Photonic Crystal Surface Emitting Lasers (PCSEL)'s inverse design demands expert knowledge in physics, materials science, and quantum mechanics which is prohibitively labor-intensive. Advanced AI technologies, especially reinforcement learning (RL), have emerged as a powerful tool to augment and accelerate this inverse design process. By modeling the inverse design of PCSEL as a sequential decision-making problem, RL approaches can construct a satisfactory PCSEL structure from scratch. However, the data inefficiency resulting from online interactions with precise and expensive simulation environments impedes the broader applicability of RL approaches. Recently, sequential models, especially the Transformer architecture, have exhibited compelling performance in sequential decision-making problems due to their simplicity and scalability to large language models. In this paper, we introduce a novel framework named PCSEL Inverse Design Transformer (PiT) that abstracts the inverse design of PCSEL as a sequence modeling problem. The central part of our PiT is a Transformer-based structure that leverages the past trajectories and current states to predict the current actions. Compared with the traditional RL approaches, PiT can output the optimal actions and achieve target PCSEL designs by leveraging offline data and conditioning on the desired return. Results demonstrate that PiT achieves superior performance and data efficiency compared to baselines.

Frame quality deterioration is one of the main challenges in the field of video understanding. To compensate for the information loss caused by deteriorated frames, recent approaches exploit transformer-based integration modules to obtain spatio-temporal information. However, these integration modules are heavy and complex. Furthermore, each integration module is specifically tailored for its target task, making it difficult to generalise to multiple tasks. In this paper, we present a neat and unified framework, called Spatio-Temporal Prompting Network (STPN). It can efficiently extract robust and accurate video features by dynamically adjusting the input features in the backbone network. Specifically, STPN predicts several video prompts containing spatio-temporal information of neighbour frames. Then, these video prompts are prepended to the patch embeddings of the current frame as the updated input for video feature extraction. Moreover, STPN is easy to generalise to various video tasks because it does not contain task-specific modules. Without bells and whistles, STPN achieves state-of-the-art performance on three widely-used datasets for different video understanding tasks, i.e., ImageNetVID for video object detection, YouTubeVIS for video instance segmentation, and GOT-10k for visual object tracking. Code is available at https://github.com/guanxiongsun/vfe.pytorch.

In high energy physics (HEP), machine learning methods have emerged as an effective way to accurately simulate particle collisions at the Large Hadron Collider (LHC). The message-passing generative adversarial network (MPGAN) was the first model to simulate collisions as point, or ``particle'', clouds, with state-of-the-art results, but suffered from quadratic time complexity. Recently, generative adversarial particle transformers (GAPTs) were introduced to address this drawback; however, results did not surpass MPGAN. We introduce induced GAPT (iGAPT) which, by integrating ``induced particle-attention blocks'' and conditioning on global jet attributes, not only offers linear time complexity but is also able to capture intricate jet substructure, surpassing MPGAN in many metrics. Our experiments demonstrate the potential of iGAPT to simulate complex HEP data accurately and efficiently.

In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [Hur\'e-Pham-Warin. Mathematics of Computation 89, no. 324 (2020)] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided including: Amerasian option under the Black-Scholes model, American option with a path-dependent geometric mean payoff function, and the Shiryaev's optimal stopping problem.

We solve a fundamental challenge in semiconductor IC design: the fast and accurate characterization of nanoscale photonic devices. Much like the fusion between AI and EDA, many efforts have been made to apply DNNs such as convolutional neural networks (CNN) to prototype and characterize next-gen optoelectronic devices commonly found in photonic integrated circuits (PIC) and LiDAR. These prior works generally strive to predict the quality factor (Q) and modal volume (V) of for instance, photonic crystals, with ultra-high accuracy and speed. However, state-of-the-art models are still far from being directly applicable in the real-world: e.g. the correlation coefficient of V ($V_{coeff}$ ) is only about 80%, which is much lower than what it takes to generate reliable and reproducible nanophotonic designs. Recently, attention-based transformer models have attracted extensive interests and been widely used in CV and NLP. In this work, we propose the first-ever Transformer model (POViT) to efficiently design and simulate semiconductor photonic devices with multiple objectives. Unlike the standard Vision Transformer (ViT), we supplied photonic crystals as data input and changed the activation layer from GELU to an absolute-value function (ABS). Our experiments show that POViT exceeds results reported by previous models significantly. The correlation coefficient $V_{coeff}$ increases by over 12% (i.e., to 92.0%) and the prediction errors of Q is reduced by an order of magnitude, among several other key metric improvements. Our work has the potential to drive the expansion of EDA to fully automated photonic design. The complete dataset and code will be released to aid researchers endeavoring in the interdisciplinary field of physics and computer science.

In this paper we propose a generalization of the Deep Galerking Method (DGM) of Sirignano and Spiliopoulos [2018] to deal with Path-Dependent Partial Differential Equations (PPDEs). These equations firstly appeared in the seminal work of Dupire [2009], where the functional Itô calculus was developed to deal with path-dependent financial derivatives contracts. The method, which we call Path-Dependent DGM (PDGM), consists of using a combination of feed-forward and Long Short-Term Memory architectures to model the solution of the PPDE. We then analyze several numerical examples, many from the Financial Mathematics literature, that show the capabilities of the method under very different situations.