NumAStAI · Numerical Analysis for Stable AI

From a numerical analysis perspective I will identify, quantify and mitigate vulnerabilities in current artificial intelligence (AI) algorithms.Novel mathematical research will emerge along six overlapping axes:Inevitability: rigorously understand the inescapable endgame of the attack-versus-defence paradigm. Under what conditions is it inevitable that adversaries willsucceed? Formalizing such conditions will allow us to understand and, where possible, overcome current AI instabilities.Editability: study algorithms that stealthily change a small number of parameters. This scenario is highly pertitent when new AI is built on top of third-party, foundation models. It also opens up the possibility of fixing errors on-the-fly without the need to re-train.Targetability: examine whether under-represented categories in the training data are more susceptible to adversarial attacks. This topic raises a key,and currently overlooked, issue in the ethical use of AI.Universality: develop linear, sparse, low rank mappings that create adversarial attacks. These new functions will expose novel, low-cost, threat mechanisms, but will also give insights into the decision boundary landscape. Roundability: use state-of-the art probabilistic rounding error analysis to justify large-scale, low precision computations.I will study (a) why current AI technologies appear to defy traditional worst-case floating point error bounds, and (b) whether low precision can be exploited byan adversary. Legislatability: devise easy-to-interpret results and practical case studies that can inform public opinion and impact the design of appropriate AI legislation.The project identifies high-profile open questions requiring tools frommatrix analysis, optimization, backward error analysis, condition number theory andstochastic computation. Some of the proposed work is highly speculative and challenging,but will significantly advance our understanding of AI vulnerabilities.