## ISL Colloquium presents "Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators"

Convolutional Neural Networks (CNNs) have emerged as highly successful tools for image generation, recovery, and restoration. This success is often attributed to large amounts of training data.

On the contrary, a number of recent experimental results suggest that a major contributing factor to this success is that convolutional networks impose strong prior assumptions about natural images. A surprising experiment that highlights this structural bias towards simple, natural images is that one can remove various kinds of noise and corruptions from a corrupted natural image by simply fitting (via gradient descent) a randomly initialized, over-parameterized convolutional generator to this single image. While this over-parameterized model can eventually fit the corrupted image perfectly, surprisingly after a few iterations of gradient descent one obtains the uncorrupted image, without using any training data. This intriguing phenomena has enabled state-of-the-art CNN-based denoising as well as regularization in linear inverse problems such as compressive sensing.

In this talk we take a step towards explaining this experimental phenomena by attributing it to particular architectural choices of convolutional networks. We then characterize the dynamics of fitting a two layer convolutional generator to a noisy signal and prove that early-stopped gradient descent denoises/regularizes. This results relies on showing that convolutional generators fit the structured part of an image significantly faster than the corrupted portion.

Based on joint work with Paul Hand and Mahdi Soltanolkotabi.

### The Information Systems Laboratory Colloquium (ISLC)

is typically held in Packard 101 every Thursday at 4:30 pm during the academic year. Coffee and refreshments are served at 4pm in the second floor kitchen of Packard Bldg.

The Colloquium is organized by graduate students Joachim Neu, Tavor Baharav and Kabir Chandrasekher. To suggest speakers, please contact any of the students.

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