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In this article, we study the Iwasawa theory for cuspidal automorphic representations of $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ over CM fields along anticyclotomic directions, in the framework of the Gan-Gross-Prasad conjecture for unitary groups. We prove one-side divisibility of the corresponding Iwasawa main conjecture: when the global root number is $1$, the $p$-adic $L$-function belongs to the characteristic ideal of the Iwasawa Bloch-Kato Selmer group; when the global root number is $-1$, the square of the characteristic ideal of a certain Iwasawa module is contained in the characteristic ideal of the torsion part of the Iwasawa Bloch-Kato Selmer group (analogous to Perrin-Riou's Heegner point main conjecture)., Comment: 105 pages; main theorems improved; comments welcome. arXiv admin note: text overlap with arXiv:2211.06673 by other authors

As a fundamental task in computational chemistry, retrosynthesis prediction aims to identify a set of reactants to synthesize a target molecule. Existing template-free approaches only consider the graph structures of the target molecule, which often cannot generalize well to rare reaction types and large molecules. Here, we propose T-Rex, a text-assisted retrosynthesis prediction approach that exploits pre-trained text language models, such as ChatGPT, to assist the generation of reactants. T-Rex first exploits ChatGPT to generate a description for the target molecule and rank candidate reaction centers based both the description and the molecular graph. It then re-ranks these candidates by querying the descriptions for each reactants and examines which group of reactants can best synthesize the target molecule. We observed that T-Rex substantially outperformed graph-based state-of-the-art approaches on two datasets, indicating the effectiveness of considering text information. We further found that T-Rex outperformed the variant that only use ChatGPT-based description without the re-ranking step, demonstrate how our framework outperformed a straightforward integration of ChatGPT and graph information. Collectively, we show that text generated by pre-trained language models can substantially improve retrosynthesis prediction, opening up new avenues for exploiting ChatGPT to advance computational chemistry. And the codes can be found at https://github.com/lauyikfung/T-Rex.

We construct $p$-adic $L$-functions for Rankin--Selberg products of automorphic forms of hermitian type in the anticyclotomic direction for both root numbers. When the root number is $+1$, the construction relies on global Bessel periods on definite unitary groups which, due to the recent advances on the global Gan--Gross--Prasad conjecture, interpolate classical central $L$-values. When the root number is $-1$, we construct an element in the Iwasawa Selmer group using the diagonal cycle on the product of unitary Shimura varieties, and conjecture that its $p$-adic height interpolates derivatives of cyclotomic $p$-adic $L$-functions. We also propose the nonvanishing conjecture and the main conjecture in both cases., Comment: typos corrected

Relational triple extraction is challenging for its difficulty in capturing rich correlations between entities and relations. Existing works suffer from 1) heterogeneous representations of entities and relations, and 2) heterogeneous modeling of entity-entity interactions and entity-relation interactions. Therefore, the rich correlations are not fully exploited by existing works. In this paper, we propose UniRel to address these challenges. Specifically, we unify the representations of entities and relations by jointly encoding them within a concatenated natural language sequence, and unify the modeling of interactions with a proposed Interaction Map, which is built upon the off-the-shelf self-attention mechanism within any Transformer block. With comprehensive experiments on two popular relational triple extraction datasets, we demonstrate that UniRel is more effective and computationally efficient. The source code is available at https://github.com/wtangdev/UniRel., Comment: Accepted at EMNLP 2022. Camera-ready version

This report describes our VolcTrans system for the WMT22 shared task on large-scale multilingual machine translation. We participated in the unconstrained track which allows the use of external resources. Our system is a transformerbased multilingual model trained on data from multiple sources including the public training set from the data track, NLLB data provided by Meta AI, self-collected parallel corpora, and pseudo bitext from back-translation. A series of heuristic rules clean both bilingual and monolingual texts. On the official test set, our system achieves 17.3 BLEU, 21.9 spBLEU, and 41.9 chrF2++ on average over all language pairs. The average inference speed is 11.5 sentences per second using a single Nvidia Tesla V100 GPU. Our code and trained models are available at https://github.com/xian8/wmt22, Comment: WMT 2022, 8 pages

Fix a prime number $p$ and let $E/F$ be a CM extension of number fields in which $p$ splits relatively. Let $\pi$ be an automorphic representation of a quasi-split unitary group of even rank with respect to $E/F$ such that $\pi$ is ordinary above $p$ with respect to the Siegel parabolic subgroup. We construct the cyclotomic $p$-adic $L$-function of $\pi$, and show, under certain conditions, that if its order of vanishing at the trivial character is $1$, then the rank of the Selmer group of the Galois representation of $E$ associated with $\pi$ is at least $1$. Furthermore, under a certain modularity hypothesis, we use special cycles on unitary Shimura varieties to construct some explicit elements in the Selmer group called Selmer theta lifts; and we prove a precise formula relating their $p$-adic heights to the derivative of the $p$-adic $L$-function. In parallel to Perrin-Riou's $p$-adic analogue of the Gross--Zagier formula, our formula is the $p$-adic analogue of the arithmetic inner product formula recently established by Chao~Li and the second author., Comment: 107 pages; layout changed + minor modifications; to appear in Invent. Math

Fine-grained Visual Classification (FGVC) aims to identify objects from subcategories. It is a very challenging task because of the subtle inter-class differences. Existing research applies large-scale convolutional neural networks or visual transformers as the feature extractor, which is extremely computationally expensive. In fact, real-world scenarios of fine-grained recognition often require a more lightweight mobile network that can be utilized offline. However, the fundamental mobile network feature extraction capability is weaker than large-scale models. In this paper, based on the lightweight MobilenetV2, we propose a Progressive Multi-Stage Interactive training method with a Recursive Mosaic Generator (RMG-PMSI). First, we propose a Recursive Mosaic Generator (RMG) that generates images with different granularities in different phases. Then, the features of different stages pass through a Multi-Stage Interaction (MSI) module, which strengthens and complements the corresponding features of different stages. Finally, using the progressive training (P), the features extracted by the model in different stages can be fully utilized and fused with each other. Experiments on three prestigious fine-grained benchmarks show that RMG-PMSI can significantly improve the performance with good robustness and transferability.

In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation., Comment: 42 pages. This article is essentially the original Appendix E of the article arXiv:1912.11942; we now decide to make that appendix an independent article

In this note, we introduce the notion of almost unramified representations of quasi-split unitary groups of even ranks with respect to an unramified quadratic extension of local fields, and study their behavior under the local theta correspondence. These representations are in some sense the least ramified representations that have root number $-1$., Comment: 23 pages, to appear in Journal of Number Theory

Anomalous users detection in social network is an imperative task for security problems. Motivated by the great power of Graph Neural Networks(GNNs), many current researches adopt GNN-based detectors to reveal the anomalous users. However, the increasing scale of social activities, explosive growth of users and manifold technical disguise render the user detection a difficult task. In this paper, we propose an innovate Relevance-aware Anomalous Users Detection model (RAU-GNN) to obtain a fine-grained detection result. RAU-GNN first extracts multiple relations of all types of users in social network, including both benign and anomalous users, and accordingly constructs the multiple user relation graph. Secondly, we employ relevance-aware GNN framework to learn the hidden features of users, and discriminate the anomalous users after discriminating. Concretely, by integrating Graph Convolution Network(GCN) and Graph Attention Network(GAT), we design a GCN-based relation fusion layer to aggregate initial information from different relations, and a GAT-based embedding layer to obtain the high-level embeddings. Lastly, we feed the learned representations to the following GNN layer in order to consolidate the node embedding by aggregating the final users' embeddings. We conduct extensive experiment on real-world datasets. The experimental results show that our approach can achieve high accuracy for anomalous users detection., Comment: Accepted by IJCNN 2021

Depth prediction plays a key role in understanding a 3D scene. Several techniques have been developed throughout the years, among which Convolutional Neural Network has recently achieved state-of-the-art performance on estimating depth from a single image. However, traditional CNNs suffer from the lower resolution and information loss caused by the pooling layers. And oversized parameters generated from fully connected layers often lead to a exploded memory usage problem. In this paper, we present an advanced Dilated Fully Convolutional Neural Network to address the deficiencies. Taking advantages of the exponential expansion of the receptive field in dilated convolutions, our model can minimize the loss of resolution. It also reduces the amount of parameters significantly by replacing the fully connected layers with the fully convolutional layers. We show experimentally on NYU Depth V2 datasets that the depth prediction obtained from our model is considerably closer to ground truth than that from traditional CNNs techniques.

In this article, we develop an arithmetic analogue of Fourier--Jacobi period integrals for a pair of unitary groups of equal rank. We construct the so-called Fourier--Jacobi cycles, which are algebraic cycles on the product of unitary Shimura varieties and abelian varieties. We propose the arithmetic Gan--Gross--Prasad conjecture for these cycles, which is related to central derivatives of certain Rankin--Selberg $L$-functions, and develop a relative trace formula approach toward this conjecture. As a necessary ingredient, we propose the conjecture of the corresponding arithmetic fundamental lemma, and confirm it for unitary groups of rank at most two and for the minuscule case., Comment: v2: minor revision, 89 pages, published on Cambridge Journal of Mathematics

In this article, we improve our main results from \emph{Chow groups and $L$-derivatives of automorphic motives for unitary groups} in two direction: First, we allow ramified places in the CM extension $E/F$ at which we consider representations that are spherical with respect to a certain special maximal compact subgroup, by formulating and proving an analogue of the Kudla--Rapoport conjecture for exotic smooth Rapoport--Zink spaces. Second, we lift the restriction on the components at split places of the automorphic representation, by proving a more general vanishing result on certain cohomology of integral models of unitary Shimura varieties with Drinfeld level structures., Comment: v2: 70 pages; revised in accordance with [LL]. arXiv admin note: text overlap with arXiv:2006.06139

In this article, we study the Chow group of the motive associated to a tempered global $L$-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is $-1$. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and $L$-functions, which generalizes the Birch and Swinnerton-Dyer conjecture. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This confirms the conjectural arithmetic inner product formula proposed by one of us, which generalizes the Gross--Zagier formula to higher dimensional motives., Comment: v5: 66 pages; revised after referee reports

In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value of the Rankin-Selberg $L$-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed from certain diagonal cycle does not vanish, which is conjecturally equivalent to the nonvanishing of the central critical first derivative of the Rankin-Selberg $L$-function, then the Bloch-Kato Selmer group is of rank one., Comment: v3: 179 page. We have separated the original Appendix E as an independent article arXiv:2108.06998, as suggested by a referee

We introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of the global Gan--Gross--Prasad conjecture and its refinement Ichino--Ikeda conjecture for $\mathrm{U}(n)\times\mathrm{U}(n+1)$ in the stable case., Comment: minor revision; 48 pages; to appear in Annals of Mathematics