Varied number of bit split: To generate the samples in this split, we first sampled the number ofbits, then sampled each bitindividually from auniform Bernoulli distribution. Variednumberofonessplit: Here, we fixed the number of bits at30. NaturalLanguageParityDataset: Inorder totapinto thenatural language understanding capabilities of pretrained language models, we situated the parity task as a"coin flip problem". We trained baseline models with the same parameter count on a modified version of the variable assignment dataset where the order of the operations were randomly shuffled. We used greedy decoding in all of our experiments (including few-shot scratchpad ones).

Moreover,doctors explicitly explore severepathologies before potentially ruling them out from the differential, especially in acute care settings. Finally, for doctors to trust a system's recommendations, they need to understand how the gathered evidences led to the predicted diseases.

Stein thinning is a promising algorithm proposed by (Riabiz et al., 2022) for post-processing outputs of Markov chain Monte Carlo (MCMC). The main principle is to greedily minimize the kernelized Stein discrepancy (KSD), which only requires the gradient of the log-target distribution, and is thus well-suited for Bayesian inference. The main advantages of Stein thinning are the automatic remove of the burn-in period, the correction of the bias introduced by recent MCMC algorithms, and the asymptotic properties of convergence towards the target distribution. Nevertheless, Stein thinning suffers from several empirical pathologies, which may result in poor approximations, as observed in the literature. In this article, we conduct a theoretical analysis of these pathologies, to clearly identify the mechanisms at stake, and suggest improved strategies. Then, we introduce the regularized Stein thinning algorithm to alleviate the identified pathologies. Finally, theoretical guarantees and extensive experiments show the high efficiency of the proposed algorithm. An implementation of regularized Stein thinning as the kernax library in python and JAX is available at https://gitlab.com/drti/kernax.