On the Convergence of Muon and Beyond

The Muon optimizer has demonstrated remarkable empirical success in handling matrix-structured parameters for training neural networks. However, a significant gap persists between its practical performance and theoretical understanding. Existing analyses indicate that the standard Muon variant achieves only a suboptimal convergence rate of $\mathcal{O}(T^{-1/4})$ in stochastic non-convex settings, where $T$ denotes the number of iterations. To explore the theoretical limits of the Muon framework, we construct and analyze a variance-reduced variant, termed Muon-VR2. We provide the first rigorous proof that incorporating a variance-reduction mechanism enables Muon-VR2 to attain an optimal convergence rate of $\tilde{\mathcal{O}}(T^{-1/3})$, thereby matching the theoretical lower bound for this class of problems. Moreover, our analysis establishes convergence guarantees for Muon variants under the Polyak-{\L}ojasiewicz (P{\L}) condition. Extensive experiments on vision (CIFAR-10) and language (C4) benchmarks corroborate our theoretical findings on per-iteration convergence. Overall, this work provides the first proof of optimality for a Muon-style optimizer and clarifies the path toward developing more practically efficient, accelerated variants.

AlphaAdam:Asynchronous Masked Optimization with Dynamic Alpha for Selective Updates

In the training of large language models (LLMs), updating parameters more efficiently and stably has always been an important challenge. To achieve efficient parameter updates, existing methods usually achieve performance comparable to full parameter updates through methods such as low-dimensional decomposition or layer-wise selective updates. In this work, we propose AlphaAdam, an optimization framework for LLM from the perspective of intra-layer parameter updates. By decoupling parameter updates and dynamically adjusting their strength, AlphaAdam accelerates convergence and improves training stability. We construct parameter masks based on the consistency of historical momentum and gradient direction and combine them with an adaptive mask strength strategy to ensure efficient optimization and theoretical convergence guarantees, which is also applicable to most momentum-based optimizers. Extensive experiments show that AlphaAdam outperforms state-of-the-art methods such as AdamW in terms of convergence speed and computational efficiency across tasks, including GPT-2 pre-trained and fine-tuned RoBERTa and Llama-7B. Our AlphaAdam implements an optimizer enhancement framework for LLMs through intra-layer asynchronous masked adaptive updates. Our code is available in this \href{https://github.com/MaeChd/AlphaAdam}{link}

IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce

Weight initialization significantly impacts the convergence and performance of neural networks. While traditional methods like Xavier and Kaiming initialization are widely used, they often fall short for spiking neural networks (SNNs), which have distinct requirements compared to artificial neural networks (ANNs). To address this, we introduce \textbf{IKUN}, a variance-stabilizing initialization method integrated with surrogate gradient functions, specifically designed for SNNs. \textbf{IKUN} stabilizes signal propagation, accelerates convergence, and enhances generalization. Experiments show \textbf{IKUN} improves training efficiency by up to \textbf{50\%}, achieving \textbf{95\%} training accuracy and \textbf{91\%} generalization accuracy. Hessian analysis reveals that \textbf{IKUN}-trained models converge to flatter minima, characterized by Hessian eigenvalues near zero on the positive side, promoting better generalization. The method is open-sourced for further exploration: \href{https://github.com/MaeChd/SurrogateVarStabe}{https://github.com/MaeChd/SurrogateVarStabe}.

DLoRA-TrOCR: Mixed Text Mode Optical Character Recognition Based On Transformer

With the continuous development of OCR technology and the expansion of application fields, text recognition in complex scenes has become a key challenge. Factors such as multiple fonts, mixed scenes and complex layouts seriously affect the recognition accuracy of traditional OCR models. Although OCR models based on deep learning have performed well in specific fields or similar data sets in recent years, the generalization ability and robustness of the model are still a big challenge when facing complex environments with multiple scenes. Furthermore, training an OCR model from scratch or fine-tuning all parameters is very demanding on computing resources and inference time, which limits the flexibility of its application. This study focuses on a fundamental aspect of mixed text recognition in response to the challenges mentioned above, which involves effectively fine-tuning the pre-trained basic OCR model to demonstrate exceptional performance across various downstream tasks. To this end, we propose a parameter-efficient hybrid text recognition method based on pre-trained OCR Transformer, namely DLoRA-TrOCR. This method embeds DoRA into the image encoder and LoRA into the internal structure of the text decoder, enabling efficient parameter fine-tuning for downstream tasks. Experimental results show that compared to similar parameter adjustment methods, our model DLoRA-TrOCR has the smallest number of parameters and performs better. It can achieve state-of-the-art performance on complex scene data sets involving simultaneous recognition of mixed handwritten, printed and street view texts.