Mengzhe Ruan

Mengzhe Ruan, Guangfeng Yan, Yuanzhang Xiao et al.

Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification, which sparsifies the gradients by a fixed degree during model training. However, there has been a lack of an adaptive approach to adjust the sparsification degree to maximize the potential of the model's performance or training speed. This paper proposes a novel adaptive Top-K in SGD framework that enables an adaptive degree of sparsification for each gradient descent step to optimize the convergence performance by balancing the trade-off between communication cost and convergence error. Firstly, an upper bound of convergence error is derived for the adaptive sparsification scheme and the loss function. Secondly, an algorithm is designed to minimize the convergence error under the communication cost constraints. Finally, numerical results on the MNIST and CIFAR-10 datasets demonstrate that the proposed adaptive Top-K algorithm in SGD achieves a significantly better convergence rate compared to state-of-the-art methods, even after considering error compensation.

Yunhe Li, Hao Shi, Bowen Deng et al.

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose a novel framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. We propose $\mathtt{DeepInsightTheorem}$, a hierarchical dataset that structures informal proofs by explicitly extracting core techniques and proof sketches alongside the final proof. To fully exploit this dataset, we design a Progressive Multi-Stage SFT strategy that mimics the human learning process, guiding the model from basic proof writing to insightful thinking. Our experiments on challenging mathematical benchmarks demonstrate that this insight-aware generation strategy significantly outperforms baselines. These results demonstrate that teaching models to identify and apply core techniques can substantially improve their mathematical reasoning.

Zhengru Fang, Senkang Forest Hu, Zhonghao Chang et al.

LLM search agents increasingly rely on tools at inference time, but their trajectories are often constrained by hard limits on both tool calls and generated tokens. Under such dual budgets, better answers require not only stronger models, but also explicit control over which search action should receive the next budget unit and when the accumulated evidence is sufficient to commit a final answer. We study this problem in multi-hop question answering (QA) and formulate it as two-stage inference-time budget control. At search time, our controller assigns each feasible action a task-level Value-of-Information (VOI) score, defined as an operational estimate of marginal task value per unit budget under the current search state and remaining dual budget, and uses this score to choose among retrieval, decomposition, and answer commitment. After search, a selective evidence-grounded finalizer compares the trajectory answer with a refined candidate and rewrites only when the residual error appears to be a low-risk answer-form error. Across four multi-hop QA benchmarks, three LLM backbones, and four budget levels, the method yields positive aggregate gains over four audited baselines under the same hard dual-budget protocol. Ablations show that search-time budget control, especially budget-dependent penalty, provides the main performance gain, while answer-time control helps mainly when the retrieval path is already adequate. These results suggest that inference-time budget control for LLM search agents should govern both how budget is spent during search and how the final answer is committed.