A central part of geometric statistics is to compute the Fréchet mean. This is a well-known intrinsic mean on a Riemannian manifold that minimizes the sum of squared Riemannian distances from the mean point to all other data points. The Fréchet mean is simple to define and generalizes the Euclidean mean, but for most manifolds even minimizing the Riemannian distance involves solving an optimization problem. Therefore, numerical computations of the Fréchet mean require solving an embedded optimization problem in each iteration. We introduce the GEORCE-FM algorithm to simultaneously compute the Fréchet mean and Riemannian distances in each iteration in a local chart, making it faster than previous methods. We extend the algorithm to Finsler manifolds and introduce an adaptive extension such that GEORCE-FM scales to a large number of data points. Theoretically, we show that GEORCE-FM has global convergence and local quadratic convergence and prove that the adaptive extension converges in expectation to the Fréchet mean. We further empirically demonstrate that GEORCE-FM outperforms existing baseline methods to estimate the Fréchet mean in terms of both accuracy and runtime.

We develop a high-dimensional scaling limit for Stochastic Gradient Descent with Polyak Momentum (SGD-M) and adaptive step-sizes. This provides a framework to rigourously compare online SGD with some of its popular variants. We show that the scaling limits of SGD-M coincide with those of online SGD after an appropriate time rescaling and a specific choice of step-size. However, if the step-size is kept the same between the two algorithms, SGD-M will amplify high-dimensional effects, potentially degrading performance relative to online SGD. We demonstrate our framework on two popular learning problems: Spiked Tensor PCA and Single Index Models. In both cases, we also examine online SGD with an adaptive step-size based on normalized gradients. In the high-dimensional regime, this algorithm yields multiple benefits: its dynamics admit fixed points closer to the population minimum and widens the range of admissible step-sizes for which the iterates converge to such solutions. These examples provide a rigorous account, aligning with empirical motivation, of how early preconditioners can stabilize and improve dynamics in settings where online SGD fails.

Transitioning from offline to online reinforcement learning (RL) poses critical challenges due to distributional shifts between the fixed behavior policy in the offline dataset and the evolving policy during online learning. Although this issue is widely recognized, few methods attempt to explicitly assess or utilize the distributional structure of the offline data itself, leaving a research gap in adapting learning strategies to different types of samples. To address this challenge, we propose an innovative method, Energy-Guided Diffusion Stratification (StratDiff), which facilitates smoother transitions in offline-to-online RL. StratDiff deploys a diffusion model to learn prior knowledge from the offline dataset. It then refines this knowledge through energy-based functions to improve policy imitation and generate offline-like actions during online fine-tuning. The KL divergence between the generated action and the corresponding sampled action is computed for each sample and used to stratify the training batch into offline-like and online-like subsets. Offline-like samples are updated using offline objectives, while online-like samples follow online learning strategies. We demonstrate the effectiveness of StratDiff by integrating it with off-the-shelf methods Cal-QL and IQL. Extensive empirical evaluations on D4RL benchmarks show that StratDiff significantly outperforms existing methods, achieving enhanced adaptability and more stable performance across diverse RL settings.

The COVID-19 pandemic disrupted healthcare systems worldwide, disproportionately impacting individuals with chronic conditions such as cardiovascular disease (CVD). These disruptions -- through delayed care and behavioral changes, affected key CVD biomarkers, including LDL cholesterol (LDL-C), HbA1c, BMI, and systolic blood pressure (SysBP). Accurate modeling of these changes is crucial for predicting disease progression and guiding preventive care. However, prior work has not addressed multi-target prediction of CVD biomarker from Electronic Health Records (EHRs) using machine learning (ML), while jointly capturing biomarker interdependencies, temporal patterns, and predictive uncertainty. In this paper, we propose MBT-CB, a Multi-target Bayesian Transformer (MBT) with pre-trained BERT-based transformer framework to jointly predict LDL-C, HbA1c, BMI and SysBP CVD biomarkers from EHR data. The model leverages Bayesian Variational Inference to estimate uncertainties, embeddings to capture temporal relationships and a DeepMTR model to capture biomarker inter-relationships. We evaluate MBT-CT on retrospective EHR data from 3,390 CVD patient records (304 unique patients) in Central Massachusetts during the Covid-19 pandemic. MBT-CB outperformed a comprehensive set of baselines including other BERT-based ML models, achieving an MAE of 0.00887, RMSE of 0.0135 and MSE of 0.00027, while effectively capturing data and model uncertainty, patient biomarker inter-relationships, and temporal dynamics via its attention and embedding mechanisms. MBT-CB's superior performance highlights its potential to improve CVD biomarker prediction and support clinical decision-making during pandemics.

The tailsitter vertical takeoff and landing (VTOL) UAV is widely used due to its lower dead weight, which eliminates the actuators and mechanisms for tilting. However, the tailsitter UAV is susceptible to wind disturbances in multi-rotor mode, as it exposes a large frontal fuselage area. To address this issue, our tailsitter UAV features a reconfigurable wing design, allowing wings to retract in multi-rotor mode and extend in fixed- wing mode. Considering power efficiency, we design a coaxial heterogeneous dual-rotor configuration, which significantly re- duces the total power consumption. To reduce structural weight and simplify structural complexity, we employ a swashplateless mechanism with an improved design to control pitch and roll in multi-rotor mode. We optimize the structure of the swashplateless mechanism by adding flapping hinges, which reduces vibration during cyclic acceleration and deceleration. Finally, we perform comprehensive transition flight tests to validate stable flight performance across the entire flight envelope of the tailsitter UAV.

Federated learning (FL) offers new opportunities in machine learning, particularly in addressing data privacy concerns. In contrast to conventional event-based federated learning, time-triggered federated learning (TT-Fed), as a general form of both asynchronous and synchronous FL, clusters users into different tiers based on fixed time intervals. However, the FL network consists of a growing number of user devices with limited wireless bandwidth, consequently magnifying issues such as stragglers and communication overhead. In this paper, we introduce adaptive model pruning to wireless TT-Fed systems and study the problem of jointly optimizing the pruning ratio and bandwidth allocation to minimize the training loss while ensuring minimal learning latency. To answer this question, we perform convergence analysis on the gradient l_2 norm of the TT-Fed model based on model pruning. Based on the obtained convergence upper bound, a joint optimization problem of pruning ratio and wireless bandwidth is formulated to minimize the model training loss under a given delay threshold. Then, we derive closed-form solutions for wireless bandwidth and pruning ratio using Karush-Kuhn-Tucker(KKT) conditions. The simulation results show that model pruning could reduce the communication cost by 40% while maintaining the model performance at the same level.

Cooperative multi-agent planning requires agents to make joint decisions with partial information and limited communication. Coordination at the trajectory level often fails, as small deviations in timing or movement cascade into conflicts. Symbolic planning mitigates this challenge by raising the level of abstraction and providing a minimal vocabulary of actions that enable synchronization and collective progress. We present DR. WELL, a decentralized neurosymbolic framework for cooperative multi-agent planning. Cooperation unfolds through a two-phase negotiation protocol: agents first propose candidate roles with reasoning and then commit to a joint allocation under consensus and environment constraints. After commitment, each agent independently generates and executes a symbolic plan for its role without revealing detailed trajectories. Plans are grounded in execution outcomes via a shared world model that encodes the current state and is updated as agents act. By reasoning over symbolic plans rather than raw trajectories, DR. WELL avoids brittle step-level alignment and enables higher-level operations that are reusable, synchronizable, and interpretable. Experiments on cooperative block-push tasks show that agents adapt across episodes, with the dynamic world model capturing reusable patterns and improving task completion rates and efficiency. Experiments on cooperative block-push tasks show that our dynamic world model improves task completion and efficiency through negotiation and self-refinement, trading a time overhead for evolving, more efficient collaboration strategies.

We study the problem of language identification in the limit, where given a sequence of examples from a target language, the goal of the learner is to output a sequence of guesses for the target language such that all the guesses beyond some finite time are correct. Classical results of Gold showed that language identification in the limit is impossible for essentially any interesting collection of languages. Later, Angluin gave a precise characterization of language collections for which this task is possible. Motivated by recent positive results for the related problem of language generation, we revisit the classic language identification problem in the setting where the learner is given the additional power of producing a list of $k$ guesses at each time step. The goal is to ensure that beyond some finite time, one of the guesses is correct at each time step. We give an exact characterization of collections of languages that can be $k$-list identified in the limit, based on a recursive version of Angluin's characterization (for language identification with a list of size $1$). This further leads to a conceptually appealing characterization: A language collection can be $k$-list identified in the limit if and only if the collection can be decomposed into $k$ collections of languages, each of which can be identified in the limit (with a list of size $1$). We also use our characterization to establish rates for list identification in the statistical setting where the input is drawn as an i.i.d. stream from a distribution supported on some language in the collection. Our results show that if a collection is $k$-list identifiable in the limit, then the collection can be $k$-list identified at an exponential rate, and this is best possible. On the other hand, if a collection is not $k$-list identifiable in the limit, then it cannot be $k$-list identified at any rate that goes to zero.

Category V ariable Definition Tax Avoidance CETR Cash Effective T ax Rate = Cash Taxes Paid / Pre - tax Income GETR GAAP Effective Tax Rate = T otal Tax Expense / Pre - tax Income CETR3 Three - year average CETR GETR3 Three - year average GETR CETR5 Five - year average CETR GETR5 Five - year average GETR A_CETR Adjusted Cash Effective Tax Rate A_GETR Adjusted GAAP Effective T ax Rate A_CETR3 Adjusted three - year average CETR A_GETR3 Adjusted three - year average GETR A_CETR5 Adjusted five - year average CETR A_GETR5 Adjusted five - year average GETR TSTA Total Book - T ax Difference (accrual - based measure) TSDA Discretionary Book - Tax Difference (discretionary accrual - based measure) Profitability ROA Return on Assets = Net Income / Lagged T otal Assets ROE Return on Equity = Net Income / Lagged Equity CFO Operating Cash Flow scaled by total assets LOSS Loss dummy (1 if prior - year net income < 0) Stability LEV Leverage = T otal Liabilities / Total Assets CUR Current Ratio = Current Assets / Current Liabilities SIZE Natural logarithm of total assets PPE Ratio of Property, Plant, and Equipment to total assets AGE Natural logarithm of firm age (based on year of establishment) INVREC Ratio of inventories and receivables to total assets Growth GRW Sales growth rate MB Market - to - Book Ratio = Market Capitalization / Book Equity TQ Tobin's Q = (Market Capitalization + Total Liabilities) / T otal Assets Market Valuation & Governance KOSPI KOSPI listing status dummy BIG4 Big4 audit dummy FORN Foreign ownership share (%) OWN Largest shareholder ownership share (%) Stability Measures Stability measures reflect a firm's financial soundness and its ability to meet obligations. Leverage (LEV) is defined as total liabilities divided by total assets, indicating the firm's degree of financial leverage. The current ratio (CUR), calculated as current assets divided by current liabilities, captures short - term liquidity and payment capacity. Firm size (SIZE) is measured as the natural logarithm of total assets, providing a quantitative indicator of scale. The proportion of property, plant, and eq uipment (PPE), defined as tangible fixed assets divided by total assets, is used to assess the structural stability of the asset base.

Recent advances in Large Language Models (LLMs) have highlighted the critical importance of extending context length, yet the quadratic complexity of attention mechanisms poses significant challenges for efficient long-context modeling. KV cache compression has emerged as a key approach to address this challenge. Through extensive empirical analysis, we reveal a fundamental yet previously overlooked asymmetry in KV caches: while adjacent keys receive similar attention weights ({\it local homogeneity}), adjacent values demonstrate distinct {\it heterogeneous} distributions. This key-value asymmetry reveals a critical limitation in existing compression methods that treat keys and values uniformly. To address the limitation, we propose a training-free compression framework (AsymKV) that combines homogeneity-based key merging with a mathematically proven lossless value compression. Extensive experiments demonstrate that AsymKV consistently outperforms existing long-context methods across various tasks and base models. For example, on LLaMA3.1-8B, AsymKV achieves an average score of 43.95 on LongBench, surpassing SOTA methods like H$_2$O (38.89) by a large margin.Our code can be found in this link:https://github.com/the-scale-lab/Asymkv.