44 citations · 84 across the 8 of their papers we have counts for
11 papers
Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs
Alexander Bastounis, Fabian Circelli, Anders C. Hansen
Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes eq…
On the consistent reasoning paradox of intelligence and optimal trust in AI: The power of 'I don't know'
Alexander Bastounis, Paolo Campodonico, Mihaela van der Schaar +2
We introduce the Consistent Reasoning Paradox (CRP). Consistent reasoning, which lies at the core of human intelligence, is the ability to handle tasks that are equivalent, yet des…
Stealth edits to large language models
Oliver J. Sutton, Qinghua Zhou, Wei Wang +4
We reveal the theoretical foundations of techniques for editing large language models, and present new methods which can do so without requiring retraining. Our theoretical insight…
When can you trust feature selection? -- II: On the effects of random data on condition in statistics and optimisation
Alexander Bastounis, Felipe Cucker, Anders C. Hansen
In Part I, we defined a LASSO condition number and developed an algorithm -- for computing support sets (feature selection) of the LASSO minimisation problem -- that runs in polyno…
When can you trust feature selection? -- I: A condition-based analysis of LASSO and generalised hardness of approximation
Alexander Bastounis, Felipe Cucker, Anders C. Hansen
The arrival of AI techniques in computations, with the potential for hallucinations and non-robustness, has made trustworthiness of algorithms a focal point. However, trustworthine…
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning
Alexander Bastounis, Alexander N. Gorban, Anders C. Hansen +5
In this work, we assess the theoretical limitations of determining guaranteed stability and accuracy of neural networks in classification tasks. We consider classical distribution-…
How adversarial attacks can disrupt seemingly stable accurate classifiers
Oliver J. Sutton, Qinghua Zhou, Ivan Y. Tyukin +3
Adversarial attacks dramatically change the output of an otherwise accurate learning system using a seemingly inconsequential modification to a piece of input data. Paradoxically,…
Generalised hardness of approximation and the SCI hierarchy -- On determining the boundaries of training algorithms in AI
Luca Eva Gazdag, Alexander Bastounis, Anders C. Hansen
Generalised hardness of approximation (GHA) is the phenomenon that one can easily compute an -approximation to a solution of a computational problem for , but for $ε…
The extended Smale's 9th problem -- On computational barriers and paradoxes in estimation, regularisation, computer-assisted proofs and learning
Alexander Bastounis, Anders C Hansen, Verner Vlačić
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assist…
The mathematics of adversarial attacks in AI -- Why deep learning is unstable despite the existence of stable neural networks
Alexander Bastounis, Anders C Hansen, Verner Vlačić
The unprecedented success of deep learning (DL) makes it unchallenged when it comes to classification problems. However, it is well established that the current DL methodology prod…
On the absence of the RIP in real-world applications of compressed sensing and the RIP in levels
Alexander Bastounis, Anders C. Hansen
The purpose of this paper is twofold. The first is to point out that the Restricted Isometry Property (RIP) does not hold in many applications where compressed sensing is successfu…