William J. Knottenbelt

Padmanaba Srinivasan, William J. Knottenbelt

Many real-world tasks are plagued by limitations on data: in some instances very little data is available and in others, data is protected by privacy enforcing regulations (e.g. GDPR). We consider limitations posed specifically on time-series data and present a model that can generate synthetic time-series which can be used in place of real data. A model that generates synthetic time-series data has two objectives: 1) to capture the stepwise conditional distribution of real sequences, and 2) to faithfully model the joint distribution of entire real sequences. Autoregressive models trained via maximum likelihood estimation can be used in a system where previous predictions are fed back in and used to predict future ones; in such models, errors can accrue over time. Furthermore, a plausible initial value is required making MLE based models not really generative. Many downstream tasks learn to model conditional distributions of the time-series, hence, synthetic data drawn from a generative model must satisfy 1) in addition to performing 2). We present TsT-GAN, a framework that capitalises on the Transformer architecture to satisfy the desiderata and compare its performance against five state-of-the-art models on five datasets and show that TsT-GAN achieves higher predictive performance on all datasets.

Christina Karakosta, Lian Alhedaithy, William J. Knottenbelt

Iris-based biometric identification is increasingly recognized for its significant accuracy and long-term stability compared to other biometric modalities such as fingerprints or facial features. However, all biometric modalities are highly sensitive data that raise serious privacy and security concerns, particularly in decentralized and untrusted environments. While Fully Homomorphic Encryption (FHE) has emerged as a promising solution for protecting sensitive data during computation, existing privacy-preserving iris recognition systems face significant performance limitations that hinder their practical deployment. This paper investigates the performance challenges of the current landscape of privacy-preserving iris recognition systems using FHE. Based on these insights, we outline a scalable privacy-preserving framework that aligns with all the requirements specified in the ISO/IEC 24745 standard. Leveraging the Open Iris library, our approach starts with robust iris segmentation, followed by normalization and feature extraction using Gabor filters to generate iris codes. We then apply binary masking to filter out unreliable regions and perform matching using Hamming distance on encrypted iris codes. The accuracy and performance of our proposed privacy-preserving framework is evaluated on the CASIA-Iris-Thousand dataset. Results show that our privacy-preserving framework yields very similar accuracy to the cleartext equivalent, but a much higher computational overhead with respect to pairwise iris template comparisons, of $\sim 120\,000 \times$. This points towards the need for the deployment of two-level schemes in the context of scalable $1-N$ template comparisons.

Edward Pearce-Crump, William J. Knottenbelt

Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph $G$ that has $n$ vertices, using the symmetric group $S_n$ as its group of symmetries does not take into account the relations that exist between the vertices. Given that the actual group of symmetries is the automorphism group Aut$(G)$, we show how to construct neural networks that are equivariant to Aut$(G)$ by obtaining a full characterisation of the learnable, linear, Aut$(G)$-equivariant functions between layers that are some tensor power of $\mathbb{R}^{n}$. In particular, we find a spanning set of matrices for these layer functions in the standard basis of $\mathbb{R}^{n}$. This result has important consequences for learning from data whose group of symmetries is a finite group because a theorem by Frucht (1938) showed that any finite group is isomorphic to the automorphism group of a graph.

Edward Pearce-Crump, William J. Knottenbelt

Group equivariant neural networks are growing in importance owing to their ability to generalise well in applications where the data has known underlying symmetries. Recent characterisations of a class of these networks that use high-order tensor power spaces as their layers suggest that they have significant potential; however, their implementation remains challenging owing to the prohibitively expensive nature of the computations that are involved. In this work, we present a fast matrix multiplication algorithm for any equivariant weight matrix that maps between tensor power layer spaces in these networks for four groups: the symmetric, orthogonal, special orthogonal, and symplectic groups. We obtain this algorithm by developing a diagrammatic framework based on category theory that enables us to not only express each weight matrix as a linear combination of diagrams but also makes it possible for us to use these diagrams to factor the original computation into a series of steps that are optimal. We show that this algorithm improves the Big-$O$ time complexity exponentially in comparison to a naïve matrix multiplication.

Sam M. Werner, Daniel Perez, Lewis Gudgeon et al.

Decentralized Finance (DeFi), a blockchain powered peer-to-peer financial system, is mushrooming. Two years ago the total value locked in DeFi systems was approximately 700m USD, now, as of April 2022, it stands at around 150bn USD. The frenetic evolution of the ecosystem has created challenges in understanding the basic principles of these systems and their security risks. In this Systematization of Knowledge (SoK) we delineate the DeFi ecosystem along the following axes: its primitives, its operational protocol types and its security. We provide a distinction between technical security, which has a healthy literature, and economic security, which is largely unexplored, connecting the latter with new models and thereby synthesizing insights from computer science, economics and finance. Finally, we outline the open research challenges in the ecosystem across these security types.

Dragos I. Ilie, Sam M. Werner, Iain Stewart et al.

In Proof-of-Work blockchains, difficulty algorithms serve the crucial purpose of maintaining a stable transaction throughput by dynamically adjusting the block difficulty in response to the miners' constantly changing computational power. Blockchains that may experience severe hash rate fluctuations need difficulty algorithms that quickly adapt the mining difficulty. However, without careful design, the system could be gamed by miners using coin-hopping strategies to manipulate the block difficulty for profit. Such miner behavior results in an unreliable system due to the unstable processing of transactions. We provide an empirical analysis of how Bitcoin Cash's difficulty algorithm design leads to cyclicality in block solve times as a consequence of a positive feedback loop. In response, we mathematically derive a difficulty algorithm using a negative exponential filter which prohibits the formation of positive feedback and exhibits additional desirable properties, such as history agnosticism. We compare the described algorithm to that of Bitcoin Cash in a simulated mining environment and verify that the former would eliminate the severe oscillations in transaction throughput.