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).

For additional motivation, it is reasonable to consider Massart noise to be a more realistic model of real-life noise (even when benign) when compared to the RCN model, as it allows for some amount of non-uniformity. This made Definition 1 a possibly tractable way to relax the noise assumption, without running intotheaforementioned computational barriers foragnostic learning.

Yet, small, distant, and incomplete objects with sparse or few points are often hard to detect.

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If the memory state can be addressed by its content, itisfurthermore called content-addressable.

After observing a sample, the analyst may update their estimate of the mean and variance of that group and choose the next group accordingly. The analyst's objective is to dynamically collect samples to minimize the

There are words with multiple clusters (Figure 1b).