One-Shot Aggregation: Concepts, Methods, and Applications

• One-shot aggregation is a non-iterative technique that combines local data, model updates, or predictions into a unified output using a single round of communication.
• It is widely applied in federated learning, conformal prediction, distributed optimization, and data summarization, offering strong theoretical guarantees on accuracy and robustness.
• The method faces challenges such as managing heterogeneity and ensuring resilience to errors and adversarial inputs without iterative refinement or historical reweighting.

One-shot aggregation denotes a broad family of algorithmic strategies in which a collection of data, model updates, or structural predictions is aggregated into a global solution in a single pass or round of communication, without iterative refinement, re-weighting, or referencing the identities or prior behavior of the sources. One-shot aggregation is central in federated learning, conformal prediction, distributed optimization, data summarization (coresets), crowdsourcing, privacy-preserving computation, and graph inference, among other areas. Despite its simplicity, it presents unique algorithmic and statistical challenges due to its irreversibility and its need to achieve robustness, accuracy, and sometimes strong formal guarantees with severely limited interaction or information.

1. Fundamental Principles and Definitions

One-shot aggregation frameworks aggregate a set of local objects (models, statistics, labels, graphs, etc.) into a global solution based on a single pass over the available data or a single round of communication, as opposed to multi-round or iterative algorithms. The one-shot property requires the aggregation to be data- and/or agent-independent, often precluding the use of historical records, repeated negotiation, or reweighting based on previous accuracy.

Formally, if each of $K$ distributed entities (clients, agents, annotators, etc.) possesses information $S_i$, a one-shot aggregation protocol defines an operator $\mathcal{A}$ acting on $(S_1,\ldots,S_K)$ such that the output $\mathcal{A}(S_1,\ldots,S_K)$ is the globally aggregated solution. The operator $\mathcal{A}$ must be defined such that each $S_i$ is submitted once, and the aggregation protocol does not require further input or iteration.

Distinct one-shot aggregation paradigms include:

• Parameter and sufficient-statistic fusion: clients send local statistics (e.g., $X_i^\top X_i$, $X_i^\top y_i$), as in federated ridge regression (Alsulaimawi, 13 Jan 2026).
• Model parameter or posterior aggregation: as in federated learning, either by layer-wise parameter averaging, Bayesian posterior product, or harmonization in multi-objective settings (Liu et al., 2023, Su et al., 2022).
• Nonparametric voting or learning-based decision rule aggregation: as in crowdsourcing or collective judgment (Shinitzky et al., 2022, Shinitzky et al., 2022).
• Graph and structure inference: per-sample or per-batch local inference, then one-shot frequency-based or adaptive fusion (Math et al., 23 Sep 2025).
• Privacy-preserving aggregation: each party encodes/masks input once; the aggregator (possibly with help of a committee) reconstructs the global sum/product (Karthikeyan et al., 2024).
• Coreset construction and data summarization: single-pass summarization for a full family of objectives (Bachem et al., 2017).
• One-shot architecture search: super-net training with one-pass evolutionary sub-net selection (Liang et al., 2021).

2. Algorithmic Methodologies

One-shot aggregation is instantiated according to the specifics of the problem domain. Several representative methodologies from recent literature include:

Federated Ridge Regression via Sufficient Statistic Aggregation

In one-shot federated ridge regression, each client $i$ computes and sends $(G_i = X_i^\top X_i,\, h_i = X_i^\top y_i)$ once to the server. The server computes $G = \sum_i G_i$, $h = \sum_i h_i$, and obtains the global minimizer $\hat w = (G + \lambda I)^{-1} h$. Under a coverage condition, this yields the exact centralized estimator in one shot, even under heterogeneity. Communication can be further compressed by random projections; differential privacy is achieved by adding noise once to each statistic (Alsulaimawi, 13 Jan 2026).

Bayesian Layer-Wise Posterior Aggregation

In settings with local overfitting and non-IID data, as in one-shot federated learning, local clients approximate their parameter posteriors $\mathcal N(\mu_{k,l}, \Sigma_{k,l})$ via Laplace or empirical Fisher/KFAC methods, and send these summaries (mean $\mu_{k,l}$ and curvature factors) to the server. The server aggregates each layer by solving a quadratic maximization corresponding to the product of Gaussians, yielding global means $\bar M_l$. This strongly outperforms naive averaging in non-IID regimes (Liu et al., 2023).

Geometric Median Aggregation with Permutation Alignment

For distributed ICA, local solutions are ambiguous up to permutation and sign. Each client sends its estimate once; the server first aligns signs, clusters all local component vectors with $k$-means (resolving permutations), and then aggregates each cluster via the geometric median, achieving robustness to adversarial and heterogeneous local errors (Jin et al., 26 May 2025).

Meta-Learning for One-Shot Crowdsourcing

In group decision aggregation, engineered response-level or answer-level meta-cognitive feature vectors are used to train ML classifiers to predict the correctness of each response or answer. The classifier's predictions are then used in a single pass to aggregate responses, with significant accuracy gains over majority or confidence-weighted rules. No iterative consensus or per-worker historical modeling is used (Shinitzky et al., 2022, Shinitzky et al., 2022).

Secure One-Shot Aggregation in Federated Learning

The OPA protocol achieves secure aggregation in a single round: each client masks its data (using PRG or DPRF mechanisms) and broadcasts it; a server and committee reconstruct the overall mask sum, enabling recovery of the total input sum without leaking individual contributions. OPA avoids the multi-round complexity of previous protocols and is robust to partial client dropout (Karthikeyan et al., 2024).

One-Shot Aggregation in Causal Discovery

CARGO infers per-sample causal graphs using neural density estimators (Transformers) in one forward pass per sequence, then aggregates the binary edge adjacencies across samples by adaptive thresholding the empirical edge frequency, producing a sparse global Markov boundary without full-dataset conditional independence testing (Math et al., 23 Sep 2025).

A summary table of typical one-shot aggregation instantiations:

Context	Local Object	Aggregation Operator
Federated regression	Sufficient statistics	Summation and closed-form inversion
Federated deep learning	Model/posterior	Averaging, posterior product, harmonized descent
ICA/factor analysis	Component estimates	Permuted clustering + geometric median
Crowdsourcing	Judgments/responses	ML classifier-based aggregation
Secure FL	Masked vectors	Masked sum with committee-enabled demasking
Causal graph discovery	Local graphs	Frequency thresholding / adaptive fusion
Coreset/data summarization	Points/sensitivities	Weighted resampling with envelope-based weights

3. Theoretical Guarantees and Limitations

One-shot aggregation methods often admit strong theoretical results, though their guarantees can be highly problem-dependent:

• Exactness: For distributed ridge regression, exact recovery of the centralized optimum is achieved under full-rank coverage, even with arbitrary heterogeneity. Communication cost is minimized to $O(d^2)$, with robustness to client dropout and a natural privacy mechanism (Alsulaimawi, 13 Jan 2026).
• Coverage/validity: In one-shot conformal aggregation (e.g., CAOS), exact finite-sample marginal coverage is attained using monotonicity arguments, despite the unavailability of classical exchangeability, provided a self-score optimality assumption holds (Waldron, 8 Jan 2026).
• Robustness to error and adversariality: In federated ICA, the two-stage (clustering + geometric median) methodology achieves minimax-optimal rates so long as fewer than half the clients are heavily corrupted, owing to both permutation error correction and the geometric median's outlier-resilience (Jin et al., 26 May 2025).
• Statistical compactness: In one-shot coresets for $k$-clustering, a single sampled, weighted subset approximates all $\ell_p$ clustering costs for $p \in [1, p_{\text{max}}]$^{} simultaneously within $1\pm\varepsilon$ multiplicative error, with sample size scaling logarithmically in $p_{\text{max}}$ and inversely in $\varepsilon$ (Bachem et al., 2017).
• Limitations and failure modes:
  • In federated learning with highly non-linear models (deep nets), no sufficient-statistic representation is available for exact one-shot aggregation; only approximate or knowledge-distillation-based methods are possible (Alsulaimawi, 13 Jan 2026).
  • Certain meta-cognitive aggregation regimes require users to self-report confidences or peer predictions, which may not be feasible in all crowd settings (Shinitzky et al., 2022).
  • The CAOS guarantee is marginal, not conditional; it relies on minimum self-score across the pool, which may be violated under some predictor constructions (Waldron, 8 Jan 2026).

4. Practical Implementations and Applications

The one-shot aggregation paradigm is implemented across a spectrum of domains to address communication, privacy, robustness, and computational bottlenecks:

• Federated Learning: Single-round model fusion schemes (via sufficient statistics (Alsulaimawi, 13 Jan 2026), harmonization (Su et al., 2022), layer-wise Bayesian aggregation (Liu et al., 2023), or privacy masks (Karthikeyan et al., 2024)) greatly reduce communication overhead and are especially favorable in high-latency or large-scale settings with frequent dropouts or strong privacy requirements. OPA achieves substantial speedups over classical Bonawitz-style and LERNA-style secure protocols and retains model accuracy within 0.5–1% of cleartext training (Karthikeyan et al., 2024).
• Conformal Prediction and Uncertainty Quantification: In low-data regimes (e.g., $n=1$ or $n=2$ per task), CAOS efficiently aggregates multiple one-shot predictors, yielding set-valued predictions with reliable finite-sample coverage and much smaller uncertainty sets compared to split conformal approaches (Waldron, 8 Jan 2026).
• Distributed Blind Source Separation: In federated ICA, one-shot robust aggregation is performed even when permutations and sign ambiguities differ across clients; sequential communication is entirely avoided (Jin et al., 26 May 2025).
• Crowdsourced Decision Aggregation: Machine-learning-based one-shot aggregators consistently outperform rule-based aggregation (majority, confidence-weighted, “surprisingly popular”) by 20–35 percentage points, establishing new benchmarks for non-iterative consensus (Shinitzky et al., 2022, Shinitzky et al., 2022).
• Data Summarization and Sketching: One-shot coresets are used in clustering, low-rank approximation, and related summarization tasks to support future queries without assuming a fixed loss function (Bachem et al., 2017).
• Causal Discovery in High-Dimensional Sequences: CARGO enables graph inference in millions of event sequences with thousands of variables; per-sequence local graph extraction and global adaptive fusion dramatically reduce computational requirements versus traditional constraint-based methods (Math et al., 23 Sep 2025).

5. Extensions, Generalizations, and Influence

A common theme is that one-shot aggregation attempts to operationalize "statistical sufficiency" under structural, computational, or privacy constraints. Several potential extension points and generalizations highlighted in the cited works include:

• Multi-scale feature aggregation: In generative modeling, as in FontDiffuser, multi-scale content aggregation via adaptive channel attention can enhance stroke- or texture-level fidelity, and the design is applicable to style transfer, medical reconstruction, and layout-guided synthesis (Yang et al., 2023).
• Meta-learning over aggregation rules: The ensemble approach in group-decision settings—machine-learned selection or combination of base aggregation strategies—demonstrates that meta-cognitive and context features can be uniquely leveraged in one-shot protocols (Shinitzky et al., 2022).
• Link to statistical sufficiency and random projections: Both in distributed regression and data summarization, random projection and sensitivity-based envelope constructions enable compact, approximate, or privacy-preserving single-pass aggregation steps (Bachem et al., 2017, Alsulaimawi, 13 Jan 2026).
• Single-round secure computation: OPA’s design generalizes to any summation- or threshold-based secure computation with efficient, minimal interaction and committee-based variance reduction for adaptive security (Karthikeyan et al., 2024).

A plausible implication is that as model and data scale continue to grow and privacy/communication constraints become more stringent, the class of one-shot aggregation techniques—unified by their non-iterative, high-efficiency, often provable properties—will become increasingly foundational in distributed learning, large-scale inference, and secure collaborative computation.

Key advances and domain exemplars:

• One-Shot Federated Ridge Regression: Exact Recovery via Sufficient Statistic Aggregation (Alsulaimawi, 13 Jan 2026)
• CAOS: Conformal Aggregation of One-Shot Predictors (Waldron, 8 Jan 2026)
• One-shot Robust Federated Learning of Independent Component Analysis (Jin et al., 26 May 2025)
• Exploiting Meta-Cognitive Features for a Machine-Learning-Based One-Shot Group-Decision Aggregation (Shinitzky et al., 2022)
• Meta-Learning Approaches for a One-Shot Collective-Decision Aggregation (Shinitzky et al., 2022)
• OPANAS: One-Shot Path Aggregation Network Architecture Search for Object Detection (Liang et al., 2021)
• “OPA”: One-shot Private Aggregation with Single Client Interaction and its Applications to Federated Learning (Karthikeyan et al., 2024)
• Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation (Math et al., 23 Sep 2025)
• One-Shot Coresets: The Case of k-Clustering (Bachem et al., 2017)
• TreeNet: A lightweight One-Shot Aggregation Convolutional Network (Rao, 2021)
• FontDiffuser: One-Shot Font Generation via Denoising Diffusion with Multi-Scale Content Aggregation and Style Contrastive Learning (Yang et al., 2023)

These works collectively define the methodological landscape, formal underpinnings, and diverse applications of one-shot aggregation across contemporary research frontiers.