Spectrum Extraction and Clipping for Implicitly Linear Layers

Ali Ebrahimpour Boroojeny, Matus Telgarsky, Hari Sundaram

Research output: Contribution to journalConference articlepeer-review


We show the effectiveness of automatic differentiation in efficiently and correctly computing and controlling the spectrum of implicitly linear operators, a rich family of layer types including all standard convolutional and dense layers. We provide the first clipping method which is correct for general convolution layers, and illuminate the representational limitation that caused correctness issues in prior work. We study the effect of the batch normalization layers when concatenated with convolutional layers and show how our clipping method can be applied to their composition. By comparing the accuracy and performance of our algorithms to the state-of-the-art methods, using various experiments, we show they are more precise and efficient and lead to better generalization and adversarial robustness. We provide the code for using our methods at https://github.com/Ali-E/FastClip.

Original languageEnglish (US)
Pages (from-to)2971-2979
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 2024
Event27th International Conference on Artificial Intelligence and Statistics, AISTATS 2024 - Valencia, Spain
Duration: May 2 2024May 4 2024

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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