Linear Attention

A recurring weakness in quantum machine learning (QML) is that reported ``quantum advantages'' are seldom tested against a \emph{capacity-matched} classical control, leaving it unclear whether a gain comes from the quantum substrate or from the architectural change that accompanies it. Our primary contribution is methodological: a protocol for attributing such gains honestly -- a capacity-matched classical bottleneck of identical parameter budget, transparent reporting of where quantum does \emph{not} help, and validation on real quantum hardware -- which we develop and apply through a concrete case study. That case study is Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection of a \emph{single} encoder layer with a 36-parameter parameterized quantum circuit (PQC), keeping all other layers classical. Across nine synthetic benchmarks and the real-world ETTh1 dataset, QASA improves on a full-capacity classical Transformer for chaotic and trend-dominated signals. To ask whether this is a genuinely \emph{quantum} effect, we introduce a control rarely applied in quantum machine learning -- a capacity-matched classical bottleneck with the same parameter budget -- and find that it matches the PQC on the error metrics. The gain is therefore attributable to the low-rank value-projection \emph{bottleneck} (an \emph{architectural parsimony} principle), not to quantumness; adding further quantum layers only degrades performance and trainability. We accordingly position the quantum layer not as a source of accuracy advantage but as a \emph{competitive} instantiation of this principle: its low-rank compression onto the signal's intrinsic dimensionality is matched by a classical bottleneck, so the gain is architectural rather than quantum.

The Transformer architecture has achieved remarkable success in natural language processing and high-level vision tasks over the past few years. However, the inherent complexity of self-attention is quadratic to the size of the image, leading to unaffordable computational costs for high-resolution vision tasks. In this paper, we introduce Concertormer, featuring a novel Concerto Self-Attention (CSA) mechanism designed for image deblurring. The proposed CSA divides self-attention into two distinct components: one emphasizes generally global and another concentrates on specifically local correspondence. By retaining partial information in additional dimensions independent from the self-attention calculations, our method effectively captures global contextual representations with complexity linear to the image size. To effectively leverage the additional dimensions, we present a Cross-Dimensional Communication module, which linearly combines attention maps and thus enhances expressiveness. Moreover, we amalgamate the two-staged Transformer design into a single stage using the proposed gated-dconv MLP architecture. While our primary objective is single-image motion deblurring, extensive quantitative and qualitative evaluations demonstrate that our approach performs favorably against the state-of-the-art methods in other tasks, such as deraining and deblurring with JPEG artifacts. The source codes and trained models will be made available to the public.

Structured data is widely used in domains such as healthcare, finance, and scientific data management. Recent studies on structured data foundation models (SFMs) aim to support data analysis and mining tasks over such data, but still face scalability and generalization challenges when applied to real-world enterprise databases. First, many SFMs rely on full self-attention, which introduces an O(N^2) computational bottleneck and limits the number of tuples that can be processed jointly. Second, directly replacing attention with linear-complexity sequence models may conflict with the permutation-invariant nature of structured data, introducing artificial order bias and degrading representation quality. Moreover, models trained only on synthetic data may struggle to generalize to the heavy-tailed and heterogeneous distributions commonly found in real-world databases. To address these challenges, we propose FEAT, a linear-complexity foundation model for extremely large structured data. FEAT replaces quadratic attention with a multi-layer dual-axis encoding architecture. It integrates an adaptive-fusion bidirectional state-space model (AFBM) with convolutional gated linear attention (Conv-GLA), enabling cross-tuple contextualization in O(N) time while supporting permutation-invariant representation learning. To improve robustness under real-world data skewness, FEAT further adopts a hybrid structural causal pre-training pipeline with a robust reconstruction objective. Experiments on 12 real-world database benchmarks show that FEAT consistently outperforms representative SFMs on zero-shot tasks and scales linearly with structured-data sample length, achieving up to 50x faster inference latency.