The "black-box" nature of representations, combined with the known susceptibility of networks to learn spurious correlations [

To address this problem, existing methods partition the overall DPDP into fixed-size sub-problems by caching online generated orders and solve each sub-problem, or on this basis to utilize the predicted future orders to optimize each sub-problem further. However, the solution quality and efficiency of these methods are unsatisfactory, especially when the problem scale is very large.

Jean-Paul Thorbjornsen is a leader of THORChain, a blockchain that is not supposed to have any leaders--and is reeling from a series of expensive controversies. We can do whatever we want," Jean-Paul Thorbjornsen tells me from the pilot's seat of his Aston Martin helicopter. As we fly over suburbs outside Melbourne, Australia, it's becoming clear that doing whatever he wants is Thorbjornsen's MO. Upper-middle-class homes give way to vineyards, and Thorbjornsen points out our landing spot outside a winery. "They're going to ask for a shot now," he says, used to the attention drawn by his luxury helicopter, emblazoned with the tail letters "BTC" for bitcoin (the price tag of $5 million in Australian dollars--$3.5 million in US dollars today--was perhaps reasonable for someone who claims a previous crypto project made more than AU$400 million, although he also says those funds were tied up in the company). Thorbjornsen is a founder of THORChain, a blockchain through which users can swap ...

First, note that we shall use the same MDPs defined in Appendix D.1 as follows

The theory of Koopman operators allows to deploy non-parametric machine learning algorithms to predict and analyze complex dynamical systems.

Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs.

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.

Reasoning over TKGs has two challenges: 1.