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Hierarchical text classification (HTC) is a special sub-task of multi-label classification (MLC) whose taxonomy is constructed as a tree and each sample is assigned with at least one path in the tree. Latest HTC models contain three modules: a text encoder, a structure encoder and a multi-label classification head. Specially, the structure encoder is designed to encode the hierarchy of taxonomy. However, the structure encoder has scale problem. As the taxonomy size increases, the learnable parameters of recent HTC works grow rapidly. Recursive regularization is another widely-used method to introduce hierarchical information but it has collapse problem and generally relaxed by assigning with a small weight (ie. 1e-6). In this paper, we propose a Hierarchy-aware Light Global model with Hierarchical local conTrastive learning (HiLight), a lightweight and efficient global model only consisting of a text encoder and a multi-label classification head. We propose a new learning task to introduce the hierarchical information, called Hierarchical Local Contrastive Learning (HiLCL). Extensive experiments are conducted on two benchmark datasets to demonstrate the effectiveness of our model.

We establish an omega theorem for logarithmic derivative of the Riemann zeta function near the 1-line by resonance method. We show that the inequality $\left| \zeta^{\prime}\left(\sigma_A+it\right)/\zeta\left(\sigma_A+it\right) \right| \geqslant \left(\left(e^A-1\right)/A\right)\log_2 T + O\left(\log_2 T / \log_3 T\right)$ has a solution $t \in [T^{\beta}, T]$ for all sufficiently large $T,$ where $\sigma_A = 1 - A / \log_2 {T}.$Furthermore, we give a conditional lower bound for the measure of the set of $t$ for which the logarithmic derivative of the Riemann zeta function is large. Moreover, similar results can be generalized to Dirichlet $L$-functions.

Lexicon-based retrieval has gained siginificant popularity in text retrieval due to its efficient and robust performance. To further enhance performance of lexicon-based retrieval, researchers have been diligently incorporating state-of-the-art methodologies like Neural retrieval and text-level contrastive learning approaches. Nonetheless, despite the promising outcomes, current lexicon-based retrieval methods have received limited attention in exploring the potential benefits of feature context representations and term-level knowledge guidance. In this paper, we introduce an innovative method by introducing FEature Context and TErm-level Knowledge modules(FecTek). To effectively enrich the feature context representations of term weight, the Feature Context Module (FCM) is introduced, which leverages the power of BERT's representation to determine dynamic weights for each element in the embedding. Additionally, we develop a term-level knowledge guidance module (TKGM) for effectively utilizing term-level knowledge to intelligently guide the modeling process of term weight. Evaluation of the proposed method on MS Marco benchmark demonstrates its superiority over the previous state-of-the-art approaches.

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in the harmonic algebra.

In this paper, using Hamilton-Jacobi method, we discuss the tunnelling of fermions when the dual influence of quantum gravity and the deformation of a parameterized black hole is taken into account. With the influence of the generalized uncertainty principle, there exists an offset around the standard Hawking temperature. We investigate a parametric deformed black hole and find that the corrected temperature is lower than the standard one,so there exists remnant of the black hole and the correction is not only determined by the mass of the emitted fermion,but also determined by the mass of the black hole and the deformation parameter.Under the dual influence of quantum gravity and deformation,the correction effect of quantum gravity is the main influencing factor, while the correction effect of deformation parameter is secondary. The quantum gravitational correction factor is only determined by the mass of the emitted fermions, while the deformation correction factor is only determined by the mass of the black hole.

Large-scale pre-trained models (PTMs) have been widely used in document-oriented NLP tasks, such as question answering. However, the encoding-task coupling requirement results in the repeated encoding of the same documents for different tasks and queries, which is highly computationally inefficient. To this end, we target to decouple document encoding from downstream tasks, and propose to represent each document as a plug-and-play document module, i.e., a document plugin, for PTMs (PlugD). By inserting document plugins into the backbone PTM for downstream tasks, we can encode a document one time to handle multiple tasks, which is more efficient than conventional encoding-task coupling methods that simultaneously encode documents and input queries using task-specific encoders. Extensive experiments on 8 datasets of 4 typical NLP tasks show that PlugD enables models to encode documents once and for all across different scenarios. Especially, PlugD can save $69\%$ computational costs while achieving comparable performance to state-of-the-art encoding-task coupling methods. Additionally, we show that PlugD can serve as an effective post-processing way to inject knowledge into task-specific models, improving model performance without any additional model training., Comment: Accepted by ACL 2023

In this paper, we study the explicit expressions of multiple t-star values with an arbitrary number of blocks of twos of general level. We give an expression of a generating function of such values, which generalizes the results for multiple zeta-star values and multiple t-star values. This derived generating function can provide expressions of multiple t-star values of general level in terms of the alternating multiple t-half values of general level with additional factorial and pochhammer symbol. As applications, some specific evaluations of multiple t-star values of general level with one-two-three or more general indices are given. These evaluations contribute to a deeper understanding of the properties of multiple t-star values of general level., Comment: arXiv admin note: substantial text overlap with arXiv:2212.09070

As Hopf truss analogues of Rota-Baxter Hopf algebras, the notion of Rota-Baxter systems of Hopf algebras is proposed. We study the relatiohship between Rota-Baxter systems of Hopf algebras and Rota-Baxter Hopf algebras, show that there is a Rota-Baxter system structure on the group algebra if the group has a Rota-Baxter system structure, investigate the descendent Hopf algebra of a Rota-Baxte system of Hopf algebras. Finally we study the local decomposition of the character group from a Rota-Baxter system of Hopf algebras to a commutative algebra.

Few-shot dense retrieval (DR) aims to effectively generalize to novel search scenarios by learning a few samples. Despite its importance, there is little study on specialized datasets and standardized evaluation protocols. As a result, current methods often resort to random sampling from supervised datasets to create "few-data" setups and employ inconsistent training strategies during evaluations, which poses a challenge in accurately comparing recent progress. In this paper, we propose a customized FewDR dataset and a unified evaluation benchmark. Specifically, FewDR employs class-wise sampling to establish a standardized "few-shot" setting with finely-defined classes, reducing variability in multiple sampling rounds. Moreover, the dataset is disjointed into base and novel classes, allowing DR models to be continuously trained on ample data from base classes and a few samples in novel classes. This benchmark eliminates the risk of novel class leakage, providing a reliable estimation of the DR model's few-shot ability. Our extensive empirical results reveal that current state-of-the-art DR models still face challenges in the standard few-shot scene. Our code and data will be open-sourced at https://github.com/OpenMatch/ANCE-Tele., Comment: Work in progress

Fashion vision-language pre-training models have shown efficacy for a wide range of downstream tasks. However, general vision-language pre-training models pay less attention to fine-grained domain features, while these features are important in distinguishing the specific domain tasks from general tasks. We propose a method for fine-grained fashion vision-language pre-training based on fashion Symbols and Attributes Prompt (FashionSAP) to model fine-grained multi-modalities fashion attributes and characteristics. Firstly, we propose the fashion symbols, a novel abstract fashion concept layer, to represent different fashion items and to generalize various kinds of fine-grained fashion features, making modelling fine-grained attributes more effective. Secondly, the attributes prompt method is proposed to make the model learn specific attributes of fashion items explicitly. We design proper prompt templates according to the format of fashion data. Comprehensive experiments are conducted on two public fashion benchmarks, i.e., FashionGen and FashionIQ, and FashionSAP gets SOTA performances for four popular fashion tasks. The ablation study also shows the proposed abstract fashion symbols, and the attribute prompt method enables the model to acquire fine-grained semantics in the fashion domain effectively. The obvious performance gains from FashionSAP provide a new baseline for future fashion task research.

Fine-grained supervision based on object annotations has been widely used for vision and language pre-training (VLP). However, in real-world application scenarios, aligned multi-modal data is usually in the image-caption format, which only provides coarse-grained supervision. It is not only cost-expensive but also compute-expensive to collect object annotations and build object annotation pre-extractor for different scenarios. In this paper, we propose a fine-grained VLP scheme without object annotations from the linguistic perspective. First, we propose a homonym sentence rewriting (HSR) algorithm to provide token-level supervision. The algorithm replaces a verb/noun/adjective/quantifier word of the caption with its homonyms from WordNet. Correspondingly, we propose refined vision-language modeling (RVLM) framework to exploit the token-level supervision. Three refined tasks, i.e., refined image-text contrastive (RITC), refined image-text matching (RITM), and replace language modeling (RLM) are proposed to learn the fine-grained alignment. Extensive experiments on several downstream tasks demonstrate the superior performance of the proposed method., Comment: Work in progress, v0.2

In this paper, we study the generating functions of multiple $t$-star values with an arbitrary number of blocks of twos, which are based on the results of the corresponding generating functions of multiple $t$-harmonic star sums. These generating functions can deduce an explicit expression of multiple $t$-star values. As applications, we obtain some evaluations of multiple $t$-star values with one-two-three or more general indices.

We study the relations of multiple $t$-values of general level. The generating function of sums of multiple $t$-(star) values of level $N$ with fixed weight, depth and height is represented by the generalized hypergeometric function $_3F_2$, which generalizes the results for multiple zeta(-star) values and multiple $t$-(star) values. As applications, we obtain formulas for the generating functions of sums of multiple $t$-(star) values of level $N$ with height one and maximal height and a weighted sum formula for sums of multiple $t$-(star) values of level $N$ with fixed weight and depth. Using the stuffle algebra, we also get the symmetric sum formulas and Hoffman's restricted sum formulas for multiple $t$-(star) values of level $N$. Some evaluations of multiple $t$-star values of level $2$ with one-two-three indices are given., Comment: 24 pages

As a generalization of skew braces, the notion of skew trusses was introduced by T. Brzezinski. It was shown that every Rota-Baxter group has the structure of skew braces by V. G. Bardakov and V. Gubarev. To investigate an analogue of Rota-Baxter groups which has the structure of skew trusses, we define RotaBaxter systems. We study the relationship between Rota-Baxter systems and Rota-Baxter groups. Furthermore, we prove that a Rota-Baxter system can be decomposed as a direct sum of two semigroups. A factorization theorem is proved, generalizing the factorization theorem of Rota-Baxter groups. The notion of Rota-Baxter systems of Lie algebras was introduced, as a generalization of Rota-Baxter Lie algebras. The connection between Rota-Baxter systems of Lie algebras and Lie groups is studied. Finally, as a generalization of the modified Yang-Baxter equation, we define twisted modified Yang-Baxter equations. We give solutions of twisted modified Yang-Baxter equations by Rota-Baxter systems of Lie algebras.

We study the Ohno-Zagier type relation for multiple $t$-values and multiple $t$-star values. We represent the generating function of sums of multiple $t$-(star) values with fixed weight, depth and height in terms of the generalized hypergeometric function $\,_3F_2$. As applications, we get a formula for the generating function of sums of multiple $t$-(star) values of maximal height and a weighted sum formula for sums of multiple $t$-(star) values with fixed weight and depth., Comment: 12 pages

In 2015, S. Hong and C. Wang proved that none of the elementary symmetric functions of $1,1/3,\ldots,1/(2n-1)$ is an integer when $n\geq 2$. In 2017, Kh. Pilehrood, T. Pilehrood and R. Tauraso proved that the multiple harmonic sums $H_n(s_1,\ldots,s_r)$ are never integers with exceptions of $H_1(s_1)=1$ and $H_3(1,1)=1$. They also proved that the multiple harmonic star sums are never integers when $n\geq 2$. In this paper, we consider the odd multiple harmonic sums and the odd multiple harmonic star sums and show that none of these sums is an integer with exception of the trivial case. Besides, we give evaluations of the odd (alternating) multiple harmonic sums with depth one., Comment: 13 pages

Existing anchor-base oriented object detection methods have achieved amazing results, but these methods require some manual preset boxes, which introduces additional hyperparameters and calculations. The existing anchor-free methods usually have complex architectures and are not easy to deploy. Our goal is to propose an algorithm which is simple and easy-to-deploy for aerial image detection. In this paper, we present a one-stage anchor-free rotated object detector (FCOSR) based on FCOS, which can be deployed on most platforms. The FCOSR has a simple architecture consisting of only convolution layers. Our work focuses on the label assignment strategy for the training phase. We use ellipse center sampling method to define a suitable sampling region for oriented bounding box (OBB). The fuzzy sample assignment strategy provides reasonable labels for overlapping objects. To solve the insufficient sampling problem, a multi-level sampling module is designed. These strategies allocate more appropriate labels to training samples. Our algorithm achieves 79.25, 75.41, and 90.15 mAP on DOTA1.0, DOTA1.5, and HRSC2016 datasets, respectively. FCOSR demonstrates superior performance to other methods in single-scale evaluation. We convert a lightweight FCOSR model to TensorRT format, which achieves 73.93 mAP on DOTA1.0 at a speed of 10.68 FPS on Jetson Xavier NX with single scale. The code is available at: https://github.com/lzh420202/FCOSR, Comment: 10 pages, 6 tables, 7 figures

Cross-model retrieval has emerged as one of the most important upgrades for text-only search engines (SE). Recently, with powerful representation for pairwise text-image inputs via early interaction, the accuracy of vision-language (VL) transformers has outperformed existing methods for text-image retrieval. However, when the same paradigm is used for inference, the efficiency of the VL transformers is still too low to be applied in a real cross-modal SE. Inspired by the mechanism of human learning and using cross-modal knowledge, this paper presents a novel Vision-Language Decomposed Transformer (VLDeformer), which greatly increases the efficiency of VL transformers while maintaining their outstanding accuracy. By the proposed method, the cross-model retrieval is separated into two stages: the VL transformer learning stage, and the VL decomposition stage. The latter stage plays the role of single modal indexing, which is to some extent like the term indexing of a text SE. The model learns cross-modal knowledge from early-interaction pre-training and is then decomposed into an individual encoder. The decomposition requires only small target datasets for supervision and achieves both $1000+$ times acceleration and less than $0.6$\% average recall drop. VLDeformer also outperforms state-of-the-art visual-semantic embedding methods on COCO and Flickr30k.

This paper introduces the notion of Rota-Baxter $C^{\ast}$-algebras. Here a Rota-Baxter $C^{\ast}$-algebra is a $C^{\ast}$-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on $C^{\ast}$-algebra, are defined and studied. A theorem of Rota-Baxter operators on concrete $C^{\ast}$-algebras is given, deriving the relationship between two kinds of Rota-Baxter algebras. As a corollary, some connection between $\ast$-representations and Rota-Baxter operators is given. The notion of representations of Rota-Baxter $C^{\ast}$-algebras are constructed, and a theorem of representations of direct sums of Rota-Baxter representations is derived. Finally using Rota-Baxter operators, the notion of quasidiagonal operators on $C^{\ast}$-algebra is reconstructed., Comment: 20 pages

We study the sum of the finite multiple harmonic $q$-series on $r\text{-}(r+1)$ indices at roots of unity with $r=1,2,3$. And we give the equivalent conditions of two conjectures regarding cyclic sums of finite multiple harmonic $q$-series on $1\text{-}2\text{-}3$ indices at roots of unity, posed recently by Kh. Pilehrood, T. Pilehrood and R. Tauraso., Comment: 15 pages