Extreme multi-label text classification (XMC) seeks to find relevant labels from an extreme large label collection for a given text input. Many real-world applications can be formulated as XMC problems, such as recommendation systems, document tagging and semantic search. Recently, transformer based XMC methods, such as XTransformer and LightXML, have shown significant improvement over other XMC methods. Despite leveraging pre-trained transformer models for text representation, the fine-tuning procedure of transformer models on large label space still has lengthy computational time even with powerful GPUs. In this paper, we propose a novel recursive approach, XR-Transformer to accelerate the procedure through recursively fine-tuning transformer models on a series of multi-resolution objectives related to the original XMC objective function. Empirical results show that XRTransformer takes significantly less training time compared to other transformerbased XMC models while yielding better state-of-the-art results. In particular, on the public Amazon-3M dataset with 3 million labels, XR-Transformer is not only 20x faster than X-Transformer but also improves the Precision@1 from 51% to 54%. Our code is publicly available at https://github.com/amzn/pecos.

While there remains a small gap between our main lower bound of Theorem 3 and the deterministic quantised gradient descent of Section 6, we can show that the gap cannot be closed by improved deterministic algorithms where the coordinator learns value of objective function F(x) in addition to the minimiser x. That is, our quantised gradient descent is the communication-optimal deterministic algorithm for variant (1) for objectives with constant condition number. Recall that in the N-player equality over universe of size d, denoted by EQd,N, each player i is given an input bi 2{ 0,1}d, and the task is to decide if all players have the same input. It is known [33] that the deterministic communication complexity of EQd,N is CC(EQd,N)= ( Nd). Theorem 8. Given parameters N, d, ", 0 and = 0N satisfying d /" = (1), any deterministic protocol solving (1) for quadratic input functions x 7! 0kx x0k22 has communication complexity Nd log( d/"), if the coordinator is also required to output estimate r 2 R for the minimum function value such that Assume is a deterministic protocol solving (1) with communication complexity C .We show that can then solve N-party equality over a universe of size D = ( dlog( d/")), implying C = ( ND)= Nd log( d/") . More specifically, let S be the set given by Lemma 2 with =(2 "/)1/2, and let D = dlog|S|e = (dlog( d/")). Note that since we assume d /" = (1), the set S has at least two elements and D 1.

Double Q-learning (Hasselt, 2010) has gained significant success in practice due to its effectiveness in overcoming the overestimation issue of Q-learning. However, the theoretical understanding of double Q-learning is rather limited. The only existing finite-time analysis was recently established in (Xiong et al., 2020), where the polynomial learning rate adopted in the analysis typically yields a slower convergence rate. This paper tackles the more challenging case of a constant learning rate, and develops new analytical tools that improve the existing convergence rate by orders of magnitude.

The recent success of transformer-based image generative models in object-centric learning highlights the importance of powerful image generators for handling complex scenes. However, despite the high expressiveness of diffusion models in image generation, their integration into object-centric learning remains largely unexplored in this domain. In this paper, we explore the feasibility and potential of integrating diffusion models into object-centric learning and investigate the pros and cons of this approach. We introduce Latent Slot Diffusion (LSD), a novel model that serves dual purposes: it is the first object-centric learning model to replace conventional slot decoders with a latent diffusion model conditioned on object slots, and it is also the first unsupervised compositional conditional diffusion model that operates without the need for supervised annotations like text. Through experiments on various object-centric tasks, including the first application of the FFHQ dataset in this field, we demonstrate that LSD significantly outperforms state-of-the-art transformer-based decoders, particularly in more complex scenes, and exhibits superior unsupervised compositional generation quality. In addition, we conduct a preliminary investigation into the integration of pre-trained diffusion models in LSD and demonstrate its effectiveness in real-world image segmentation and generation.

In a broad Degree-Corrected Mixed-Membership (DCMM) setting, we test whether a non-uniform hypergraph has only one community or has multiple communities. Since both the null and alternative hypotheses have many unknown parameters, the challenge is, given an alternative, how to identify the null that is hardest to separate from the alternative. We approach this by proposing a degree matching strategy where the main idea is leveraging the theory for tensor scaling to create a least favorable pair of hypotheses. We present a result on standard minimax lower bound theory and a result on Region of Impossibility (which is more informative than the minimax lower bound). We show that our lower bounds are tight by introducing a new test that attains the lower bound up to a logarithmic factor. We also discuss the case where the hypergraphs may have mixed-memberships.

We consider the task of training machine learning models with data-dependent constraints. Such constraints often arise as empirical versions of expected value constraints that enforce fairness or stability goals. We reformulate data-dependent constraints so that they are calibrated: enforcing the reformulated constraints guarantees that their expected value counterparts are satisfied with a user-prescribed probability. The resulting optimization problem is amendable to standard stochastic optimization algorithms, and we demonstrate the efficacy of our method on a fairness-sensitive classification task where we wish to guarantee the classifier's fairness (at test time).