Variance-Adaptive Muon: Accelerating LLM Pretraining with NSR-Modulated and Variance-Scaled Momentum

Large Language Models (LLMs) achieve competitive performance across diverse natural language processing (NLP) tasks, yet pretraining is computationally demanding, making optimizer efficiency an important practical consideration. Muon accelerates LLM pretraining via orthogonal momentum updates that serve as a matrix analogue of the element-wise sign operator. Motivated by the recent perspective that Adam is a variance-adaptive sign update algorithm, we propose two variants of Muon, Muon-NSR and Muon-VS, which apply variance-adaptive normalization to momentum before orthogonalization. Muon-NSR applies noise-to-signal ratio (NSR) modulation, while Muon-VS performs variance-based scaling without introducing additional hyperparameters. Experiments on GPT-2 and LLaMA pretraining demonstrate that our proposed methods accelerate convergence and consistently achieve lower validation loss than both competitive, well-tuned AdamW and Muon baselines. For example, on the LLaMA-1.2B model, Muon-NSR and Muon-VS reduce the iterations required to reach the target validation loss by $1.36\times$ relative to the well-tuned Muon following the recent benchmark.

Convergence Rate Analysis of the AdamW-Style Shampoo: Unifying One-sided and Two-Sided Preconditioning

This paper studies the AdamW-style Shampoo optimizer, an effective implementation of classical Shampoo that notably won the external tuning track of the AlgoPerf neural network training algorithm competition. Our analysis unifies one-sided and two-sided preconditioning and establishes the convergence rate $\frac{1}{K}\sum_{k=1}^K E\left[\|\nabla f(X_k)\|_*\right]\leq O(\frac{\sqrt{m+n}C}{K^{1/4}})$ measured by nuclear norm, where $K$ represents the iteration number, $(m,n)$ denotes the size of matrix parameters, and $C$ matches the constant in the optimal convergence rate of SGD. Theoretically, we have $\|\nabla f(X)\|_F\leq \|\nabla f(X)\|_*\leq \sqrt{m+n}\|\nabla f(X)\|_F$, supporting that our convergence rate can be considered to be analogous to the optimal $\frac{1}{K}\sum_{k=1}^KE\left[\|\nabla f(X_k)\|_F\right]\leq O(\frac{C}{K^{1/4}})$ convergence rate of SGD in the ideal case of $\|\nabla f(X)\|_*= Θ(\sqrt{m+n})\|\nabla f(X)\|_F$.

SafeLoad: Efficient Admission Control Framework for Identifying Memory-Overloading Queries in Cloud Data Warehouses

Memory overload is a common form of resource exhaustion in cloud data warehouses. When database queries fail due to memory overload, it not only wastes critical resources such as CPU time but also disrupts the execution of core business processes, as memory-overloading (MO) queries are typically part of complex workflows. If such queries are identified in advance and scheduled to memory-rich serverless clusters, it can prevent resource wastage and query execution failure. Therefore, cloud data warehouses desire an admission control framework with high prediction precision, interpretability, efficiency, and adaptability to effectively identify MO queries. However, existing admission control frameworks primarily focus on scenarios like SLA satisfaction and resource isolation, with limited precision in identifying MO queries. Moreover, there is a lack of publicly available MO-labeled datasets with workloads for training and benchmarking. To tackle these challenges, we propose SafeLoad, the first query admission control framework specifically designed to identify MO queries. Alongside, we release SafeBench, an open-source, industrial-scale benchmark for this task, which includes 150 million real queries. SafeLoad first filters out memory-safe queries using the interpretable discriminative rule. It then applies a hybrid architecture that integrates both a global model and cluster-level models, supplemented by a misprediction correction module to identify MO queries. Additionally, a self-tuning quota management mechanism dynamically adjusts prediction quotas per cluster to improve precision. Experimental results show that SafeLoad achieves state-of-the-art prediction performance with low online and offline time overhead. Specifically, SafeLoad improves precision by up to 66% over the best baseline and reduces wasted CPU time by up to 8.09x compared to scenarios without SafeLoad.

Analyzing the Mechanism of Attention Collapse in VGGT from a Dynamics Perspective

Visual Geometry Grounded Transformer (VGGT) delivers state-of-the-art feed-forward 3D reconstruction, yet its global self-attention layer suffers from a drastic collapse phenomenon when the input sequence exceeds a few hundred frames: attention matrices rapidly become near rank-one, token geometry degenerates to an almost one-dimensional subspace, and reconstruction error accumulates super-linearly.In this report,we establish a rigorous mathematical explanation of the collapse by viewing the global-attention iteration as a degenerate diffusion process.We prove that,in VGGT, the token-feature flow converges toward a Dirac-type measure at a $O(1/L)$ rate, where $L$ is the layer index, yielding a closed-form mean-field partial differential equation that precisely predicts the empirically observed rank profile.The theory quantitatively matches the attention-heat-map evolution and a series of experiments outcomes reported in relevant works and explains why its token-merging remedy -- which periodically removes redundant tokens -- slows the effective diffusion coefficient and thereby delays collapse without additional training.We believe the analysis provides a principled lens for interpreting future scalable 3D-vision transformers,and we highlight its potential for multi-modal generalization.

CTkvr: KV Cache Retrieval for Long-Context LLMs via Centroid then Token Indexing

Large language models (LLMs) are increasingly applied in long-context scenarios such as multi-turn conversations. However, long contexts pose significant challenges for inference efficiency, including high memory overhead from Key-Value (KV) cache and increased latency due to excessive memory accesses. Recent methods for dynamic KV selection struggle with trade-offs: block-level indexing degrades accuracy by retrieving irrelevant KV entries, while token-level indexing incurs high latency from inefficient retrieval mechanisms. In this paper, we propose CTKVR, a novel centroid-then-token KV retrieval scheme that addresses these limitations. CTKVR leverages a key observation: query vectors adjacent in position exhibit high similarity after Rotary Position Embedding (RoPE) and share most of their top-k KV cache entries. Based on this insight, CTKVR employs a two-stage retrieval strategy: lightweight centroids are precomputed during prefilling for centroid-grained indexing, followed by token-level refinement for precise KV retrieval. This approach balances retrieval efficiency and accuracy. To further enhance performance, we implement an optimized system for indexing construction and search using CPU-GPU co-execution. Experimentally, CTKVR achieves superior performance across multiple benchmarks with less than 1% accuracy degradation. Meanwhile, CTKVR delivers 3 times and 4 times throughput speedups on Llama-3-8B and Yi-9B at 96K context length across diverse GPU hardware.

MovSemCL: Movement-Semantics Contrastive Learning for Trajectory Similarity

Trajectory similarity computation is fundamental functionality that is used for, e.g., clustering, prediction, and anomaly detection. However, existing learning-based methods exhibit three key limitations: (1) insufficient modeling of trajectory semantics and hierarchy, lacking both movement dynamics extraction and multi-scale structural representation; (2) high computational costs due to point-wise encoding; and (3) use of physically implausible augmentations that distort trajectory semantics. To address these issues, we propose MovSemCL, a movement-semantics contrastive learning framework for trajectory similarity computation. MovSemCL first transforms raw GPS trajectories into movement-semantics features and then segments them into patches. Next, MovSemCL employs intra- and inter-patch attentions to encode local as well as global trajectory patterns, enabling efficient hierarchical representation and reducing computational costs. Moreover, MovSemCL includes a curvature-guided augmentation strategy that preserves informative segments (e.g., turns and intersections) and masks redundant ones, generating physically plausible augmented views. Experiments on real-world datasets show that MovSemCL is capable of outperforming state-of-the-art methods, achieving mean ranks close to the ideal value of 1 at similarity search tasks and improvements by up to 20.3% at heuristic approximation, while reducing inference latency by up to 43.4%.

QuiZSF: An efficient data-model interaction framework for zero-shot time-series forecasting

Time series forecasting has become increasingly important to empower diverse applications with streaming data. Zero-shot time-series forecasting (ZSF), particularly valuable in data-scarce scenarios, such as domain transfer or forecasting under extreme conditions, is difficult for traditional models to deal with. While time series pre-trained models (TSPMs) have demonstrated strong performance in ZSF, they often lack mechanisms to dynamically incorporate external knowledge. Fortunately, emerging retrieval-augmented generation (RAG) offers a promising path for injecting such knowledge on demand, yet they are rarely integrated with TSPMs. To leverage the strengths of both worlds, we introduce RAG into TSPMs to enhance zero-shot time series forecasting. In this paper, we propose QuiZSF (Quick Zero-Shot Time Series Forecaster), a lightweight and modular framework that couples efficient retrieval with representation learning and model adaptation for ZSF. Specifically, we construct a hierarchical tree-structured ChronoRAG Base (CRB) for scalable time-series storage and domain-aware retrieval, introduce a Multi-grained Series Interaction Learner (MSIL) to extract fine- and coarse-grained relational features, and develop a dual-branch Model Cooperation Coherer (MCC) that aligns retrieved knowledge with two kinds of TSPMs: Non-LLM based and LLM based. Compared with contemporary baselines, QuiZSF, with Non-LLM based and LLM based TSPMs as base model, respectively, ranks Top1 in 75% and 87.5% of prediction settings, while maintaining high efficiency in memory and inference time.

On the $O(\frac{\sqrt{d}}{K^{1/4}})$ Convergence Rate of AdamW Measured by $\ell_1$ Norm

As the default optimizer for training large language models, AdamW has achieved remarkable success in deep learning. However, its convergence behavior is not theoretically well-understood. This paper establishes the convergence rate $\frac{1}{K}\sum_{k=1}^KE\left[\|\nabla f(x^k)\|_1\right]\leq O(\frac{\sqrt{d}C}{K^{1/4}})$ for AdamW measured by $\ell_1$ norm, where $K$ represents the iteration number, $d$ denotes the model dimension, and $C$ matches the constant in the optimal convergence rate of SGD. Theoretically, we have $E\left[\|\nabla f(x)\|_1\right]\geq\sqrt{\frac{2d}{\pi}}E\left[\|\nabla f(x)\|_2\right]$ when each element of $\nabla f(x)$ is generated from Gaussian distribution $\mathcal N(0,1)$. Empirically, our experimental results on real-world deep learning tasks reveal $\|\nabla f(x)\|_1=\varTheta(\sqrt{d})\|\nabla f(x)\|_2$. Both support that our convergence rate can be considered to be analogous to the optimal $\frac{1}{K}\sum_{k=1}^KE\left[\|\nabla f(x^k)\|_2\right]\leq O(\frac{C}{K^{1/4}})$ convergence rate of SGD.

CHASe: Client Heterogeneity-Aware Data Selection for Effective Federated Active Learning

Active learning (AL) reduces human annotation costs for machine learning systems by strategically selecting the most informative unlabeled data for annotation, but performing it individually may still be insufficient due to restricted data diversity and annotation budget. Federated Active Learning (FAL) addresses this by facilitating collaborative data selection and model training, while preserving the confidentiality of raw data samples. Yet, existing FAL methods fail to account for the heterogeneity of data distribution across clients and the associated fluctuations in global and local model parameters, adversely affecting model accuracy. To overcome these challenges, we propose CHASe (Client Heterogeneity-Aware Data Selection), specifically designed for FAL. CHASe focuses on identifying those unlabeled samples with high epistemic variations (EVs), which notably oscillate around the decision boundaries during training. To achieve both effectiveness and efficiency, \model{} encompasses techniques for 1) tracking EVs by analyzing inference inconsistencies across training epochs, 2) calibrating decision boundaries of inaccurate models with a new alignment loss, and 3) enhancing data selection efficiency via a data freeze and awaken mechanism with subset sampling. Experiments show that CHASe surpasses various established baselines in terms of effectiveness and efficiency, validated across diverse datasets, model complexities, and heterogeneous federation settings.

HMI: Hierarchical Knowledge Management for Efficient Multi-Tenant Inference in Pretrained Language Models

The significant computational demands of pretrained language models (PLMs), which often require dedicated hardware, present a substantial challenge in serving them efficiently, especially in multi-tenant environments. To address this, we introduce HMI, a Hierarchical knowledge management-based Multi-tenant Inference system, designed to manage tenants with distinct PLMs resource-efficiently. Our approach is three-fold: Firstly, we categorize PLM knowledge into general, domain-specific, and task-specific. Leveraging insights on knowledge acquisition across different model layers, we construct hierarchical PLMs (hPLMs) by extracting and storing knowledge at different levels, significantly reducing GPU memory usage per tenant. Secondly, we establish hierarchical knowledge management for hPLMs generated by various tenants in HMI. We manage domain-specific knowledge with acceptable storage increases by constructing and updating domain-specific knowledge trees based on frequency. We manage task-specific knowledge within limited GPU memory through parameter swapping. Finally, we propose system optimizations to enhance resource utilization and inference throughput. These include fine-grained pipelining via hierarchical knowledge prefetching to overlap CPU and I/O operations with GPU computations, and optimizing parallel implementations with batched matrix multiplications. Our experimental results demonstrate that the proposed HMI can efficiently serve up to 10,000 hPLMs (hBERTs and hGPTs) on a single GPU, with only a negligible compromise in accuracy.