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We study theoretically the nonlinear optical response of disordered electrons in the regime of weak (anti)localization. Our analytical and numerical calculations reveal that, in orthogonal/symplectic class systems, two consecutive, phase coherent optical pulses generates an electric current echo that appears after the second pulse, and at a time equal to the pulse delay time. The current echo reflects the quantum interference between a self-intersecting electron path and its time reversal partner, and, therefore, provide a time-domain interferometry of weak (anti)localization. Our results can be potentially tested on disordered metal films by using terahertz two-dimensional coherent spectroscopy or ultrafast transport measurements., Comment: 14 pages, 6 figures

The need to explain the output of a deep neural network classifier is now widely recognized. While previous methods typically explain a single class in the output, we advocate explaining the whole output, which is a probability distribution over multiple classes. A whole-output explanation can help a human user gain an overall understanding of model behaviour instead of only one aspect of it. It can also provide a natural framework where one can examine the evidence used to discriminate between competing classes, and thereby obtain contrastive explanations. In this paper, we propose a contrastive whole-output explanation (CWOX) method for image classification, and evaluate it using quantitative metrics and through human subject studies. The source code of CWOX is available at https://github.com/vaynexie/CWOX., Comment: To appear at UAI 2023

Despite the popularity of Vision Transformers (ViTs) and eXplainable AI (XAI), only a few explanation methods have been designed specially for ViTs thus far. They mostly use attention weights of the [CLS] token on patch embeddings and often produce unsatisfactory saliency maps. This paper proposes a novel method for explaining ViTs called ViT-CX. It is based on patch embeddings, rather than attentions paid to them, and their causal impacts on the model output. Other characteristics of ViTs such as causal overdetermination are also considered in the design of ViT-CX. The empirical results show that ViT-CX produces more meaningful saliency maps and does a better job revealing all important evidence for the predictions than previous methods. The explanation generated by ViT-CX also shows significantly better faithfulness to the model. The codes and appendix are available at https://github.com/vaynexie/CausalX-ViT., Comment: IJCAI2023 Camera-ready

Some examples are easier for humans to classify than others. The same should be true for deep neural networks (DNNs). We use the term example perplexity to refer to the level of difficulty of classifying an example. In this paper, we propose a method to measure the perplexity of an example and investigate what factors contribute to high example perplexity. The related codes and resources are available at https://github.com/vaynexie/Example-Perplexity.

It has been long debated that eXplainable AI (XAI) is an important topic, but it lacks rigorous definition and fair metrics. In this paper, we briefly summarize the status quo of the metrics, along with an exhaustive experimental study based on them, including faithfulness, localization, false-positives, sensitivity check, and stability. With the experimental results, we conclude that among all the methods we compare, no single explanation method dominates others in all metrics. Nonetheless, Gradient-weighted Class Activation Mapping (Grad-CAM) and Randomly Input Sampling for Explanation (RISE) perform fairly well in most of the metrics. Utilizing a set of filtered metrics, we further present a case study to diagnose the classification bases for models. While providing a comprehensive experimental study of metrics, we also examine measuring factors that are missed in current metrics and hope this valuable work could serve as a guide for future research., Comment: 14 pages, 16 figures

In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the "quasi-particles" entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, including a brief discussion on the case where the Majorana fermions represent spins, but not real fermion particles., Comment: 9 pages, 6 figures

In this work, we study a molecular graphene model on the top of a superconductor in the presence of pseudomagnetic fields induced by coplanar strain fields. With the pseudomagnetic fields and the attractive interaction induced from the substrate, a flat band superconductor can be achieved according to mean field analysis on the effective Hamiltonian. Based on a semiclassical approximation, we first show that the orbital limit is hugely enhanced by the pseudomagnetic fields. The physical reason is that the orbital angular momenta locking at $K$ and $K'$ valleys due to the pseudomagnetic fields suppress the orbital magnetization from external magnetic fields. Considering the vanishing band width in this system, we then study the effects of Gaussian fluctuations in both Hartree and pairing channels. We show that in the dilute limit, the phase transition is dominated by collective modes with critical temperatures much lower than the mean field results. At half filling, our method gives no corrections to the mean field critical temperatures.

In this paper, we first characterize the finiteness of fractal interpolation functions (FIFs) on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on Sierpinski gasket (SG). As an application, we prove that the solution of the following Dirichlet problem on SG is an FIF with uniform vertical scaling factor $\frac{1}{5}$: $\Delta u=0$ on $SG\setminus \{q_1,q_2,q_3\}$, and $u(q_i)=a_i$, $i=1,2,3$, where $q_i$, $i=1,2,3$, are boundary points of SG., Comment: 10 papges