Organizing Committee
Simon Fraser University
Concordia University
University of Cambridge
University of Texas
Abstract
Deep learning is profoundly reshaping the research directions of entire scientific communities across mathematics, computer science, and statistics, as well as the physical, biological and medical sciences . Yet, despite their indisputable success, deep neural networks are known to be universally unstable. That is, small changes in the input that are almost undetectable produce significant changes in the output. This happens in applications such as image recognition and classification, speech and audio recognition, automatic diagnosis in medicine, image reconstruction and medical imaging as well as inverse problems in general. This phenomenon is now very well documented and yields non-human-like behaviour of neural networks in the cases where they replace humans, and unexpected and unreliable behaviour where they replace standard algorithms in the sciences.
The many examples produced over the last years demonstrate the intricacy of this complex problem and the questions of safety and security of deep learning become crucial. Moreover, the ubiquitous phenomenon of instability combined with the lack of interpretability of deep neural networks makes the reproducibility of scientific results based on deep learning at stake.
For these reasons, the development of mathematical foundations aimed at improving the safety and security of deep learning is of key importance. The goal of this workshop is to bring together experts from mathematics, computer science, and statistics in order to accelerate the exploration of breakthroughs and of emerging mathematical ideas in this area.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
The many examples produced over the last years demonstrate the intricacy of this complex problem and the questions of safety and security of deep learning become crucial. Moreover, the ubiquitous phenomenon of instability combined with the lack of interpretability of deep neural networks makes the reproducibility of scientific results based on deep learning at stake.
For these reasons, the development of mathematical foundations aimed at improving the safety and security of deep learning is of key importance. The goal of this workshop is to bring together experts from mathematics, computer science, and statistics in order to accelerate the exploration of breakthroughs and of emerging mathematical ideas in this area.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
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Workshop Schedule
Saturday, April 10, 2021
10:00 - 10:15 AM EDT
Welcome
Welcome - Virtual
Brendan Hassett, ICERM/Brown University
10:15 - 10:55 AM EDT
An Information Theoretic Approach to Validate Deep Learning-Based Algorithms
Virtual
Speaker
Gitta Kutyniok, LMU Munich
Session Chair
Simone Brugiapaglia, Concordia University
Abstract
In this talk, we provide a theoretical framework for interpreting neural network decisions by formalizing the problem in a rate-distortion framework. The solver of the associated optimization, which we coin Rate-Distortion Explanation (RDE), is then accessible to a mathematical analysis. We will discuss theoretical results as well as present numerical experiments showing that our algorithmic approach outperforms established methods, in particular, for sparse explanations of neural network decisions.
11:55 AM - 1:30 PM EDT
Lunch/Free Time
Virtual
1:30 - 2:10 PM EDT
Data Matters in Robust ML
Virtual
Speaker
Aleksander Madry, Massachusetts Institute of Technology
Session Chair
Clayton Webster, University of Texas
2:20 - 3:00 PM EDT
Breaking into a Deep Learning box
Virtual
Speaker
Ivan Tyukin, University of Leicester
Session Chair
Clayton Webster, University of Texas
Abstract
Recent decade brought explosive progress in the applications of Machine Learning and data-driven Artificial Intelligence (AI) to real-life problems across sectors. Autonomous cars and automated passport control are examples of the new reality. Deep Learning models, or more generally, models with multiple learnable processing stages constitute a large class of models to which a significant part of the recent successes has been apportioned. Notwithstanding these successes, there are emerging challenges too.
In this talk we will discuss a set of vulnerabilities which may typically arise in large Deep Learning models. These vulnerabilities are extreme sensitivities of the models to data or structure perturbations. We will present a formal theoretical framework for assessing and analysing two classes of such vulnerabilities. The first class is linked with adversarial examples. Vulnerabilities of the second class are linked with purposeful malicious structure perturbations which may be, with high probability, undetectable through input-output validation. We name these perturbations “stealth attacks”. We will show how to construct stealth attacks on Deep Learning models that are hard to spot unless the validation set is made exponentially large.
For both classes of attacks, the high dimensionality of the AI’s decision-making space appears to be a major contributor to the AI’s vulnerability. We conclude with recommendations of how robustness to malicious perturbations of data and structure can be mitigated by ensuring that the data dimensionality at relevant processing stages in Deep Learning models is kept sufficiently small.
3:10 - 4:00 PM EDT
Gathertown Afternoon Coffee Break
Coffee Break - Virtual
Sunday, April 11, 2021
9:10 - 9:50 AM EDT
Deep Learning and Neural Networks: The Mathematical View
Virtual
Speaker
Ronald DeVore, Texas A&M University
Session Chair
Anders Hansen, University of Cambridge
Abstract
Deep Learning is much publicized and has had great empirical success on challenging problems in learning. Yet there is no quantifiable proof of performance and certified guarantees for these methods. This talk will give an overview of Deep Learning from the viewpoint of mathematics and numerical computation.
10:00 - 10:30 AM EDT
Gathertown Morning Coffee Break
Coffee Break - Virtual
10:30 - 11:10 AM EDT
Can we design deep learning models that are inherently interpretable?
Virtual
Speaker
Cynthia Rudin, Duke University
Session Chair
Anders Hansen, University of Cambridge
Abstract
Black box deep learning models are difficult to troubleshoot. In practice, it can be difficult to tell whether their reasoning process is correct, and ""explanations"" have repeatedly been shown to be ineffective. In this talk I will discuss two possible approaches to create deep learning methods that are inherently interpretable. The first is to use case-based reasoning, through a neural architecture called ProtoPNet, where an extra ""prototype"" layer in the network allows it to reason about an image based on how similar it looks to other images (the network says ""this looks like that""). Second, I will describe ""concept whitening,"" a method for disentangling the latent space of a neural network by decorrelating concepts in the latent space and aligning them along the axes.
This Looks Like That: Deep Learning for Interpretable Image Recognition. NeurIPS spotlight, 2019.
https://arxiv.org/abs/1806.10574
Concept Whitening for Interpretable Image Recognition. Nature Machine Intelligence, 2020.
https://rdcu.be/cbOKj
11:20 AM - 12:00 PM EDT
Differential privacy, deep learning, and synthetic data generation
Virtual
Speaker
Rachel Cummings, Columbia University
Session Chair
Anders Hansen, University of Cambridge
Abstract
Differential privacy is a parameterized notion of database privacy that gives a mathematically rigorous worst-case bound on the maximum amount of information that can be learned about an individual's data from the output of a computation. Recent work has provided tools for differentially private stochastic gradient decent, which enables differentially private deep learning. These in turn enable differentially private synthetic data generation, to provide synthetic versions of sensitive datasets that share statistical properties with the original data while additionally providing formal privacy guarantees for the training dataset. This talk will first give an introduction to differential privacy, and then survey recent advances in differentially private deep learning and its application to synthetic data generation.
12:10 - 1:30 PM EDT
Lunch/Free Time
Virtual
1:30 - 2:10 PM EDT
Reliability, Robustness and Minipatch Learning
Virtual
Speaker
Genevera Allen, Rice University
Session Chair
Ben Adcock, Simon Fraser University
Abstract
Many have noted and lamented a reproducibility crisis in science with more recent discussion and interest on the reproducibility and reliability of data science and machine learning techniques. In this talk, I will introduce the Four R's, a tiered framework for discussing and assessing the reproducibility, replicability, reliability, and robustness of a data science or machine learning pipeline. Then, I will introduce a new minipatch learning framework that helps to improve the reliability and robustness of machine learning procedures. Inspired by stability approaches from high-dimensional statistics, random forests, and dropout training in deep learning, minipatch learning is an ensemble approach where we train on very tiny randomly or adaptively chosen subsets of both observations and features or parameters. Beyond the obvious computational and memory efficiency advantages, we show that minipatch learning also yields more reliable and robust solutions by providing implicit regularization.