Numerical estimator of Pointwise Sliced Mutual Information (PSMI).

Jérémie Dentan, École Polytechnique

Setup

Our library is published on PyPI!

bash pip install psmi

Usage

We implement a class PSMI which should be used in a similar way to scikit-learn classes, with fit, transform and fit_transform methods.

We only implement PSMI between scalar feature and integer labels belonging to a finite number of classes. We use algorithm 1 in [1] to estimate PSMI. The only hyperparameter of this algorithm is the number of estimator (i.e. the number of directions samples to estimate PSMI).

We propose two approaches to compute PSMI.

1. Manual. You simply pass argument n_estimators with the desired value.

2. Automatic. In that cas, you pass n_estimators="auto" and an algorithm will be used to determine a suitable value for n_estimators.

Example

```python import numpy as np from psmi import PSMI

Generating data

nsamples, dim, nlabels = 100, 1024, 5 features = np.random.random((nsamples, dim)) labels = np.random.randint(nlabels, size=n_samples)

Manual number of estimator

psmiestimator = PSMI(nestimators=500) psmimean, psmistd, psmifull = psmiestimator.fittransform(features, labels) print(f"psmimean: {psmimean.shape}") # Should be (100,) print(f"psmistd: {psmistd.shape}") # Should be (100,) print(f"psmifull: {psmifull.shape}") # Should be (100,500) print(f"Num of estimator: {psmiestimator.n_estimators}") # Should be 500

Automatic number of estimator

psmiestimator = PSMI() psmimean, psmistd, psmifull = psmiestimator.fittransform(features, labels) print(f"psmimean: {psmimean.shape}") # Should be (100,) print(f"psmistd: {psmistd.shape}") # Should be (100,) print(f"psmifull: {psmifull.shape}") # Should be (100,) print(f"Num of estimator: {psmiestimator.nestimators}")

You can separate the fit and transform

ntest = 5 featurestest = np.random.random((ntest, dim)) labelstest = np.random.randint(nlabels, size=ntest) psmiestimator = PSMI() psmiestimator.fit(features, labels) psmimean, psmistd, psmifull = psmiestimator.transform(featurestest, labelstest) print(f"psmimean: {psmimean.shape}") # Should be (5,) print(f"psmistd: {psmistd.shape}") # Should be (5,) print(f"psmifull: {psmifull.shape}") # Should be (5,) print(f"Num of estimator: {psmiestimator.nestimators}") ```

Details on the auto mode

More specifically, we will iteratively add more and more estimators, in blocks of min_n_estimators. We stop this process when the PSMI of the elements that have the lowest PSMI minimally evolved between the current step and the one with half as many estimators.

More specifically, if lowest_psmi_quantile=0.05, we consider the 5% of elements with the lowest PSMI at current step. Then, we compare this value to the PSMI of theses elements using only the first int(n*milestone) blocks of estimators, where n is the current number of blocks that was added. Then we compare the absolute value of the variation divided by the PSMI at the current step. If it is below max_variation_of_the_lowest, we stop. Else, we add another block of min_n_estimators estimators.

For example, the default values corresponds to blocks of 500 estimators. We add blocks untill the 5% of elements with lowest PSMI have varied of less than 5% between the current step and the one with half as many blocks.

[1] Shelvia Wongso et al. Pointwise Sliced Mutual Information for Neural Network Explainability. IEEE International Symposium on Information Theory (ISIT). 2023. DOI: 10.1109/ISIT54713.2023.10207010

Contributing

You are welcome to submit pull requests! Please use pre-commit to correctly format your code:

bash pip install -r .github/dev-requirements.txt pre-commit install

Please test your code:

bash pytest

License and Copyright

Copyright 2024-present Laboratoire d'Informatique de Polytechnique. This project is licensed under the GNU Lesser General Public License v3.0. See the LICENSE file for details.

Please cite this work as follows:

bibtex @misc{dentan_predicting_2024, title = {Predicting and analysing memorization within fine-tuned Large Language Models}, url = {https://arxiv.org/abs/2409.18858}, author = {Dentan, Jérémie and Buscaldi, Davide and Shabou, Aymen and Vanier, Sonia}, month = sep, year = {2024}, }

Acknowldgements

This work received financial support from Crédit Agricole SA through the research chair ”Trustworthy and responsible AI” with École Polytechnique.