The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become trapped in sharp local minima. In this work, we present **MONA**, an optimizer that bridges Muon’s orthogonalization framework with curvature-aware acceleration. MONA adds an acceleration term directly into Muon’s gradient processing pipeline. This term is calculated from the exponential moving average of gradient differences. We provide a detailed convergence analysis for MONA, showing that the acceleration term enables escape from sharp minima while preserving Muon’s spectral-norm regularization. Empirically, MONA achieves better convergence and downstream task performance compared to both Muon and AdamW across three scales of Mixture-of-Experts pretraining, spanning from 1B to 68B parameters, with the largest model trained on 1 trillion tokens. Furthermore, we conduct supervised fine-tuning on the MOE-68B-A3B model and evaluate it on general capability, mathematical reasoning, and code generation benchmarks, where MONA achieves **SOTA** performance.

Speculative decoding accelerates autoregressive language model inference by verifying multiple draft tokens in parallel. However, the verification stage often becomes the dominant computational bottleneck, especially for long-context inputs and mixture-of-experts (MoE) models. Existing sparsification methods are designed primarily for token-by-token autoregressive decoding to remove substantial computational redundancy in LLMs. This work systematically adopts different sparse methods on the verification stage of the speculative decoding and identifies structured redundancy across multiple dimensions. Based on these observations, we propose a sparse verification framework that jointly sparsifies attention, FFN, and MoE components during the verification stage to reduce the dominant computation cost. The framework further incorporates an inter-draft token and inter-layer retrieval reuse strategy to further reduce redundant computation without introducing additional training. Extensive experiments across summarization, question answering, and mathematical reasoning datasets demonstrate that the proposed methods achieve favorable efficiency-accuracy trade-offs and can be translated into practical latency reduction with optimized sparse kernels.

Linear attention mechanisms have emerged as promising alternatives to softmax attention, offering linear-time complexity during inference. Recent advances such as Gated DeltaNet (GDN) and Kimi Delta Attention (KDA) have demonstrated that the delta rule (an online gradient descent update) enables superior associative recall compared to simple additive updates. While KDA refined the coarse head-wise decay gate into channel-wise decay, the learning rate 𝛽_t in the delta update remains a scalar, limiting the model’s capacity for dimension-specific adaptation. We introduce FG²-GDN, which replaces the scalar 𝛽_t with a channel-wise vector in a manner analogous to the transition from SGD to per-coordinate adaptive optimizers such as AdaGrad and Adam. We further propose FG²-GDN+, which decouples the scaling for keys and values, enabling independent control of erasure strength and write strength. Experiments on synthetic and real-world benchmarks show that FG²-GDN and its variant improve associative recall and long-context understanding over GDN and KDA, with comparable computational efficiency.