aggregation function design

This work addresses subdomain aggregation over time-series and image data, proposing the first unified modeling framework grounded in category theory. Methodologically, it formalizes classical aggregation operations—including summation, extremum computation, and sliding-window statistics—as bifunctors on double categories, thereby achieving functional abstraction of aggregation semantics across diverse data structures. Integrating functorial semantic modeling with Blelloch’s parallel scan algorithm, the framework derives novel aggregation operators with provably parallel implementations, substantially extending the applicability of the scan paradigm. Key contributions are: (1) the first functional aggregation framework supporting formal verification of parallelizability; (2) systematic definition and generation of previously unformalized subdomain aggregation patterns; and (3) a composable, extensible mathematical foundation for cross-modal data aggregation. The approach bridges abstract categorical semantics with practical parallel computation, enabling rigorous, scalable, and interoperable aggregation across heterogeneous data modalities.

This work addresses the lack of systematic and reproducible benchmarks for evaluating robustness in federated learning across diverse datasets and model architectures. It introduces the first comprehensive evaluation matrix comprising 500 experimental configurations, spanning five aggregation methods, five datasets, five model architectures, and four attack types—including sign-flipping, Gaussian noise, and BadNets backdoor attacks. Through rigorous reproduction and log-based auditing, the study systematically compares method performance under both clean and adversarial conditions. Results show that Trimmed Mean achieves the highest average accuracy (76.02%) in clean settings, while Krum demonstrates superior robustness against specific attacks. The analysis also uncovers critical implementation flaws—such as the misuse of the TTLR metric and inconsistencies between prediction and aggregation updates in FedPARETO—thereby significantly enhancing the transparency and auditability of robustness evaluations in federated learning.

This work addresses the limitations of existing black-box model ensembling approaches—namely, their reliance on model architecture and poor generalization. We propose Minimal Empirical Variance Aggregation (MEVA), a model-agnostic linear ensemble method that performs end-to-end optimization solely on model predictions. Its core innovation lies in replacing conventional error minimization with empirical variance minimization as the aggregation objective; we theoretically establish that this strategy yields superior statistical robustness under finite-sample regimes and unifies ensemble learning with general error estimation. MEVA requires no access to internal model parameters or gradients, making it compatible with diverse predictors—including machine learning models and numerical PDE solvers. Extensive experiments across data science and partial differential equation solving tasks demonstrate consistent improvements in both predictive accuracy and stability, validating MEVA’s generality and practical efficacy.

This work addresses the inefficiency and suboptimal energy consumption of data aggregation operations on heterogeneous hardware platforms. To bridge this gap, the authors propose a hybrid hardware acceleration framework that synergistically combines unified abstractions with platform-specific optimizations, effectively balancing programmability, portability, and architectural specialization across CPUs, GPUs, and FPGAs. By introducing a common abstraction layer while incorporating tailored optimization strategies for each hardware target, the approach achieves significant improvements in both performance and energy efficiency across all three mainstream architectures. The evaluation demonstrates consistent gains not only in device-level computation but also in end-to-end processing metrics, thereby establishing an effective trade-off between generality and high performance for data aggregation workloads.

This work investigates the interplay between interpolation and aggregation in regression tasks and its implications for learnability. By introducing the γ-graph dimension, the study characterizes the learnability boundary for a broad class of natural aggregation procedures and proposes a minimalist aggregation method that takes the median of three interpolating hypotheses. Theoretical analysis demonstrates that this median aggregation achieves optimal sample complexity among all finite interpolating aggregations and strictly outperforms standard interpolating learning. Moreover, the work reveals that certain hypothesis classes are learnable only via infinite or non-interpolating aggregations, thereby establishing fundamental limitations and optimality conditions for finite interpolating aggregation schemes.

In federated learning, aggregated local evaluation metrics often diverge from centralized assessment results, leading to misleading performance estimates. This work presents the first systematic analysis of the root causes of this discrepancy and introduces FLAM (Federated Learning Aggregatable Metrics), a general framework for consistent metric aggregation. Through rigorous mathematical derivation, FLAM establishes necessary conditions for metrics to ensure global consistency and devises a distributed evaluation protocol that enables accurate aggregation of diverse performance measures without requiring a global test set. Empirical evaluations across multiple benchmark tasks demonstrate that FLAM precisely reproduces centralized evaluation outcomes, substantially enhancing the reliability and applicability of model assessment in federated settings and overcoming the prevailing limitation of existing approaches to accuracy alone.

This study systematically investigates the impact of aggregation strategies on model performance, robustness, and system efficiency in federated learning under diverse data distributions. Within a unified experimental framework, the authors evaluate multiple state-of-the-art aggregation algorithms across both homogeneous and heterogeneous data settings, using several standard image classification benchmarks. By comprehensively analyzing metrics including model accuracy, convergence loss, and communication overhead, the work elucidates the strengths, limitations, and operational boundaries of each aggregation approach. The findings provide empirical insights and practical design guidelines for selecting and deploying aggregation strategies in real-world federated learning systems.

This work addresses the challenge of effectively aggregating statistical evidence under unknown dependence structures by proposing a unified framework grounded in permutation invariance. The approach constructs exchangeable data units, aggregates statistics within transformed datasets, and calibrates results across transformations, accommodating single-batch, sequential, and two-stage strategies. By integrating group invariance, exchangeability modeling, sequential alpha-spending, and a decoupling of standardization from calibration, the method achieves high power and adaptivity in finite samples, substantially outperforming traditional calibration techniques such as Bonferroni correction. Empirical evaluations demonstrate that the framework guarantees valid inference under arbitrary dependence structures in tasks including nonparametric testing and conformal prediction, while supporting data-driven aggregation rules and early rejection mechanisms.