Top-$nσ$: Not All Logits Are You Need

Large language models (LLMs) typically employ greedy decoding or low-temperature sampling for reasoning tasks, reflecting a perceived trade-off between diversity and accuracy. We challenge this convention by introducing top-$n\sigma$, a novel sampling method that operates directly on pre-softmax logits by leveraging a statistical threshold. Our key insight is that logits naturally separate into a Gaussian-distributed noisy region and a distinct informative region, enabling efficient token filtering without complex probability manipulations. Unlike existing methods (e.g., top-$p$, min-$p$) that inadvertently include more noise tokens at higher temperatures, top-$n\sigma$ maintains a stable sampling space regardless of temperature scaling. We also provide a theoretical analysis of top-$n\sigma$ to better understand its behavior. The extensive experimental results across four reasoning-focused datasets demonstrate that our method not only outperforms existing sampling approaches but also surpasses greedy decoding, while maintaining consistent performance even at high temperatures.

Optimizing Federated Graph Learning with Inherent Structural Knowledge and Dual-Densely Connected GNNs

Federated Graph Learning (FGL) is an emerging technology that enables clients to collaboratively train powerful Graph Neural Networks (GNNs) in a distributed manner without exposing their private data. Nevertheless, FGL still faces the challenge of the severe non-Independent and Identically Distributed (non-IID) nature of graphs, which possess diverse node and edge structures, especially across varied domains. Thus, exploring the knowledge inherent in these structures becomes significantly crucial. Existing methods, however, either overlook the inherent structural knowledge in graph data or capture it at the cost of significantly increased resource demands (e.g., FLOPs and communication bandwidth), which can be detrimental to distributed paradigms. Inspired by this, we propose FedDense, a novel FGL framework that optimizes the utilization efficiency of inherent structural knowledge. To better acquire knowledge of diverse and underexploited structures, FedDense first explicitly encodes the structural knowledge inherent within graph data itself alongside node features. Besides, FedDense introduces a Dual-Densely Connected (DDC) GNN architecture that exploits the multi-scale (i.e., one-hop to multi-hop) feature and structure insights embedded in the aggregated feature maps at each layer. In addition to the exploitation of inherent structures, we consider resource limitations in FGL, devising exceedingly narrow layers atop the DDC architecture and adopting a selective parameter sharing strategy to reduce resource costs substantially. We conduct extensive experiments using 15 datasets across 4 different domains, demonstrating that FedDense consistently surpasses baselines by a large margin in training performance, while demanding minimal resources.