Distributional Learning

Probabilistic circuits (PCs) can model complex joint distributions while supporting exact and efficient computation of many inference queries. However, standard likelihood-based PC learning is vulnerable to overfitting and fragile generalization when confronted with data noise, small sample sizes, or distribution shifts. This can be mitigated using distributionally-robust optimization which consider worst-case distributions within a Wasserstein ball of the empirical distribution, but current methods are limited to training a model from scratch in this framework. Instead, we propose PeTeR: a novel, data-free post-training framework designed to robustify pre-trained PCs against distribution shifts without retraining from scratch. Empirical evaluations across multiple density estimation benchmarks demonstrate that PeTeR effectively robustifies baseline models against both random and adversarial perturbations, achieving competitive or superior performance to data-dependent robust learning baselines.

One-shot federated learning (OSFL) addresses the communication overhead of federated learning by limiting training to a single round, but doing so without sacrificing model quality is non-trivial, particularly when client data distributions diverge. Recent work has addressed this challenge by aggregating client knowledge on the server through the construction of transferable synthetic datasets or distillates. However, most of these methods lack formal privacy guarantees, leaving a gap in jointly achieving low communication, robustness to heterogeneity, and rigorous privacy. We propose FedKT-CSD (Federated Knowledge Transfer via Collaborative Synthetic Data), a framework inspired by neural image compression that closes this gap by leveraging publicly pretrained autoencoders as a shared latent space. Each client encodes its private data in a single forward pass, computes class-conditional latent statistics, and transmits these to the server. The server aggregates these statistics via secure aggregation, adds calibrated differential privacy noise, and decodes a synthetic dataset for training a global model and further downstream tasks. This design provides formal $(\varepsilon,δ)$-differential privacy by construction, while keeping client-side computation and communication lightweight. Despite operating under privacy constraints, FedKT-CSD is competitive with and even outperforms non-private baselines across diverse datasets and heterogeneity settings, and scales to a large number of clients. Our code is available at: https://github.com/an7123/FedKT-CSD

Semi-supervised 3D medical image segmentation reduces the need for dense voxel-level annotations by exploiting unlabeled volumes. Although existing methods such as consistency regularization, pseudo-labeling, and co-training improve prediction-level robustness, they often provide insufficient feature-space organization for anatomically complex structures, especially small organs and ambiguous boundary regions with large intra-class variations. To address this issue, we propose Variation-Conditioned Distributional Proxy Learning (VCDP), a plug-and-play training-only regularization module for semi-supervised 3D medical image segmentation. VCDP represents each class with a learnable Gaussian distribution for shared class semantics and multiple variation prototypes for fine-grained intra-class patterns. A unified variation-conditioned compatibility score is further formulated to fuse distributional similarity and soft variation aggregation, guiding voxel embeddings to align with both global organ identity and local anatomical variations. VCDP is attached to decoder features during training and removed during inference, introducing no additional inference cost. Experiments on multi-organ segmentation benchmarks show that VCDP improves most evaluated baselines, particularly for small, ambiguous, and highly variable organs. Our anonymous code is released at https://anonymous.4open.science/r/VCDP_code-41ED.

Subsampling significantly reduces the number of measurements, thereby streamlining data processing and transfer overhead, and shortening acquisition time across diverse real-world applications. The recently introduced Active Deep Probabilistic Subsampling (A-DPS) approach jointly optimizes both the subsampling pattern and the downstream task model, enabling instance- and subject-specific sampling trajectories and effective adaptation to new data at inference time. However, this approach does not fully leverage valuable dataset priors and relies on top-1 sampling, which can impede the optimization process. Herein, we enhance A-DPS by integrating a deterministic (fixed) prior-informed sampling pattern derived from the training dataset, along with group-based sampling via top-k sampling, to achieve more robust optimization, method we call Prior-aware and context-guided Group-based Active DPS (PGA-DPS). We also provide a theoretical analysis supporting improved optimization via group sampling, and validate this with empirical results. We evaluated PGA-DPS on three tasks: classification, image reconstruction, and segmentation, using the MNIST, CIFAR-10, fastMRI knee, and hyperspectral AeroRIT datasets, respectively. In every case, PGA-DPS outperformed A-DPS, DPS, and all other sampling methods.

Federated Learning (FL) enables training shared models on private, on-device data, but production deployments remain constrained to slow, multi-day refresh cycles due to the complexity of coordinating massive client populations. For applications such as feed ranking, ad targeting, and personalized recommendation, model freshness: the ability to rapidly adapt to new user-local data is critical for maximizing objectives like click-through rate. This lag leaves models stale and unresponsive to volatile data distributions driven by viral trends and shifting user intent. Bridging this gap requires addressing three challenges overlooked by existing FL systems: transient client availability, dynamic data heterogeneity, and delays between model predictions and observable outcomes. We present FeLiX, an FL orchestration framework that minimizes wall-clock time-to-target accuracy on live interaction streams. FeLiX introduces three primitives: (i) streaming-aware availability tiers that leverage lightweight telemetry to identify ready clients at scale; (ii) fresh-utility selection, a dual-tier mechanism that prioritizes statistically valuable updates from devices able to meet tight refresh deadlines; and (iii) informativeness-aware, delay-robust aggregation that incorporates late, high-value updates containing ground-truth outcomes without biasing the global model toward stale distributions. Unlike prior systems that rely on unrealistic oracular knowledge of client availability, FeLiX achieves near-oracular performance in real-world settings. Across CIFAR-10, Google Speech, and realistic low-availability traces, FeLiX reduces wall-clock time-to-target accuracy by up to 2.37X while reducing communication bandwidth by 1.30X compared to state-of-the-art synchronous and asynchronous FL baselines.

Federated Learning (FL) is fundamentally challenged by statistical heterogeneity, where non-identically distributed (non-IID) data induces client drift that severely hampers global convergence. While existing approaches attempt to mitigate this drift through spatial-domain gradient correction or regularization, they overlook the intrinsic spectral structure of optimization signals. In this work, we revisit client drift from a novel frequency-domain perspective and uncover a critical Spectral Bias of Drift: inter-client gradient divergence is predominantly concentrated in low-frequency components which encode client-specific distributional shifts, while high-frequency components representing fine-grained features remain relatively consistent. Motivated by this, we propose SpecGradFilter, a unified Spectral Gradient Filtering Framework that tames heterogeneity by suppressing discordant low-frequency signals. Crucially, we demonstrate that SpecGradFilter is a generalizable principle, effective not only via precise FFT-based truncation but also through spatial approximations like Gaussian detrending. Extensive experiments on benchmarks such as CIFAR-10/100 and Tiny-ImageNet demonstrate that SpecGradFilter significantly performs better performance in highly Non-IID settings with negligible communication overhead, establishing a new paradigm for robust federated optimization.

Federated Learning (FL) enables decentralized training without data sharing, but suffers from statistical heterogeneity across clients, leading to client drift, poor generalization, and sharp minima compared to centralized training. Sharpness-Aware Minimization (SAM) has emerged as a promising approach to improve generalization, yet its application in federated learning still suffers from divergence problems, since perturbations are computed locally and reflect client-specific loss geometries. To better understand this issue, we provide experimental evidence from a new perspective, the frequency domain, for SAM perturbations in federated settings, revealing that inter-client perturbation inconsistencies are predominantly concentrated in the low-frequency spectrum. Motivated by this insight, we propose Federated learning with Frequency-domain Filtering of SAM perturbations (FedFFT). It is a lightweight and plug-and-play method that filters out low-frequency components of SAM perturbations without requiring additional communication, thereby suppressing inconsistent components in client updates while preserving consistent learning signals. Extensive experiments across multiple benchmarks and diverse backbones demonstrate that FedFFT consistently outperforms SAM-based FL methods, particularly under severe non-IID distributions. These results highlight the effectiveness, scalability, and general applicability of our frequency-domain perspective for sharpness-aware federated optimization.

Federated learning (FL) is severely hindered by statistical heterogeneity due to variations in scanners, acquisition protocols, and patient populations. Such non-IID data induces client drift during local optimization, leading to unstable convergence and suboptimal global models when parameter-based aggregation is applied. We propose a prototype-based, influence-aware federated learning framework (FedProIn) that uses multiple learnable class prototypes to capture shared semantic structures across heterogeneous clients. We introduce feature divergence loss and prototype contrastive loss to mitigate client drift by decomposing it into feature drift and prototype drift. In addition, we propose a normalized influence aggregation strategy that adaptively weights client prototypes according to their contribution to the global representation, reducing the impact of biased or low-quality updates. Experimental results on two publicly available medical datasets, HAM10000 and Matek-19, demonstrate that FedProIn achieves accuracies of (83.5% IID, 81.1% non-IID) on HAM10000 and (96.2% IID, 95.8% non-IID) on Matek-19, respectively, outperforming existing baselines in both conditions. Our code is available at https://github.com/harsh-kmr/FedProIn.

Routing-prediction federated learning has emerged as a new paradigm that reframes inter-client heterogeneity as a resource for system-level intelligence: at inference time, the server routes each external query to the best-matched client for prediction. Existing approaches, however, typically treat each client as internally homogeneous, overlooking latent subpopulations within local data. For example, patients with the same diagnosis at one hospital may exhibit morphologically distinct disease subtypes. The coexistence of inter-client and intra-client heterogeneity, which we call dual heterogeneity, can impair both routing and prediction. To address this challenge, we propose FedSPM, a routing-enabled semiparametric mixture framework that represents each client using client-specific latent components. Each component combines a predictive distribution for classification with a feature distribution for routing. To flexibly model feature distributions while effectively sharing information across clients, FedSPM models their density ratios relative to a common nonparametric measure estimated via empirical likelihood. We develop a federated expectation-maximization algorithm that optimizes a tractable surrogate and prove convergence of the exact profiled objective at the standard $\mathcal{O}(1/\sqrt{T})$ rate when the surrogate errors are properly controlled. Experiments on controlled benchmarks and real-world medical data demonstrate consistent improvements in routing and prediction under dual heterogeneity. Code is available at https://github.com/zijianwang0510/FedSPM.

The federated learning (FL) paradigm fosters distributed pervasive computing combined with artificial intelligence techniques, allowing for optimized data usage and improved mitigation of privacy concerns. Indeed, model training occurs on the client's local devices, and model parameters are subsequently shared with a centralized server. However, there is a need to find a tradeoff between models' personalization and generalization capabilities. In this paper, we design and implement several testing scenarios devoted to evaluating and comparing the centralized, local, and federated paradigm performances. We also design and implement a scenario that emulates a change in clients' data. We then present experimental results of the FedAvg algorithm applied to the Human Activity Recognition (HAR) domain to understand the trade-off between personalized and generalized accuracy. Results show that, although FedAvg confirms a higher degree of personalization capabilities while keeping a high degree of generalization with respect to the traditional centralized learning, this result is not so obvious under stressful conditions, such as when varying class distribution over clients.

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.

Recent research has introduced distributed self-supervised learning (D-SSL) approaches to leverage vast amounts of unlabeled decentralized data. However, D-SSL faces the critical challenge of data heterogeneity, and there is limited theoretical understanding of how different D-SSL frameworks respond to this challenge. To fill this gap, we present a rigorous theoretical analysis of the robustness of D-SSL frameworks under non-IID (non-independent and identically distributed) settings. Our results show that pre-training with Masked Image Modeling (MIM) is inherently more robust to heterogeneous data than Contrastive Learning (CL), and that the robustness of decentralized SSL increases with average network connectivity, implying that federated learning (FL) is no less robust than decentralized learning (DecL). These findings provide a solid theoretical foundation for guiding the design of future D-SSL algorithms. To further illustrate the practical implications of our theory, we introduce MAR loss, a refinement of the MIM objective with local-to-global alignment regularization. Extensive experiments across model architectures and distributed settings validate our theoretical insights, and additionally confirm the effectiveness of MAR loss as an application of our analysis.

Distributed machine learning enables collaborative model training without centralizing data, but it also exposes learning processes to privacy leakage and malicious manipulation. Existing defenses typically address these threats in isolation and are often tailored to specific learning paradigms or model architectures, limiting their applicability in realistic deployments. In particular, federated learning and decentralized learning exhibit distinct adversarial surfaces that are rarely addressed within a unified framework. In this paper, we present a model-agnostic framework for adversary-resistant distributed learning that jointly addresses privacy preservation and malicious behavior across both federated and decentralized settings. Our approach combines paradigm-specific defense mechanisms with GPBACC, a privacy-enhancing coded computing technique applicable to arbitrary machine learning models. For federated learning, we integrate robust aggregation strategies to mitigate the impact of malicious participants, while for decentralized learning we employ approximate decode-and-compare and group testing techniques to enable lightweight verification and adversary isolation without relying on a trusted aggregator. Crucially, we evaluate the proposed framework through an explicit, attack-driven analysis. We implement representative privacy attacks and malicious behaviors, and empirically demonstrate that the combination of GPBACC with robust aggregation and verification mechanisms significantly reduces privacy leakage and improves resilience against active adversaries. These results suggest that privacy-enhancing coded computing, when combined with appropriate adversary-resistance strategies, provides a practical and deployable foundation for secure distributed machine learning.

Performance evaluation in AI systems commonly assumes that random dataset splits produce independent and identically distributed (i.i.d.) subsets. We show that this assumption often breaks down in spatiotemporally correlated domains such as aerial surveillance, precision agriculture, and medical imaging, leading to two systematic failures: data leakage, where correlated samples span training and validation splits and inflate performance estimates, and hidden stratification, where errors on minority subpopulations are obscured by aggregate metrics. To address these issues, we propose a unified evaluation and training framework for spatially correlated data. We introduce Structure-Aware Stratified Partitioning (SASP), which constructs validation splits that reduce spatiotemporal leakage while preserving meaningful class balance, and Curriculum Distributionally Robust Optimization (CDRO), a curriculum-based relaxation of distributionally robust training that stabilizes optimization under these stricter splits. Across multiple benchmarks, this combination yields consistently improved generalization, more reliable confidence calibration, and exposes failure modes that remain hidden under conventional random-split evaluation.

Value functions are an essential component in actor-critic based deep reinforcement learning (RL). Conventionally, these functions are trained as a regression task by minimising the mean squared error (MSE) relative to bootstrapped target values. Meanwhile, in distributional RL, a distribution of returns is modelled based on the distributional Bellman operator. This work investigates the Gaussian Histogram Loss (HL-Gauss), a recent approach that reframes value estimation as classification by encoding each scalar Bellman target as a Gaussian-smoothed categorical target. Despite its potential, applying histogram-based losses to RL presents inherent challenges, most notably the requirement to pre-define a fixed support interval, which is often complicated by the non-stationary and stochastic nature of target values typically found in RL tasks. In this work, we propose an approach that dynamically learns the lower and upper bounds of the support instead of assigning them beforehand. We derive an objective that jointly learns these bounds whilst learning the categorical representation of the scalar values, and we show that this objective forms an upper bound on the mean-squared Bellman error. Our theoretical analysis further shows that this bound is tighter than that of non-learned supports of HL-Gauss. Empirically, the proposed objective enables stable adaptation of the support interval and matches HL-Gauss-based actor-critic algorithms on most continuous-control tasks whilst improving on a subset, without requiring a pre-specified support interval.

Recent work has established a fundamental trilemma between Byzantine robustness, local differential privacy (LDP), and optimization error in distributed learning. We show that this trilemma does not universally extend to generalization error, but instead depends critically on the privacy regime. Specifically, in the high-noise regime (strong privacy), we prove that increasing privacy reduces the generalization error, i.e., there is no tension between robustness and privacy. In the low-noise regime (weaker privacy), however, the tension between robustness and privacy reappears and increasing privacy indeed degrades generalization. Our theory explains this surprising non-monotonic behavior of the generalization error via matching lower and upper bounds on the algorithmic stability of Byzantine-robust distributed learning under LDP constraints. We corroborate and further analyze these theoretical findings with empirical evaluations.

Generalizing machine learning models to environments that differ from their training distribution remains a critical hurdle, particularly when data from the target domain is entirely or partially unavailable. We propose Generative Meta-Learning with Human Feedback (GMHF), a novel framework that bridges this domain gap by leveraging expert intuition to guide data synthesis. Grounded in a theoretical analysis of generalization error, we derive bounds demonstrating that aligning the distribution of generated data with human beliefs regarding the target physics significantly mitigates risk. GMHF operationalizes this insight by employing a Conditional Neural ODE (cNODE) as a generative digital twin, coupled with a Reinforcement Learning (RL) agent. The agent iteratively refines the latent physical parameters of the generated trajectories based on feedback, effectively steering the meta-learner toward the unobserved target distribution. Empirical validation on a nonlinear Duffing oscillator shows that GMHF substantially reduces deployment loss as expert reliability increases, and that the divergence between generated and target data falls under reliable feedback, directly corroborating the divergence-minimisation mechanism predicted by our theory. Further experiments on a non-dynamical probabilistic model confirm that the framework extends beyond ODE-governed systems, establishing human-AI collaboration as a rigorous catalyst for robust generalisation under distribution shift.

Federated Learning (FL) is a distributed machine learning (ML) paradigm with collaboration among multiple clients without sharing data. FL is challenging under data heterogeneity and partial client participation. Learning sparse models is useful for communication and computational efficiency in FL, but it is especially difficult in the small-sample high-dimensional regime (d >> N) where optimization can yield parameter configurations that fail to generalize to unseen test data. While magnitude-based pruning doesn't account for uncertainty exploration in the parameter space, a formulation with probabilistic gates and an L0 constraint allows sampling from competing sparse configurations during training. In this work, we study entropy regularization of gate distributions as a mechanism to maintain uncertainty in sparse federated optimization by preventing early commitment to sparse support. We examine its impact under data heterogeneity, client participation heterogeneity, and sparsity. Experiments on synthetic and real-world benchmarks show consistent improvements over federated iterative hard thresholding (Fed-IHT) and pruning after dense federated averaging (FedAvg) training, both in statistical performance on test data and in sparsity recovery accuracy.

We present an algorithm for the group distributionally robust (GDR) least squares problem. Given $m$ groups, a parameter vector in $\mathbb{R}^d$, and stacked design matrices and responses $\mathbf{A}$ and $\mathbf{b}$, our algorithm obtains a $(1+\varepsilon)$-multiplicative optimal solution using $\widetilde{O}(\min\{\mathsf{rank}(\mathbf{A}),m\}^{1/3}\varepsilon^{-2/3})$ linear-system-solves of matrices of the form $\mathbf{A}^{\top}\mathbf{B}\mathbf{A}$ for block-diagonal $\mathbf{B}$. Our technical methods follow from a recent geometric construction, block Lewis weights, that relates the empirical GDR problem to a carefully chosen least squares problem and an application of accelerated proximal methods. Our algorithm improves over known interior point methods for moderate accuracy regimes and matches the state-of-the-art guarantees for the special case of $\ell_{\infty}$ regression. We also give algorithms that smoothly interpolate between minimizing the average least squares loss and the distributionally robust loss.

Federated Learning often suffers under non-independently and identically distributed data, where a single global model may fail to represent the diversity of client distributions. Clustered Federated Learning mitigates this issue by training specialized models for groups of similar clients, but existing approaches often couple cluster assignment with the main training loop, increasing computational and communication costs. We propose a lightweight clustering approach based on Random Network Distillation. Each client trains a compact Random Network Distillation predictor on its local data and uses its prediction error as a novelty signal to estimate similarity with other clients. This enables the discovery of meaningful client groups before federated training, without sharing raw data or repeatedly evaluating the main model. Crucially, the resulting federations emerge from local novelty estimates at runtime, making the method suitable for autonomous large-scale distributed systems where neither the number of clusters nor the collaboration structure can be specified a priori. Overall, by decoupling clustering from learning, the method provides a task-agnostic and efficient mechanism for autonomous collaboration under non-independently and identically distributed data.

Federated learning typically aggregates client updates using fixed or heuristic weighting rules, which can be suboptimal when clients have heterogeneous data and varying contributions to the global model. We propose a framework that refines client aggregation weights using Conditional Random Fields (CRFs). Our method defines unary potentials for individual clients and pairwise potentials for all client pairs, allowing the server to model both client-specific reliability and interactions between clients. The resulting CRF inference produces aggregation weights that enable better convergence of the global training objective. Experiments show that, under non-IID heterogeneity, our approach consistently improves performance over well-established federated learning baselines.

Federated Learning (FL) emerged as a promising distributed machine learning paradigm. However, extending FL to the class incremental learning scenarios introduces unique challenges: 1) Capacity conflict and catastrophic forgetting from the shared model overloading, 2) Heterogeneity from Non-Independent and Identically Distributed (Non-IID) data, and 3) Synchronized class misalignment. In this paper, we propose \textbf{F}isher-Routed \textbf{M}i\textbf{X}ture of Experts for \textbf{Fed}erated Class-Incremental Learning (\textsc{FedFMX}), a novel framework to address these challenges via adaptive expert specialization across clients. The crucial insight is to route each sample to an expert subset that jointly optimizes knowledge acquisition and retention. Specifically, we introduce a Fisher-Routed Expert Scoring (FRES) module to estimate expert importance via Fisher-based stability cost and gradient-based plasticity gain. Then, we design an Adaptive Expert Selection (AES) module by quantifying marginal contributions for adaptive expert subset determination. Finally, by the routing-aware regularization (RAR), we achieve load balance and efficient FL training. We theoretically prove the $\mathcal{O}(T^{-1})$ convergence rate. Extensive experiments on multiple benchmarks compared with state-of-the-art methods demonstrate the superiority of \textsc{FedFMX}.

Byzantine-robust federated learning seeks to protect distributed model training from malicious or corrupted clients without requiring access to their private data. FLTrust addresses this challenge by introducing a trusted server-side root dataset that assigns trust scores to client updates for more robust aggregation. In this work, we propose FOGGYTRUST, a hierarchical extension of FLTrust that localizes trust computation to fog nodes, allowing the framework to better handle globally heterogeneous data while preserving robustness within locally homogeneous client groups. We further show that this two-level architecture can simultaneously address distribution mismatch in trust estimation and client drift across groups by combining local trust-based aggregation with heterogeneity-aware global optimizers such as FedAdam and SCAFFOLD. Across benchmark datasets, FOGGYTRUST achieves its strongest gains on more challenging heterogeneous settings, particularly on CIFAR-10 under Krum and Trim attacks, where it achieves an over 50% improvement over FLTrust. We also test FOGGYTRUST in a real-world safari dataset to show the promise of hierarchical trust networks for robust federated learning in socially impactful, safety-critical settings such as distributed wildlife monitoring.

Domain generalization (DG) aims to learn a model from one or more source domains that generalizes to an unseen target domain without accessing target data during training. A common approach enforces invariance of representations across all source domains, assuming predictive structure is globally shared. However, we demonstrate that enforcing invariance across more domains gradually restricts the feasible representation space, discarding transferable predictive factors that are not universally shared. To address this limitation, we propose subset-shared invariance, where predictive structure is assumed stable only within domain subsets. We implement this principle with a mixture-of-experts architecture, where each expert aligns the specific domains it serves and a routing mechanism composes subset-invariant components for prediction. This creates a routing-conditioned invariance, jointly learned with the representation. To facilitate effective decomposition, we develop training objectives that encourage selective alignment, confident and balanced routing, and diverse expert specialization. Experiments on DomainBed benchmarks demonstrate improved out-of-domain generalization and greater robustness under increasing domain heterogeneity. Our results suggest that DG should move beyond enforcing a single global invariance and instead model invariance through partially shared structure across domain subsets.

Distributed intelligent systems increasingly need to train across data silos without centralizing raw data. Federated learning keeps data local but can suffer under heterogeneous partitions and requires repeated full-model exchange. Split learning reduces communication through cut-layer activations, but standard protocols generally do not recover centralized mini-batch gradient behavior and may expose activations and gradients in plaintext. We present TL++, a two-mode traversal-learning framework that constructs virtual batches across nodes to recover centralized mini-batch gradient behavior under explicit synchronization assumptions. Base mode exchanges cut-layer activations and gradients rather than full models. Secure mode secret-shares each cut-layer activation and gradient between an orchestrator and a non-colluding helper, preventing either server from observing plaintext cut-layer tensors. This protection is limited to a semi-honest two-server setting; labels and loss-related outputs remain visible to the orchestrator. In the lightweight secure path evaluated here, exactness requires a linear or affine server path, while nonlinear operations require nonlinear MPC or approximation. We formalize TL++, analyze communication and computation costs, and evaluate it against federated and split-learning baselines on CIFAR-10 and BioGPT/PubMedQA using full fine-tuning and LoRA. On CIFAR-10, TL++ base cut 1 and exact secure cut 3 achieve accuracies of 91.41% (SD 0.19) and 90.93% (SD 0.17), respectively, exceeding the strongest measured non-TL++ baseline by more than 12 percentage points. TL++ base cut 1 also reduces per-step communication by 13.1-fold relative to full-model synchronization. PubMedQA results similarly favor TL++. Overall, TL++ approaches centralized-training performance while reducing communication and providing activation-level secret sharing.

Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems. Given a group acting on the input space, one augments the training set with transformed copies of each sample. Because it exploits symmetries without modifying the underlying learning algorithm, data augmentation can be applied broadly across learning methods. However, this universality comes at a computational cost: when the group is large, full group-sized augmentation quickly becomes computationally infeasible. This raises a fundamental question: Can partial data augmentation achieve the same statistical benefits as full augmentation in terms of generalization and sample complexity? We develop a general framework for investigating this question using Fourier analysis and the representation theory of finite groups. We show that, for a broad class of classical learning problems, partial data augmentation based on a randomly sampled subset of group elements achieves the same minimax rates as full augmentation, up to an approximation error that vanishes as the subset size increases. Our results provide a theoretical explanation for why partial augmentation can retain the statistical benefits of full augmentation despite enforcing symmetry only approximately, and shed light on a recently raised question in learning with symmetries: whether statistically optimal learning under general group invariances can be achieved using computationally scalable methods. Moreover, we prove a complementary impossibility result: enforcing exact invariance via data augmentation requires averaging over the entire group, and cannot be achieved by any strict subset when the hypothesis space is sufficiently expressive. Together, these results provide a unified perspective on full and partial data augmentation, as well as exact and approximate symmetry enforcement.

To make large-scale distributed training practical outside high-bandwidth datacenters, we must reduce blocking, high-volume synchronization. While DiLoCo communicates infrequently, its outer synchronization remains bandwidth-heavy and brittle to stragglers and transient failures. We relax exact synchronization to approximate synchronization via mixing/gossip, which degrades gracefully under delays and communication failures. This allows us to factorize DiLoCo synchronization into a non-blocking mixing step that overlaps computation with no staleness, and a blocking mixing step that tightens worker agreement, yielding a tunable trade-off between compute utilization and optimization stability. On up to billion-parameter language models in low-bandwidth settings, our framework substantially improves compute utilization compared to DiLoCo, with training progress ranging from comparable to closely matching it, and is more robust to failures.

Federated learning (FL) is an emerging distributed machine learning paradigm that enables local devices to jointly train a global model while keeping data decentralized and private. We propose a variance-reduction based algorithm, VRA-FedSGD, for FL in the presence of heavy-tailed gradient noise and communication noise, where these noises are prevalent in large-scale machine learning over wireless networks and Internet of Things deployments. VRA-FedSGD employs a momentum variance reduction technique together with a nonlinear mapping to mitigate heavy-tailed gradient noise, and uses a variance-reduced aggregation mechanism to suppress heavy-tailed communication noise. In the mean sense, VRA-FedSGD achieves a convergence rate of {\small$\mathcal{O}\left(K^{-(p-1)/(2p-1)}\right)$} for nonconvex objective functions, where $p$ is the tail index of heavy-tailed noise. In the almost sure sense, VRA-FedSGD achieves a convergence rate of $\tilde{\mathcal{O}}\left(K^{-(1-1/(p-ε))}\right)$ for strongly convex objective functions, where $ε$ is an arbitrarily small constant. Simulated experiments on a logistic regression problem with real-world data verify the effectiveness of VRA-FedSGD.

Plugging predictions of unknown parameters into downstream optimization problems, often referred to as the ``predict-then-optimize'' paradigm, has long been a standard approach in decision-making under uncertainty. However, improved predictive accuracy does not, in general, translate into improved decision quality. This disconnect has motivated growing interest in decision-focused learning (DFL) within the operations research community. This tutorial reviews recent developments in DFL and highlights key methodological insights, with a particular focus on stochastic linear programming as the downstream decision-making problem. We discuss why several widely used tools in traditional statistical learning are not directly suited to decision-focused settings and must be rethought, including (i) data collection strategies driven purely by predictive uncertainty and (ii) distributional distance measures such as the Wasserstein distance. We summarize properties of DFL that distinguish it from conventional predictive modeling and provide insights into the development of new decision-focused tools.

Stochastic segmentation seeks to represent multiple plausible masks for a single image, which is essential in safety- and quality-critical applications such as medical imaging or building defect inspection. Most existing methods introduce stochasticity by injecting continuous latent variables or by iterative denoising trajectories, whose stochastic sources are difficult to search or audit directly. We propose architecture distributions as a new stochastic source for segmentation: instead of sampling a latent variable or noise, we sample a discrete architecture from a learned distribution over operator choices at multiple searchable positions in a segmentation backbone. Each sampled architecture yields one mask through the selected active path, so inference depends on the executed subnet rather than the complete candidate bank. This approach also supports architectural provenance, since each output corresponds to a specific architecture configuration. To reduce collapse toward averaged masks, we train with set-level supervision by matching a set of architecture-sampled predictions to the annotation set using an IoU-based energy-distance surrogate. We further construct the candidate bank with evolutionary search, making the support of the stochastic source optimizable before distribution learning. The proposed method achieves state-of-the-art distribution matching and hypothesis coverage on LIDC-IDRI, and remains effective on two extension tasks. To the best of our knowledge, this is the first work to formulate stochastic segmentation as learning an architecture distribution and realizing output diversity through architecture sampling.

Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines, and CNN-based classification further demonstrates the practical effectiveness of the proposed methods in nonconvex neural network settings.

Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on $\mathbb{R}$ and the reward is defined through a utility functional applied to the Wasserstein barycenter of induced outcome distributions. We establish statistical guarantees for the policy learning framework based on both Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators. By handling the challenging uniform deviation over the product of the combinatorial policy class and the infinite-dimensional quantile domain, we prove that the finite-sample regret has leading dependence $\widetilde{\mathcal{O}}(\sqrt{\mathrm{N\text{-}dim}(Π)/N})$. In the one-dimensional Wasserstein setting and under the stated regularity conditions, the leading regret rate is still governed by the policy-class complexity. Moreover, we provide a minimax lower bound establishing the sharpness of the leading dependence on $N$ and $\mathrm{N\text{-}dim}(Π)$.

Online learning in non-stationary streams is often formulated as tracking a point estimate, but many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and adversarial corruption. Our approach represents each candidate law through a latent cluster geometry: a variable-size configuration of centers that organizes probability mass and induces a predictive distribution. A Gibbs quasi-posterior over these configurations yields an online predictor by posterior averaging, and the resulting variable-dimensional posterior can be sampled with reversible-jump MCMC. The method therefore avoids specifying a parametric streaming law while retaining a structured latent space for uncertainty, regularization, and comparison. We evaluate performance by cumulative Wasserstein-1 regret against the time-varying true law. The analysis separates two effects: corruption perturbs the loss-based posterior update, whereas drift makes long-horizon posterior memory stale. We address the latter with a restarted variant that temporally localizes the same quasi-Bayesian update. The resulting high-probability bounds decompose into a PAC-Bayesian complexity term, a corruption-sensitive posterior perturbation term, and a dynamic optimal-transport term driven by $A_T^{\mathrm{OT}}=\sum_{t=2}^T W_2^2(p_{t-1}^*,p_t^*)$. Under bounded support, stable latent geometry, predictive-map regularity, oracle realizability, localized restart windows, sublinear transport action, and sublinear corruption budget, the restarted predictor achieves sublinear cumulative Wasserstein regret. These guarantees require no parametric model for the stream, drift mechanism, or corruption process.

In Self-Supervised Learning (SSL), preventing representation collapse by explicitly enforcing a uniform distribution on the unit hypersphere has proven to be effective. However, current frameworks typically rely on sliced statistical regularizers such as SIGReg (used in LeJEPA) and SUSReg (used in SPHERE-JEPA), which approximate this continuous objective via Monte Carlo sampling along random 1D directions. This stochasticity injects projection variance into the training gradients, destabilizing optimization, and hindering convergence. In this work, we first show that analytically integrating out these random projections natively yields a deterministic Maximum Mean Discrepancy (MMD), bypassing the variance of sliced methods. Motivated by this equivalence, we formulate full-dimensional objectives for MMD, Kernel Stein Discrepancy (KSD), and Kullback-Leibler (KL) divergence directly on the sphere to enforce a uniform distribution. To prevent spatial bias, we equip these tests with rotationally invariant kernels constructed via spectral theory, systematically evaluating two canonical families: smooth exponential decay (Heat) and strict frequency cutoff (Bandlimited) filters. Empirically, removing projection-induced noise results in more stable optimization, faster convergence, and consistent improvements over stochastic sliced regularizers on ImageNet and Galaxy10. Furthermore, we reveal that the choice of the statistical test shapes the geometry of the learned latent space: MMD and KSD favor locally clustered organization suitable for object-centric domains, whereas the continuous KDE-based KL divergence promotes fine-grained instance separation, yielding the strongest results on unclustered procedural texture retrieval.

Federated class-incremental learning (FCIL) becomes substantially harder when clients observe different label subsets, progress through tasks at different stages, and provide uneven supervision for the same semantic concepts. Existing FCIL methods often preserve old knowledge through input-space synthesis, but they can be fragile under heterogeneous task streams and difficult to transfer across modalities. To alleviate such issues, we propose PRO, a framework that replaces synthetic input replay with projected rehearsal orchestration. To remove external pretraining, we evaluate all methods under the same warmup. After this, PRO maintains compact class-level projected memories on the server and allows clients perform balanced pseudo multi-task training over current examples and old projected memories. To handle stronger representation drift, we further introduce PRO-MAX, which augments PRO with neighborhood-weighted memory alignment while preserving the same server-light principle that the server only aggregates model updates and memory statistics. Across image, text, and graph benchmarks, PRO and PRO-MAX improve retention and final utility under heterogeneous streams while remaining competitive in homogeneous FCIL. Even when baselines are given expanded replay budgets, they degrade under supervision imbalance and stage misalignment, indicating that replay quantity alone does not resolve replay-quality failures. Additional weak-task diagnostics further show that larger replay mismatch is associated with larger downstream degradation, while our method keeps projected memories better aligned with the evolving representation.

Federated learning is well suited to edge environments but is often limited by the uplink cost of transmitting model updates. This Work-in-Progress paper presents MUFFLe, a communication-efficient update compression scheme that integrates generalized deduplication (GD) into the FedAvg pipeline. MUFFLe deduplicates repeated patterns across the update vector, yielding a fixed-rate, variable-count compression scheme. Preliminary experiments on IID MNIST with 20 clients show that MUFFLe reaches the target accuracy of $92.93\%$ with 38MB cumulative uplink communication, compared with 75MB for 8-bit quantization, 86MB for Top-$k$ sparsification, and 310MB for uncompressed FedAvg. These results demonstrate the feasibility of applying GD to communication-efficient federated learning.

Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to $0$ asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10.

We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larger overlap with the ground-truth signal. We derive the optimal Bayesian conditions for teacher recovery as functions of the sample complexity, noise level, and interaction strength, and validate these predictions through numerical simulations. The resulting dynamics can be mapped onto equilibrium sampling in a Restricted Boltzmann Machine with a structured hidden layer, providing a principled theoretical understanding of how interactions improve distributed generative modeling.

Federated continual learning (FCL) must learn from distributed task streams under limited resources, such as communication, computation, memory, and label availability. Existing FCL methods often rely on repeated local optimization, replay, and full supervision. Analytic alternatives avoid iterative training and replay, but using high-dimensional random features to improve accuracy requires a second-order feature statistic, the Gram matrix, which has a quadratic communication cost in the random feature size $M$. We propose FedRAN, a resource-aware analytic FCL framework that replaces gradient-based updates with compact random feature statistics. Each client transmits a truncated-SVD summary of its Gram matrix, reducing the dominant second-order upload from quadratic to linear in $M$ for fixed rank. The server performs a two-level QR-SVD subspace merge, spatially across clients and temporally across tasks, and solves a ridge classifier in closed form. FedRAN further supports label scarcity through prototype-based pseudo-labeling. Across CIFAR-100, ImageNet-R, and VTAB datasets, FedRAN improves average accuracy by up to 4.8 percentage points over the strongest baseline, uses 30.6-121.8$\times$ less per-client communication than optimization-based FCL, and is 190.3$\times$ faster on average than gradient-based baselines; with only 20% labels, pseudo-labeling improves average accuracy by up to 6.61 points. These results show that FedRAN enables accurate and resource-efficient FCL under communication, computation, and label constraints. The source code is available at https://github.com/JebacyrilArockiaraj/Fed-RAN-SSL.

Efficiently sampling from a complex probability distribution is a fundamental problem which has become increasingly pertinent in recent years with the rise of generative AI, as sophisticated sampling procedures from LLMs have been proposed to solve challenging reasoning problems. The efficacy of such sampling algorithms is limited, however, by the relationship between the LLM and the particular sampling task at hand, which has motivated the framework of test-time training (TTT). TTT works by updating a model's weights in response to partial generations and reward feedback received at inference time, thus adapting to the particular problem. In this work, we propose a formalization for TTT as the problem of producing a sample from a given probability measure $μ^\star$ belonging to a known class ${F}$ of distributions, given an oracle $\hat μ$ which yields approximate density estimates for $μ^\star$. This is closely related to the problem of reducing sampling to approximate counting studied in seminal works of Jerrum, Valiant & Vazirani (1986) and Jerrum & Sinclair (1989): namely, when ${F}$ is the class of all distributions, it coincides exactly with the aforementioned counting-to-sampling reduction. In this paper, we first show a quadratic lower bound on the query complexity of sampling from $μ^\star$ given query access to $\hat μ$ (for sufficiently large classes ${F}$), thus showing that the random walk approach proposed by Jerrum & Sinclair (1989) and refined by Hayes & Sinclair (2010), is optimal. This answers an open question posed by Hayes & Sinclair. We then show that this lower bound can be circumvented if the size of ${F}$ is bounded appropriately. As we discuss, this latter result can be viewed as an abstraction of TTT, and thus represents a starting point for the development of a principled theoretical framework for TTT.

Data pruning (DP), as an oft-stated strategy to alleviate heavy training burdens, reduces the volume of training samples according to a well-defined pruning method while striving for near-lossless performance. However, existing approaches, which commonly select highly informative samples, can lead to biased gradient estimation compared to full-dataset training. Furthermore, the analysis of this bias and its impact on final performance remains ambiguous. To address these challenges, we propose OrderDP, a plug-and-play framework that aims to obtain stable, unbiased, and near-lossless training acceleration with theoretical guarantees. Specifically, OrderDP first randomly selects a subset and then chooses the top-$q$ samples, where unbiasedness is established with respect to a surrogate loss. This ensures that OrderDP conducts unbiased training in terms of the surrogate objective. We further establish convergence and generalization analyses, elucidating how OrderDP affects optimal performance and enables well-controlled acceleration while ensuring guaranteed final performance. Empirically, we evaluate OrderDP against comprehensive baselines on CIFAR-10, CIFAR-100, and ImageNet-1K, demonstrating competitive accuracy, stable convergence, and exact control -- all with a simpler design and faster runtime, while reducing training cost by over 40%. Delivering both strong performance and computational efficiency, our method serves as a robust and easily adaptable tool for data-efficient learning. The code is publicly available at https://github.com/shengze-xu/OrderDP.

Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$. To align with this goal, information-based acquisition functions such as Predictive Entropy Search (PES) model $\mathbf{x}^{\star}$ as a random variable and reduce the entropy of its distribution, but approximating this distribution via traditional GP posterior sampling is computationally expensive. To address this limitation, we leverage Conditional Diffusion Models (CDMs) to efficiently approximate the distribution of $\mathbf{x}^{\star}$ and develop BO-inherent training strategies for CDMs. Motivated by the structural properties of the CDM-learned distribution, we further develop an acquisition strategy termed Diffusion-based Mode Seeking (DMS) to guide the sequential evaluation. We establish a sub-optimality guarantee for the CDM-learned distribution and demonstrate through extensive experiments that DMS outperforms standard BO baselines.

A small Wasserstein distance does not certify that a transformation is admissible. In evidence-constrained, semantic, causal, physical, monotone, or risk-sensitive learning, one must ask not only how far two probability laws are, but whether mass has moved in a direction allowed by available information. We introduce conditional random ordered transport spaces (CROTS), a class of $L^0$-valued spaces of random probability measures equipped with a Wasserstein ambient metric, a closed stochastic order, hard and soft ordered transport discrepancies, and a conditional risk functional for evaluating order violation under an evidence sigma-field. The central object is an order-admissible transport geometry for random measure-valued dynamics, distinct from cone-valued metrics, ordered Kantorovich constructions, random Wasserstein spaces alone, and model-specific residuals for generative paths. We develop the foundations of CROTS as a space theory for reliable distributional learning. The results include well-posedness and duality for hard and soft ordered transport, soft-to-hard variational convergence, measurability and completeness of the random lifted space, reductions to classical Wasserstein and ordered geometries, ordered geodesics, constrained barycenters and projections, conditional risk-transport duality, and separation of order-violating distributions. The main stability theorem shows that random learning dynamics may converge in the ambient Wasserstein metric while its local admissibility leakage follows a separate conditional order-risk recursion. The resulting asymptotic order-risk floor provides a mathematical language for evidence overreach, ordered distribution shift, robustness failure, and admissible distributional dynamics.

Performative prediction studies feedback loops that arise when predictive models are deployed in consequential domains. In these settings, deploying a model can change the population whose patterns the model aims to predict, inducing a distribution shift that is endogenous to the learning system. This perspective departs from classical treatments of distribution shift, where shifts are typically modeled as exogenous changes in the data-generating process. Yet, in practice, distribution shift is rarely one or the other. Predictive models may influence future data through the decisions they support, while the world itself continues to drift for reasons beyond the learner's control. We study partially performative prediction, a framework that captures both endogenous and exogenous sources of distribution shift. The framework generalizes performative prediction by allowing the data distribution to evolve both in response to the deployed model and according to an external, time-varying process. We extend the central notions of performative stability and performative optimality to this setting by defining their online analogues that track the evolving partially performative environment. We analyze practical learning heuristics, including repeated retraining, and characterize when they successfully adapt to partially performative environments.

In the paradigm of decentralized learning, a group of agents collaborate to train a global model using distributed datasets without a central server. Although the power of collaboration has been verified by many state-of-the-art studies, it entails extensive gradient information exchanging among the agents and thus induces high risk of privacy leakage for the individual agents. Moreover, in real-world applications, the training data are usually non-identically and independently distributed across the agents, inducing more challenges to enable privacy-preserved decentralized learning. To address these issues, we propose a privacy-preserved decentralized learning algorithm with non-IID data, DPDL, which leverages the notion of Differential Privacy (DP) in cross-gradient aggregation through a similarity-based calibration technique. Specifically, in each round, each agent perturbs the cross-gradients (i.e., the derivatives of its neighbors' local model in its private local data) by Gaussian noise mechanism before sharing them with its neighbors; it then adopt cosine similarity to calibrate the received perturbed cross-gradients such that the aggregation of the calibrated cross-gradients can be utilized to effectively update local model in a momentum-like manner. Our rigorous theoretical analysis not only reveals the minimum noise level required to achieve a specific level of privacy preservation, but also illustrates that our algorithm still achieves a linear speedup in training with non-IID data. We finally conduct extensive experiments on real-world dataset to validate the effectiveness of our algorithm in defending privacy attacks and in training accurate models.

Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching intervention that enters or exits the EoS regime from the same training state, we causally demonstrate this trade-off and identify two necessary conditions for a group to benefit. First, its aggregate gradient must align with the top Hessian eigenvector. We isolate this mechanism with a controlled perturbation that preserves distance but randomizes direction, destroying alignment and eliminating the advantage. Second, the group must sustain non-vanishing gradient magnitude over time. Under cross-entropy loss, gradient saturation decouples confidently classified groups, shifting the advantage to output-outliers, whose gradients persist. Together, these results show that EoS functions not only as a stability boundary, but as a mechanism governing the allocation of learning across the data distribution.

Federated Learning (FL) of foundation and edge models increasingly targets deployments where client data distributions drift over time, yet existing forgetting-mitigation methods assume each client's distribution is stationary. Flashback, the strongest recent FL method against cross-client (spatial) forgetting, uses monotonically accumulating per-class label counts as a knowledge proxy; this proxy becomes miscalibrated under temporal distribution shift and anchors the global model to an outdated class balance. We formalise temporal forgetting in FL with a per-phase metric isolated from protocol-level fluctuations and propose Flashback Continual Learning (FlashbackCL), a drop-in extension of Flashback with (i) temporally-decayed label counts; (ii) a device-aware replay buffer with Class-Balanced Reservoir Sampling (CBRS); and (iii) server-side active coreset curation on the public distillation set. The results show that FlashbackCL achieves 6.9% to 10.0% relative improvement relative to Flashback, on CIFAR-10 with 50 clients and three controlled temporal shift modes, while simultaneously reducing temporal forgetting by up to 68%. A 5-variant ablation identifies CBRS replay as the critical component. FlashbackCL also improves Flashback by 3.5 points on stationary CIFAR-100, suggesting that class-balanced replay regularises spatial heterogeneity as well as temporal shift.

Idioms can be analysed in terms of their decomposability, the extent to which constituent meanings contribute to the figurative whole. Decomposability is thought to predict syntactic flexibility. Usage-based accounts instead attribute idiom behaviour to distributional experience, such as speaker familiarity and predictability. We examine these views using contextualised language models as controlled distributional learners. We propose a model-internal measure of decomposability and relate it to human ratings, syntactic flexibility, and predictability while tracking idiom learning during pretraining. Model-derived decomposability correlates weakly with human judgments and shows a small but consistent negative relationship with syntactic flexibility. Pretraining analyses show that stabilisation of idiom representations in models is not explained by frequency alone. Instead, surprisal, decomposability, and frequency all contribute, with decomposability showing the strongest training-dependent effect.

Learning discriminative visual representations from distributed, heterogeneous data is a fundamental challenge in Federated Learning (FL). Prototype-based methods address statistical heterogeneity by sharing class-level representations across clients but create a distance-dependent gradient pressure that is particularly severe during early training rounds: alignment pressure applied to immature global prototypes, aggregated from noisy local representations, generates large gradients that suppress the emergence of local discriminative structure. The result is a poorly organized embedding space and degraded recognition performance, particularly under severe non-IID conditions. We propose FedSAP, a framework that stabilises federated representation learning through two complementary mechanisms: a deterministic alignment curriculum that delays global alignment until local representations become stable and a geometry-driven proxy separation loss that enforces inter-class structure on the unit hypersphere using the existing prototype bank without introducing additional parameters or communication overhead. Together, these mechanisms produce compact, well-separated class clusters without altering the underlying communication protocol between federation's participants. Experiments across three benchmarks and varying degrees of heterogeneity show gains of up to 4 percentage points over the prototype-based baselines evaluated, with improvements most pronounced under high heterogeneity. The representational nature of our framework further enables a straightforward extension to semi-supervised settings, where unlabelled data is incorporated with minimal modification, underscoring the generality of scheduled alignment as a design principle.

Federated Learning (FL) combined with Split Learning (SL) is a privacy preserving paradigm that enables training deep neural networks (DNNs) on resource constrained devices while reducing overall training cost. However, determining the optimal split point, meaning the layer where the model is divided still remains a critical challenge, especially when clients have heterogeneous hardware capabilities. Fixed split points can overload weak devices and increase the communication and server load, which slows convergence and reduces stability. This paper introduces QSplitFL, a novel capability-aware Deep Q-Network (DQN) framework for optimal split point selection in Split learning based Federated Learning (SFL) environments. Unlike existing approaches that rely on high-dimensional model weight representations, QSplitFL employs a lightweight state representation derived directly from client hardware metrics, including CPU utilization, memory, battery level, and network latency. The proposed framework incorporates a decayed loss-drop reward function that prioritizes early convergence, and a committee-based DQN architecture with majority voting to mitigate reward hacking. Extensive experiments on MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets using CNN, ResNet50, MobileNetV4, and ConvNeXt architectures demonstrate that our approach achieves better convergence and higher accuracy compared to existing methods, while effectively adapting to heterogeneous device resources. The source code is publicly available at https://github.com/AIPO-Lab/QSplitFL.

Communication overhead is a crucial bottleneck in scalable distributed learning. While existing methods aim to efficiently utilize data points, such as Local SGD, Minibatch SGD, and their accelerated variants, they still exhibit communication-round complexity that scales with the total number of samples $N$. In this paper, we introduce Local MixVR, a distributed framework that integrates local updates with variance-reduction techniques to mitigate local noise. We show that Local MixVR is the first distributed method to eliminate the dependence of communication complexity on $N$, achieving a complexity that scales only with the number of workers $M$. In common regimes where $M<O\left(N^{1/4}\right)$, Local MixVR outperforms the state-of-the-art Minibatch Accelerated SGD baseline, bridging a long-standing gap in distributed optimization and establishing a new paradigm for communication-efficient training.

Recent advances in artificial intelligence have expanded the focus from classical optimization to include equilibrium analysis in noncooperative games. Many such games involve shared constraints, leading to Generalized Nash Equilibrium Problems (GNEPs). Existing distributed algorithms typically require agents to exchange Lagrange multipliers to enforce consensus and compute variational-GNEs (v-GNEs). This work introduces fully distributed continuous-time algorithms and establishes convergence without requiring multiplier exchange, thereby reducing information exchange per iteration while improving privacy preservation. The analysis focuses on strongly monotone games with convex individual constraints and linear shared constraints. I also propose several discretization schemes for the continuous-time algorithms. The proposed approach converges to general GNEs, rather than being restricted to v-GNEs, with the attained equilibrium depending on the initialization. The effectiveness of the proposed method is demonstrated through applications in multi-robot coordination and placement. In the second part, this work includes research conducted in collaboration with Amazon scientists. One of the most challenging problems in real-world machine learning is labeled data collection, which typically requires substantial human effort and cost. Active learning aims to reduce this labeling requirement. Existing handcrafted active learning strategies, however, generally perform well only on specific types of datasets, which are often unknown in advance. In this work, I propose using contextual bandits to adaptively select the most suitable active learning strategy. The effectiveness of the proposed approach is demonstrated on publicly available external datasets.

Sequential conformal prediction (CP) provides valid uncertainty quantification under the assumption of residual exchangeability. However, this assumption is often violated in real-world time series due to temporal dependencies and distributional shifts. While recent methods attempt to approximate exchangeability through reweighting, identifying optimal weights remains an open challenge. To address this limitation, we propose DistMatch, a binning-based method that recursively partitions residuals within a binary tree using the Kolmogorov-Smirnov (KS) statistic. We theoretically show that this partitioning induces approximately exchangeable leaves, thereby avoiding the need for reweighting. By applying quantile regression with online updates within each leaf, DistMatch enables locally adaptive inference and improves robustness to distributional shifts. Extensive experiments demonstrate that DistMatch outperforms existing sequential CP methods.

Federated continual learning (FCL) lets distributed clients adapt language-model heads to evolving NLP tasks without sharing raw text. Under user-level differential privacy (DP), replay-based continual learning faces a structural obstacle: clients can release only small noisy lists of candidate replay summaries, and those lists are unordered across clients. We introduce Canonicalized Stable-List Replay (CSLR), where clients privately produce candidate replay distributions over a shared sentence-embedding space and the server aligns them using signatures induced by public anchor sentences. The anchors provide identifiability for aggregation rather than additional replay data. We prove that, under an observable anchor-signature margin, $O(\log(N/η)/p)$ anchors distinguish $N$ candidate list elements with probability at least $1-η$, and we give a scoped anchorless non-identifiability result for unordered-label oracle models. Across five seeds on continual classification, NER, and dialogue benchmarks, CSLR improves the final average task metric by 3.9--5.6 points over the strongest non-CSLR DP baseline at $\eps=4$ under the reported replay-release budget, while also outperforming Hungarian and optimal-transport matchers. The formal privacy guarantee covers replay release; end-to-end private training additionally requires composition with a private optimizer for task-head updates.

A long-standing challenge in distributed wireless systems is ensuring efficient and fair random channel access. Existing solutions often address specific constraints related to timing, periodicity, or centralization, but they typically rely on fixed heuristics. Motivated by recent advances in machine learning (ML), we investigate whether ML agents can autonomously learn efficient and fair access strategies, and whether such learning can offer new insights into medium access control (MAC) design. Rather than proposing a deployable protocol, our aim is to examine whether decentralized learning can rediscover or approximate theoretically efficient random-access mechanisms under minimal assumptions. To this end, we deploy an off-policy Double Deep Q-Network (DDQN) with Bayesian inference to train agents operating over a slotted channel. The resulting method is fully online (no pre-training), fully distributed (independent multi-agent learners), stochastic (non-periodic), and requires no coordination or explicit communication. Extensive simulations show that the learned strategy adapts to varying network conditions and achieves near-theoretical efficiency while maintaining fairness. Ablation studies further reveal that the learned behavior resembles slotted ALOHA with a dynamically adjusted transmission probability, leading us to refer to the method as KISS: Keeping It Simple and Slotted.

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most $\widetilde{O}(\varepsilon^{-k \vee 2})$ samples to achieve $\varepsilon$ error in 1-Wasserstein distance, where $k$ is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.

Standard Set Representation Learning methods typically excel on curated data but often overlook the challenge of inference-time element corruption. This refers to scenarios where deployed models encounter element-level degradations, such as outliers or missing components, that may distort set representation and degrade performance. We propose SW-DRSO, a distributionally robust optimization framework tailored for sets. Rather than minimizing loss solely on observed training data, SW-DRSO optimizes a tractable surrogate of the worst-case expected loss over a family of plausible inference-time variations. We introduce a barycentric adversary that approximates the intractable search over corrupted sets by a differentiable training-time optimization over simplex weights. Extensive experiments across four tasks demonstrate that SW-DRSO effectively enhances robustness against corruption while maintaining high overall performance.

Supervised Causal Learning (SCL) has shown promise in causal discovery by framing it as a supervised learning problem. However, it suffers from significant out-of-distribution generalization challenges. We reveal three limitations of previous SCL practices: a significant performance gap between synthetic benchmarks and real-world data, fragility to distribution shifts, and failure in compositional generalization, collectively questioning its real-world applicability. To address this, we propose Test-Time Training for Supervised Causal Learning (TTT-SCL), a novel framework that dynamically generates training sets explicitly aligned with any specific test instance. We demonstrate the correlation between TTT-SCL and score-based methods, and design an efficient module for generating training sets based on the classic scoring function. Experiments on synthetic benchmarks, pseudo-real and real-world datasets demonstrate that TTT-SCL significantly outperforms existing SCL and traditional causal discovery methods.

Compute governance proposals often rely on the assumption that frontier AI training requires large, detectable computing clusters. However, recent advances in distributed training algorithms could allow developers to conduct frontier-scale training on distributed agglomerations of hardware, rather than needing large datacenter facilities. Developers who prefer not to be constrained by regulations may structure their hardware in a manner that evades the registration and monitoring requirements associated with compute governance. Therefore, regulations must be designed to detect and prevent illicit distributed training operations. This paper evaluates the feasibility of such evasion and outlines recommended countermeasures, including whistleblowing, chip tracking, forensic accounting, and memory and compute thresholds for clusters.

Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While distributional reduction-encompassing joint clustering and dimensionality reduction-offers a principled way to summarize data, its supervised variants remain relatively under-explored, despite the importance of retaining task-relevant signal for downstream prediction and decision-making. We propose Supervised Distributional Reduction (SDR), an algorithm for learning target-aware representations by combining optimal transport with explicit dependence maximization. SDR builds on the Fused Gromov-Wasserstein (FGW) objective to align the relational structure of the input distribution with a set of representative points, while augmenting it with a direct dependence term that encourages the learned embeddings to capture predictive signal more explicitly. This results in compact representations that reflect both geometric structure and supervision. Beyond representation learning, SDR naturally induces a data-dependent, non-stationary geometry that can be leveraged for settings such as Gaussian Process (GP) modelling. By redefining distances through target-aware distributional alignment, SDR enables the construction of adaptive kernels that respond to local variations in both data geometry and supervision, offering an optimal transport-based perspective on non-stationary kernel design.