The first goal of this article is to introduce a new type of p-adic
reaction-diffusion cellular neural network with delay. We study the stability
of these networks and provide numerical simulations of their responses. The
second goal is to provide a quick review of the state of the art of p-adic
cellular neural networks and their applications to image processing.

介绍了一种新类型的带延迟的 p-adic 反应扩散细胞神经网络，并研究了这些网络的稳定性和它们的响应的数值模拟。同时，对 p-adic 细胞神经网络及其在图像处理中的应用进行了快速回顾。

层次神经网络、p - 适应性的偏微分方程及其在图像处理中的应用

Hierarchical Neural Networks, p-Adic PDEs, and Applications to Image  Processing

Recurrent Neural Networks (RNNs) are renowned for their adeptness in modeling
temporal dependencies, a trait that has driven their widespread adoption for
sequential data processing. Nevertheless, vanilla RNNs are confronted with the
well-known issue of gradient vanishing and exploding, posing a significant
challenge for learning and establishing long-range dependencies. Additionally,
gated RNNs tend to be over-parameterized, resulting in poor network
generalization. To address these challenges, we propose a novel Delayed Memory
Unit (DMU) in this paper, wherein a delay line structure, coupled with delay
gates, is introduced to facilitate temporal interaction and temporal credit
assignment, so as to enhance the temporal modeling capabilities of vanilla
RNNs. Particularly, the DMU is designed to directly distribute the input
information to the optimal time instant in the future, rather than aggregating
and redistributing it over time through intricate network dynamics. Our
proposed DMU demonstrates superior temporal modeling capabilities across a
broad range of sequential modeling tasks, utilizing considerably fewer
parameters than other state-of-the-art gated RNN models in applications such as
speech recognition, radar gesture recognition, ECG waveform segmentation, and
permuted sequential image classification.

提出了一种新颖的延迟记忆单元（DMU），通过引入延迟线结构和延迟门，来增强普通 RNN 的时间建模能力，以解决梯度消失和梯度爆炸等问题，并在语音识别、雷达手势识别、心电波形分割和串联顺序图像分类等应用中展示出优越的时间建模能力。

延迟记忆单元：通过延迟门建模时间依赖

Delayed Memory Unit: Modelling Temporal Dependency Through Delay Gate

We propose a new algorithm for adversarial multi-armed bandits with
unrestricted delays. The algorithm is based on a novel hybrid regularizer
applied in the Follow the Regularized Leader (FTRL) framework. It achieves
$\mathcal{O}(\sqrt{kn}+\sqrt{D\log(k)})$ regret guarantee, where $k$ is the
number of arms, $n$ is the number of rounds, and $D$ is the total delay. The
result matches the lower bound within constants and requires no prior knowledge
of $n$ or $D$. Additionally, we propose a refined tuning of the algorithm,
which achieves $\mathcal{O}(\sqrt{kn}+\min_{S}|S|+\sqrt{D_{\bar S}\log(k)})$
regret guarantee, where $S$ is a set of rounds excluded from delay counting,
$\bar S = [n]\setminus S$ are the counted rounds, and $D_{\bar S}$ is the total
delay in the counted rounds. If the delays are highly unbalanced, the latter
regret guarantee can be significantly tighter than the former. The result
requires no advance knowledge of the delays and resolves an open problem of
Thune et al. (2019). The new FTRL algorithm and its refined tuning are anytime
and require no doubling, which resolves another open problem of Thune et al.
(2019).

提出一个新的算法，针对有无限延迟的对抗多臂老虎机问题，该算法是基于一种新型的混合规则制定的，采用 Follow the Regularized Leader (FTRL) 框架，可实现 $O (\sqrt {kn}+\sqrt {D\log (k)})$ 的遗憾保证，并且不需要预先了解 $n$ 或 $D$, 还提出了一种新的调优算法，遗憾保证可达到 $O (\sqrt {kn}+\min_{S}|S|+\sqrt {D_{\bar S}\log (k)})$，用于解决了 Thune 等人 (2019) 提出的未解决问题。