Robustifying convolutional neural networks (CNNs) against adversarial attacks remains challenging and often requires resource-intensive countermeasures. W e explore the use of sparse mixture-of-experts (MoE) layers to improve robustness by replacing selected residual blocks or convolu-tional layers, thereby increasing model capacity without additional inference cost. On ResNet architectures trained on CIF AR-100, we find that inserting a single MoE layer in the deeper stages leads to consistent improvements in robustness under PGD and AutoPGD attacks when combined with adversarial training. Furthermore, we discover that when switch loss is used for balancing, it causes routing to collapse onto a small set of overused experts, thereby concentrating adversarial training on these paths and inadvertently making them more robust. As a result, some individual experts outperform the gated MoE model in robustness, suggesting that robust subpaths emerge through specialization. Our code is available at https:// github.com/

Link prediction algorithms for multilayer networks are in principle required to effectively account for the entire layered structure while capturing the unique contexts offered by each layer. However, many existing approaches excel at predicting specific links in certain layers but struggle with others, as they fail to effectively leverage the diverse information encoded across different network layers. In this paper, we present MoE-ML-LP, the first Mixture-of-Experts (MoE) framework specifically designed for multilayer link prediction. Building on top of multilayer heuristics for link prediction, MoE-ML-LP synthesizes the decisions taken by diverse experts, resulting in significantly enhanced predictive capabilities. Our extensive experimental evaluation on real-world and synthetic networks demonstrates that MoE-ML-LP consistently outperforms several baselines and competing methods, achieving remarkable improvements of +60% in Mean Reciprocal Rank, +82% in Hits@1, +55% in Hits@5, and +41% in Hits@10. Furthermore, MoE-ML-LP features a modular architecture that enables the seamless integration of newly developed experts without necessitating the re-training of the entire framework, fostering efficiency and scalability to new experts, paving the way for future advancements in link prediction.

In this brief paper, we present a naive aggregation algorithm for a typical learning problem with expert advice setting, in which the task of improving generalization, i.e., model validation, is embedded in the learning process as a sequential decision-making problem. In particular, we consider a class of learning problem of point estimations for modeling high-dimensional nonlinear functions, where a group of experts update their parameter estimates using the discrete-time version of gradient systems, with small additive noise term, guided by the corresponding subsample datasets obtained from the original dataset. Here, our main objective is to provide conditions under which such an algorithm will sequentially determine a set of mixing distribution strategies used for aggregating the experts' estimates that ultimately leading to an optimal parameter estimate, i.e., as a consensus solution for all experts, which is better than any individual expert's estimate in terms of improved generalization or learning performances. Finally, as part of this work, we present some numerical results for a typical case of nonlinear regression problem.

The application of mixture-of-experts (MoE) is gaining popularity due to its ability to improve model's performance. In an MoE structure, the gate layer plays a significant role in distinguishing and routing input features to different experts. This enables each expert to specialize in processing their corresponding sub-tasks. However, the gate's routing mechanism also gives rise to narrow vision: the individual MoE's expert fails to use more samples in learning the allocated sub-task, which in turn limits the MoE to further improve its generalization ability. To effectively address this, we propose a method called Mixture-of-Distilled-Expert (MoDE), which applies moderate mutual distillation among experts to enable each expert to pick up more features learned by other experts and gain more accurate perceptions on their original allocated sub-tasks. We conduct plenty experiments including tabular, NLP and CV datasets, which shows MoDE's effectiveness, universality and robustness. Furthermore, we develop a parallel study through innovatively constructing "expert probing", to experimentally prove why MoDE works: moderate distilling knowledge can improve each individual expert's test performances on their assigned tasks, leading to MoE's overall performance improvement.

Machine learning algorithms dedicated to financial time series forecasting have gained a lot of interest. But choosing between several algorithms can be challenging, as their estimation accuracy may be unstable over time. Online aggregation of experts combine the forecasts of a finite set of models in a single approach without making any assumption about the models. In this paper, a Bernstein Online Aggregation (BOA) procedure is applied to the construction of long-short strategies built from individual stock return forecasts coming from different machine learning models. The online mixture of experts leads to attractive portfolio performances even in environments characterised by non-stationarity. The aggregation outperforms individual algorithms, offering a higher portfolio Sharpe Ratio, lower shortfall, with a similar turnover. Extensions to expert and aggregation specialisations are also proposed to improve the overall mixture on a family of portfolio evaluation metrics.

When dealing with time series with complex non-stationarities, low retrospective regret on individual realizations is a more appropriate goal than low prospective risk in expectation. Online learning algorithms provide powerful guarantees of this form, and have often been proposed for use with non-stationary processes because of their ability to switch between different forecasters or ``experts''. However, existing methods assume that the set of experts whose forecasts are to be combined are all given at the start, which is not plausible when dealing with a genuinely historical or evolutionary system. We show how to modify the ``fixed shares'' algorithm for tracking the best expert to cope with a steadily growing set of experts, obtained by fitting new models to new data as it becomes available, and obtain regret bounds for the growing ensemble.