Linear attention offers a linear-time alternative to self-attention but often struggles to capture long-range patterns. We revisit linear attention through a prediction-correction lens and show that prevalent variants can be written as a combination of a historical prediction and a single-token correction, which creates an expressivity bottleneck. To address this bottleneck, we introduce Residual Linear Attention (RLA), a framework that equips linear attention with an explicit residual-fitting mechanism. RLA maintains an auxiliary recurrent state that learns to accumulate residual errors over time and correct the base prediction. Our implementation leverages highly optimized linear attention kernels and preserves linear time and memory. Across language modeling and recall-intensive evaluations, RLA and RDN consistently outperform their respective baselines and other modern linear-attention methods, narrowing the gap to standard Transformers while retaining linear scaling. The Transformer (V aswani et al., 2017) architecture has become the standard for large language models. However, the quadratic time complexity of its self-attention mechanism remains a critical bottleneck, limiting its application to long sequences (Li et al., 2024).

A BSTRACT Effectively modeling multimodal longitudinal data is a pressing need in various application areas, especially biomedicine. Despite this, few approaches exist in the literature for this problem, with most not adequately taking into account the multimodality of the data. In this study, we developed multiple configurations of a novel multimodal and longitudinal learning framework, Longitudinal Ensemble Integration (LEI), for sequential classification. We evaluated LEI's performance, and compared it against existing approaches, for the early detection of dementia, which is among the most studied multimodal sequential classification tasks. LEI outperformed these approaches due to its use of intermediate base predictions arising from the individual data modalities, which enabled their better integration over time. LEI's design also enabled the identification of features that were consistently important across time for the effective prediction of dementia-related diagnoses. Overall, our work demonstrates the potential of LEI for sequential classification from longitudinal multimodal data. 1 I NTRODUCTION Data that are both longitudinal/temporal and multimodal are increasingly being used in combination with machine learning for forecasting, especially in medical diagnosis (Brand et al., 2019; Zhang & Shen, 2012; Feis et al., 2019; Li et al., 2023). Recently, a number of promising approaches for sequential classification from such data have been introduced (Eslami et al., 2023; Zhang et al., 2011; Wang et al., 2016; Zhang et al., 2024). For instance, some approaches have used recurrent neural network (RNN)-based models applied to data sequences where the modalities at each time point have been concatenated into a long feature vector, sometimes referred to as early fusion (Nguyen et al., 2020; Olaimat et al., 2023; Maheux et al., 2023).

Graph-based semi-supervised learning (GSSL) has been used successfully in various applications. Existing methods leverage the graph structure and labeled samples for classification. Label Propagation (LP) and Graph Neural Networks (GNNs) both iteratively pass messages on graphs, where LP propagates node labels through edges and GNN aggregates node features from the neighborhood. Recently, combining LP and GNN has led to improved performance. However, utilizing labels and features jointly in higher-order graphs has not been explored. Therefore, we propose Nonlinear Correct and Smooth (NLCS), which improves the existing post-processing approach by incorporating non-linearity and higher-order representation into the residual propagation to handle intricate node relationships effectively. Systematic evaluations show that our method achieves remarkable average improvements of 13.71% over base prediction and 2.16% over the state-of-the-art post-processing method on six commonly used datasets. Comparisons and analyses show our method effectively utilizes labels and features jointly in higher-order graphs to resolve challenging graph relationships.

Blockchains with smart contracts are distributed ledger systems that achieve block-state consistency among distributed nodes by only allowing deterministic operations of smart contracts. However, the power of smart contracts is enabled by interacting with stochastic off-chain data, which in turn opens the possibility to undermine the block-state consistency. To address this issue, an oracle smart contract is used to provide a single consistent source of external data; but, simultaneously, this introduces a single point of failure, which is called the oracle problem. To address the oracle problem, we propose an adaptive conformal consensus (ACon$^2$) algorithm that derives a consensus set of data from multiple oracle contracts via the recent advance in online uncertainty quantification learning. Interesting, the consensus set provides a desired correctness guarantee under distribution shift and Byzantine adversaries. We demonstrate the efficacy of the proposed algorithm on two price datasets and an Ethereum case study. In particular, the Solidity implementation of the proposed algorithm shows the potential practicality of the proposed algorithm, implying that online machine learning algorithms are applicable to address security issues in blockchains.

We investigate ensemble methods for prediction in an online setting. Unlike all the literature in ensembling, for the first time, we introduce a new approach using a meta learner that effectively combines the base model predictions via using a superset of the features that is the union of the base models' feature vectors instead of the predictions themselves. Here, our model does not use the predictions of the base models as inputs to a machine learning algorithm, but choose the best possible combination at each time step based on the state of the problem. We explore three different constraint spaces for the ensembling of the base learners that linearly combines the base predictions, which are convex combinations where the components of the ensembling vector are all nonnegative and sum up to 1; affine combinations where the weight vector components are required to sum up to 1; and the unconstrained combinations where the components are free to take any real value. The constraints are both theoretically analyzed under known statistics and integrated into the learning procedure of the meta learner as a part of the optimization in an automated manner. To show the practical efficiency of the proposed method, we employ a gradient-boosted decision tree and a multi-layer perceptron separately as the meta learners. Our framework is generic so that one can use other machine learning architectures as the ensembler as long as they allow for a custom differentiable loss for minimization. We demonstrate the learning behavior of our algorithm on synthetic data and the significant performance improvements over the conventional methods over various real life datasets, extensively used in the well-known data competitions. Furthermore, we openly share the source code of the proposed method to facilitate further research and comparison.