Distributed Estimation and Inference with Statistical Guarantees

This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from $k$ subsamples of size $n/k$, where $n$ is the sample size. In both low dimensional and high dimensional settings, we address the important question of how to choose $k$ as $n$ grows large, providing a theoretical upper bound on $k$ such that the information loss due to the divide and conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as a practically infeasible oracle with access to the full sample. Thorough numerical results are provided to back up the theory

Hierarchy Flow For High-Fidelity Image-to-Image Translation

Image-to-image (I2I) translation comprises a wide spectrum of tasks. Here we divide this problem into three levels: strong-fidelity translation, normal-fidelity translation, and weak-fidelity translation, indicating the extent to which the content of the original image is preserved. Although existing methods achieve good performance in weak-fidelity translation, they fail to fully preserve the content in both strong- and normal-fidelity tasks, e.g. sim2real, style transfer and low-level vision. In this work, we propose Hierarchy Flow, a novel flow-based model to achieve better content preservation during translation. Specifically, 1) we first unveil the drawbacks of standard flow-based models when applied to I2I translation. 2) Next, we propose a new design, namely hierarchical coupling for reversible feature transformation and multi-scale modeling, to constitute Hierarchy Flow. 3) Finally, we present a dedicated aligned-style loss for a better trade-off between content preservation and stylization during translation. Extensive experiments on a wide range of I2I translation benchmarks demonstrate that our approach achieves state-of-the-art performance, with convincing advantages in both strong- and normal-fidelity tasks. Code and models will be at https://github.com/WeichenFan/HierarchyFlow.Comment: arXiv admin note: text overlap with arXiv:2207.0190

Mutual Wasserstein Discrepancy Minimization for Sequential Recommendation

Self-supervised sequential recommendation significantly improves recommendation performance by maximizing mutual information with well-designed data augmentations. However, the mutual information estimation is based on the calculation of Kullback Leibler divergence with several limitations, including asymmetrical estimation, the exponential need of the sample size, and training instability. Also, existing data augmentations are mostly stochastic and can potentially break sequential correlations with random modifications. These two issues motivate us to investigate an alternative robust mutual information measurement capable of modeling uncertainty and alleviating KL divergence limitations. To this end, we propose a novel self-supervised learning framework based on Mutual WasserStein discrepancy minimization MStein for the sequential recommendation. We propose the Wasserstein Discrepancy Measurement to measure the mutual information between augmented sequences. Wasserstein Discrepancy Measurement builds upon the 2-Wasserstein distance, which is more robust, more efficient in small batch sizes, and able to model the uncertainty of stochastic augmentation processes. We also propose a novel contrastive learning loss based on Wasserstein Discrepancy Measurement. Extensive experiments on four benchmark datasets demonstrate the effectiveness of MStein over baselines. More quantitative analyses show the robustness against perturbations and training efficiency in batch size. Finally, improvements analysis indicates better representations of popular users or items with significant uncertainty. The source code is at https://github.com/zfan20/MStein.Comment: Updated with the correction of the asymmetric mistake on the mutual information connectio

The nanohertz stochastic gravitational-wave background from cosmic string Loops and the abundant high redshift massive galaxies

Very recently, the Pulsar Timing Array (PTA) experiments reported strong evidence for the presence of the nanohertz stochastic gravitational wave background (SGWB). In this work we show that the cosmic string loops can account for the nanohertz SGWB data with a $G\mu \sim 2\times 10^{-12}$ and the loops number density $N \sim 10^{4}$. Though the presence of cosmic string loops can also effectively enhance the number density of massive galaxies at high redshifts, we do not find a reasonable parameter space to self-consistently interpret both the SGWB data and the JWST observations. This implies either an extension of the model adopted in this work or the different physical origins of these two phenomena

Link-Context Learning for Multimodal LLMs

The ability to learn from context with novel concepts, and deliver appropriate responses are essential in human conversations. Despite current Multimodal Large Language Models (MLLMs) and Large Language Models (LLMs) being trained on mega-scale datasets, recognizing unseen images or understanding novel concepts in a training-free manner remains a challenge. In-Context Learning (ICL) explores training-free few-shot learning, where models are encouraged to ``learn to learn" from limited tasks and generalize to unseen tasks. In this work, we propose link-context learning (LCL), which emphasizes "reasoning from cause and effect" to augment the learning capabilities of MLLMs. LCL goes beyond traditional ICL by explicitly strengthening the causal relationship between the support set and the query set. By providing demonstrations with causal links, LCL guides the model to discern not only the analogy but also the underlying causal associations between data points, which empowers MLLMs to recognize unseen images and understand novel concepts more effectively. To facilitate the evaluation of this novel approach, we introduce the ISEKAI dataset, comprising exclusively of unseen generated image-label pairs designed for link-context learning. Extensive experiments show that our LCL-MLLM exhibits strong link-context learning capabilities to novel concepts over vanilla MLLMs. Code and data will be released at https://github.com/isekai-portal/Link-Context-Learning.Comment: 10 pages, 8 figure