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PoincareProbe

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Implementation of ICLR 21 paper: Probing BERT in Hyperbolic Spaces

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Boli Chen\*, Yao Fu\*, Guangwei Xu, Pengjun Xie, Chuanqi Tan, Mosha Chen, Liping Jing. _Probing BERT in Hyperbolic Spaces_. ICLR 2021.

## Requirements

$ pip install -r requirements.txt

## Sentiment Visualization with Pretrained Probes

Probe checkpoints are in the folder `./SentimentProbe/checkpoint`.

Use the Jupyter Notebook `Sentiment-Visualization-Poincare/Euclidean.ipynb`.

Play with it by changing the input text.

### Example

_BERT is a good model_

## Syntax Visualization with Pretrained Probes

Use the Jupyter Notebook `SyntaxProbe/Syntax-Visualization-Poincare/Euclidean.ipynb`.

## Key Implementation 
Equation (1), the poincare distance is implemented within the [geoopt](https://github.com/geoopt/geoopt) library, `Stereographic` class. In our work we just call its implementation.

Our Poincare probe is implemented in `SyntaxProbe/probe/hyper.py`, `PoincareProbe` class and `SentimentProbe/probe/probe.py`, `PoincareProbe` class.

Equation (2) and (3) in the paper correspond to:
* `SyntaxProbe/probe/hyper.py` line 80 to 82 for syntax
* `SentimentProbe/probe/probe.py` line 60 - 62 for sentiment

Equation (4) and (5) in the paper correspond to `SyntaxProbe/probe/hyper.py`, `PoincareProbeBase` class, function `distance` (line 16 - 34) and `depth` (line 36 - 50).

Equation (6) in the paper correspond to `SentimentProbe/probe/probe.py` line 63 - 64.

Optimization:
* For the syntax probe, there is no parameters lay in the hyperbolic space (we project embeddings into the hyperbolic space, but the parameters for the projections are themselves in euclidean). So we use normal Adam optimizer.
* For the sentiment probe, the two meta embeddings are in the hyperbolic space (`SentimentProbe/probe/probe.py` line 51 - 52) while the rest are in the euclidean space. So we use `RiemannianAdam` for the meta embeddings in ``SentimentProbe/run.py` line 91-92. Note that this optimizer will different the space of the parameters and [operate accordingly](https://github.com/geoopt/geoopt/blob/master/geoopt/optim/radam.py).

## Reproduction

### Data preparation
You will need access to the PTB dataset from [LDC](https://catalog.ldc.upenn.edu/LDC99T42).
Then use the [scripts from Hewitt](https://github.com/john-hewitt/structural-probes/tree/master/scripts) to preprocess the data. You only need the `convert_splits_to_depparse.sh` and `convert_conll_to_raw.py` file since we will use our own in `SyntaxProbe/data.py` to get BERT embeddings from the current huggingface transformers library (current = 2021.03.19).

You will need to name the datasets and create folders accordingly, checkout `SyntaxProbe/data.py` for the directory names.

### Reproducing Table 1 and 2 
Then use `run.py`, which can be found in the sub-folders `./SyntaxProbe` and `./SentimentProbe`. This would enable you to reproduce Table 1 and Table 2, which are our major results.

We do not use fixed random seeds. Generally we do not recommend using any fixed seeds. We recommend doing multiple runs for training and observe the mean and variance of the performance.

### Visualization of Figure 4, 5, 6, 7  
can be reproduced by modifying the jupyter notebooks.

## Background Knowledge

Q: if I only know sequence to sequence, but I want to really understand what you are doing, what should I read to get sufficient background knowledge?

A: to understand our paper, you will need (a) background about dependency parsing, (b) background about hyperbolic geometry, (c) background about probing BERT.

For parsing, start with [slp chap 14](https://web.stanford.edu/~jurafsky/slp3/14.pdf) to learn what is dependency parsing and read [biaffine](https://arxiv.org/abs/1611.01734) to know what makes a good parser. A good practice is to put the two side by side and do [comparative-contrastive reading](https://writingcenter.unc.edu/tips-and-tools/comparing-and-contrasting/). After reading them, you will know the basics about parsing used in our paper (e.g., the meaning of UUAS in Table 1, the meaning of edges in Figure 3)

For hyperbolic geometry, start with the blog posts about differential geometry ([tensors](https://bjlkeng.github.io/posts/tensors-tensors-tensors/), [manifolds](https://bjlkeng.github.io/posts/manifolds/)). Then read the [Poincare embeddings paper](https://arxiv.org/abs/1705.08039) and a [blog post](https://bjlkeng.github.io/posts/hyperbolic-geometry-and-poincare-embeddings/) about it. After reading them, you should have deep enough knowledge to understand the techniques in our chapter 3.

For probing syntax in BERT, start with the [structural probe paper](https://www.aclweb.org/anthology/N19-1419/) (this is the primary paper we follow) then [a discussion paper about a probe and a parser](https://arxiv.org/abs/2005.01641) (this paper motivates our heavy discussion about the probe sensitivity in our introduction).

PoincareProbe

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