Open Access

Federated learning (FL) enables collaborative model training across distributed clients while preserving data privacy by keeping data local. A central challenge in FL is determining which client updates are beneficial for aggregation with respect to each client’s target domain. Existing methods typically address this problem in parameter space by comparing model parameters or gradients. However, parameter-space similarity is often a poor proxy for predictive behavior, particularly in heterogeneous settings where client data is not independent and identically distributed. As a result, updates that are misaligned with a client’s target domain, including those arising from heterogeneous data distributions or malfunctioning clients, may be incorporated into aggregation and degrade local model performance. In this work, we propose Local Inference Guided Aggregation for Heterogeneous Training Environments to Yield Enhancement Through Agreement and Regularization (LIGHTYEAR), a federated learning framework that performs update selection in the function space. Central to our method is an NTK-based agreement score that characterizes predictive behavior and is used to determine the optimal aggregation set for each client. By relating model parameters to local predictive responses, the Neural Tangent Kernel (NTK) enables a function-space characterization of model updates and provides a more expressive criterion for update selection than parameter-space similarity alone. Since access to function-space information before aggregation is not available in conventional centralized FL, LIGHTYEAR leverages a peer-to-peer (P2P) topology, where clients exchange updates directly and can locally evaluate incoming models on private validation data. This enables each client to construct a personalized aggregation set consisting only of updates that are beneficial with respect to its own target domain. The selected updates are then aggregated using a regularized aggregation rule that further stabilizes training under heterogeneity. Our empirical evaluation across five datasets and nine baseline methods demonstrates that LIGHTYEAR consistently outperforms both centralized FL baselines and existing P2P approaches.

Closed-loop generative selection has become a workhorse of computational drug discovery: a learned generative model proposes candidate molecules, a fitness oracle scores them, the best are kept, and the model is retrained on this elite set before the next round. Despite its wide use, the method has lacked a rigorous convergence theory, largely because retraining the model each round breaks the Markov property on which classical evolutionary-algorithm analysis relies. We develop a self-contained theory of convergence and expected running time for this class of algorithms. By recovering a Markov structure on an enlarged state space, we show that elitism makes the search absorbing, and we prove almost-sure convergence together with a runtime bound that decomposes the search into the time spent escaping each fitness level. We then analyse the role of the model's memory---how much of the past it is trained on. When learning improves steadily with more data, deeper memory never hurts; when it does not, an exit-time analysis pinpoints the optimal memory depth and shows that excess memory can actually slow convergence. The theory extends to multi-objective search and to noisy oracles: we quantify how many repeated evaluations certify progress under light-tailed noise, and how robust estimators restore guarantees under heavy tails. Recast in terms of oracle evaluations - the true bottleneck in drug design - the analysis yields a concrete, evaluation-minimal strategy. Areproducible study confirms the predictions, including the surprising cost of excess memory. We close with three open problems.

Estimating the mean of manifold-valued data is a central problem in modern statistics, yet it remains challenging due to the lack of a closed-form expression for the Fréchet mean. The gradient descent algorithm is widely used to approximate this quantity across various applications. Although generally effective, it can be computationally intensive for large datasets, as each iteration requires evaluating gradients with respect to the entire dataset. To address these limitations, we propose a tree-based, Recursive Fréchet Mean Estimator (RFME), tailored to data on manifolds. The proposed method leverages a hierarchical aggregation strategy to reduce computational complexity while preserving statistical accuracy. We establish the weak consistency of RFME with respect to the population Fréchet mean and discuss its computational properties. Through simulation studies and real-world applications, we demonstrate that RFME achieves competitive estimation accuracy with substantially improved efficiency. Moreover, as a generalization of the incremental Fréchet mean estimator, RFME also offers enhanced flexibility while maintaining practical advantages.

Grinding stones are widely distributed across prehistoric contexts, yet linking their use to specific processing strategies and food products remains challenging. This study introduces a methodological approach that combines extended experimental replication with computational shape analysis to investigate the long-term morphological change in grinding tools. Focusing on the Early Neolithic site of Göbekli Tepe (9600-8000 BC), we analyze one of the earliest large-scale assemblages of grinding stones associated with cereal processing. Experimental produced replicas of original handstones made of basaltic rocks were used to process einkorn under controlled grinding motions, generating coarse and fine flour through contrasting movement and pressure regimes. Successive wear states were captured using high-resolution photogrammetry and reconstructed as three-dimensional models, allowing cumulative deformation trajectories to be quantified and compared. The results demonstrate that long-term shape alteration reflects consistent patterns linked to grinding behavior and product characteristics. The proposed framework extends functional interpretation beyond surface wear alone and offers a transferable analytical model applicable to other tool classes and archaeological contexts, supporting comparative and computational studies of food-processing technologies in cultural heritage research.