Verified Deep Learning [CS 839 / S20]
Aws Albarghouthi
Office hrs: Tue, 1300-1415, CS 6363
TA: Swati Anand, sanand24@wisc.edu

Deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security, correctness, or robustness of neural networks. This course covers foundational ideas from formal verification and their application to deep learning.


The couse is based on chapters from the instructor's ongoing book on the subject and research papers from machine learning and verification.

1.20 Overview of verified deep learning
Tue  chapter 1 / slides
Thu  chapter 2

1.27 Correctness properties of neural networks
Tue  chapter 3 / Hoare's classic paper / Floyd's paper / Turing's obscure paper
Thu  chapter 4 / see also slides from Dillig's course

2.3 Logical encodings of neural networks
Tue  chapter 5 / see also encodings of traditional programs
Thu  cancelled

2.10 Encodings and decision procedures
Tue  chapter 5, continued / see Z3 tutorial
Thu  chapter 6 / see abstract DPPL paper

2.17 SMT solving
Tue  ✈️ Aws out of town for a PC meeting on Tuesday
Thu  chapter 6 / see abstract DPPL paper

2.25 Neural-network specialized theory solvers
Tue  chapter 7 / see paper from Dutertre & de Moura
Thu  chapter 7 / see Reluplex paper

3.2 A taste of abstract interpretation
Tue  chapter 8 / Lifting neural networks to operate on sets
Thu  chapter 8 / Interval abstraction of neural operations

3.9 Advanced abstract domains for neural networks
Tue  chapter 9 / Zonotope abstraction / see DeepZ paper
Thu  chapter 9 / Polyhedra abstraction / see Stars and DeepPoly papers

3.16 🌷Spring break

3.23 More on abstraction
Tue  tuning virtual lectures + asn 2 preview
Thu  Joint abstraction / see k-ReLU paper

3.30 Abstract training
Tue  Abstract training / see DiffAI and IBP papers (IBP is an easier read)
Thu  Randomized smoothing + NLP / see Cohen et al. and Huang et al.

4.6 Verified RL
Tue  Invariants and NNs / see Zhu et al.
Thu  MDPs and verification / see Zhu et al.

4.13 TBD
Tue 
Thu 

4.20 Project presentations
Tue  presentations
Thu  presentations

4.27 Project presentations
Tue  presentations
Thu  presentations + farewell



Grade distribution
75% project (mid March review 15%, mid April review 15%, paper 30%, 15% presentation)
25% assignments (5% participation + 3 assignments)

Project details
Find project partner and choose project
Create GitHub repository in CS839 organization
Weekly update README.md with new developments, problems, etc.