Revealing Modular Gradient Noise Imbalance in LLMs: Calibrating Adam via Signal-to-Noise Ratio

The impressive performance of large language models (LLMs) arises from their massive scale and heterogeneous module composition. However, this structural heterogeneity introduces additional optimization challenges. While adaptive optimizers such as Adam(W) provide per-parameter adaptivity, they do not explicitly account for module-level gradient heterogeneity, resulting in slower convergence, suboptimal performance, or training instability. Existing approaches typically rely on manually tuned module-specific learning rates or specific optimization strategies, which are computationally costly and difficult to generalize across tasks or models. To establish a more principled approach, we first analyze the noise-damping behavior of Adam in high-noise modules and introduce \textbf{Module-wise Learning Rate Scaling via SNR (MoLS)}. MoLS estimates module-level SNRs to scale Adam updates, allowing automated module-wise learning rate allocation without manual tuning. Empirical results through multiple LLM training benchmarks demonstrate that MoLS improves convergence speed and generalization, achieving performance comparable to carefully tuned module-specific learning rates, while remaining compatible with memory-efficient training algorithms.

Flexible Graph Similarity Computation With A Proactive Optimization Strategy

Graph Edit Distance (GED) is an important similarity measure in graph retrieval, which quantifies the minimum cost of transforming one graph into another through edit operations, and offers flexibility by allowing customizable operation costs. Recent learning-based approaches approximate GEDs with the distances between representations in vector spaces. However, these methods often struggle with varying operation costs due to neglecting the impact of these costs on determining optimal graph mappings. Furthermore, they rely on isolated node distances as guidance, necessitating inefficient reactive refinements of mappings. To address these issues, we propose Graph Edit Network (GEN), a novel learning-based approach for flexible GED computation. By identifying the limitations of existing methods in capturing flexibility of GED, we introduce a principled yet simple solution that incorporates the operation costs before establishing mappings. To improve matching efficiency, we propose a strategy that proactively optimizes guidance from a graph perspective. This strategy initializes guidance as each node's alignment difficulty and captures the interdependencies between matches within and across graphs through a difficulty propagation mechanism, enabling more informed decisions. As a result, GEN selects optimal matches in a single step, minimizing the need for costly refinements. Results on real-world and synthetic datasets demonstrate the effectiveness, time efficiency, and adaptability of GEN, achieving up to 37.8\% error reduction and 72.7\% inference time reduction compared with state-of-the-art models, while performing robustly under varying cost settings and graph sizes.