Secure Aggregation

Standard ensemble methods can improve robustness by mitigating individual model stochasticity, but they frequently fail to generalize beyond the training distribution, leaving systems vulnerable to out-of-distribution (OOD) data. We introduce the Robust Satisficing Ensemble (RSE), a scalable probabilistic aggregation framework designed to secure model combinations by minimizing their fragility against distributional changes. By bridging a robust satisficing objective with a quadratic risk surrogate, RSE derives a closed-form analytical inner adversary. This fundamental reformulation enables highly efficient weight updates without the computational bottleneck of standard minimax optimization, crucially decoupling optimization complexity from sample size to scale effectively to large datasets. In particular, we prove a geometrically decaying truncation error for the fragility approximation via Lagrange-Bürmann expansion and show that the proximal RSE updates converge to a stationary point. We evaluate RSE across a comprehensive spectrum of distribution shifts, including adversarial label shift (SST-5, TREC), natural subpopulation and temporal shifts (CivilComments, HuffPost). Our results demonstrate that RSE consistently outperforms strong robust baselines, including GroupDRO, IRM, and SRM. These findings establish RSE as a practical, theoretically grounded safeguard for reliable model aggregation in dynamic environments.

This paper studies test-time aggregation, an approach that generates multiple reasoning traces and aggregates them into a final answer. Most existing methods rely on evaluation signals collected from candidate traces in isolation or answer frequencies, while ignoring comparative interactions among candidates. We propose *Joint Consistency* (JC), formulated as a constrained Ising-type energy minimization problem, where independent evaluation signals act as external fields and pairwise comparisons act as interactions. JC provides a unified framework for test-time aggregation that subsumes existing voting and weighted aggregation methods as special cases. Our construction of the interaction matrix leverages LLM-as-a-judge comparisons, and admits a theoretical interpretation under answer-level homogeneity assumptions. Moreover, we develop an efficient approximation strategy that makes interaction modeling practical for large-scale test-time aggregation. Experiments on math and code reasoning benchmarks show that JC consistently outperforms existing baselines across tasks, judge models, trace budgets, and trace-generation settings.

Conditional independence (CI) testing is a fundamental problem in statistics. However, classical nonparametric CI tests suffer from the curse of dimensionality, as nonparametric estimation degrades rapidly in high dimensions. This paper proposes RP-CIT, a random-projection-aggregated CI test that remains effective in the high-dimensional regime. The central idea is to project $X$ and $Y$ onto random one-dimensional subspaces before applying a univariate base CI test. This projection (i) preserves conditional independence under the null hypothesis and (ii) reduces the original high-dimensional problem to a collection of univariate CI subproblems, thereby avoiding high-dimensional nonparametric estimation. Since a single projection may miss the dependence signal, we aggregate the $p$-values from $k$ independent projections via a Bonferroni-max rule, which asymptotically controls the Type~I error at the nominal level and yields a limiting Type~II error bound that decreases exponentially in $k$ under a detectable-projection condition. The paper also develops a top-$r$ aggregation extension for alternatives whose signal is spread across multiple projection directions. More broadly, the random-projection aggregation framework can be combined with other scalar base tests; as one example, we use a projected GCM base test to accommodate higher-dimensional conditioning variables. Experiments on synthetic benchmarks, image-valued CI tasks, and Norman Perturb-seq module skeleton learning illustrate the calibration, power, and practical utility of the framework.

Federated Learning (FL) algorithms implicitly assume that clients passively comply with server-side orchestration by sharing local model updates upon server request. However, this overlooks an important aspect in real-world cross-silo environments: clients are often rational agents who may prioritize their utilities such as local model performance over that of the global model. In settings with significant statistical heterogeneity, rational clients may opt out of the federation if the perceived benefits of collaboration fail to meet their local utility thresholds. Such attrition degrades the global model performance and can lead to the collapse of the federated training process. In this work, we introduce FedUCA: Federated Learning by Utility-Constrained Stochastic Aggregation for Improving Rational Participation, a framework that formalizes the server's role as an optimizer seeking to maximize global model performance by sustaining client participation. We substantiate our framework through extensive experiments on standard datasets demonstrating that by prioritizing participation feasibility, FedUCA achieves significantly higher client retention and, consequently, a superior global model performance.

We propose WALLA, a decentralized mechanism for aggregating probabilistic predictions from multiple LLMs using wagering mechanisms. Each model reports a prediction and a learned wager reflecting its expected score advantage; predictions are then aggregated using wagers as weights. Our mechanism introduces a leave-one-out baseline that yields three key properties: dominant-strategy incentive compatibility under general belief structures, a best-response wager proportional to expected score advantage, and decoupling of prediction and wager optimization. We instantiate two mechanism variants trading off normality and no-arbitrage, both with bounded worst-case deficit independent of the number of participants. Experiments on QA benchmarks and a forecasting benchmark show that WALLA matches centralized baselines while simultaneously achieving advantage-weighted aggregation, uncertainty-awareness, fully decentralized learning, and incentive-compatibility guarantees.

Message-passing graph neural networks (MPGNNs) dominate modern graph learning. Typical efforts enhance MPGNN's expressive power by enriching the adjacency-based aggregation. In contrast, we introduce a graph-level aggregation over walk incidence-based matrices that are constructed to deliberately trade off some expressivity for stronger and more structured inductive bias. This approach allows for gradual scaling between classical message-passing and simpler methods based on walks. Our second result characterizes the expressive power at each scale using homomorphism counts over a hierarchy of generalized caterpillar graphs. Based on these foundations, we propose Caterpillar GNNs that substantially reduce the number of nodes in the hidden layers of the computational graphs on real-world datasets. This gradual reduction does not obstruct learning, enabling a systematic study of lower-order expressivity. We further describe benchmark settings where a task-aligned expressivity supports learning.

Model merging techniques, which aggregate independently finetuned models into one to combine their capabilities, have become a topic of significant interest in recent years, with a broad array of methods having been proposed to tackle this problem. Simultaneously, an emerging trend in distributed learning has been the use of methods such as local SGD and DiLoCo, which greatly reduce communication costs by periodically aggregating the independently trained local models. However, these communication-efficient methods have been shown to degrade in performance relative to the FLOP-matched data-parallel gold standard as the number of independent local models grows and as the number of local training steps before global communication is increased. In this work, we draw an explicit analogy between the pseudo-gradient aggregation step in local SGD/DiLoCo and task arithmetic-based model merging, establishing a straightforward way to utilize merging methods in the context of distributed optimization. We then evaluate multiple state-of-the-art model merging methods in this setting and identify one method in particular, Iso-C, as a promising approach for improving DiLoCo. We find that DiLoCo SGD with Iso-C aggregation outperforms not only simple pseudo-gradient averaging but even the momentum-based DiLoCo, despite lacking a momentum mechanism itself. Building on this finding, we propose IsoLoCo, which adapts Iso-C for distributed training by equipping it with Nesterov momentum. Our empirical evaluations on language model pre-training across varying numbers of local workers show that IsoLoCo significantly outperforms DiLoCo, with the gap between them widening as the number of workers increases. This advantage remains present across model sizes and inner step counts, confirming that merging-inspired aggregation is an effective strategy for low-communication distributed training.

Federated fine-tuning of large language models (LLMs) under heterogeneous client capacities is increasingly important, and low-rank adaptation (LoRA) with heterogeneous ranks makes it practical. Existing server-side aggregators compose local matrix updates $\Delta W_i$ from client-specific LoRA factors $(A_i,B_i)$ before aggregating them. Although these matrix updates lie in the same weight space $\mathbb{R}^{m\times n}$ and can be averaged directly, the LoRA factors that generate them may expressed client-specific local basis. In the typical compose--aggregate--factorize--dispatch loop, this basis inconsistency can make the rank-$r_i$ reference prefix dispatched to lower-rank clients unstable after server-side refactorization. In this work, we propose FedAbA, a basis-consistent federated LoRA aggregation framework for heterogeneous ranks. FedAbA first extracts each client's local basis, aligns it to the corresponding prefix of the global reference basis, and constructs a basis-consistent reconstruction of each local matrix update before aggregation. It then aggregates these reconstructions with weights that combine client data size and consistency score, followed by exact coefficient-space SVD refactorization and gauge fixing before rank-prefix dispatch. Our theoretical analysis clarifies the role of basis consistency and supports the proposed consistency-aware aggregation mechanism. Extensive experiments show that FedAbA outperforms representative federated LoRA baselines, with the largest gains under the strongest rank heterogeneity.