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Found 7 papers, 5 papers with code
When can you trust feature selection? -- I: A condition-based analysis of LASSO and generalised hardness of approximation
However, we define a LASSO condition number and design an efficient algorithm for computing these support sets provided the input data is well-posed (has finite condition number) in time polynomial in the dimensions and logarithm of the condition number.
The Boundaries of Verifiable Accuracy, Robustness, and Generalisation in Deep Learning
We consider classical distribution-agnostic framework and algorithms minimising empirical risks and potentially subjected to some weights regularisation.
Implicit regularization in AI meets generalized hardness of approximation in optimization -- Sharp results for diagonal linear networks
In this work we provide sharp results for the implicit regularization imposed by the gradient flow of Diagonal Linear Networks (DLNs) in the over-parameterized regression setting and, potentially surprisingly, link this to the phenomenon of phase transitions in generalized hardness of approximation (GHA).
Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem
We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities, however, there does not exist any algorithm, even randomised, that can train (or compute) such a NN.
The troublesome kernel -- On hallucinations, no free lunches and the accuracy-stability trade-off in inverse problems
In inverse problems in imaging, the focus of this paper, there is increasing empirical evidence that methods may suffer from hallucinations, i. e., false, but realistic-looking artifacts; instability, i. e., sensitivity to perturbations in the data; and unpredictable generalization, i. e., excellent performance on some images, but significant deterioration on others.
What do AI algorithms actually learn? - On false structures in deep learning
We provide the foundations for such a program establishing the existence of the false structures in practice.
On instabilities of deep learning in image reconstruction - Does AI come at a cost?
Deep learning, due to its unprecedented success in tasks such as image classification, has emerged as a new tool in image reconstruction with potential to change the field.
