Electronic Structure and Linear Optical Properties of Sr2_{2}CuO2_{2}Cl2_{2} Studied from the First Principles Calculation

First-principles calculations with the full-potential linearized augmented plane-wave (FP-LAPW) method have been performed to investigate detailed electronic and linear optical properties of Sr$_{2}$CuO$_{2}$Cl$_{2}$, which is a classical low-dimensional antiferromagnet (AFM) charge transfer ({\it CT}) insulator. Within the local-spin-density approximation (LSDA) plus the on-site Coulomb interaction $U$ (LADA+$U$) added on Cu 3d orbitals, our calculated band gap and spin moments are well consistent with the experimental and other theoretical values. The energy dispersion relation agrees well with the angle resolved photoemission measurements. Its linear optical properties are calculated within the electric-dipole approximation. The absorption spectrum is found to agree well with the experimental result.Comment: 5 pages, 5 figure

On the Dimensionality of Sentence Embeddings

Learning sentence embeddings is a fundamental problem in natural language processing. While existing research primarily focuses on enhancing the quality of sentence embeddings, the exploration of sentence embedding dimensions is limited. Here we present a comprehensive and empirical analysis of the dimensionality of sentence embeddings. First, we demonstrate that the optimal dimension of sentence embeddings is usually smaller than the default value. Subsequently, to compress the dimension of sentence embeddings with minimum performance degradation, we identify two components contributing to the overall performance loss: the encoder's performance loss and the pooler's performance loss. Therefore, we propose a two-step training method for sentence representation learning models, wherein the encoder and the pooler are optimized separately to mitigate the overall performance loss in low-dimension scenarios. Experimental results on seven STS tasks and seven sentence classification tasks demonstrate that our method significantly improves the performance of low-dimensional sentence embeddings

First principles investigation of transition-metal doped group-IV semiconductors: Rx{_x}Y1−x_{1-x} (R=Cr, Mn, Fe; Y=Si, Ge)

A number of transition-metal (TM) doped group-IV semiconductors, R$_{x}$Y$_{1-x}$ (R=Cr, Mn and Fe; Y=Si, Ge), have been studied by the first principles calculations. The obtained results show that antiferromagnetic (AFM) order is energetically more favored than ferromagnetic (FM) order in Cr-doped Ge and Si with $x$=0.03125 and 0.0625. In 6.25% Fe-doped Ge, FM interaction dominates in all range of the R-R distances while for Fe-doped Ge at 3.125% and Fe-doped Si at both concentrations of 3.125% and 6.25%, only in a short R-R range can the FM states exist. In the Mn-doped case, the RKKY-like mechanism seems to be suitable for the Ge host matrix, while for the Mn-doped Si, the short-range AFM interaction competes with the long-range FM interaction. The different origin of the magnetic orders in these diluted magnetic semiconductors (DMSs) makes the microscopic mechanism of the ferromagnetism in the DMSs more complex and attractive.Comment: 14 pages, 2 figures, 6 table

A Closer Look at the Self-Verification Abilities of Large Language Models in Logical Reasoning

Logical reasoning has been an ongoing pursuit in the field of AI. Despite significant advancements made by large language models (LLMs), they still struggle with complex logical reasoning problems. To enhance reasoning performance, one promising direction is scalable oversight, which requires LLMs to identify their own errors and then improve by themselves. Various self-verification methods have been proposed in pursuit of this goal. Nevertheless, whether existing models understand their own errors well is still under investigation. In this paper, we take a closer look at the self-verification abilities of LLMs in the context of logical reasoning, focusing on their ability to identify logical fallacies accurately. We introduce a dataset, FALLACIES, containing 232 types of reasoning fallacies categorized in a hierarchical taxonomy. By conducting exhaustive experiments on FALLACIES, we obtain comprehensive and detailed analyses of a series of models on their verification abilities. Our main findings suggest that existing LLMs could struggle to identify fallacious reasoning steps accurately and may fall short of guaranteeing the validity of self-verification methods. Drawing from these observations, we offer suggestions for future research and practical applications of self-verification methods.Comment: work in progres

A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation

Recently developed large language models have achieved remarkable success in generating fluent and coherent text. However, these models often tend to 'hallucinate' which critically hampers their reliability. In this work, we address this crucial problem and propose an approach that actively detects and mitigates hallucinations during the generation process. Specifically, we first identify the candidates of potential hallucination leveraging the model's logit output values, check their correctness through a validation procedure, mitigate the detected hallucinations, and then continue with the generation process. Through extensive experiments with the 'article generation task', we first demonstrate the individual efficacy of our detection and mitigation techniques. Specifically, the detection technique achieves a recall of 88% and the mitigation technique successfully mitigates 57.6% of the correctly detected hallucinations. Importantly, our mitigation technique does not introduce new hallucinations even in the case of incorrectly detected hallucinations, i.e., false positives. Then, we show that the proposed active detection and mitigation approach successfully reduces the hallucinations of the GPT-3 model from 47.5% to 14.5% on average. In summary, our work contributes to improving the reliability and trustworthiness of large language models, a crucial step en route to enabling their widespread adoption in real-world applications

Spin-orbit interaction in Au structures of various dimensionalities

Variation of the geometrical and electronic properties of the gold materials in different dimensions has been investigated by $ab$ $initio$ method, taking into account the spin-orbit (SO) interaction. It is found that SO effects in different dimensional Au materials depend greatly on fundamental symmetry and dimensionality. For single walled gold nanotubes (SWGNTs), SO interaction decreases significantly the conducting channel number of achiral SWGNT (4, 0), and leads to spin splitting at Fermi level of chiral SWGNT, indicating that quasi-1D SWGNT can be a good candidate for the spin-electron devices. Furthermore, our results suggest that cage cluster might be synthesizable experimentally by taking gold tube structure as parent material.Comment: 11 pages, 4 figure

Thrust: Adaptively Propels Large Language Models with External Knowledge

Although large-scale pre-trained language models (PTLMs) are shown to encode rich knowledge in their model parameters, the inherent knowledge in PTLMs can be opaque or static, making external knowledge necessary. However, the existing information retrieval techniques could be costly and may even introduce noisy and sometimes misleading knowledge. To address these challenges, we propose the instance-level adaptive propulsion of external knowledge (IAPEK), where we only conduct the retrieval when necessary. To achieve this goal, we propose measuring whether a PTLM contains enough knowledge to solve an instance with a novel metric, Thrust, which leverages the representation distribution of a small number of seen instances. Extensive experiments demonstrate that thrust is a good measurement of PTLM models' instance-level knowledgeability. Moreover, we can achieve significantly higher cost-efficiency with the Thrust score as the retrieval indicator than the naive usage of external knowledge on 88% of the evaluated tasks with 26% average performance improvement. Such findings shed light on the real-world practice of knowledge-enhanced LMs with a limited knowledge-seeking budget due to computation latency or costs.Comment: 13 pages, 6 figure

Chain-of-Note: Enhancing Robustness in Retrieval-Augmented Language Models

Retrieval-augmented language models (RALMs) represent a substantial advancement in the capabilities of large language models, notably in reducing factual hallucination by leveraging external knowledge sources. However, the reliability of the retrieved information is not always guaranteed. The retrieval of irrelevant data can lead to misguided responses, and potentially causing the model to overlook its inherent knowledge, even when it possesses adequate information to address the query. Moreover, standard RALMs often struggle to assess whether they possess adequate knowledge, both intrinsic and retrieved, to provide an accurate answer. In situations where knowledge is lacking, these systems should ideally respond with "unknown" when the answer is unattainable. In response to these challenges, we introduces Chain-of-Noting (CoN), a novel approach aimed at improving the robustness of RALMs in facing noisy, irrelevant documents and in handling unknown scenarios. The core idea of CoN is to generate sequential reading notes for retrieved documents, enabling a thorough evaluation of their relevance to the given question and integrating this information to formulate the final answer. We employed ChatGPT to create training data for CoN, which was subsequently trained on an LLaMa-2 7B model. Our experiments across four open-domain QA benchmarks show that RALMs equipped with CoN significantly outperform standard RALMs. Notably, CoN achieves an average improvement of +7.9 in EM score given entirely noisy retrieved documents and +10.5 in rejection rates for real-time questions that fall outside the pre-training knowledge scope.Comment: Preprin