A.1 Creation of the Multimodal Web Document Dataset A.1.1 Collecting of a Large Number of HTMLFiles Our data collection process begins by considering the 25 most recent Common Crawl6 dumps available at the time of dataset creation. It contains webpages spanning from February 2020 to January/February 2023. We use a modified version of readability-lxml7 to extract the main text from the pages, discarding any pages that contain text of excessively high perplexity. This process yields a total of 41.2 billion documents. Selection of English content To identify non-English content, we apply the FastText classifier (Joulin et al., 2017) to the extracted text, e ectively filtering out 63.6% of the documents. Early text deduplication Often, a set of URLs is crawled repeatedly across di erent Common Crawl snapshots. However, the content of these websites may vary as web administrators make changes over time. Hence, at this stage, we refrain from deduplicating documents based on their URLs. Instead, we perform MinHash (Broder, 1997) deduplication with 16 hashes calculated over 5-grams. To further refine the data, we eliminate documents containing substantial proportions of repeated paragraphs and n-grams, employing the methodology described in MassiveText (Rae et al., 2022).

In this paper, we consider how to construct best-of-both-worlds linear bandit algorithms that achieve nearly optimal performance for both stochastic and adversarial environments. For this purpose, we show that a natural approach referred to as exploration by optimization [Lattimore and Szepesvári, 2020b] works well.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning.

Data-driven models learned often struggle to generalize due to widespread subpopulation shifts, especially the presence of both spurious correlations and group imbalance (SC-GI). To learn models more powerful for defending against SC-GI, we propose a Correlation-Oriented Disentanglement and Augmentation (CODA) modeling scheme, which includes two unique developments: (1) correlation-oriented disentanglement and (2) strategic sample augmentation with reweighted consistency (RWC) loss. In (1), a bi-branch encoding process is developed to enable the disentangling of variant and invariant correlations by coordinating with a decoy classifier and the decoder reconstruction. In (2), a strategic sample augmentation based on disentangled latent features with RWC loss is designed to reinforce the training of a more generalizable model. The effectiveness of CODA is verified by benchmarking against a set of SOTA models in terms of worst-group accuracy and maximum group accuracy gap based on two famous datasets, ColoredMNIST and CelebA.

The proliferation of 2D foundation models has sparked research into adapting them for open-world 3D instance segmentation. Recent methods introduce a paradigm that leverages superpoints as geometric primitives and incorporates 2D multi-view masks from Segment Anything model (SAM) as merging guidance, achieving outstanding zero-shot instance segmentation results. However, the limited use of 3D priors restricts the segmentation performance. Previous methods calculate the 3D superpoints solely based on estimated normal from spatial coordinates, resulting in under-segmentation for instances with similar geometry. Besides, the heavy reliance on SAM and hand-crafted algorithms in 2D space suffers from over-segmentation due to SAM's inherent part-level segmentation tendency. To address these issues, we propose SA3DIP, a novel method for Segmenting Any 3D Instances via exploiting potential 3DPriors.

As illustrated by the success of integer linear programming, linear integer arithmetic is a powerful tool for modelling combinatorial problems. Furthermore, the probabilistic extension of linear programming has been used to formulate problems in neurosymbolic AI. However, two key problems persist that prevent the adoption of neurosymbolic techniques beyond toy problems. First, probabilistic inference is inherently hard, #P-hard to be precise. Second, the discrete nature of integers renders the construction of meaningful gradients challenging, which is problematic for learning. In order to mitigate these issues, we formulate linear arithmetic over integer-valued random variables as tensor manipulations that can be implemented in a straightforward fashion using modern deep learning libraries. At the core of our formulation lies the observation that the addition of two integer-valued random variables can be performed by adapting the fast Fourier transform to probabilities in the log-domain. By relying on tensor operations we obtain a differentiable data structure, which unlocks, virtually for free, gradient-based learning. In our experimental validation we show that tensorising probabilistic linear integer arithmetic and leveraging the fast Fourier transform allows us to push the state of the art by several orders of magnitude in terms of inference and learning times.