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Generalized Category Discovery (GCD) aims to classify both base and novel images using labeled base data. However, current approaches inadequately address the intrinsic optimization of the co-occurrence matrix $\bar{A}$ based on cosine similarity, failing to achieve zero base-novel regions and adequate sparsity in base and novel domains. To address these deficiencies, we propose a Non-Negative Generalized Category Discovery (NN-GCD) framework. It employs Symmetric Non-negative Matrix Factorization (SNMF) as a mathematical medium to prove the equivalence of optimal K-means with optimal SNMF, and the equivalence of SNMF solver with non-negative contrastive learning (NCL) optimization. Utilizing these theoretical equivalences, it reframes the optimization of $\bar{A}$ and K-means clustering as an NCL optimization problem. Moreover, to satisfy the non-negative constraints and make a GCD model converge to a near-optimal region, we propose a GELU activation function and an NMF NCE loss. To transition $\bar{A}$ from a suboptimal state to the desired $\bar{A}^*$, we introduce a hybrid sparse regularization approach to impose sparsity constraints. Experimental results show NN-GCD outperforms state-of-the-art methods on GCD benchmarks, achieving an average accuracy of 66.1\% on the Semantic Shift Benchmark, surpassing prior counterparts by 4.7\%., Comment: 13 pages, 8 figures

Deep learning models have become pivotal in the field of video processing and is increasingly critical in practical applications such as autonomous driving and object detection. Although Vision Transformers (ViTs) have demonstrated their power, Convolutional Neural Networks (CNNs) remain a highly efficient and high-performance choice for feature extraction and encoding. However, the intensive computational demands of convolution operations hinder its broader adoption as a video encoder. Given the inherent temporal continuity in video frames, changes between consecutive frames are minimal, allowing for the skipping of redundant computations. This technique, which we term as Diff Computation, presents two primary challenges. First, Diff Computation requires to cache intermediate feature maps to ensure the correctness of non-linear computations, leading to significant memory consumption. Second, the imbalance of sparsity among layers, introduced by Diff Computation, incurs accuracy degradation. To address these issues, we propose a memory-efficient scheduling method to eliminate memory overhead and an online adjustment mechanism to minimize accuracy degradation. We integrate these techniques into our framework, SparseTem, to seamlessly support various CNN-based video encoders. SparseTem achieves speedup of 1.79x for EfficientDet and 4.72x for CRNN, with minimal accuracy drop and no additional memory overhead. Extensive experimental results demonstrate that SparseTem sets a new state-of-the-art by effectively utilizing temporal continuity to accelerate CNN-based video encoders., Comment: 9 pages, 13 figures

Recent studies have unveiled new possibilities for discovering intrinsic quantum phases that are unique to open systems, including phases with average symmetry-protected topological (ASPT) order and strong-to-weak spontaneous symmetry breaking (SWSSB) order in systems with global symmetry. In this work, we propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders. This new phase is absent from prior studies and cannot exist in conventional closed systems. Using the recently developed imaginary-Lindbladian formalism, we explore the phase diagram of a one-dimensional open system with $\mathbb{Z}_2^{\sigma}\times \mathbb{Z}_2^{\tau}$ symmetry. We identify universal critical behaviors along each critical line and observe the emergence of an intermediate phase that completely breaks the $\mathbb{Z}_2^{\sigma}$ symmetry, leading to the formation of two triple points in the phase diagram. These two triple points are topologically distinct and connected by a domain-wall decoration duality map. Our results promote the establishment of a complete classification for quantum phases in open systems with various symmetry conditions., Comment: 10 pages, 5 figures

Edge Intelligence (EI) has been instrumental in delivering real-time, localized services by leveraging the computational capabilities of edge networks. The integration of Large Language Models (LLMs) empowers EI to evolve into the next stage: Edge General Intelligence (EGI), enabling more adaptive and versatile applications that require advanced understanding and reasoning capabilities. However, systematic exploration in this area remains insufficient. This survey delineates the distinctions between EGI and traditional EI, categorizing LLM-empowered EGI into three conceptual systems: centralized, hybrid, and decentralized. For each system, we detail the framework designs and review existing implementations. Furthermore, we evaluate the performance and throughput of various Small Language Models (SLMs) that are more suitable for development on edge devices. This survey provides researchers with a comprehensive vision of EGI, offering insights into its vast potential and establishing a foundation for future advancements in this rapidly evolving field.

Large Language Models (LLMs) often suffer from catastrophic forgetting when learning multiple tasks sequentially, making continual learning (CL) essential for their dynamic deployment. Existing state-of-the-art (SOTA) methods, such as O-LoRA, typically focus on constructing orthogonality tasks to decouple parameter interdependence from various domains.In this paper, we reveal that building non-collision parameters is a more critical factor in addressing CL challenges. Our theoretical and experimental analyses demonstrate that non-collision parameters can provide better task orthogonality, which is a sufficient but unnecessary condition. Furthermore, knowledge from multiple domains will be preserved in non-collision parameter subspaces, making it more difficult to forget previously seen data. Leveraging this insight, we propose Non-collision Low-Rank Adaptation (N-LoRA), a simple yet effective approach leveraging low collision rates to enhance CL in LLMs. Experimental results on multiple CL benchmarks indicate that N-LoRA achieves superior performance (+2.9), higher task orthogonality (*4.1 times), and lower parameter collision (*58.1 times) than SOTA methods.

Proximity graphs (PG) have gained increasing popularity as the state-of-the-art (SOTA) solutions to $k$-approximate nearest neighbor ($k$-ANN) search on high-dimensional data, which serves as a fundamental function in various fields, e.g. information retrieval and retrieval-augmented generation~(RAG). Although PG-based approaches have the best $k$-ANN search performance, their index construction cost is superlinear to the number of points, since they have to identify close neighbors for each point to establish the edges. Such superlinear cost substantially limits their scalability in the era of big data. Hence, the goal of this paper is to accelerate the construction of PG-based methods without compromising their $k$-ANN search performance. To achieve this goal, two mainstream categories of PG are revisited: relative neighborhood graph (RNG) and navigable small world graph (NSWG). By revisiting their construction process, we find the issues of construction efficiency. To address these issues, we propose a new construction framework with a novel pruning strategy for edge selection, which accelerates RNG construction while keeping its $k$-ANN search performance. Then, we integrate this framework into NSWG construction to enhance both the construction efficiency and $k$-ANN search performance. Moreover, extensive experiments are conducted to validate our construction framework for both RNG and NSWG. The results demonstrate that it significantly reduces the PG construction cost, achieving up to 5.6x speedup while not compromising the $k$-ANN search performance.

We present a set of novel accelerated gradient flow methods for solving quadratic energy minimization problems with nonconvex constraints. Our algorithms are built on novel evolutionary equations that combine projection-free approximations for nonconvex constraints with first- and higher-order backward differentiation formulas (BDFs) for {artificial} temporal derivatives. We focus on examining the asymptotic consistency of constraints achieved by the accelerated gradient flow using the BDF schemes. Both unconditional and conditional high-order estimates for constraint violations in these schemes are established. Numerical results not only validate our theoretical findings but also demonstrate that the proposed methods outperform existing gradient flow approaches in terms of both efficiency and accuracy.

Open-vocabulary video visual relationship detection aims to expand video visual relationship detection beyond annotated categories by detecting unseen relationships between both seen and unseen objects in videos. Existing methods usually use trajectory detectors trained on closed datasets to detect object trajectories, and then feed these trajectories into large-scale pre-trained vision-language models to achieve open-vocabulary classification. Such heavy dependence on the pre-trained trajectory detectors limits their ability to generalize to novel object categories, leading to performance degradation. To address this challenge, we propose to unify object trajectory detection and relationship classification into an end-to-end open-vocabulary framework. Under this framework, we propose a relationship-aware open-vocabulary trajectory detector. It primarily consists of a query-based Transformer decoder, where the visual encoder of CLIP is distilled for frame-wise open-vocabulary object detection, and a trajectory associator. To exploit relationship context during trajectory detection, a relationship query is embedded into the Transformer decoder, and accordingly, an auxiliary relationship loss is designed to enable the decoder to perceive the relationships between objects explicitly. Moreover, we propose an open-vocabulary relationship classifier that leverages the rich semantic knowledge of CLIP to discover novel relationships. To adapt CLIP well to relationship classification, we design a multi-modal prompting method that employs spatio-temporal visual prompting for visual representation and vision-guided language prompting for language input. Extensive experiments on two public datasets, VidVRD and VidOR, demonstrate the effectiveness of our framework. Our framework is also applied to a more difficult cross-dataset scenario to further demonstrate its generalization ability.

We present a model-predictive control (MPC) framework for legged robots that avoids the singularities associated with common three-parameter attitude representations like Euler angles during large-angle rotations. Our method parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry. The derivation of our algorithm requires only elementary calculus and linear algebra, deliberately avoiding the abstraction and notation of Lie groups. We demonstrate the performance and computational efficiency of quaternion MPC in several experiments on quadruped and humanoid robots.

Group activities are important behaviors in human society, providing personalized recommendations for groups is referred to as the group recommendation task. Existing methods can usually be categorized into two strategies to infer group preferences: 1) determining group preferences by aggregating members' personalized preferences, and 2) inferring group consensus by capturing group members' coherent decisions after common compromises. However, the former would suffer from the lack of group-level considerations, and the latter overlooks the fine-grained preferences of individual users. To this end, we propose a novel group recommendation method AlignGroup, which focuses on both group consensus and individual preferences of group members to infer the group decision-making. Specifically, AlignGroup explores group consensus through a well-designed hypergraph neural network that efficiently learns intra- and inter-group relationships. Moreover, AlignGroup innovatively utilizes a self-supervised alignment task to capture fine-grained group decision-making by aligning the group consensus with members' common preferences. Extensive experiments on two real-world datasets validate that our AlignGroup outperforms the state-of-the-art on both the group recommendation task and the user recommendation task, as well as outperforms the efficiency of most baselines., Comment: 10 pages, accepted by CIKM 2024

Knowledge Distillation (KD) is a powerful approach for compressing a large model into a smaller, more efficient model, particularly beneficial for latency-sensitive applications like recommender systems. However, current KD research predominantly focuses on Computer Vision (CV) and NLP tasks, overlooking unique data characteristics and challenges inherent to recommender systems. This paper addresses these overlooked challenges, specifically: (1) mitigating data distribution shifts between teacher and student models, (2) efficiently identifying optimal teacher configurations within time and budgetary constraints, and (3) enabling computationally efficient and rapid sharing of teacher labels to support multiple students. We present a robust KD system developed and rigorously evaluated on multiple large-scale personalized video recommendation systems within Google. Our live experiment results demonstrate significant improvements in student model performance while ensuring consistent and reliable generation of high quality teacher labels from a continuous data stream of data.

Adversarial scenario generation is crucial for autonomous driving testing because it can efficiently simulate various challenge and complex traffic conditions. However, it is difficult to control current existing methods to generate desired scenarios, such as the ones with different conflict levels. Therefore, this paper proposes a data-driven quantitative method to represent scenario difficulty. Compared with rule-based discrete scenario difficulty representation method, the proposed algorithm can achieve continuous difficulty representation. Specifically, the environment agent is introduced, and a reinforcement learning method combined with mechanism knowledge is constructed for policy search to obtain an agent with adversarial behavior. The model parameters of the environment agent at different stages in the training process are extracted to construct a policy group, and then the agents with different adversarial intensity are obtained, which are used to realize data generation in different difficulty scenarios through the simulation environment. Finally, a data-driven scenario difficulty quantitative representation model is constructed, which is used to output the environment agent policy under different difficulties. The result analysis shows that the proposed algorithm can generate reasonable and interpretable scenarios with high discrimination, and can provide quantifiable difficulty representation without any expert logic rule design. The video link is https://www.youtube.com/watch?v=GceGdqAm9Ys.

Autonomous driving vehicles with self-learning capabilities are expected to evolve in complex environments to improve their ability to cope with different scenarios. However, most self-learning algorithms suffer from low learning efficiency and lacking safety, which limits their applications. This paper proposes a safety-oriented self-learning algorithm for autonomous driving, which focuses on how to achieve evolution from a basic model. Specifically, a basic model based on the transformer encoder is designed to extract and output policy features from a small number of demonstration trajectories. To improve the learning efficiency, a policy mixed approach is developed. The basic model provides initial values to improve exploration efficiency, and the self-learning algorithm enhances the adaptability and generalization of the model, enabling continuous improvement without external intervention. Finally, an actor approximator based on receding horizon optimization is designed considering the constraints of the environmental input to ensure safety. The proposed method is verified in a challenging mixed traffic environment with pedestrians and vehicles. Simulation and real-vehicle test results show that the proposed method can safely and efficiently learn appropriate autonomous driving behaviors. Compared reinforcement learning and behavior cloning methods, it can achieve comprehensive improvement in learning efficiency and performance under the premise of ensuring safety.

Autonomous vehicles with a self-evolving ability are expected to cope with unknown scenarios in the real-world environment. Take advantage of trial and error mechanism, reinforcement learning is able to self evolve by learning the optimal policy, and it is particularly well suitable for solving decision-making problems. However, reinforcement learning suffers from safety issues and low learning efficiency, especially in the continuous action space. Therefore, the motivation of this paper is to address the above problem by proposing a hybrid Mechanism-Experience-Learning augmented approach. Specifically, to realize the efficient self-evolution, the driving tendency by analogy with human driving experience is proposed to reduce the search space of the autonomous driving problem, while the constrained optimization problem based on a mechanistic model is designed to ensure safety during the self-evolving process. Experimental results show that the proposed method is capable of generating safe and reasonable actions in various complex scenarios, improving the performance of the autonomous driving system. Compared to conventional reinforcement learning, the safety and efficiency of the proposed algorithm are greatly improved. The training process is collision-free, and the training time is equivalent to less than 10 minutes in the real world.

Autonomous driving systems with self-evolution capabilities have the potential to independently evolve in complex and open environments, allowing to handle more unknown scenarios. However, as a result of the safety-performance trade-off mechanism of evolutionary algorithms, it is difficult to ensure safe exploration without sacrificing the improvement ability. This problem is especially prominent in dynamic traffic scenarios. Therefore, this paper proposes a safe self-evolution algorithm for autonomous driving based on data-driven risk quantification model. Specifically, a risk quantification model based on the attention mechanism is proposed by modeling the way humans perceive risks during driving, with the idea of achieving safety situation estimation of the surrounding environment through a data-driven approach. To prevent the impact of over-conservative safety guarding policies on the self-evolution capability of the algorithm, a safety-evolutionary decision-control integration algorithm with adjustable safety limits is proposed, and the proposed risk quantization model is integrated into it. Simulation and real-vehicle experiments results illustrate the effectiveness of the proposed method. The results show that the proposed algorithm can generate safe and reasonable actions in a variety of complex scenarios and guarantee safety without losing the evolutionary potential of learning-based autonomous driving systems.

This paper focuses on target-oriented grasping in occluded scenes, where the target object is specified by a binary mask and the goal is to grasp the target object with as few robotic manipulations as possible. Most existing methods rely on a push-grasping synergy to complete this task. To deliver a more powerful target-oriented grasping pipeline, we present MPGNet, a three-branch network for learning a synergy between moving, pushing, and grasping actions. We also propose a multi-stage training strategy to train the MPGNet which contains three policy networks corresponding to the three actions. The effectiveness of our method is demonstrated via both simulated and real-world experiments., Comment: Accepted to IROS 2024

We study the task of language instruction-guided robotic manipulation, in which an embodied robot is supposed to manipulate the target objects based on the language instructions. In previous studies, the predicted manipulation regions of the target object typically do not change with specification from the language instructions, which means that the language perception and manipulation prediction are separate. However, in human behavioral patterns, the manipulation regions of the same object will change for different language instructions. In this paper, we propose Instruction-Guided Affordance Net (IGANet) for predicting affordance maps of instruction-guided robotic manipulation tasks by utilizing powerful priors from vision and language encoders pre-trained on large-scale datasets. We develop a Vison-Language-Models(VLMs)-based data augmentation pipeline, which can generate a large amount of data automatically for model training. Besides, with the help of Large-Language-Models(LLMs), actions can be effectively executed to finish the tasks defined by instructions. A series of real-world experiments revealed that our method can achieve better performance with generated data. Moreover, our model can generalize better to scenarios with unseen objects and language instructions., Comment: Accepted to ICARM 2024

Inspired by recent experimental findings, we investigate various scenarios of the doped Hubbard model with impurity potentials. We calculate the lattice Green's function in a finite-size cluster and then map it to the continuum real space, which allows for a direct comparison with scanning-tunneling-microscopy measurements on the local density of states. Our simulations successfully reproduce experimental data, including the characteristic stripe- and ladder-shaped structures observed in cuprate systems. Moreover, our results establish a connection between previous numerical findings on stripe-ordered ground states and experimental observations, thereby providing new insights into doped Mott insulators., Comment: 11 pages, 7 figures

Recent studies have found that all three materials within the vanadium-based kagome superconductors ($\textit{A}$V$_{3}$Sb$_{5}$, $\textit{A}$ = K, Cs, Rb) exhibit time-reversal symmetry-breaking behaviors in the superconducting states. Among the three, the Josephson junctions structured Nb/K$_{1-x}$V$_{3}$Sb$_{5}$/Nb and RbV$_{3}$Sb$_{5}$ show magnetic hysteresis below the superconducting transition temperature. CsV$_{3}$Sb$_{5}$ exhibits a zero-field superconducting diode effect, meaning the magnitude of the positive and negative superconducting critical currents are different. We first discuss the similarities and differences among the three above-mentioned experiments. Then, we discuss the possible mechanisms responsible for the unconventional superconducting transport phenomena: such as a chiral superconducting order parameter, and chiral pair density waves arising from the intertwining of the chiral charge order with superconductivity.

The rapid advancement of blockchain platforms has significantly accelerated the growth of decentralized applications (DApps). Similar to traditional applications, DApps integrate front-end descriptions that showcase their features to attract users, and back-end smart contracts for executing their business logic. However, inconsistencies between the features promoted in front-end descriptions and those actually implemented in the contract can confuse users and undermine DApps's trustworthiness. In this paper, we first conducted an empirical study to identify seven types of inconsistencies, each exemplified by a real-world DApp. Furthermore, we introduce HYPERION, an approach designed to automatically identify inconsistencies between front-end descriptions and back-end code implementation in DApps. This method leverages a fine-tuned large language model LLaMA2 to analyze DApp descriptions and employs dataflow-guided symbolic execution for contract bytecode analysis. Finally, HYPERION reports the inconsistency based on predefined detection patterns. The experiment on our ground truth dataset consisting of 54 DApps shows that HYPERION reaches 84.06% overall recall and 92.06% overall precision in reporting DApp inconsistencies. We also implement HYPERION to analyze 835 real-world DApps. The experimental results show that HYPERION discovers 459 real-world DApps containing at least one inconsistency., Comment: Accepted by ICSE 2025

The inference process for large language models is slow and memory-intensive, with one of the most critical bottlenecks being excessive Key-Value (KV) cache accesses. This paper introduces "Double Sparsity," a novel post-training sparse attention technique designed to alleviate this bottleneck by reducing KV cache access. Double Sparsity combines token sparsity, which focuses on utilizing only the important tokens for computing self-attention, with channel sparsity, an approach that uses important feature channels for identifying important tokens. Our key insight is that the pattern of channel sparsity is relatively static, allowing us to use offline calibration to make it efficient at runtime, thereby enabling accurate and efficient identification of important tokens. Moreover, this method can be combined with offloading to achieve significant memory usage reduction. Experimental results demonstrate that Double Sparsity can achieve $\frac{1}{16}$ token and channel sparsity with minimal impact on accuracy across various tasks, including wiki-2 perplexity, key-value retrieval, and long context benchmarks with models including Llama-2-7B, Llama-2-70B, and Mixtral-8x7B. It brings up to a 14.1$\times$ acceleration in attention operations and a 1.9$\times$ improvement in end-to-end inference on GPUs. With offloading, it achieves a decoding speed acceleration of 16.3$\times$ compared to state-of-the-art solutions at a sequence length of 256K. Our code is publicly available at https://github.com/andy-yang-1/DoubleSparse.

This study delves into the concept of quantum phases in open quantum systems, examining the shortcomings of existing approaches that focus on steady states of Lindbladians and highlighting their limitations in capturing key phase transitions. In contrast to these methods, we introduce the concept of imaginary-time Lindbladian evolution as an alternative framework. This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator. We find that, in addition to all pure gapped ground states, the Gibbs state of a stabilizer Hamiltonian at any finite temperature can also be characterized by our scheme, demonstrated through explicit construction. To illustrate the effectiveness of this framework, we apply it to investigate the phase diagram for open systems with $\mathbb{Z}_{2}^{\sigma} \times \mathbb{Z}_{2}^{\tau}$ symmetry, including cases with nontrivial average symmetry protected topological order or spontaneous symmetry breaking order. Our findings demonstrate universal properties at quantum criticality, such as nonanalytic behaviors of steady-state observables, divergence of correlation lengths, and closing of the imaginary-Liouville gap. These results advance our understanding of quantum phase transitions in open quantum systems., Comment: 13 pages, 4 figures

With the widespread use of power electronic devices, modern distribution networks are turning into flexible distribution networks (FDNs), which have enhanced active and reactive power flexibility at the transmission-distribution-interface (TDI). However, owing to the stochastics and volatility of distributed generation, the flexibility can change in real time and can hardly be accurately captured using conventional discrete-time (DT) assessment methods. This paper first proposes the notion of continuous-time (CT) TDI active and reactive flexibility and establishes its mathematical model. This model comprehensively considers the flexible devices in the FDN and the impact of uncertainty of photovoltaic power generation and load. In particular, a novel direction-factor-based metric is proposed to model CT-TDI PQ flexibility. Moreover, an efficient solution method is designed to address the difficulties in handling the infinite dimension of CT model and the complexity of bi-objectivity from assessing both active and reactive flexibility to be assessed. The solution successfully transforms the infinite dimensional optimization into a finite dimensional problem and effectively explores the PQ plane in a parallel pattern. Case studies show that the method can more effectively assess the real-time TDI flexibility of an FDN relative to conventional DT counterparts, and also reveals the impact of the relevant factors, such as penetrations of flexible devices and levels of uncertainty.

A multitude of industries depend on accurate and reasonable tabular data augmentation for their business processes. Contemporary methodologies in generating tabular data revolve around utilizing Generative Adversarial Networks (GAN) or fine-tuning Large Language Models (LLM). However, GAN-based approaches are documented to produce samples with common-sense errors attributed to the absence of external knowledge. On the other hand, LLM-based methods exhibit a limited capacity to capture the disparities between synthesized and actual data distribution due to the absence of feedback from a discriminator during training. Furthermore, the decoding of LLM-based generation introduces gradient breakpoints, impeding the backpropagation of loss from a discriminator, thereby complicating the integration of these two approaches. To solve this challenge, we propose using proximal policy optimization (PPO) to apply GANs, guiding LLMs to enhance the probability distribution of tabular features. This approach enables the utilization of LLMs as generators for GANs in synthesizing tabular data. Our experiments demonstrate that PPO leads to an approximately 4\% improvement in the accuracy of models trained on synthetically generated data over state-of-the-art across three real-world datasets., Comment: The paper was accepted by findings of ACL 2024

Graph Collaborative Filtering (GCF) has achieved state-of-the-art performance for recommendation tasks. However, most GCF structures simplify the feature transformation and nonlinear operation during message passing in the graph convolution network (GCN). We revisit these two components and discover that a part of feature transformation and nonlinear operation during message passing in GCN can improve the representation of GCF, but increase the difficulty of training. In this work, we propose a simple and effective graph-based recommendation model called FourierKAN-GCF. Specifically, it utilizes a novel Fourier Kolmogorov-Arnold Network (KAN) to replace the multilayer perceptron (MLP) as a part of the feature transformation during message passing in GCN, which improves the representation power of GCF and is easy to train. We further employ message dropout and node dropout strategies to improve the representation power and robustness of the model. Extensive experiments on two public datasets demonstrate the superiority of FourierKAN-GCF over most state-of-the-art methods. The implementation code is available at https://github.com/Jinfeng-Xu/FKAN-GCF.

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature language processing tasks. One of the key factors that contribute to the success of these networks is that spherical and hyperbolic manifolds have the rich algebraic structures of gyrogroups and gyrovector spaces. This enables principled and effective generalizations of the most successful DNNs to these manifolds. Recently, some works have shown that many concepts in the theory of gyrogroups and gyrovector spaces can also be generalized to matrix manifolds such as Symmetric Positive Definite (SPD) and Grassmann manifolds. As a result, some building blocks for SPD and Grassmann neural networks, e.g., isometric models and multinomial logistic regression (MLR) can be derived in a way that is fully analogous to their spherical and hyperbolic counterparts. Building upon these works, we design fully-connected (FC) and convolutional layers for SPD neural networks. We also develop MLR on Symmetric Positive Semi-definite (SPSD) manifolds, and propose a method for performing backpropagation with the Grassmann logarithmic map in the projector perspective. We demonstrate the effectiveness of the proposed approach in the human action recognition and node classification tasks.

High-accuracy microwave sensing is widely demanded in various fields, ranging from cosmology to microwave quantum technology. Quantum receivers based on inorganic solid-state spin systems are promising candidates for such purpose because of the stability and compatibility, but their best sensitivity is currently limited to a few pT/$\sqrt{\rm{Hz}}$. Here, by utilising an enhanced readout scheme with the state-of-the-art solid-state maser technology, we develop a robust microwave quantum receiver functioned by organic molecular spins at ambient conditions. Owing to the maser amplification, the sensitivity of the receiver achieves 6.14 $\pm$ 0.17 fT/$\sqrt{\rm{Hz}}$ which exceeds three orders of magnitude than that of the inorganic solid-state quantum receivers. The heterodyne detection without additional local oscillators improves bandwidth of the receiver and allows frequency detection. The scheme can be extended to other solid-state spin systems without complicated control pulses and thus enables practical applications such as electron spin resonance spectroscopy, dark matter searches, and astronomical observations., Comment: 10 pages, 4 figures

The physical nature of pseudogap phase is one of the most important and intriguing problems towards understanding the key mechanism of high temperature superconductivity in cuprates. Theoretically, the square-lattice $t$-$J$ model is widely believed to be the simplest toy model that captures the essential physics of cuprate superconductors. We employ the Grassmann tensor product state approach to investigate uniform states in the underdoped ($\delta \lesssim 0.1$) region. In addition to the previously known uniform $d$-wave state, we discover a strongly fluctuating pair density wave (PDW) state with wave vector $Q = (\pi, \pi)$. This fluctuating PDW state weakly breaks the $C_4$ rotational symmetry of the square lattice and has a lower or comparable energy to the $d$-wave state (depending on doping and the $t/J$ ratio), making it a promising candidate state for describing the pseudogap phase., Comment: 10 pages, 13 figures, references added