Convolutional neural networks use kernels to extract informative motifs from massive amount of sequence datasets. However, the only way to distill the motifs from these kernels is a heuristic one from Deepbind (Alipanahi et al., 2015) that aligns all matched sequence segments altogether and calculate the frequency directly, leading to one Position Weight Matrix (PWM) for each kernel.

Here we proposed an exact transformation from kernel to PWM, in the sense that the convolution result of the kernel on a given sequence fragment is identical to the sum of a sequence-independent constant and the log-likelihood of the PWM on the same sequence.

Steps of this exact transformation are detailed below:

The k2p toolbox implements the transformation described in our manuscript. All codes are available from the k2p-1.0 directory. The current implementatin depends on the python packages numpy, pandas, and keras. Below is a copy of README in this archive:

The python scripts in this toolbox allow the user to transform a kernel that is applied directly to nucleotide sequences into a PWM, or vice versa. Specifically,

• ./code/kernel2PWM.py : transform a kernel into a PWM with a given base. The resulting PWM is in meme motif format.

• ./code/PWM2kernel.py : transform a PWM into a kernel with a given base. The PWM must be in meme motif format.

• ./code/kernel2PWM_MLE.py : transform a series of kernels into PWMs with the base estimated by Maximum Likelihood Estimation (MLE), which requires the user to provide sequences from which the kernels have been trained. These kernels are assumed to come from a model with the following structure: input -> convolution -> linear or ReLU activation -> global max-pooling -> arbitrary layers. The kernels, sequences, and PWMs are all stored as hdf5 tensors.

The following datasets are for testing purposes, and they also illustrates how the input should be formatted. For the details of input formats, please refer to the help message of each script (use "-h" to show the help message).

• ./data/toy_kernel_matrix.txt : a toy example of the kernel file describing the kernel matrix.

• ./data/toy_PWM.meme : a toy example of the PWM file describing the PWM matrix.

• ./data/toy_PWM_2_with_zero.meme : another toy example of the PWM file. This PWM contains a zero element, which will be detected and corrected by ./code/PWM2kernel.py.

• ./data/for.3..1.kernel.tensor.hdf5 and ./data/for.3..1.sequence.tensor.hdf5 : a toy example of the kernel and sequence tensors.

• Python 2.7 and the following packages:
  • numpy
  • h5py (for ./code/kernel2PWM_MLE.py only)
  • scipy (for ./code/kernel2PWM_MLE.py only)

Run the following commands under the root directory (where the "code" and "data" directories are):

$ python ./code/kernel2PWM.py ./data/toy_kernel_matrix.txt ./data/toy_kernel_transformed_PWM.meme

$ python ./code/PWM2kernel.py ./data/toy_PWM.meme ./data/toy_PWM_transformed_kernel.txt

$ python ./code/PWM2kernel.py ./data/toy_PWM_2_with_zero.meme ./data/toy_PWM_2_with_zero_transformed_kernel.txt

$ python ./code/kernel2PWM_MLE.py ./data/for.3..1.kernel.tensor.hdf5 ./data/for.3..1.sequence.tensor.hdf5 ./data/for.3..1.PWM.tensor.hdf5

Please cite the following bioRxiv prepint ( https://dx.doi.org/10.1101/163220 ):

Ding,Y. et al. (2018) An exact transformation for CNN kernel enables accurate sequence motif identification and leads to a potentially full probabilistic interpretation of CNN. bioRxiv, 163220.

This will be updated once the work is accepted by a particular journal or conference.

The following directories in supplements are for reproducing the corresponding figures in the manuscript:

• Wilcoxon signed test results: standard output of work03 (see work03_simulate.simple.case.3/README.md for more details).
• Figure 3 : work05_retrain.Deepbind.model/data/for.2..3.MAPE.and.MSE.comparison.result.for.all.motifs.png (see ``work05_retrain.Deepbind.model/README.md` for more details).
• Validation accuracies for the AddGene case: see work06_compare.k2p.and.Deepbind.heuristic.for.complex.models/README.md for more details.

Codes and guidelines (described by README.md )for reproducing these figures are also available in the corresponding work* directories.

• text01_supplementary.information: this directory contains the PDF file for the Supplementary Notes.
• tool02_k2p: this directory contains several python scripts used by work* directories above.