A.1 Datasets fMoWRGBFunctional Map of the World (fMoW) [17] is a dataset of high-resolution satellite image time series across the world, with a task of classification among 62 architecture categories such as airport, shipyard, and zoo. The license is provided here 2. Co-located images of different timestamps, or sequences, are provided in fMoW. They are of different length, and around 60% of the samples have length larger than 2. Readers can refer to the fMoW paper [17] for statistics on the distribution of sequence lengths. We construct a temporal version of fMoW by randomly associating every single image with two images of the same location but of different timestamps if possible. For a given spatial location loc, we define Tloc as the number of temporally distinct snapshots present in the dataset. We crop surface reflectance images from the Sentinel-2 (ESA) satellite (courtesy of the U.S. Geological Survey), consisting of 90-day composites of images at the same locations as fMoW images (to reduce the impacts of cloud coverage). At each fMoW datapoint location, we collect a time series of Sentinel-2 images, using the provided geo-coordinate bounding boxes.

A.1 Detailed Re-alignment Task Formulation and Training Setup In Figure A1, we show the procedure for converting the data samples in the alignment datasets into training data of AEM (negative samples used in AIL are generated similarly). In DP-inferred chain-of-edits (CoEs), we use a few special tokens to mark the editing operations (with their position and content). Then our decipher module will translate these special tokens into natural language. As the final step, we add a special token [SEP] between Context + Source and the ground truth Chain-of-Edits (CoEs) and Target, as a boundary signal similar to the settings in text-to-text training. During inference, we input a certain Context + Source, and the LM trained by SECONDTHOUGHTS can generate CoEs and the corresponding Target.

Molecular Representation Learning (MRL) has emerged as a powerful tool for drug and materials discovery in a variety of tasks such as virtual screening and inverse design. While there has been a surge of interest in advancing modelcentric techniques, the influence of both data quantity and quality on molecular representations is not yet clearly understood within this field.

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Learning methods for generic object recognition with invariance to pose and lighting.

We study a generalization of boosting to the multiclass setting. We introduce a weak learning condition for multiclass classification that captures the original notion of weak learnability as being "slightly better than random guessing". We give a simple and efficient boosting algorithm, that does not require realizability assumptions and its sample and oracle complexity bounds are independent of the number of classes. In addition, we utilize our new boosting technique in several theoretical applications within the context of List PACLearning. First, we establish an equivalence to weak PAC learning. Furthermore, we present a new result on boosting for list learners, as well as provide a novel proof for the characterization of multiclass PAC learning and List PAC learning. Notably, our technique gives rise to a simplified analysis, and also implies an improved error bound for large list sizes, compared to previous results.