Federated Edge Inference

Data heterogeneity is a fundamental challenge in Federated Learning (FL), where induced model drift often results in "negative gains" for global models on data-abundant clients, with performance falling below that of local training. To address this issue, we propose FedGain, a novel framework that optimizes collaborative client clustering to mitigate the negative gain. We are the first to develop a modified Scaling Law (SL) to quantify the reduction in data utility caused by heterogeneity and define Effective Federated Capacity to align clients with the highest potential collaboration gains. Extensive experiments demonstrate that our modified SL strictly adheres to the power-law learning discipline in non-IID scenarios. FedGain effectively suppresses negative gains to a negligible level across various FL algorithms and outperforms other Clustered FL methods.

Federated learning has emerged as the foremost approach for decentralized model training with privacy preserving. The global class imbalance and cross-client data heterogeneity naturally coexist, and the mismatch between local and global imbalances exacerbates the performance degradation of the aggregated model. The agnosticism of global class distribution poses significant challenges for data-level methods, especially under extreme conditions with severe class absence across clients. In this paper, we propose FedReLa, a novel data-level approach that tackles the coexistence of data heterogeneity and class imbalance in federated learning. By re-labeling samples with a feature-dependent label re-allocator, FedReLa corrects biased global decision boundaries without requiring knowledge of the global class distribution. This modular, model-agnostic approach can be integrated with algorithmic methods to deliver consistent improvements without additional communication overhead. Through extensive experiments, our method significantly improves the accuracy of minority classes and the overall accuracy on stepwise-imbalanced and long-tailed datasets, outperforming the previous state of the art.

The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian approaches and then hovers near the stability threshold $2/\eta$ during gradient descent (GD) with step size $\eta$. Despite (apparently) violating classical smoothness assumptions, EoS has been widely observed in deep learning, but its theoretical foundations remain incomplete. We provide an interpretation of EoS through the lens of Directional Smoothness [Mishkin et al., 2024]. This interpretation naturally extends to non-Euclidean norms, which we use to define generalized sharpness under an arbitrary norm. Our generalized sharpness measure includes previously studied vanilla GD and preconditioned GD as special cases, as well as methods for which EoS has not been studied, such as $\ell_{\infty}$-descent, Block CD, Spectral GD, and their normalized versions. Through experiments on neural networks, we show that non-Euclidean GD with our generalized sharpness also exhibits progressive sharpening followed by oscillations around or above the threshold $2/\eta$. Practically, our framework provides a geometry-aware spectral diagnostic that can be applied across a broad class of non-Euclidean gradient methods.

Federated learning (FL) enables collaborative training across distributed edge devices, but deploying lightweight models in dynamic edge environments remains challenging. Existing methods typically require retraining whenever device resource constraints change, resulting in excessive computational overhead. We propose DFMPQ, a dynamic federated mixed-precision quantization framework that enables retraining-free deployment at the edge. DFMPQ trains a weight-sharing mixed-precision supernet via FL, which jointly represents diverse bit-width configurations. After training, resource-aware quantized subnets can be derived on demand to satisfy heterogeneous and time-varying resource constraints without additional optimization. Optimizing such a supernet in federated settings is difficult due to optimization interference among heterogeneous bit-widths and the coupling of quantization noise with non-IID data. DFMPQ addresses these issues through semantic-aware training and aggregation mechanisms that stabilize supernet optimization. In addition, a sensitivity-guided greedy search strategy is adopted to efficiently identify suitable quantization configurations under given resource budgets. Extensive experiments on multiple datasets and network architectures demonstrate that DFMPQ achieves competitive accuracy with significantly reduced computational cost, enabling efficient deployment for dynamic edge computing environments.

Recent work suggests that (stochastic) gradient descent self-organizes near the instability boundary, shaping both optimization and the solutions found. Momentum and mini-batch gradients are widely used in practical deep learning optimization, but it remains unclear whether they operate in a comparable regime of instability. We demonstrate that SGD with momentum exhibits an Edge of Stochastic Stability (EoSS)-like regime with \textit{batch-size--dependent behavior} that cannot be explained by a single momentum-adjusted stability threshold. Batch Sharpness (the expected directional mini-batch curvature) stabilizes in two distinct regimes: at small batch sizes it converges to a lower plateau $2(1-\beta)/\eta$, reflecting amplification of stochastic fluctuations by momentum and favoring flatter regions than vanilla SGD; at large batch sizes it converges to a higher plateau $2(1+\beta)/\eta$, where momentum recovers its classical stabilizing effect and favors sharper regions consistent with full-batch dynamics. We further show this aligns with linear stability thresholds and we discuss the implications on hyperparameters tuning and coupling.

Federated learning (FL) enables distributed model training, yet in heterogeneous deployments, Bandwidth-Constrained Clients (BCCs) often contribute inefficiently due to limited uplink bandwidth. In model-heterogeneous FL with fixed small sub-models, BCCs with sub-models may improve quickly in early rounds but become under-parameterized later, resulting in slow convergence and poor generalization. To address this challenge, we propose **FedGMR**, a federated learning framework centered around **Gradual Model Restoration (GMR)**, where GMR progressively increases each client’s sub-model density during training, allowing BCCs to remain effective contributors throughout optimization. To make GMR practical under real-world heterogeneity, FedGMR is realized as an end-to-end workflow with asynchronous coordination and stable, mask-aware aggregation. We further establish convergence guarantees, showing that the aggregation error scales with the **average** sub-model density across clients and rounds, and that GMR provably narrows the gap toward full-model FL. Extensive experiments on FEMNIST, CIFAR-10, ImageNet-100, and StackOverflow demonstrate that FedGMR improves both convergence speed and final accuracy, especially under severe heterogeneity and non-IID data distributions. Code is available at https://github.com/machengjie321/ICML2026-FedGMR.

Federated causal discovery for time series is becoming increasingly important in many application domains. In practice, intervention policies on each client often change over time, causing the local underlying causal mechanisms to drift rather than remain fixed. Moreover, different sampling frequencies across clients yield incompatible time scales in the observed data, making the resulting local causal graphs naturally heterogeneous and difficult to aggregate consistently. Accordingly, we propose Fed-CAW, a Credibility-Aware Weighting Federated causal discovery framework for time series. Specifically, we define edge-level credibility scores that quantify per-edge reliability by summarizing (i) within-client temporal stability across windows and (ii) cross-client temporal consistency after mapping heterogeneous sampling frequencies onto a unified time scale. We then aggregate privatized edge statistics under differential privacy, treating credibility scores as weights to recover a global causal graph while preserving personalized local structures without sharing raw data. Theoretically, we demonstrate the rationale for the unified time scale mapping and establish rigorous differential privacy guarantees. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our proposed method.

Heterogeneous federated learning (HtFL) has emerged as a promising approach to address heterogeneity in local computational resources and data distribution. However, existing methods cause performance degradation of model personalization because personalized and generalized knowledge are either intertwined or dominated by one of them. To address this issue, we propose a novel Elastic Mixture of Experts (EMoE) architecture on HtFL, namely FedEMoE, decoupling personalization from generalization. Specially, FedEMoE employs a multi-scale feature extraction mechanism via personalized experts to enrich personalized knowledge. Furthermore, we design an elastic shared expert to break the transferred knowledge bottleneck across heterogeneous client models. The elastic shared expert can adaptively expand or shrink according to the status of each expert by the weight spectrum analysis, respectively. Extensive experiments across statistical and model heterogeneity settings demonstrate that FedEMoE significantly outperforms state-of-the art methods on the accuracy of each heterogeneous model over diverse datasets.

Computation overhead has emerged as a critical bottleneck in Federated Learning (FL). Coreset selection tackles this challenge by constructing an informative subset to represent the full dataset. However, existing approaches optimize coreset construction solely at the data level and enforce a uniform retention ratio across all clients, ignoring client heterogeneity and introducing detrimental fragmented clients. In this paper, we first introduce a *gradient projection Shapley value* (GPSV) to evaluate client contributions. GPSV captures both the directional and magnitude information of client updates and enables exact Shapley value calculation with $\mathcal{O}(1)$ per-coalition evaluation. Building on GPSV, we then propose ShapCCS, the first client-level coreset selection strategy for FL. ShapCCS prioritizes clients with high GPSV scores while excluding fragmented clients with negligible or even negative GPSV. As a client-level coreset selection strategy, ShapCCS can be integrated with a data-level selection approach, and additionally reduces communication costs, an advantage unattainable by data-level methods alone. Extensive experiments demonstrate the superiority of ShapCCS on model performance and robustness to noise. The code is available at https://anonymous.4open.science/r/ShapCCS-5CBB.

Cross-device Federated Learning (FL) is frequently bottlenecked by the prohibitive memory and communication costs of training deep neural networks on resource-constrained edge hardware. While federated dynamic sparse training aims to alleviate these costs by adjusting sparse structures during training, existing methods rely on magnitude-based heuristics that are fundamentally ill-suited for the non-convergent, heterogeneous environments inherent to FL. To address this challenge, we propose FedFit, a federated dynamic sparse training framework that replaces simple heuristics with optimization-centric criteria for structure adjustment. By leveraging a second-order approximation of the loss landscape via the Fisher Information Matrix, FedFit enables precise and efficient structure adjustment without the overhead of explicit Hessian computation. Empirical evaluations across computer vision and natural language processing benchmarks demonstrate that FedFit significantly narrows the sparse-to-dense accuracy gap, outperforming state-of-the-art methods while maintaining high communication efficiency. Our code is available at https://github.com/Serena-28/Fedfit.git.

Label Distribution Learning (LDL) models supervision as an instance-wise probability distribution, enabling fine-grained learning under inherent ambiguity, but its success relies on high-fidelity label distributions that are costly to obtain and thus often noisy. Motivated by privacy-sensitive applications, we study Federated Label Distribution Learning (Fed-LDL), where data isolation further induces heterogeneous annotation quality across clients, making local updates unevenly reliable and breaking sample-size-based aggregation (e.g., FedAvg). To address this trust dilemma, we propose FedQual, a quality-aware Fed-LDL framework with two coupled mechanisms: (i) quality-adaptive client training guided by a global semantic anchor that calibrates low-quality clients while preserving high-quality autonomy, and (ii) reliability-aware server aggregation that reweights client contributions by effective reliable information rather than raw sample size. To enable rigorous evaluation, we construct four new Fed-LDL benchmarks (FER-LDL, FI-LDL, PIPAL-LDL, and KADID-LDL) with controlled annotation quality disparity. We further provide a theoretical guarantee showing that under heterogeneous supervision quality, client-specific calibration is strictly better than any uniform calibration. Experiments on the proposed benchmarks demonstrate the effectiveness of FedQual.

We study the MaxECC problem, where given an edge-colored hypergraph with $k$ colors and edge size $r$, we seek to color the vertices of the graph in order to maximize the number of satisfied edges (edges having the same color as their extremities): this is an effective mechanism for clustering (coloring) objects based on their multi-way interactions with one another in a system, providing significant applications in machine learning, clustering, and data mining. We exponentially improve upon the approximation ratio of an existing algorithm to $\frac{1}{r+1}$, present another novel dependent-rounding algorithm with an approximation ratio of $1/ \lceil \frac{k}{2}\rceil$, and modify the initial algorithm via analytical scaling techniques in order to achieve an approximation factor of $(1-e^{-r})/r$. We then apply our scaling algorithm to graph MaxECC and improve the best-known approximation factor for all hypergraphs: in particular, our algorithm provides an approximation factor of $0.43$ as opposed to the previously-known $0.38$ factor for graphs.

Federated learning increasingly faces deletion requests that require client-level unlearning without sacrificing model quality, yet a client’s influence is often deeply entangled after many rounds of aggregation. We aim to make unlearning fast, stable, and predictable by reducing the gap to leave-one-out retraining under realistic heterogeneity. We propose Influence-Disentangled Federated Training (IDFT), which instruments standard FedAvg with training-time influence logging: each round’s updates are decomposed into shared covarying directions and a client-separable residual trace, and an entanglement-aware shrinkage suppresses non-removable components. Deletion then becomes a single subtraction followed by a short anchored repair, yielding a stability-style characterization of retrain fidelity driven by the unremoved residual. Across representative benchmarks, IDFT consistently attains the lowest retrain gap (Avg. Gap) on multiple dataset--architecture pairs and improves the fidelity--cost frontier, matching retrain-level forgetting with substantially lower communication/compute than history-heavy baselines. These results suggest a practical pathway to unlearning-friendly federated systems by designing for removability during training rather than relying solely on post-hoc corrections.

Graph Neural Networks (GNNs) suffer from overfitting and over-squashing of long-range information. Stochastic graph augmentations (e.g., edge deletion) regularize training against overfitting but can introduce train-inference misalignment and do not improve over-squashing. In contrast, rewiring methods improve connectivity to mitigate over-squashing, but are not designed to regularize training. We propose *Random Add-Drop Edge (RADE)*, a stochastic graph augmentation method that jointly drops and adds edges to address both overfitting and over-squashing simultaneously. RADE is provably designed to align training and inference so that random augmentations regularize training without distribution shift, while supporting long-range communication at inference. We further propose and study a mini-batch gradient-norm balancing algorithm that adapts deletion and addition rates during training, rendering RADE hyperparameter-free in practice. Experiments on node- and graph-classification benchmarks show that RADE is a strong regularizer and mitigates over-squashing. Ablations support the roles of train-inference alignment, adaptive rate selection, and the complementary effects of random edge deletion and edge addition.

As frontier Large Language Models (LLMs) increasingly saturate new benchmarks shortly after they are published, benchmarking itself is at a juncture: if frontier models keep improving, it will become increasingly hard for humans to generate discriminative tasks, provide accurate ground-truth answers, or evaluate complex solutions. If benchmarking becomes infeasible, our ability to measure any progress in AI is at stake. We refer to this scenario as the *post-comprehension regime*. In this work, we propose Critique-Resilient Benchmarking, an adversarial framework designed to compare models even when full human understanding is infeasible. Our technique relies on the notion of *critique-resilient correctness*: an answer is deemed correct if no adversary has convincingly proved otherwise. Unlike standard benchmarking, humans serve as bounded verifiers and focus on localized claims, which preserves evaluation integrity beyond full comprehension of the task. Using an itemized bipartite Bradley-Terry model, we jointly rank LLMs by their ability to solve challenging tasks and to generate difficult yet solvable questions. We showcase the effectiveness of our method in the mathematical domain across eight frontier LLMs, showing that the resulting scores are stable and correlate with external capability measures. Our framework reformulates benchmarking as an adversarial generation-evaluation game in which humans serve as final adjudicators.

The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime. In this work, we argue that a comprehensive understanding of the generalization performance of gradient descent requires analyzing the interaction between these various forms of implicit regularization. We empirically demonstrate that the learning rate interpolates between low parameter norm and low sharpness of the trained model. We furthermore prove that neither implicit bias alone minimizes the generalization error for diagonal linear networks trained on a simple regression task. These findings demonstrate that focusing on a single implicit bias is insufficient to explain good generalization, and they motivate a broader view of implicit regularization that captures the dynamic trade-off between norm and sharpness induced by non-negligible learning rates.

Federated Incremental Learning (FIL) aims to learn streaming tasks across distributed clients without catastrophic forgetting while preserving privacy. Most existing methods mitigate forgetting by replaying historical samples, but it can pose privacy risks and incur high resource overhead, limiting deployment on resource-constrained edge devices. To address this challenge, we propose a novel **Li**ghtweight **F**ederated **I**ncremental **L**earning framework called **Li-FIL** that leverages dense features synthesized by a server-side secure generator to enable efficient feature-based decoupled replay. More specifically, each client extracts high-confidence features from new tasks, enrich them via mixup, and privatize them before uploading to the server, which reduces both storage and communication overhead. A generator is deployed on the server to learn the distributions of clients and generate global features for replay. Moreover, to enable clients to better learn from these dense features, we decouple local training into classifier stabilization and encoder regularization. This design allows feature replay and alignment between new and previous features to be conducted separately and more effectively. Extensive experiments demonstrate that Li-FIL outperforms other state-of-the-art methods by up to 10.14% in terms of accuracy on both old and new tasks with superior resource efficiency.

Speculative decoding can significantly accelerate LLM inference, especially given that its cloud-edge collaborative deployment offers cloud workload offloading, offline robustness, and privacy enhancement. However, existing collaborative inference frameworks with speculative decoding are constrained by (i) sequential token generation and communication with low resource utilization, and (ii) inflexible cloud non-autoregressive verification (NAV) triggering that induces premature verification or costly rollbacks. In this paper, we propose PipeSD, an efficient cloud-edge collaborative pipeline inference framework with speculative decoding. PipeSD overlaps token generation and communication by a token-batch pipeline scheduling mechanism optimized by dynamic programming, and improves verification flexibility through a dual-threshold NAV triggering mechanism with a lightweight Bayesian optimization autotuner. We implement PipeSD using llama-cpp-python, PyTorch, and FastAPI, and evaluate it on a real-world cloud-edge testbed with two draft-target model pairs across four scenarios. Results show that PipeSD consistently outperforms state-of-the-art baselines, achieving $1.16\times$-$2.16\times$ speedup and reducing energy consumption by $14.3$%-$25.3$%. Our code is available at https://github.com/Ghanyunhe/PipeSD.