This paper studies the landscape of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Since the complicated sensing structure makes direct landscape analysis technically challenging, we introduce a tractable tensor sensing surrogate that preserves the essential low-rank structure. We first analyze its population risk, characterize the global landscape on the unit sphere, and establish local linear convergence of Riemannian gradient descent (RGD) under mild conditions. We then extend the analysis to tensor sensing under a tensor restricted isometry property (TRIP), establishing local geometric and RGD convergence guarantees, and quantify robustness to measurement noise. Our theoretical results are further supported by extensive numerical experiments. These findings offer insights into the optimization landscape of the surrogate tensor sensing problem, thereby providing guidance for studying and solving the original BDPR problem.
Autoregressive (AR) models have recently emerged as a promising paradigm for image generation, as they can model visual tokens through the same next-token prediction principle that underlies large language models. However, most competitive AR image generators still rely on Transformer attention, whose quadratic token interaction cost and growing key-value cache become increasingly expensive for high-resolution visual sequences. Linear attention provides an attractive route to efficient AR generation, but our study shows that directly importing linear or decay-based attention from language modeling leads to clear quality degradation. We identify a key cause: after a 2D token map is flattened by raster scan, 1D sequence locality no longer faithfully reflects spatial locality, and conventional decay mechanisms may introduce a false-locality bias at row transitions. To address this problem, we propose Linear Attention with Spatial-Aware Decay (LASAD), a simple recurrent attention mechanism that modulates decay according to the original 2D token geometry while preserving linear complexity. Built upon this layer, LASADGen replaces standard attention in an AR image generator with spatial-aware linear attention. Experiments on ImageNet demonstrate that LASADGen achieves a favorable quality-efficiency tradeoff, improving generation quality over linear-attention baselines while reducing inference cost and memory usage compared with Transformer-based AR models.
Alireza Goldar, Zhen Qin, Zhihui Zhu, Zhe-Xuan Gong, Michael B. Wakin
Can measurements chosen adaptively, in response to earlier outcomes, be exponentially more informative than measurements fixed in advance? In many quantum settings, adaptivity helps at most polynomially; known exponential advantages require coherent measurements across copies or restricted measurements. We show an exponential advantage measuring one copy at a time, with no quantum memory kept between state copies, even when the nonadaptive learner may perform arbitrary global measurements on each copy. We construct explicit families of multi-qubit states in which a scalar parameter is encoded in one of exponentially many candidate observables, with an auxiliary marker indicating which one. An adaptive protocol identifies the relevant observable and then measures it using only single-qubit measurements and one round of adaptation. At fixed accuracy, it needs logarithmically many copies as the qubit count grows, whereas every nonadaptive protocol needs exponentially many. The same mechanism yields an exponential gap in local asymptotic minimax mean squared error constants, tight up to the exponential base. The states are separable and classical in label-dependent product bases; no entanglement or other nonclassical correlations are required. The gap comes from measurement incompatibility: the candidate observables cannot be measured jointly, so a fixed measurement must divide its information budget among them, while adaptivity selects the informative one. Accordingly, the separation disappears when the candidate observables commute, and cannot occur with fully observed classical samples. Measurement incompatibility thus emerges as a resource for quantum learning, distinct from entanglement and quantum memory, that classical feedback alone can exploit.