathematical formulas. math_10 was fine-tuned on a classification task to determine whether a given question (sequence 1) matches a given answer (sequence 2). The classification output can be used for ranking the best answers. For further details, please read our paper: http://ceur-ws.org/Vol-3180/paper-07.pdf.
Other Models for ARQMath 3
We plan on also publishing the other fine-tuned models as well as the base models. Links to these repositories will be added here soon.
| Model | Initialised from | Pre-training | Fine-Tuned | Link |
|---|---|---|---|---|
| roberta_10 | RoBERTa | MathSE (1) | yes, N=10 MathSE | |
| base_10 | ALBERT | MathSE (1) | yes, N=10 MathSE | |
| math_10_add | ALBERT | MathSE (1)-(3) | yes, N=10 MathSE and annotated data | |
| Khan_SE_10 | ALBERT | MathSE (1) | yes, N=10 MathSE | |
| roberta | RoBERTa | MathSE (1) | no | AnReu/math_pretrained_roberta |
| math albert | ALBERT | MathSE (1)-(3) | no | AnReu/math_albert |
| base | ALBERT | MathSE (1) | no | |
| Khan_SE | ALBERT | MathSE (1) mixed with Khan | no |
Update
We have also further pre-trained a BERT-base-cased model in the same way as our ALBERT model. You can find it here: AnReu/math_pretrained_bert.
Usage
# based on https://huggingface.co/docs/transformers/main/en/task_summary#sequence-classification
from transformers import AutoTokenizer, AutoModelForSequenceClassification
tokenizer = AutoTokenizer.from_pretrained("AnReu/albert-for-arqmath-3")
model = AutoModelForSequenceClassification.from_pretrained("AnReu/albert-for-arqmath-3")
classes = ["non relevant", "relevant"]
sequence_0 = "How can I calculate x in $3x = 5$"
sequence_1 = "Just divide by 3: $x = \\frac{5}{3}$"
sequence_2 = "The general rule for squaring a sum is $(a+b)^2=a^2+2ab+b^2$"
# The tokenizer will automatically add any model specific separators (i.e. <CLS> and <SEP>) and tokens to
# the sequence, as well as compute the attention masks.
irrelevant = tokenizer(sequence_0, sequence_2, return_tensors="pt")
relevant = tokenizer(sequence_0, sequence_1, return_tensors="pt")
irrelevant_classification_logits = model(**irrelevant).logits
relevant_classification_logits = model(**relevant).logits
irrelevant_results = torch.softmax(irrelevant_classification_logits, dim=1).tolist()[0]
relevant_results = torch.softmax(relevant_classification_logits, dim=1).tolist()[0]
# Should be irrelevant
for i in range(len(classes)):
print(f"{classes[i]}: {int(round(irrelevant_results[i] * 100))}%")
# Should be relevant
for i in range(len(classes)):
print(f"{classes[i]}: {int(round(relevant_results[i] * 100))}%")
Citation
If you find this model useful, consider citing our paper:
@article{reusch2022transformer,
title={Transformer-Encoder and Decoder Models for Questions on Math},
author={Reusch, Anja and Thiele, Maik and Lehner, Wolfgang},
year={2022},
organization={CLEF}
}