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Traditional superoscillation focusing typically requires complex optimization of the incident light field. These complexities may limit the practical application of superoscillation. High-order radially polarized Laguerre-Gaussian beams inherently support superoscillation focusing due to their multi-ring amplitude distribution and 0 ~ \pi phase alternation, which align with the necessary destructive interference mechanisms. In this study, we demonstrate that by adjusting the beam mode order together with the incident beam size, we can easily control the full width at half maximum, field of view, and energy distribution of superoscillation focusing. Moreover, high-order azimuthally polarized vortex-phase Laguerre-Gaussian beams can also achieve superoscillation focusing, offering even better super-resolution effects. The distinct focusing behaviors of their circular components present unique opportunities for applications involving circular dichroism materials., Comment: 5 pages, 4 figures

Blind or Low-Vision (BLV) users often rely on audio descriptions (AD) to access video content. However, conventional static ADs can leave out detailed information in videos, impose a high mental load, neglect the diverse needs and preferences of BLV users, and lack immersion. To tackle these challenges, we introduce SPICA, an AI-powered system that enables BLV users to interactively explore video content. Informed by prior empirical studies on BLV video consumption, SPICA offers novel interactive mechanisms for supporting temporal navigation of frame captions and spatial exploration of objects within key frames. Leveraging an audio-visual machine learning pipeline, SPICA augments existing ADs by adding interactivity, spatial sound effects, and individual object descriptions without requiring additional human annotation. Through a user study with 14 BLV participants, we evaluated the usability and usefulness of SPICA and explored user behaviors, preferences, and mental models when interacting with augmented ADs.

Due to its speed and simplicity, subgradient descent is one of the most used optimization algorithms in convex machine learning algorithms. However, tuning its learning rate is probably its most severe bottleneck to achieve consistent good performance. A common way to reduce the dependency on the learning rate is to use implicit/proximal updates. One such variant is the Importance Weight Aware (IWA) updates, which consist of infinitely many infinitesimal updates on each loss function. However, IWA updates' empirical success is not completely explained by their theory. In this paper, we show for the first time that IWA updates have a strictly better regret upper bound than plain gradient updates in the online learning setting. Our analysis is based on the new framework, generalized implicit Follow-the-Regularized-Leader (FTRL) (Chen and Orabona, 2023), to analyze generalized implicit updates using a dual formulation. In particular, our results imply that IWA updates can be considered as approximate implicit/proximal updates., Comment: arXiv admin note: text overlap with arXiv:2306.00201

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

Parameter-free algorithms are online learning algorithms that do not require setting learning rates. They achieve optimal regret with respect to the distance between the initial point and any competitor. Yet, parameter-free algorithms do not take into account the geometry of the losses. Recently, in the stochastic optimization literature, it has been proposed to instead use truncated linear lower bounds, which produce better performance by more closely modeling the losses. In particular, truncated linear models greatly reduce the problem of overshooting the minimum of the loss function. Unfortunately, truncated linear models cannot be used with parameter-free algorithms because the updates become very expensive to compute. In this paper, we propose new parameter-free algorithms that can take advantage of truncated linear models through a new update that has an "implicit" flavor. Based on a novel decomposition of the regret, the new update is efficient, requires only one gradient at each step, never overshoots the minimum of the truncated model, and retains the favorable parameter-free properties. We also conduct an empirical study demonstrating the practical utility of our algorithms.

Parameter-free stochastic gradient descent (PFSGD) algorithms do not require setting learning rates while achieving optimal theoretical performance. In practical applications, however, there remains an empirical gap between tuned stochastic gradient descent (SGD) and PFSGD. In this paper, we close the empirical gap with a new parameter-free algorithm based on continuous-time Coin-Betting on truncated models. The new update is derived through the solution of an Ordinary Differential Equation (ODE) and solved in a closed form. We show empirically that this new parameter-free algorithm outperforms algorithms with the "best default" learning rates and almost matches the performance of finely tuned baselines without anything to tune.