Annie Gray

Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy

The Manifold Hypothesis is a widely accepted tenet of Machine Learning which asserts that nominally high-dimensional data are in fact concentrated near a low-dimensional manifold, embedded in high-dimensional space. This phenomenon is observed empirically in many real world situations, has led to development of a wide range of statistical methods in the last few decades, and has been suggested as a key factor in the success of modern AI technologies. We show that rich and sometimes intricate manifold structure in data can emerge from a generic and remarkably simple statistical model -- the Latent Metric Model -- via elementary concepts such as latent variables, correlation and stationarity. This establishes a general statistical explanation for why the Manifold Hypothesis seems to hold in so many situations. Informed by the Latent Metric Model we derive procedures to discover and interpret the geometry of high-dimensional data, and explore hypotheses about the data generating mechanism. These procedures operate under minimal assumptions and make use of well known graph-analytic algorithms.

Mary Llewellyn, Annie Gray, Josh Collyer et al.

Before adopting a new large language model (LLM) architecture, it is critical to understand vulnerabilities accurately. Existing evaluations can be difficult to trust, often drawing conclusions from LLMs that are not meaningfully comparable, relying on heuristic inputs or employing metrics that fail to capture the inherent uncertainty. In this paper, we propose a principled and practical end-to-end framework for evaluating LLM vulnerabilities to prompt injection attacks. First, we propose practical approaches to experimental design, tackling unfair LLM comparisons by considering two practitioner scenarios: when training an LLM and when deploying a pre-trained LLM. Second, we address the analysis of experiments and propose a Bayesian hierarchical model with embedding-space clustering. This model is designed to improve uncertainty quantification in the common scenario that LLM outputs are not deterministic, test prompts are designed imperfectly, and practitioners only have a limited amount of compute to evaluate vulnerabilities. We show the improved inferential capabilities of the model in several prompt injection attack settings. Finally, we demonstrate the pipeline to evaluate the security of Transformer versus Mamba architectures. Our findings show that consideration of output variability can suggest less definitive findings. However, for some attacks, we find notably increased Transformer and Mamba-variant vulnerabilities across LLMs with the same training data or mathematical ability.

Annie Gray, Alexander Modell, Patrick Rubin-Delanchy et al.

In this paper we offer a new perspective on the well established agglomerative clustering algorithm, focusing on recovery of hierarchical structure. We recommend a simple variant of the standard algorithm, in which clusters are merged by maximum average dot product and not, for example, by minimum distance or within-cluster variance. We demonstrate that the tree output by this algorithm provides a bona fide estimate of generative hierarchical structure in data, under a generic probabilistic graphical model. The key technical innovations are to understand how hierarchical information in this model translates into tree geometry which can be recovered from data, and to characterise the benefits of simultaneously growing sample size and data dimension. We demonstrate superior tree recovery performance with real data over existing approaches such as UPGMA, Ward's method, and HDBSCAN.

Nick Whiteley, Annie Gray, Patrick Rubin-Delanchy

Given a graph or similarity matrix, we consider the problem of recovering a notion of true distance between the nodes, and so their true positions. We show that this can be accomplished in two steps: matrix factorisation, followed by nonlinear dimension reduction. This combination is effective because the point cloud obtained in the first step lives close to a manifold in which latent distance is encoded as geodesic distance. Hence, a nonlinear dimension reduction tool, approximating geodesic distance, can recover the latent positions, up to a simple transformation. We give a detailed account of the case where spectral embedding is used, followed by Isomap, and provide encouraging experimental evidence for other combinations of techniques.