Herald: A Natural Language Annotated Lean 4 Dataset

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

Distortion-Aware Phase Retrieval Receiver for High-Order QAM Transmission with Carrierless Intensity-Only Measurements

We experimentally investigate transmitting high-order quadrature amplitude modulation (QAM) signals with carrierless and intensity-only measurements with phase retrieval (PR) receiving techniques. The intensity errors during measurement, including noise and distortions, are found to be a limiting factor for the precise convergence of the PR algorithm. To improve the PR reconstruction accuracy, we propose a distortion-aware PR scheme comprising both training and reconstruction stages. By estimating and emulating the distortion caused by various channel impairments, the proposed scheme enables enhanced agreement between the estimated and measured amplitudes throughout the PR iteration, thus resulting in improved reconstruction performance to support high-order QAM transmission. With the aid of proposed techniques, we experimentally demonstrate 50-GBaud 16QAM and 32QAM signals transmitting through a standard single-mode optical fiber (SSMF) span of 40 and 80 km, and achieve bit error rates (BERs) below the 6.25% hard decision (HD)-forward error correction (FEC) and 25% soft decision (SD)-FEC thresholds for the two modulation formats, respectively. By tuning the pilot symbol ratio and applying concatenated coding, we also demonstrate that a post-FEC data rate of up to 140 Gb/s can be achieved for both distances at an optimal pilot symbol ratio of 20%.

Agent Teaming Situation Awareness (ATSA): A Situation Awareness Framework for Human-AI Teaming

The rapid advancements in artificial intelligence (AI) have led to a growing trend of human-AI teaming (HAT) in various fields. As machines continue to evolve from mere automation to a state of autonomy, they are increasingly exhibiting unexpected behaviors and human-like cognitive/intelligent capabilities, including situation awareness (SA). This shift has the potential to enhance the performance of mixed human-AI teams over all-human teams, underscoring the need for a better understanding of the dynamic SA interactions between humans and machines. To this end, we provide a review of leading SA theoretical models and a new framework for SA in the HAT context based on the key features and processes of HAT. The Agent Teaming Situation Awareness (ATSA) framework unifies human and AI behavior, and involves bidirectional, and dynamic interaction. The framework is based on the individual and team SA models and elaborates on the cognitive mechanisms for modeling HAT. Similar perceptual cycles are adopted for the individual (including both human and AI) and the whole team, which is tailored to the unique requirements of the HAT context. ATSA emphasizes cohesive and effective HAT through structures and components, including teaming understanding, teaming control, and the world, as well as adhesive transactive part. We further propose several future research directions to expand on the distinctive contributions of ATSA and address the specific and pressing next steps.

Color Image Recovery Using Generalized Matrix Completion over Higher-Order Finite Dimensional Algebra

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent, called the "t-matrix" model, which incorporates a pixel neighborhood expansion strategy to characterize the local pixel constraints. This "t-matrix" model is then used to extend some commonly used matrix and tensor completion algorithms to their higher-order versions. We perform extensive experiments on various algorithms using simulated data and algorithms on simulated data and publicly available images and compare their performance. The results show that our generalized matrix completion model and the corresponding algorithm compare favorably with their lower-order tensor and conventional matrix counterparts.

ASCON: Anatomy-aware Supervised Contrastive Learning Framework for Low-dose CT Denoising

While various deep learning methods have been proposed for low-dose computed tomography (CT) denoising, most of them leverage the normal-dose CT images as the ground-truth to supervise the denoising process. These methods typically ignore the inherent correlation within a single CT image, especially the anatomical semantics of human tissues, and lack the interpretability on the denoising process. In this paper, we propose a novel Anatomy-aware Supervised CONtrastive learning framework, termed ASCON, which can explore the anatomical semantics for low-dose CT denoising while providing anatomical interpretability. The proposed ASCON consists of two novel designs: an efficient self-attention-based U-Net (ESAU-Net) and a multi-scale anatomical contrastive network (MAC-Net). First, to better capture global-local interactions and adapt to the high-resolution input, an efficient ESAU-Net is introduced by using a channel-wise self-attention mechanism. Second, MAC-Net incorporates a patch-wise non-contrastive module to capture inherent anatomical information and a pixel-wise contrastive module to maintain intrinsic anatomical consistency. Extensive experimental results on two public low-dose CT denoising datasets demonstrate superior performance of ASCON over state-of-the-art models. Remarkably, our ASCON provides anatomical interpretability for low-dose CT denoising for the first time. Source code is available at https://github.com/hao1635/ASCON.

CoreDiff: Contextual Error-Modulated Generalized Diffusion Model for Low-Dose CT Denoising and Generalization

Low-dose computed tomography (CT) images suffer from noise and artifacts due to photon starvation and electronic noise. Recently, some works have attempted to use diffusion models to address the over-smoothness and training instability encountered by previous deep-learning-based denoising models. However, diffusion models suffer from long inference times due to the large number of sampling steps involved. Very recently, cold diffusion model generalizes classical diffusion models and has greater flexibility. Inspired by the cold diffusion, this paper presents a novel COntextual eRror-modulated gEneralized Diffusion model for low-dose CT (LDCT) denoising, termed CoreDiff. First, CoreDiff utilizes LDCT images to displace the random Gaussian noise and employs a novel mean-preserving degradation operator to mimic the physical process of CT degradation, significantly reducing sampling steps thanks to the informative LDCT images as the starting point of the sampling process. Second, to alleviate the error accumulation problem caused by the imperfect restoration operator in the sampling process, we propose a novel ContextuaL Error-modulAted Restoration Network (CLEAR-Net), which can leverage contextual information to constrain the sampling process from structural distortion and modulate time step embedding features for better alignment with the input at the next time step. Third, to rapidly generalize to a new, unseen dose level with as few resources as possible, we devise a one-shot learning framework to make CoreDiff generalize faster and better using only a single LDCT image (un)paired with NDCT. Extensive experimental results on two datasets demonstrate that our CoreDiff outperforms competing methods in denoising and generalization performance, with a clinically acceptable inference time.

ConstGCN: Constrained Transmission-based Graph Convolutional Networks for Document-level Relation Extraction

Document-level relation extraction with graph neural networks faces a fundamental graph construction gap between training and inference - the golden graph structure only available during training, which causes that most methods adopt heuristic or syntactic rules to construct a prior graph as a pseudo proxy. In this paper, we propose $\textbf{ConstGCN}$, a novel graph convolutional network which performs knowledge-based information propagation between entities along with all specific relation spaces without any prior graph construction. Specifically, it updates the entity representation by aggregating information from all other entities along with each relation space, thus modeling the relation-aware spatial information. To control the information flow passing through the indeterminate relation spaces, we propose to constrain the propagation using transmitting scores learned from the Noise Contrastive Estimation between fact triples. Experimental results show that our method outperforms the previous state-of-the-art (SOTA) approaches on the DocRE dataset.

FD-MAR: Fourier Dual-domain Network for CT Metal Artifact Reduction

The presence of high-density objects such as metal implants and dental fillings can introduce severely streak-like artifacts in computed tomography (CT) images, greatly limiting subsequent diagnosis. Although various deep neural networks-based methods have been proposed for metal artifact reduction (MAR), they usually suffer from poor performance due to limited exploitation of global context in the sinogram domain, secondary artifacts introduced in the image domain, and the requirement of precise metal masks. To address these issues, this paper explores fast Fourier convolution for MAR in both sinogram and image domains, and proposes a Fourier dual-domain network for MAR, termed FD-MAR. Specifically, we first propose a Fourier sinogram restoration network, which can leverage sinogram-wide receptive context to fill in the metal-corrupted region from uncorrupted region and, hence, is robust to the metal trace. Second, we propose a Fourier refinement network in the image domain, which can refine the reconstructed images in a local-to-global manner by exploring image-wide context information. As a result, the proposed FD-MAR can explore the sinogram- and image-wide receptive fields for MAR. By optimizing FD-MAR with a composite loss function, extensive experimental results demonstrate the superiority of the proposed FD-MAR over the state-of-the-art MAR methods in terms of quantitative metrics and visual comparison. Notably, FD-MAR does not require precise metal masks, which is of great importance in clinical routine.

PETRv2: A Unified Framework for 3D Perception from Multi-Camera Images

In this paper, we propose PETRv2, a unified framework for 3D perception from multi-view images. Based on PETR, PETRv2 explores the effectiveness of temporal modeling, which utilizes the temporal information of previous frames to boost 3D object detection. More specifically, we extend the 3D position embedding (3D PE) in PETR for temporal modeling. The 3D PE achieves the temporal alignment on object position of different frames. A feature-guided position encoder is further introduced to improve the data adaptability of 3D PE. To support for high-quality BEV segmentation, PETRv2 provides a simply yet effective solution by adding a set of segmentation queries. Each segmentation query is responsible for segmenting one specific patch of BEV map. PETRv2 achieves state-of-the-art performance on 3D object detection and BEV segmentation. Detailed robustness analysis is also conducted on PETR framework. We hope PETRv2 can serve as a unified framework for 3D perception.

Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra

Low-rank approximation of images via singular value decomposition is well-received in the era of big data. However, singular value decomposition (SVD) is only for order-two data, i.e., matrices. It is necessary to flatten a higher order input into a matrix or break it into a series of order-two slices to tackle higher order data such as multispectral images and videos with the SVD. Higher order singular value decomposition (HOSVD) extends the SVD and can approximate higher order data using sums of a few rank-one components. We consider the problem of generalizing HOSVD over a finite dimensional commutative algebra. This algebra, referred to as a t-algebra, generalizes the field of complex numbers. The elements of the algebra, called t-scalars, are fix-sized arrays of complex numbers. One can generalize matrices and tensors over t-scalars and then extend many canonical matrix and tensor algorithms, including HOSVD, to obtain higher-performance versions. The generalization of HOSVD is called THOSVD. Its performance of approximating multi-way data can be further improved by an alternating algorithm. THOSVD also unifies a wide range of principal component analysis algorithms. To exploit the potential of generalized algorithms using t-scalars for approximating images, we use a pixel neighborhood strategy to convert each pixel to "deeper-order" t-scalar. Experiments on publicly available images show that the generalized algorithm over t-scalars, namely THOSVD, compares favorably with its canonical counterparts.