7 citations · 7 across the 6 of their papers we have counts for
7 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…
Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
Emil Haugen, Alexei Stepanenko, Anders C. Hansen
We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. We use numerical quadrature to compute upper bounds for norm…
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…
Do stable neural networks exist for classification problems? -- A new view on stability in AI
Z. N. D. Liu, A. C. Hansen
In deep learning (DL) the instability phenomenon is widespread and well documented, most commonly using the classical measure of stability, the Lipschitz constant. While a small Li…
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-…