Grounding Representation Similarity with Statistical Testing

This repo contains code to replicate the results in our paper, which evaluates representation similarity measures with a series of benchmark tasks. The experiments in the paper require first computing neural network embeddings of a dataset and computing accuracy scores of that neural network, which we provide pre-computed. This repo contains the code that implements our benchmark evaluation, given these embeddings and performance scores.

File descriptions

This repo: sim_metric

This repo is organized as follows:

• experiments/ contains code to run the experiments in part 4 of the paper:
  • layer_exp is the first experiment in part 4, with different random seeds and layer depths
  • pca_deletion is the second experiment in part 4, with different numbers of principal components deleted
  • feather is the first experiment in part 4.1, with different finetuning seeds
  • pretrain_finetune is the second experiment in part 4.2, with different pretraining and finetuning seeds
• dists/ contains functions to compute dissimilarities between representations.

Pre-computed resources: sim_metric_resources

The pre-computed embeddings and scores available at https://zenodo.org/record/5117844 can be downloaded and unzipped into a folder titled sim_metric_resources, which is organized as follows:

• embeddings contains the embeddings between which we are computing dissimilarities
• dists contains, for every experiment, the dissimilarities between the corresponding embeddings, for every metric:
  • dists.csv contains the precomputed dissimilarities
  • dists_self_computed.csv contains the dissimilarities computed by running compute_dists.py (see below)
• scores contains, for every experiment, the accuracy scores of the embeddings
• full_dfs contains, for every experiment, a csv file aggregating the dissimilarities and accuracy differences between the embeddings

Instructions

• clone this repository
• go to https://zenodo.org/record/5117844 and download sim_metric_resources.tar
• untar it with tar -xvf sim_metric_resources sim_metric_resources.tar
• in sim_metric/paths.py, modify the path to sim_metric_resources

Replicating the results

For every experiment (eg feather, pretrain_finetune, layer_exp, or pca_deletion):

• the relevant dissimilarities and accuracies differences have already been precomputed and aggregated in a dataframe full_df
• make sure that dists_path and full_df_path in compute_full_df.py, script.py and notebook.ipynb are set to dists.csv and full_df.csv, and not dists_self_computed.csv and full_df_self_computed.csv.
• to get the results, you can:
  • run the notebook notebook.ipynb, or
  • run script.py in the experiment's folder, and find the results in results.txt, in the same folder To run the scripts for all four experiments, run experiments/script.py.

Recomputing dissimilarities

For every experiment, you can:

• recompute the dissimilarities between embeddings by running compute_dists.py in this experiment's folder
• use these and the accuracy scores to recompute the aggregate dataframe by running compute_full_df.py in this experiment's folder
• change dists_path and full_df_path in compute_full_df.py, script.py and notebook.ipynb from dists.csv and full_df.csv to dists_self_computed.csv and full_df_self_computed.csv
• run the experiments with script.py or notebook.ipynb as above.

Adding a new metric

This repo also allows you to test a new representational similarity metric and see how it compares according to our benchmark. To add a new metric:

• add the corresponding function at the end of dists/scoring.py
• add a condition in dists/score_pair.py, around line 160
• for every experiment in experiments, add the name of the metric to the metrics list in compute_dists.py