Nonetheless, modern machine learning is adaptive in its nature. Prior information about a model's performance on the test set inevitably influences

We propose below the proofs of the results presented in the main text. RKBS developed in (Zhang et al., 2009; Song et al., 2013) to develop the notion of vector-valued (Giles, 1967). " 0, @ j ď n, @ u P U (9) which allows us to say that O P RKBS (Corollary 3.2 of Zhang (2013)) that we recall hereafter: We first define for any linear operator We show our result in the case J=1 and can be directly extended to any cardinality J. Specifically, we tested three expressions: Exp. The two first expressions yield similar result in the ADR experiment at an equal compute cost. We also tried a'branch' and'trunk' networks formulation of the model as in DeepONet (Lu T able S.2: Summary of the architectural hyperparameters used to build the Transducer in the four experiments. 'Depth' corresponds to network number of layers, 'MLP dim' to the dimensionality of the hidden layer As stated, we used for all experiments, the same meta-training procedure. T able S.3: Summary of the meta-learning hyperparameters used to meta-train the Transducer in our four Figure S.1: Examples of sampled functions δ p xq and ν px q used to build operators O We train Tranducers for 200K gradient steps. Flow library (Holl et al., 2020) that allows for batched and differentiable simulations of fluid dynamics Figure S.5: Magnitude of the complex coefficients of the Fourier transform of an exemple pair of input and In order to tackle the high-resolution climate modeling experiment, we take inspiration from Pathak et al. (2022), which combines neural operators with the patch splitting L " 12, in order to match number of trainable parameters.

The most forceful driver of advancements in the field of Machine Learning over the past decades has been the success of deep neural networks.

We thank the reviewers for their insightful feedback, and we appreciate the opportunity to improve our paper. We would like to emphasize that Theorem 1 is the most important contribution of our paper due to its generality. In the Gaussian case, our sample complexity result follows directly from the expression for the optimal loss. Finally, while Dohmatob's bounds become non-trivial only when the adversarial We will also add a clearer description of the "translate and pair in place" coupling. Comparisons with Sinha et al. are in Section 7 and we compare to Dohmatob above.

The notoriously challenging book is being re-released for its 30th anniversary. Its fandom is annoying, sure--but at least they read. The host had been grilling Wallace, ostensibly invited on to discuss his own literary and journalistic output, on range of topics: tennis, teaching, why women don't like Westerns, depression, and, yes, Anthony Minghella's Academy Award-winning epic war drama, which had by the time the interview aired already become a punch line . Watching the interview, it's clear Wallace, who died by suicide in 2008, bristles at being pressed to purvey rank punditry on the popular culture at large like some kind of dancing monkey. But the exercise revealed how Rose, and large swaths of American intellectual culture circa the late-1990s, thought of Wallace.