Yueyao Yu

Xinyu Chen, Renjie Li, Yueyao Yu et al.

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.

Yueyao Yu, Yin Zhang

Since its introduction in 2017, Transformer has emerged as the leading neural network architecture, catalyzing revolutionary advancements in many AI disciplines. The key innovation in Transformer is a Self-Attention (SA) mechanism designed to capture contextual information. However, extending the original Transformer design to models of greater depth has proven exceedingly challenging, if not impossible. Even though various modifications have been proposed in order to stack more layers of SA mechanism into deeper models, a full understanding of this depth problem remains lacking. In this paper, we conduct a comprehensive investigation, both theoretically and empirically, to substantiate the claim that the depth problem is caused by \emph{token similarity escalation}; that is, tokens grow increasingly alike after repeated applications of the SA mechanism. Our analysis reveals that, driven by the invariant leading eigenspace and large spectral gaps of attention matrices, token similarity provably escalates at a linear rate. Based on the gained insight, we propose a new strategy of surgically removing excessive similarity in contrast to the existing approach of diminishing the SA mechanism explicitly or implicitly (such as in pre-norm transformers). Preliminary experimental results confirm the effectiveness of the proposed strategy in small-scale post-norm Transformer models.

Yueyao Yu, Yin Zhang

To enhance resource efficiency and model deployability of neural networks, we propose a neural-layer architecture based on Householder weighting and absolute-value activating, called Householder-absolute neural layer or simply Han-layer. Compared to a fully connected layer with $d$-neurons and $d$ outputs, a Han-layer reduces the number of parameters and the corresponding computational complexity from $O(d^2)$ to $O(d)$. {The Han-layer structure guarantees that the Jacobian of the layer function is always orthogonal, thus ensuring gradient stability (i.e., free of gradient vanishing or exploding issues) for any Han-layer sub-networks.} Extensive numerical experiments show that one can strategically use Han-layers to replace fully connected (FC) layers, reducing the number of model parameters while maintaining or even improving the generalization performance. We will also showcase the capabilities of the Han-layer architecture on a few small stylized models, and discuss its current limitations.

Yueyao Yu, Yin Zhang

Despite the tremendous successes of deep neural networks (DNNs) in various applications, many fundamental aspects of deep learning remain incompletely understood, including DNN trainability. In a trainability study, one aims to discern what makes one DNN model easier to train than another under comparable conditions. In particular, our study focuses on multi-layer perceptron (MLP) models equipped with the same number of parameters. We introduce a new notion called variability to help explain the benefits of deep learning and the difficulties in training very deep MLPs. Simply put, variability of a neural network represents the richness of landscape patterns in the data space with respect to well-scaled random weights. We empirically show that variability is positively correlated to the number of activations and negatively correlated to a phenomenon called "Collapse to Constant", which is related but not identical to the well-known vanishing gradient phenomenon. Experiments on a small stylized model problem confirm that variability can indeed accurately predict MLP trainability. In addition, we demonstrate that, as an activation function in MLP models, the absolute value function can offer better variability than the popular ReLU function can.