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In this paper, we explore sampling from strongly log-concave distributions defined on convex and compact supports. We propose a general proximal framework that involves projecting onto the constrained set, which is highly flexible and supports various projection options. Specifically, we consider the cases of Euclidean and Gauge projections, with the latter having the advantage of being performed efficiently using a membership oracle. This framework can be seamlessly integrated with multiple sampling methods. Our analysis focuses on Langevin-type sampling algorithms within the context of constrained sampling. We provide nonasymptotic upper bounds on the W1 and W2 errors, offering a detailed comparison of the performance of these methods in constrained sampling.

The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify chain-of-thought reasoning, reward modeling, formal reasoning, data augmentation, and code interpreter in a unified seq2seq format and supervise our model to be a versatile math reasoner, verifier, prover, and augmenter. These abilities can be used to develop the next math LLMs or self-iteration. InternLM-Math obtains open-sourced state-of-the-art performance under the setting of in-context learning, supervised fine-tuning, and code-assisted reasoning in various informal and formal benchmarks including GSM8K, MATH, Hungary math exam, MathBench-ZH, and MiniF2F. Our pre-trained model achieves 30.3 on the MiniF2F test set without fine-tuning. We further explore how to use LEAN to solve math problems and study its performance under the setting of multi-task learning which shows the possibility of using LEAN as a unified platform for solving and proving in math. Our models, codes, and data are released at \url{//github.com/InternLM/InternLM-Math}.

In this paper, we study the partitioning of a context-aware shared memory data structure so that it can be implemented as a distributed data structure running on multiple machines. By context-aware data structures, we mean that the result of an operation not only depends upon the value of the shared data but also upon the previous operations performed by the same client. While there is substantial work on designing distributed data structures, designing distributed context-aware data structures has not received much attention. We focus on singly-linked lists as a case study of the context-aware data structure. We start with a shared memory context-aware lock-free singly-linked list and show how it can be transformed into a distributed lock-free context-aware singly-linked list. The main challenge in such a transformation is to preserve properties of client-visible operations of the underlying data structure. We present two protocols that preserve these properties of client-visible operations of the linked list. In the first protocol, the distribution is done in the background as a low priority task, while in the second protocol the client-visible operations help the task of distribution without affecting client latency. In both protocols, the client-visible operations remain lock-free. Also, our transformation approach does not utilize any hardware primitives (except a compare-and-swap operation on a single word). We note that our transformation is generic and can be used for other lock-free context-aware data structures that can be constructed from singly-linked lists.

In this paper, we propose a novel approach called DIffusion-guided DIversity (DIDI) for offline behavioral generation. The goal of DIDI is to learn a diverse set of skills from a mixture of label-free offline data. We achieve this by leveraging diffusion probabilistic models as priors to guide the learning process and regularize the policy. By optimizing a joint objective that incorporates diversity and diffusion-guided regularization, we encourage the emergence of diverse behaviors while maintaining the similarity to the offline data. Experimental results in four decision-making domains (Push, Kitchen, Humanoid, and D4RL tasks) show that DIDI is effective in discovering diverse and discriminative skills. We also introduce skill stitching and skill interpolation, which highlight the generalist nature of the learned skill space. Further, by incorporating an extrinsic reward function, DIDI enables reward-guided behavior generation, facilitating the learning of diverse and optimal behaviors from sub-optimal data.

In this paper, we investigate the challenging framework of Byzantine-robust training in distributed machine learning (ML) systems, focusing on enhancing both efficiency and practicality. As distributed ML systems become integral for complex ML tasks, ensuring resilience against Byzantine failures-where workers may contribute incorrect updates due to malice or error-gains paramount importance. Our first contribution is the introduction of the Centered Trimmed Meta Aggregator (CTMA), an efficient meta-aggregator that upgrades baseline aggregators to optimal performance levels, while requiring low computational demands. Additionally, we propose harnessing a recently developed gradient estimation technique based on a double-momentum strategy within the Byzantine context. Our paper highlights its theoretical and practical advantages for Byzantine-robust training, especially in simplifying the tuning process and reducing the reliance on numerous hyperparameters. The effectiveness of this technique is supported by theoretical insights within the stochastic convex optimization (SCO) framework.

In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and data heterogeneity. However, the non-smoothness of the check loss function poses big challenges to both computation and theory in the distributed setting. To tackle these problems, we transform the original quantile regression into the least-squares optimization. By applying a double-smoothing approach, we extend a previous Newton-type distributed approach without the restrictive independent assumption between the error term and covariates. An efficient algorithm is developed, which enjoys high computation and communication efficiency. Theoretically, the proposed distributed estimator achieves a near-oracle convergence rate and high support recovery accuracy after a constant number of iterations. Extensive experiments on synthetic examples and a real data application further demonstrate the effectiveness of the proposed method.

In this paper, we propose low-complexity local detectors and log-likelihood ratio (LLR) refinement techniques for a coded cell-free massive multiple input multiple output (CF- mMIMO) systems, where an iterative detection and decoding (IDD) scheme is applied using parallel interference cancellation (PIC) and access point (AP) selection. In particular, we propose three LLR processing schemes based on the individual processing of the LLRs of each AP, LLR censoring, and a linear combination of LLRs by assuming statistical independence. We derive new closed-form expressions for the local soft minimum mean square error (MMSE)-PIC detector and receive matched filter (RMF). We also examine the system performance as the number of iterations increases. Simulations assess the performance of the proposed techniques against existing approaches.

In this paper, we present a comprehensive review of the imbalance problems in object detection. To analyze the problems in a systematic manner, we introduce a problem-based taxonomy. Following this taxonomy, we discuss each problem in depth and present a unifying yet critical perspective on the solutions in the literature. In addition, we identify major open issues regarding the existing imbalance problems as well as imbalance problems that have not been discussed before. Moreover, in order to keep our review up to date, we provide an accompanying webpage which catalogs papers addressing imbalance problems, according to our problem-based taxonomy. Researchers can track newer studies on this webpage available at: //github.com/kemaloksuz/ObjectDetectionImbalance .

We consider an interesting problem-salient instance segmentation in this paper. Other than producing bounding boxes, our network also outputs high-quality instance-level segments. Taking into account the category-independent property of each target, we design a single stage salient instance segmentation framework, with a novel segmentation branch. Our new branch regards not only local context inside each detection window but also its surrounding context, enabling us to distinguish the instances in the same scope even with obstruction. Our network is end-to-end trainable and runs at a fast speed (40 fps when processing an image with resolution 320x320). We evaluate our approach on a publicly available benchmark and show that it outperforms other alternative solutions. We also provide a thorough analysis of the design choices to help readers better understand the functions of each part of our network. The source code can be found at \url{//github.com/RuochenFan/S4Net}.

In this paper we address issues with image retrieval benchmarking on standard and popular Oxford 5k and Paris 6k datasets. In particular, annotation errors, the size of the dataset, and the level of challenge are addressed: new annotation for both datasets is created with an extra attention to the reliability of the ground truth. Three new protocols of varying difficulty are introduced. The protocols allow fair comparison between different methods, including those using a dataset pre-processing stage. For each dataset, 15 new challenging queries are introduced. Finally, a new set of 1M hard, semi-automatically cleaned distractors is selected. An extensive comparison of the state-of-the-art methods is performed on the new benchmark. Different types of methods are evaluated, ranging from local-feature-based to modern CNN based methods. The best results are achieved by taking the best of the two worlds. Most importantly, image retrieval appears far from being solved.