QK-Normed MLA: QK normalization without full key caching

Query-key (QK) normalization stabilizes attention by controlling the scale of queries and keys before the dot product, but is not immediately compatible with Multi-head Latent Attention (MLA). MLA achieves efficient decoding by caching low-dimensional latent states instead of full keys, whereas post-projection QK RMSNorm appears to require the fully projected key for every cached token. We show this apparent incompatibility is an implementation artifact, not an architectural constraint. RMSNorm decomposes into a static affine weight and a dynamic scalar RMS statistic. The static key-side weight can be absorbed into the MLA query-side projection; the dynamic key statistic reduces to one inverse-RMS scalar per token and KV group. The resulting formulation is exactly equivalent to explicit post-projection QK RMSNorm in exact arithmetic and preserves MLA's latent decode path. In our 400M runs trained for up to 100B tokens, QK-Normed MLA achieves lower training loss and better downstream accuracy than QK clipping, while H800 decode benchmarks show less than 2% latency overhead up to 256k context. These results make QK normalization a practical stabilization option for MLA models without requiring full-key caching.

Addressing Market Regime Changes and Heavy-Tailed Returns in Portfolio Optimization via Bayesian VAR and Elliptical Black-Litterman

Deep reinforcement learning (DRL) frameworks for portfolio optimization have shown promise for their ability to learn allocation rules dynamically from market data. However, these models fail to account for fat-tailed returns, which characterize actual market behavior with more frequent extreme events. Furthermore, historical data is treated homogeneously, without accounting for temporal importance, leading models to fail during regime changes. We propose a new BAVAR-BLED algorithm that combines methods derived from Bayesian-Averaging Vector Autoregressive (BAVAR) and the Black-Litterman model using Elliptical Distributions (BLED) within a TD3 architecture. BAVAR captures a set of vector autoregressive representations that consider multi-scale temporal features, enabling adaptive allocation decisions based on regime-aware estimates of return expectations and dispersion matrices. These estimates serve as prior inputs to BLED, a model that uses Student's t-distributions, allowing for more realistic fat tail return estimates. The BAVAR-BLED algorithm uses transformer networks for view construction and CNNs for risk-aversion estimates, which modify dynamic allocation decisions based on market conditions. An evaluation of 29 Dow Jones Industrial Average constituents over a decade-long market period shows that BAVAR-BLED significantly outperforms state-of-the-art methods, achieving Sharpe and Sortino ratios of 1.72 and 2.70, respectively, and total returns of 57.26%.

PC Layer: Polynomial Weight Preconditioning for Improving LLM Pre-Training

We propose a preconditioning (PC) layer, a weight parameterization via polynomial preconditioner that ensures stable weight conditioning throughout LLM training. The PC module reshapes the singular-value spectrum of weight matrices via low-degree polynomial preconditioning. After training, the preconditioned weights can be merged back into the original architecture, incurring no inference overhead. We demonstrate the advantage of the proposed PC layer over standard transformers in Llama-1B pre-training, for both the AdamW and Muon optimizers. Theoretically, we justify this spectrum-control principle by proving that uniformly bounding each layer's singular values ensures geometric convergence of gradient descent to global minima, for certain deep linear networks. Our code is available at https://github.com/Empath-aln/PC-layer.

A Geometric Characterization of the Stationary Plateau for Two-Layer Neural Networks

We investigate the geometric structure of stationary plateaus that arise in the loss landscape of two-layer neural networks with smooth activation functions. We focus on the phenomenon of "neuron splitting" where duplicating a hidden neuron yields an affine set of stationary points in a wider network. We provide a comprehensive classification of all stationary points on these plateaus, determining under what conditions they constitute local minima or saddle points. Our characterization hinges on a per-neuron curvature object we term the "inner Hessian" matrix. Our analysis reveals that the definiteness of the inner Hessian and the choice of splitting coefficients jointly dictate the local geometry of the plateau. We show that "splitting" a local minimum can yield either a mixture of local minima and saddles or an all-saddle plateau, with a concrete sure-saddle region identified under mild assumptions. In contrast, splitting a saddle point always produces a plateau of saddle points. Our results unify and extend prior landscape analyses, elucidating when and how model expansion preserves or alters the nature of stationary points. These findings offer new geometric insights into the effects of width expansion and reparameterization in neural networks.

FineViT: Progressively Unlocking Fine-Grained Perception with Dense Recaptions

While Multimodal Large Language Models (MLLMs) have experienced rapid advancements, their visual encoders frequently remain a performance bottleneck. Conventional CLIP-based encoders struggle with dense spatial tasks due to the loss of visual details caused by low-resolution pretraining and the reliance on noisy, coarse web-crawled image-text pairs. To overcome these limitations, we introduce FineViT, a novel vision encoder specifically designed to unlock fine-grained perception. By replacing coarse web data with dense recaptions, we systematically mitigate information loss through a progressive training paradigm.: first, the encoder is trained from scratch at a high native resolution on billions of global recaptioned image-text pairs, establishing a robust, detail rich semantic foundation. Subsequently, we further enhance its local perception through LLM alignment, utilizing our curated FineCap-450M dataset that comprises over $450$ million high quality local captions. Extensive experiments validate the effectiveness of the progressive strategy. FineViT achieves state-of-the-art zero-shot recognition and retrieval performance, especially in long-context retrieval, and consistently outperforms multimodal visual encoders such as SigLIP2 and Qwen-ViT when integrated into MLLMs. We hope FineViT could serve as a powerful new baseline for fine-grained visual perception.

Adam Converges Without Any Modification On Update Rules

Adam is the default algorithm for training neural networks, including large language models (LLMs). However, \citet{reddi2019convergence} provided an example that Adam diverges, raising concerns for its deployment in AI model training. We identify a key mismatch between the divergence example and practice: \citet{reddi2019convergence} pick the problem after picking the hyperparameters of Adam, i.e., $(β_1,β_2)$; while practical applications often fix the problem first and then tune $(β_1,β_2)$. In this work, we prove that Adam converges with proper problem-dependent hyperparameters. First, we prove that Adam converges when $β_2$ is large and $β_1 < \sqrt{β_2}$. Second, when $β_2$ is small, we point out a region of $(β_1,β_2)$ combinations where Adam can diverge to infinity. Our results indicate a phase transition for Adam from divergence to convergence when changing the $(β_1, β_2)$ combination. To our knowledge, this is the first phase transition in $(β_1,β_2)$ 2D-plane reported in the literature, providing rigorous theoretical guarantees for Adam optimizer. We further point out that the critical boundary $(β_1^*, β_2^*)$ is problem-dependent, and particularly, dependent on batch size. This provides suggestions on how to tune $β_1$ and $β_2$: when Adam does not work well, we suggest tuning up $β_2$ inversely with batch size to surpass the threshold $β_2^*$, and then trying $β_1< \sqrt{β_2}$. Our suggestions are supported by reports from several empirical studies, which observe improved LLM training performance when applying them.

AI-Driven Spectrum Occupancy Prediction Using Real-World Spectrum Measurements

Spectrum occupancy prediction is a critical enabler for real-time and proactive dynamic spectrum sharing (DSS), as it can provide short-term channel availability information to support more efficient spectrum access decisions in wireless communication systems. Instead of relying on open-source datasets or simulated data, commonly used in the literature, this paper investigates short-horizon spectrum occupancy prediction using mid-band, 24X7 real-world spectrum measurement data collected in the United States. We construct a multi-band channel occupancy dataset through analyzing 61 days of empirical data and formulate a next-minute channel occupancy prediction task across all frequency channels. This study focuses on AI-driven prediction methods, including Random Forest, Extreme Gradient Boosting (XGBoost), and a Long Short-Term Memory (LSTM) network, and compares their performance against a conventional Markov chain-based statistical baseline. Numerical results show that learning-based methods outperform the statistical baseline on dynamic channels, particularly under fixed false-alarm constraints. These results demonstrate the effectiveness of AI-driven spectrum occupancy prediction, indicating that lightweight learning models can effectively support future deployment-oriented DSS systems.

LarS-Net: A Large-Scale Framework for Network-Level Spectrum Sensing

As the demand of wireless communication continues to rise, the radio spectrum (a finite resource) requires increasingly efficient utilization. This trend is driving the evolution from static, stand-alone spectrum allocation toward spectrum sharing and dynamic spectrum sharing. A critical element of this transition is spectrum sensing, which facilitates informed decision-making in shared environments. Previous studies on spectrum sensing and cognitive radio have been largely limited to individual sensors or small sensor groups. In this work, a large-scale spectrum sensing network (LarS-Net) is designed in a cost-effective manner. Spectrum sensors are either co-located with base stations (BSs) to share the tower, backhaul, and power infrastructure, or integrated directly into BSs as a new feature leveraging active BS antenna systems. As an example incumbent system, fixed service microwave link operating in the lower-7 GHz band is investigated. This band is a primary candidate for 6G, being considered by the WRC-23, ITU, and FCC. Based on Monte Carlo simulations, we determine the minimum subset of BSs equipped with sensing capability to guarantee a target incumbent detection probability. The simulations account for various sensor antenna configurations, propagation channel models, and duty cycles for both incumbent transmissions and sensing operations. Building on this framework, we introduce three network-level sensing performance metrics: Emission Detection Probability (EDP), Temporal Detection Probability (TDP), and Temporal Mis-detection Probability (TMP), which jointly capture spatial coverage, temporal detectability, and multi-node diversity effects. Using these metrics, we analyze the impact of LarS-Net inter-site distance, noise uncertainty, and sensing duty-cycle on large-scale sensing performance.

Automated Spectrum Sensing and Analysis Framework

Spectrum sensing and analysis is crucial for a variety of reasons, including regulatory compliance, interference detection and mitigation, and spectrum resource planning and optimization. Effective, real-time spectrum analysis remains a challenge, stemming from the need to analyse an increasingly complex and dynamic environment with limited resources. The vast amount of data generated from sensing the spectrum at multiple sites requires sophisticated data analysis and processing techniques, which can be technically demanding and expensive. This paper presents a novel, holistic framework developed and deployed at multiple locations across the USA for spectrum analysis and describes the different parts of the end-to-end pipeline. The details of each of the modules of the pipeline, data collection and pre-processing at remote locations, transfer to a centralized location, post-processing analysis, visualization, and long-term storage, are reported. The motivation behind this work is to develop a robust spectrum analysis framework that can help gain greater insights into the spectrum usage across the country and augment additional use cases such as dynamic spectrum sharing.

VCORE: Variance-Controlled Optimization-based Reweighting for Chain-of-Thought Supervision

Supervised fine-tuning (SFT) on long chain-of-thought (CoT) trajectories has emerged as a crucial technique for enhancing the reasoning abilities of large language models (LLMs). However, the standard cross-entropy loss treats all tokens equally, ignoring their heterogeneous contributions across a reasoning trajectory. This uniform treatment leads to misallocated supervision and weak generalization, especially in complex, long-form reasoning tasks. To address this, we introduce \textbf{V}ariance-\textbf{C}ontrolled \textbf{O}ptimization-based \textbf{RE}weighting (VCORE), a principled framework that reformulates CoT supervision as a constrained optimization problem. By adopting an optimization-theoretic perspective, VCORE enables a principled and adaptive allocation of supervision across tokens, thereby aligning the training objective more closely with the goal of robust reasoning generalization. Empirical evaluations demonstrate that VCORE consistently outperforms existing token reweighting methods. Across both in-domain and out-of-domain settings, VCORE achieves substantial performance gains on mathematical and coding benchmarks, using models from the Qwen3 series (4B, 8B, 32B) and LLaMA-3.1-8B-Instruct. Moreover, we show that VCORE serves as a more effective initialization for subsequent reinforcement learning, establishing a stronger foundation for advancing the reasoning capabilities of LLMs. The Code will be released at https://github.com/coder-gx/VCORE.