Abstract: A machine learning system includes encoder and decoder networks. The machine learning system is configured to obtain input data, which includes sensor data and a radius of an p norm ball of admissible perturbations. Input bounding data is generated based on the input data. First bounding data and second bounding data are generated by respectively propagating the input bounding data on first and second outputs of the encoder network. Third bounding data is generated in association with a latent variable based on the first bounding data and the second bounding data. Fourth bounding data is generated by propagating the third bounding data on an output of the decoder network. A robustness certificate is established with respect to the input data by generating a lower bound of an evidence lower bound based on the first, second, third, and fourth bounding data.

Abstract: A computer-implemented method includes applying a filter to input data based on an initial set of parameters to generate an initial feature map. The filter is configured to activate a filter function that involves a periodic function. The method includes performing a first linear transform on the initial feature map based on a subset of a first set of parameters to generate a first linear transform. The method includes applying the filter to the input data based on another subset of the first set of parameters to generate a first feature map. The method includes performing a multiplicative operation on the first linear transform and the first feature map to generate a first product. The method includes performing a second linear transform on the first product based on a subset of a second set of parameters to generate a second linear transform. The method includes generating output data that takes into account at least the second linear transform.

Abstract: A computer-implemented method includes applying a filter to input data based on an initial set of parameters to generate an initial feature map. The filter is configured to activate a filter function that involves a periodic function. The method includes performing a first linear transform on the initial feature map based on a subset of a first set of parameters to generate a first linear transform. The method includes applying the filter to the input data based on another subset of the first set of parameters to generate a first feature map. The method includes performing a multiplicative operation on the first linear transform and the first feature map to generate a first product. The method includes performing a second linear transform on the first product based on a subset of a second set of parameters to generate a second linear transform. The method includes generating output data that takes into account at least the second linear transform.

Abstract: A machine learning system includes encoder and decoder networks. The machine learning system is configured to obtain input data, which includes sensor data and a radius of an p norm ball of admissible perturbations. Input bounding data is generated based on the input data. First bounding data and second bounding data are generated by respectively propagating the input bounding data on first and second outputs of the encoder network. Third bounding data is generated in association with a latent variable based on the first bounding data and the second bounding data. Fourth bounding data is generated by propagating the third bounding data on an output of the decoder network. A robustness certificate is established with respect to the input data by generating a lower bound of an evidence lower bound based on the first, second, third, and fourth bounding data.