Federated learning enables institutions to train predictive models collaboratively without sharing raw data, addressing privacy and regulatory constraints. In the standard horizontal setting, clients hold disjoint cohorts of individuals and collaborate to learn a shared predictor. Most existing methods, however, assume that all clients measure the same features. We study the more realistic setting of covariate mismatch, where each client observes a different subset of features, which typically arises in multicenter collaborations with no prior agreement on data collection. We formalize learning a linear prediction under client-wise MCAR patterns and develop two modular approaches tailored to the dimensional regime and communication budget. In the low-dimensional setting, we propose a plug-in estimator that approximates the oracle linear predictor by aggregating sufficient statistics to estimate the covariance and cross-moment terms. In higher dimensions, we study an impute-then-regress strategy: (i) impute missing covariates using any exchangeability-preserving imputation procedure, and (ii) fit a ridge-regularized linear model on the completed data. We provide asymptotic and finite-sample learning rates for our predictors, explicitly characterizing their behaviour with the global dimension, the client-specific feature partition, and the distribution of samples across sites.

Equilibrium systems are a powerful way to express neural computations. As special cases, they include models of great current interest in both neuroscience and machine learning, such as deep neural networks, equilibrium recurrent neural networks, deep equilibrium models, or meta-learning. Here, we present a new principle for learning such systems with a temporally-and spatially-local rule. Our principle casts learning as a \emph{least-control} problem, where we first introduce an optimal controller to lead the system towards a solution state, and then define learning as reducing the amount of control needed to reach such a state. We show that incorporating learning signals within a dynamics as an optimal control enables transmitting activity-dependent credit assignment information, avoids storing intermediate states in memory, and does not rely on infinitesimal learning signals. In practice, our principle leads to strong performance matching that of leading gradient-based learning methods when applied to an array of problems involving recurrent neural networks and meta-learning. Our results shed light on how the brain might learn and offer new ways of approaching a broad class of machine learning problems.

Training deep neural networks (DNNs) with backpropagation (BP) achieves state-of-the-art accuracy but requires global error propagation and full parameterization, leading to substantial memory and computational overhead. Direct Feedback Alignment (DFA) enables local, parallelizable updates with lower memory requirements but is limited by unstructured feedback and poor scalability in deeper architectures, specially convolutional neural networks. To address these limitations, we propose a structured local learning framework that operates directly on low-rank manifolds defined by the Singular Value Decomposition (SVD) of weight matrices. Each layer is trained in its decomposed form, with updates applied to the SVD components using a composite loss that integrates cross-entropy, subspace alignment, and orthogonality regularization. Feedback matrices are constructed to match the SVD structure, ensuring consistent alignment between forward and feedback pathways. Our method reduces the number of trainable parameters relative to the original DFA model, without relying on pruning or post hoc compression. Experiments on CIFAR-10, CIFAR-100, and ImageNet show that our method achieves accuracy comparable to that of BP. Ablation studies confirm the importance of each loss term in the low-rank setting. These results establish local learning on low-rank manifolds as a principled and scalable alternative to full-rank gradient-based training.

We thank the reviewers for their time and insightful comments. We address the specific concerns and questions below. Sorry if it was not very clear in the paper. SimCLR with 65.7% in Table 1 is the original SimCLR The 1.4% accuracy gap is comparing 4-layer MLP versus Meanwhile, adding two more MLP layers can also help boost performance of GIM: 62.3% (Row 5) vs 60.9% The results match Fig.9 in the SimCLR paper which shows We also include results trained with 800 epochs in the Supp.

Crop disease detection and classification is a critical challenge in agriculture, with major implications for productivity, food security, and environmental sustainability. While deep learning models such as CNN and ViT have shown excellent performance in classifying plant diseases from images, their large-scale deployment is often limited by data privacy concerns. Federated Learning (FL) addresses this issue, but centralized FL remains vulnerable to single-point failures and scalability limits. In this paper, we introduce a novel Decentralized Federated Learning (DFL) framework that uses validation loss (Loss_val) both to guide model sharing between peers and to correct local training via an adaptive loss function controlled by weighting parameter. We conduct extensive experiments using PlantVillage datasets with three deep learning architectures (ResNet50, VGG16, and ViT_B16), analyzing the impact of weighting parameter, the number of shared models, the number of clients, and the use of Loss_val versus Loss_train of other clients. Results demonstrate that our DFL approach not only improves accuracy and convergence speed, but also ensures better generalization and robustness across heterogeneous data environments making it particularly well-suited for privacy-preserving agricultural applications.

In connected and autonomous vehicles, machine learning for safety message classification has become critical for detecting malicious or anomalous behavior. However, conventional approaches that rely on centralized data collection or purely local training face limitations due to the large scale, high mobility, and heterogeneous data distributions inherent in inter-vehicle networks. To overcome these challenges, this paper explores Distributed Federated Learning (DFL), whereby vehicles collaboratively train deep learning models by exchanging model updates among one-hop neighbors and propagating models over multiple hops. Using the Vehicular Reference Misbehavior (VeReMi) Extension Dataset, we show that DFL can significantly improve classification accuracy across all vehicles compared to learning strictly with local data. Notably, vehicles with low individual accuracy see substantial accuracy gains through DFL, illustrating the benefit of knowledge sharing across the network. We further show that local training data size and time-varying network connectivity correlate strongly with the model's overall accuracy. We investigate DFL's resilience and vulnerabilities under attacks in multiple domains, namely wireless jamming and training data poisoning attacks. Our results reveal important insights into the vulnerabilities of DFL when confronted with multi-domain attacks, underlining the need for more robust strategies to secure DFL in vehicular networks.

Lazy local learning methods train a classifier "on the fly" at test time, using only a subset of the training instances that are most relevant to the novel test example. The goal is to tailor the classifier to the properties of the data surrounding the test example. Existing methods assume that the instances most useful for building the local model are strictly those closest to the test example. However, this fails to account for the fact that the success of the resulting classifier depends on the full distribution of selected training instances. Rather than simply gathering the test example's nearest neighbors, we propose to predict the subset of training data that is jointly relevant to training its local model. We develop an approach to discover patterns between queries and their "good" neighborhoods using large-scale multilabel classification with compressed sensing. Given a novel test point, we estimate both the composition and size of the training subset likely to yield an accurate local model. We demonstrate the approach on image classification tasks on SUN and aPascal and show its advantages over traditional global and local approaches.