7 accepted papers
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for architectures that explicitly preserve Lipschitz continuity have ye…
$1$-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on $1$-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and study their approximation capabilities. Leveraging the R…
Neural operators serve as universal approximators for general continuous operators. In this paper, we derive the approximation rate of solution operators for the nonlinear parabolic partial differential equations (PDEs), contributing to the quantitative approximation theorem for solution operators o…
Transformers are deep architectures that define ``in-context mappings'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In this work, we study in particular the ability of these architectures to ha…
In this work we consider the problem of discretization of neural operators in a general setting. Using category theory, we give a no-go theorem that shows that diffeomorphisms between Hilbert spaces may not admit any continuous approximations by diffeomorphisms on finite spaces, even if the discreti…
Recently there has been great interest in operator learning, where networks learn operators between function spaces from an essentially infinite-dimensional perspective. In this work we present results for when the operators learned by these networks are injective and surjective. As a warmup, we com…
Recurrent neural networks (RNNs) are a class of neural networks used in sequential tasks. However, in general, RNNs have a large number of parameters and involve enormous computational costs by repeating the recurrent structures in many time steps. As a method to overcome this difficulty, RNN prunin…