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In this article, we provide a comprehensive characterization of invariants of classical Lie superalgebras from the super-analog of the Schur-Weyl duality in a unified way. We establish $\mathfrak{g}$-invariants of the tensor algebra $T(\mathfrak{g})$, the supersymmetric algebra $S(\mathfrak{g})$, and the universal enveloping algebra $\mathrm{U}(\mathfrak{g})$ of a classical Lie superalgebra $\mathfrak{g}$ corresponding to every element in centralizer algebras and their relationship under supersymmetrization. As a byproduct, we prove that the restriction on $T(\mathfrak{g})^{\mathfrak{g}}$ of the projection from $T(\mathfrak{g})$ to $\mathrm{U}(\mathfrak{g})$ is surjective, which enables us to determine the generators of the center $\mathcal{Z}(\mathfrak{g})$ except for $\mathfrak{g}=\mathfrak{osp}_{2m|2n}$. Additionally, we present an alternative algebraic proof of the triviality of $\mathcal{Z}(\mathfrak{p}_n)$. The key ingredient involves a technique lemma related to the symmetric group and Brauer diagrams., Comment: 31 pages, 18 figures, comments welcome!

Achieving low-threshold infrared stimulated emission in solution-processed quantum dots is critical to enable real-life application including photonic integrated circuits (PICs), LIDAR application and optical telecommunication. However, realization of low threshold infrared gain is fundamentally challenging due to high degeneracy of the first emissive state (e.g., 8-fold) and fast Auger recombination. In this letter, we demonstrate ultralow-threshold infrared stimulated emission with an onset of 110 uJ.cm-2 employing cascade charge transfer (CT) in Pb-chalcogenide colloidal quantum dot (CQD) solids. In doing so, we investigate this idea in two different architectures including a mixture of multiband gap CQDs and layer-by-layer (LBL) configuration. Using transient absorption spectroscopy, we show ultrafast cascade CT from large band-gap PbS CQD to small band-gap PbS/PbSSe core/shell CQDs in LBL (~ 2 ps) and mixture (~ 9 ps) configuration. These results indicate the feasibility of using cascade CT as an efficient method to reduce optical gain threshold in CQD solid films.

Natural language counterfactual generation aims to minimally modify a given text such that the modified text will be classified into a different class. The generated counterfactuals provide insight into the reasoning behind a model's predictions by highlighting which words significantly influence the outcomes. Additionally, they can be used to detect model fairness issues and augment the training data to enhance the model's robustness. A substantial amount of research has been conducted to generate counterfactuals for various NLP tasks, employing different models and methodologies. With the rapid growth of studies in this field, a systematic review is crucial to guide future researchers and developers. To bridge this gap, this survey provides a comprehensive overview of textual counterfactual generation methods, particularly those based on Large Language Models. We propose a new taxonomy that systematically categorizes the generation methods into four groups and summarizes the metrics for evaluating the generation quality. Finally, we discuss ongoing research challenges and outline promising directions for future work., Comment: Accepted by EMNLP 2024 Findings

Counterfactually Augmented Data (CAD) involves creating new data samples by applying minimal yet sufficient modifications to flip the label of existing data samples to other classes. Training with CAD enhances model robustness against spurious features that happen to correlate with labels by spreading the casual relationships across different classes. Yet, recent research reveals that training with CAD may lead models to overly focus on modified features while ignoring other important contextual information, inadvertently introducing biases that may impair performance on out-ofdistribution (OOD) datasets. To mitigate this issue, we employ contrastive learning to promote global feature alignment in addition to learning counterfactual clues. We theoretically prove that contrastive loss can encourage models to leverage a broader range of features beyond those modified ones. Comprehensive experiments on two human-edited CAD datasets demonstrate that our proposed method outperforms the state-of-the-art on OOD datasets., Comment: Accepted by ACL 2024 main conference

We study the simplicity of Kac induced modules over the $\ell$-th Takiff superalgebras $\widetilde{\mathfrak g}_\ell:= \widetilde{\mathfrak g}\otimes \mathbb C[\theta]/(\theta^{\ell+1})$, for $\ell>0$, associated with the Lie superalgebras $\widetilde{\mathfrak g}$ of type I. We formulate a general notion of typical weights and typical Jordan blocks of the category $\mathcal O$ for $\widetilde{\mathfrak g}_\ell$ associated with Lie superalgebras $\mathfrak{gl}(m|n)$, $\mathfrak{osp}(2|2n)$ and $\mathfrak{pe}(n)$. For Lie superalgebras $\mathfrak{gl}(m|n)$ and $\mathfrak{osp}(2|2n)$, we establish an equivalence from an arbitrary typical Jordan block of the category $\mathcal O$ for $\widetilde{\mathfrak g}_\ell$ to a Jordan block of the category $\mathcal O$ for the even subalgebra of $\widetilde{\mathfrak g}_\ell$. This provides a solution to the problem of determining the composition multiplicities of the Verma modules over $\widetilde{\mathfrak g}_\ell$ with typical highest weights. We also investigate non-singular Whittaker modules over these Takiff superalgebras. In particular, we obtain a classification of non-singular simple Whittaker modules and a criterion for simplicity of non-singular standard Whittaker modules., Comment: 34 pages

Near-infrared phosphor-converted light-emitting diodes (NIR pc-LEDs) are compact light sources of great interest for NIR spectroscopy applications. Beyond typical Cr3+-activated NIR-emitting phosphors, there exists a strong demand for Cr3+-free alternatives with high efficiency and broadband emission to rich the landscape of NIR luminescent materials and extend their range of application fields. Here, we report a series of Fe3+-activated Ca3Ga2Sn3O12 garnet-type phosphors exhibiting broadband NIR emission in the 650-1000 nm range attributed to 4T1(G)-->6A1(S) transition, with a maximum at 754 nm and a FWHM of 89 nm upon UV excitation. The spectroscopic results were analyzed according to the Tanabe-Sugano theory from which the crystal field parameter Dq and Racah parameters B and C were obtained for the octahedrally coordinated Fe3+ ion. Notably, the NIR persistent luminescence lasting over 1 h was detected following UV or X-ray irradiation. The possible mechanism involving electron traps was proposed to explain the observed persistent luminescence. Furthermore, a NIR pc-LED was fabricated by coating synthesized phosphor on a UV chip, and its performance was evaluated to assess its potential suitability as a NIR light source. Our discovery of novel type of nontoxic Fe3+-activated broadband NIR luminescence phosphors with efficient NIR persistent luminescence paves the way for discovering Cr3+-free multifunctional NIR luminescence materials, thereby expanding their application possibilities., Comment: 18 pages, 5 fugures

The synthesis, structural, and luminescence properties have been carried out for Cr3+-activated Al2(WO4)3 (AWO) and Sc2(WO4)3 (SWO) phosphors for application in pc-NIR LED. Upon blue excitation, these compounds are capable of exhibiting broadband NIR emission stems primarily from 4T2-->4A2 transition in the range of 670-1200 nm (maxima ~808 nm, FWHM ~140 nm) for AWO:Cr and of 700-1300 nm (maxima ~870 nm, FWHM ~164 nm) for SWO:Cr. The significant shift of NIR emission is attributed to the substitution of AlO6 with larger ScO6 octahedrons. To gain insight into the luminescence the crystal field strength, Racah parameters, nephelauxetic effect, and electron-phonon coupling have been analyzed based on spectroscopic results. The electron-phonon coupling parameter S for SWO:Cr was determined to be 11.5, twice as large as that for AWO:Cr, which is in accordance with its strong thermal quenching. The abrupt changes occurring at 275 K in temperature-dependent luminescence spectra and decay lifetime of AWO:Cr is associated with temperature-driven phase transformation from low-temperature monoclinic to high-temperature orthorhombic phase. Pressure induced amorphization of AWO:Cr at pressures higher than 25 kbar was confirmed by employing high pressure evolution of Raman spectra. A high-power NIR pc-LED, fabricated by coating AWO:0.04Cr on a commercial 470 nm LED chip, shows good performance with an output power of 17.1 mW driven by a current of 320 mA, revealing potential application of studied materials for NIR light source., Comment: 19 pages, 7 figures

The surge in black-box AI models has prompted the need to explain the internal mechanism and justify their reliability, especially in high-stakes applications, such as healthcare and autonomous driving. Due to the lack of a rigorous definition of explainable AI (XAI), a plethora of research related to explainability, interpretability, and transparency has been developed to explain and analyze the model from various perspectives. Consequently, with an exhaustive list of papers, it becomes challenging to have a comprehensive overview of XAI research from all aspects. Considering the popularity of neural networks in AI research, we narrow our focus to a specific area of XAI research: gradient based explanations, which can be directly adopted for neural network models. In this review, we systematically explore gradient based explanation methods to date and introduce a novel taxonomy to categorize them into four distinct classes. Then, we present the essence of technique details in chronological order and underscore the evolution of algorithms. Next, we introduce both human and quantitative evaluations to measure algorithm performance. More importantly, we demonstrate the general challenges in XAI and specific challenges in gradient based explanations. We hope that this survey can help researchers understand state-of-the-art progress and their corresponding disadvantages, which could spark their interest in addressing these issues in future work.

Photodetectors that are sensitive in shortwave infrared (SWIR) range (1 um - 2 um) are of significant interest for applications in 3D, night and adverse weather imaging, machine vision and autonomous driving, among others. Currently available technologies in the SWIR rely on costly epitaxial semiconductors that are not monolithically integrated with CMOS electronics. Solution-processed quantum dots can address this challenge by enabling low-cost manufacturing and simple monolithic integration on silicon in a back-end-of-line (BEOL) process. To date, colloidal quantum dot (CQD) materials to access the SWIR are mostly based on lead sulfide (PbS) and mercury telluride (HgTe) compounds, imposing major regulatory concerns and impeding their deployment in consumer electronics due to toxicity concerns. Here we report a new synthesis method for environmentally-friendly silver telluride (Ag2Te) quantum dots and their application in high-performance SWIR photodetectors. The CQD photodetector stack employs materials compliant with the Restriction of Hazardous Substance (RoHS) directives and is sensitive in the spectral range from 350 nm - 1600 nm. The room-temperature detectivity is of the order 1012 Jones, the 3dB bandwidth is in excess of 0.1 MHz and the linear dynamic range is over 118 dB. We also realize a monolithically integrated SWIR imager based on solution processed, heavy-metal-free materials, thus paving the way of this technology to consumer electronics market.

Counterfactual explanations (CFEs) exemplify how to minimally modify a feature vector to achieve a different prediction for an instance. CFEs can enhance informational fairness and trustworthiness, and provide suggestions for users who receive adverse predictions. However, recent research has shown that multiple CFEs can be offered for the same instance or instances with slight differences. Multiple CFEs provide flexible choices and cover diverse desiderata for user selection. However, individual fairness and model reliability will be damaged if unstable CFEs with different costs are returned. Existing methods fail to exploit flexibility and address the concerns of non-robustness simultaneously. To address these issues, we propose a conceptually simple yet effective solution named Counterfactual Explanations with Minimal Satisfiable Perturbations (CEMSP). Specifically, CEMSP constrains changing values of abnormal features with the help of their semantically meaningful normal ranges. For efficiency, we model the problem as a Boolean satisfiability problem to modify as few features as possible. Additionally, CEMSP is a general framework and can easily accommodate more practical requirements, e.g., casualty and actionability. Compared to existing methods, we conduct comprehensive experiments on both synthetic and real-world datasets to demonstrate that our method provides more robust explanations while preserving flexibility., Comment: Accepted by CIKM 2023

The classical invariant theory for the queer Lie superalgebra $\mathfrak{q}_n$ investigates its invariants in the supersymmetric algebra $$\mathcal{U}_{s,l}^{r,k}:=\mathrm{Sym}\left(V^{\oplus r}\oplus \Pi(V)^{\oplus k}\oplus V^{*\oplus s}\oplus \Pi(V^*)^{\oplus l} \right),$$ where $V=\mathbb{C}^{n|n}$ is the natural supermodule, $V^*$ is its dual and $\Pi$ is the parity reversing functor. This paper aims to construct a quantum analogue $\mathcal{B}^{r,k}_{s,l}$ of $\mathcal{U}_{s,l}^{r,k}$ and to explore the quantum queer superalgebra $\mathrm{U}_q(\mathfrak{q}_n)$-invariants in $\mathcal{B}^{r,k}_{s,l}$. The strategy involves braided tensor products of the quantum analogues $\mathsf{A}_{r,n}$, $\mathsf{A}_{k,n}^{\Pi}$ of the supersymmetric algebras $\mathrm{Sym}\left(V^{\oplus r}\right)$, $\mathrm{Sym}\left(\Pi(V)^{\oplus k}\right)$, and their dual partners $\bar{\mathsf{A}}_{s,n}$, and $\bar{\mathsf{A}}_{l,n}^{\Pi}$. These braided tensor products are defined using explicit braiding operator due to the absence of a universal R-matrix for $\mathrm{U}_q(\mathfrak{q}_n)$. Furthermore, we obtain an isomorphism between the braided tensor product $\mathsf{A}_{r,n}\otimes\mathsf{A}_{k,n}$ and $\mathsf{A}_{r+k,n}$, an isomorphism between $\mathsf{A}_{k,n}^{\Pi}$ and $\mathsf{A}_{k,n}$, as well as the corresponding isomorphisms for their dual parts. Consequently, the $\mathrm{U}_q(\mathfrak{q}_n)$-supermodule superalgebra $\mathcal{B}^{r,k}_{s,l}$ is identified with $\mathcal{B}^{r+k,0}_{s+l,0}$. This allows us to obtain a set of generators of $\mathrm{U}_q(\mathfrak{q}_n)$-invariants in $\mathcal{B}^{r,k}_{s,l}$.

The goal of this paper is to generalize a statement by Drinfeld, asserting that Yangians can be constructed as limit forms of the quantum loop algebras, to the super case. We establish a connection between quantum loop superalgebra and super Yangian of the general linear Lie superalgebra $\mathfrak{gl}_{M|N}$ in RTT type presentation. In particular, we derive the Poincar\'e-Birkhoff-Witt(PBW) theorem for the quantum loop superalgebra $\mathrm{U}_q\big(\mathfrak{Lgl}_{M|N}\big)$. Additionally, we investigate the application of the same argument to twisted super Yangian of the ortho-symplectic Lie superalgebra. For this purpose, we introduce the twisted quantum loop superalgebra as a one-sided coideal of $\mathrm{U}_q\big(\mathfrak{Lgl}_{M|2n}\big)$ with respect to the comultiplication., Comment: 34 pages, 2 figures.Comments are welcome!

The emergence of large-scale pretrained language models has posed unprecedented challenges in deriving explanations of why the model has made some predictions. Stemmed from the compositional nature of languages, spurious correlations have further undermined the trustworthiness of NLP systems, leading to unreliable model explanations that are merely correlated with the output predictions. To encourage fairness and transparency, there exists an urgent demand for reliable explanations that allow users to consistently understand the model's behavior. In this work, we propose a complete framework for extending concept-based interpretability methods to NLP. Specifically, we propose a post-hoc interpretability method for extracting predictive high-level features (concepts) from the pretrained model's hidden layer activations. We optimize for features whose existence causes the output predictions to change substantially, \ie generates a high impact. Moreover, we devise several evaluation metrics that can be universally applied. Extensive experiments on real and synthetic tasks demonstrate that our method achieves superior results on {predictive impact}, usability, and faithfulness compared to the baselines.

The classical invariant theory for the queer Lie superalgebra is an investigation of the $\mathrm{U}(\mathfrak{q}_n)$-invariant sub-superalgebra of the symmetric superalgebra $\mathrm{Sym}(V^{\oplus r}\oplus V^{*\oplus s})$ for $V=\mathbb{C}^{n|n}$. We establish the first fundamental theorem of invariant theory for the quantum queer superalgebra $\mathrm{U}_q(\mathfrak{q}_n)$. The key ingredient is a quantum analog $\mathcal{O}_{r,s}$ of the symmetric superalgebra $\mathrm{Sym}(V^{\oplus r}\oplus V^{*\oplus s})$ that is created as a braided tensor product of a quantization $\mathsf{A}_{r,n}$ of $\mathrm{Sym}(V^{\oplus r})$ and a quantization $\bar{\mathsf{A}}_{s,n}$ of $\mathrm{Sym}(V^{*\oplus s})$. Since the quantum queer superalgebra $\mathrm{U}_q(\mathfrak{q}_n)$ is not quasi-triangular, our braided tensor product is created via an explicit intertwining operator instead of the universal $\mathcal{R}$-matrix., Comment: 34 pages, 2 figures

Cloud service providers have launched Machine-Learning-as-a-Service (MLaaS) platforms to allow users to access large-scale cloudbased models via APIs. In addition to prediction outputs, these APIs can also provide other information in a more human-understandable way, such as counterfactual explanations (CF). However, such extra information inevitably causes the cloud models to be more vulnerable to extraction attacks which aim to steal the internal functionality of models in the cloud. Due to the black-box nature of cloud models, however, a vast number of queries are inevitably required by existing attack strategies before the substitute model achieves high fidelity. In this paper, we propose a novel simple yet efficient querying strategy to greatly enhance the querying efficiency to steal a classification model. This is motivated by our observation that current querying strategies suffer from decision boundary shift issue induced by taking far-distant queries and close-to-boundary CFs into substitute model training. We then propose DualCF strategy to circumvent the above issues, which is achieved by taking not only CF but also counterfactual explanation of CF (CCF) as pairs of training samples for the substitute model. Extensive and comprehensive experimental evaluations are conducted on both synthetic and real-world datasets. The experimental results favorably illustrate that DualCF can produce a high-fidelity model with fewer queries efficiently and effectively., Comment: in Proceedings of the 2022 ACM Conference on Fairness, Accountability, and Transparency (FAccT '22), June 21-24, 2022, Seoul, Republic of Korea

In recent years, pre-trained models have become dominant in most natural language processing (NLP) tasks. However, in the area of Automated Essay Scoring (AES), pre-trained models such as BERT have not been properly used to outperform other deep learning models such as LSTM. In this paper, we introduce a novel multi-scale essay representation for BERT that can be jointly learned. We also employ multiple losses and transfer learning from out-of-domain essays to further improve the performance. Experiment results show that our approach derives much benefit from joint learning of multi-scale essay representation and obtains almost the state-of-the-art result among all deep learning models in the ASAP task. Our multi-scale essay representation also generalizes well to CommonLit Readability Prize data set, which suggests that the novel text representation proposed in this paper may be a new and effective choice for long-text tasks., Comment: Accepted to NAACL 2022 as a long paper

Pb-chalcogenide colloidal quantum dots (CQDs) are attractive materials to be used as tuneable laser media across the infrared spectrum. However, excessive nonradiative Auger recombination due to the presence of trap states outcompetes light amplification by rapidly annihilating the exciton population, leading to high gain thresholds. Here, we employ a binary blend of CQDs and ZnO nanocrystals in order to passivate the in-gap trap states of PbS-CQD gain medium. Using transient absorption, we measure a five-fold increase in Auger lifetime demonstrating the suppression of trap-assisted Auger recombination. By doing so, we achieve a two-fold reduction in amplified spontaneous emission (ASE) threshold. Finally, by integrating our proposed binary blend to a DFB resonator, we demonstrate single-mode lasing emission at 1650 nm with a linewidth of 1.23 nm (0.62 meV), operating at a low lasing threshold of ~385 {\mu}J.cm-2. The Auger suppression in this system has allowed to achieve unprecedented lasing emission stability for a CQD laser with recorded continuous operation of 5 hours at room temperature and ambient conditions.