Skip to main content

Learning Minimum-Entropy Couplings using AlphaZero and Geometric Deep Learning

Supervisors

Suitable for

MSc in Advanced Computer Science
Mathematics and Computer Science, Part C
Computer Science and Philosophy, Part C
Computer Science, Part C
Computer Science, Part B

Abstract

Steganography is the practice of encoding a plaintext message into another piece of content, called a stegotext, in such a way that an adversary would not realise that hidden communication is occurring. In a recent breakthrough [1,2,3], we showed that messages can be encoded into the output distribution of arbitrary autoregressive neural networks with perfect security [4], i.e. without changing the output distribution, hence rendering the hiding of secret messages information-theoretically undetectable. In this project, we seek to improve the heart of our perfectly-secure encoding algorithm, namely minimum entropy couplings. As constructing exact minimum entropy couplings is known to be NP-hard, we currently use an approximation algorithm that runs in loglinear time. For large block sizes, which are crucial to achieving good transmission rates, this algorithm is slow as it is not readily parallelisable. In this project, we will build upon recent advances in deep reinforcement learning self-play [5] and leverage graph networks to implement constraints on the sparse neural network outputs [6] in order to learn deep minimum entropy coupling networks. If successful, this project will greatly increase the feasibility of AI-generated steganography on mobile devices, as well as lead to novel methodological approaches for neural network architectures for sparse doubly-stochastic matrix outputs.

In this project, we will be working with state-of-the-art MARL implementations in JAX [2]. This project is designed to lead to publication. We are looking for a highly-motivated student.

[1] https://arxiv.org/abs/2210.14889

[2] https://www.quantamagazine.org/secret-messages-can-hide-in-ai-generated-media-20230518/

[3] https://www.scientificamerican.com/article/ai-could-smuggle-secret-messages-in-memes/

[4] https://www.sciencedirect.com/science/article/pii/S0890540104000409

[5] https://deepmind.google/discover/blog/alphadev-discovers-faster-sorting-algorithms/

[6] Modeling relational data with graph convolutional networks, M Schlichtkrull, TN Kipf, P Bloem, R Van Den Berg, I Titov, M Welling, The Semantic Web: 15th International Conference, ESWC 2018

[7] Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges, Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković, arXiv:2104.13478 [cs.LG]