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Characterizing Structural Regularities of Labeled Data in Overparameterized Models

PaperProjectC-scores for CIFAR-10C-scores for CIFAR-100C-scores for ImageNetCheckpoints

We demonstrate the held out training algorithm and c-score estimation procedure with an example on MNIST. The c-score estimation on larger and more challenging datasets (CIFAR / ImageNet) are essentially the same as this example shows, except that extra infrastructures such as GPU clusters, job scheduling, checkpoint saving and resuming, are needed. Because MNIST is small and can be easily fit with a small network and very few epochs, we are able to provide a demo to show the core algorithm with minimum dependency on irrelevant infrastructure code, which could run in reasonable time on a single GPU. We also provide pre-computed c-scores on CIFAR-10/CIFAR-100 and ImageNet for people who are interested in playing with those datasets.

Example Code on MNIST

The demo contains a single python file mnist.py, which train multi-layer perceptrons on MNIST to estimate the C-scores, and plot examples as ranked by the estimated C-scores.

The code has the following dependencies:

After running, the code will save the computed cscores in cscores.npy and export a figure in mnist-examples.pdf like the one below. It shows some MNIST training examples from each of the 10 classes. The left block shows the examples with the highest C-scores, and the right block shows the examples with the lowest C-scores.

MNIST Examples

On a single NVidia V100 GPU, with subset ratio being 0.1, 0.2, ..., 0.9 and 200 runs for each subset ratio, it takes less than 2 hours to run.

Note: tensorflow-datasets stores the MNIST examples in a different order from the official MNIST dataset binary.

Pre-computed Scores and Pre-trained Checkpoints

We provide pre-computed C-score for download. The files are in Numpy's data format exported via numpy.savez. Please see the project website for detailed description of the file format and download links.

Pre-trained model checkpoints can be found here with supportive code to load and run evaluations with those models.

Disclaimer

This is not an officially supported Google product.

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