We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence, and uniqueness statements of the corresponding variational methods. We also obtain optimal error estimates of the semidiscrete scheme in corresponding B\^ochner spaces. Finally, we construct a fully discrete scheme through a backward Euler discretization of the time derivative, and prove well-posedness statements for this fully discrete scheme. Our findings show that the mixed approach removes some theoretical impediments to analysis and is numerically easier to implement. We provide numerical simulations for the mixed formulation approach using $C^0$ Taylor-Hood finite elements on several domains. Our numerical results confirm that the algorithm has optimal convergence in accordance with the observed theoretical results.
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Recent thrilling progress in large-scale text-to-image (T2I) models has unlocked unprecedented synthesis quality of AI-generated content (AIGC) including image generation, 3D and video composition. Further, personalized techniques enable appealing customized production of a novel concept given only several images as reference. However, an intriguing problem persists: Is it possible to capture multiple, novel concepts from one single reference image? In this paper, we identify that existing approaches fail to preserve visual consistency with the reference image and eliminate cross-influence from concepts. To alleviate this, we propose an attention calibration mechanism to improve the concept-level understanding of the T2I model. Specifically, we first introduce new learnable modifiers bound with classes to capture attributes of multiple concepts. Then, the classes are separated and strengthened following the activation of the cross-attention operation, ensuring comprehensive and self-contained concepts. Additionally, we suppress the attention activation of different classes to mitigate mutual influence among concepts. Together, our proposed method, dubbed DisenDiff, can learn disentangled multiple concepts from one single image and produce novel customized images with learned concepts. We demonstrate that our method outperforms the current state of the art in both qualitative and quantitative evaluations. More importantly, our proposed techniques are compatible with LoRA and inpainting pipelines, enabling more interactive experiences.
Recent studies reveal a significant theoretical link between variational autoencoders (VAEs) and rate-distortion theory, notably in utilizing VAEs to estimate the theoretical upper bound of the information rate-distortion function of images. Such estimated theoretical bounds substantially exceed the performance of existing neural image codecs (NICs). To narrow this gap, we propose a theoretical bound-guided hierarchical VAE (BG-VAE) for NIC. The proposed BG-VAE leverages the theoretical bound to guide the NIC model towards enhanced performance. We implement the BG-VAE using Hierarchical VAEs and demonstrate its effectiveness through extensive experiments. Along with advanced neural network blocks, we provide a versatile, variable-rate NIC that outperforms existing methods when considering both rate-distortion performance and computational complexity. The code is available at BG-VAE.
In the context of emerging stacked intelligent metasurface (SIM)-based holographic MIMO (HMIMO) systems, a fundamental problem is to study the mutual information (MI) between transmitted and received signals to establish their capacity. However, direct optimization or analytical evaluation of the MI, particularly for discrete signaling, is often intractable. To address this challenge, we adopt the channel cutoff rate (CR) as an alternative optimization metric for the MI maximization. In this regard, we propose an alternating projected gradient method (APGM), which optimizes the CR of a SIM-based HMIMO system by adjusting signal precoding and the phase shifts across the transmit and receive SIMs in a layer-by-layer basis. Simulation results indicate that the proposed algorithm significantly enhances the CR, achieving substantial gains proportional to those observed for the corresponding MI. This justifies the effectiveness of using the channel CR for the MI optimization. Moreover, we demonstrate that the integration of digital precoding, even on a modest scale, has a significant impact on the ultimate performance of SIM-aided systems.
We generalize the problem of online submodular welfare maximization to incorporate a variety of new elements arising from reusability, stochastic rewards, combinatorial actions and similar features that have received significant attention in recent years. For our general formulation, we show that a non-adaptive Greedy algorithm achieves the highest possible competitive ratio against an adaptive offline benchmark in the adversarial arrival model and in the unknown IID stochastic arrival model. In addition to generalizing several previous results, this shows that, in general, adaptivity to stochastic rewards (and similar features) offers no theoretical (worst-case) benefits.
Reconfigurable intelligent surface (RIS)-assisted index modulation system schemes are considered a promising technology for sixth-generation (6G) wireless communication systems, which can enhance various system capabilities such as coverage and reliability. However, obtaining perfect channel state information (CSI) is challenging due to the lack of a radio frequency chain in RIS. In this paper, we investigate the RIS-assisted full-duplex (FD) two-way space shift keying (SSK) system under imperfect CSI, where the signal emissions are augmented by deploying RISs in the vicinity of two FD users. The maximum likelihood detector is utilized to recover the transmit antenna index. With this in mind, we derive closed-form average bit error probability (ABEP) expression based on the Gaussian-Chebyshev quadrature (GCQ) method and provide the upper bound and asymptotic ABEP expressions in the presence of channel estimation errors. To gain more insights, we also derive the outage probability and provide the throughput of the proposed scheme with imperfect CSI. The correctness of the analytical derivation results is confirmed via Monte Carlo simulations. It is demonstrated that increasing the number of elements of RIS can significantly improve the ABEP performance of the FD system over the half-duplex (HD) system. Furthermore, in the high SNR region, the ABEP performance of the FD system is better than that of the HD system.
Underlying data distributions of natural language, programming code, and mathematical symbols vary vastly, presenting a complex challenge for large language models (LLMs) that strive to achieve high performance across all three domains simultaneously. Achieving a very high level of proficiency for an LLM within a specific domain often requires extensive training with relevant corpora, which is typically accompanied by a sacrifice in performance in other domains. In this paper, we propose to fuse models that are already highly-specialized directly. The proposed fusing framework, UltraFuser, consists of three distinct specialists that are already sufficiently trained on language, coding, and mathematics. A token-level gating mechanism is introduced to blend the specialists' outputs. A two-stage training strategy accompanied by balanced sampling is designed to ensure stability. To effectively train the fused model, we further construct a high-quality supervised instruction tuning dataset, UltraChat 2, which includes text, code, and mathematical content. This dataset comprises approximately 300,000 instructions and covers a wide range of topics in each domain. Experiments show that our model could simultaneously achieve mastery of the three crucial domains.
The formation trajectory planning using complete graphs to model collaborative constraints becomes computationally intractable as the number of drones increases due to the curse of dimensionality. To tackle this issue, this paper presents a sparse graph construction method for formation planning to realize better efficiency-performance trade-off. Firstly, a sparsification mechanism for complete graphs is designed to ensure the global rigidity of sparsified graphs, which is a necessary condition for uniquely corresponding to a geometric shape. Secondly, a good sparse graph is constructed to preserve the main structural feature of complete graphs sufficiently. Since the graph-based formation constraint is described by Laplacian matrix, the sparse graph construction problem is equivalent to submatrix selection, which has combinatorial time complexity and needs a scoring metric. Via comparative simulations, the Max-Trace matrix-revealing metric shows the promising performance. The sparse graph is integrated into the formation planning. Simulation results with 72 drones in complex environments demonstrate that when preserving 30\% connection edges, our method has comparative formation error and recovery performance w.r.t. complete graphs. Meanwhile, the planning efficiency is improved by approximate an order of magnitude. Benchmark comparisons and ablation studies are conducted to fully validate the merits of our method.
Decision-Oriented Learning Using Differentiable Submodular Maximization for Multi-Robot Coordination
We present a differentiable, decision-oriented learning framework for cost prediction in a class of multi-robot decision-making problems, in which the robots need to trade off the task performance with the costs of taking actions when they select actions to take. Specifically, we consider the cases where the task performance is measured by a known monotone submodular function (e.g., coverage, mutual information), and the cost of actions depends on the context (e.g., wind and terrain conditions). We need to learn a function that maps the context to the costs. Classically, we treat such a learning problem and the downstream decision-making problem as two decoupled problems, i.e., we first learn to predict the cost function without considering the downstream decision-making problem, and then use the learned function for predicting the cost and using it in the decision-making problem. However, the loss function used in learning a prediction function may not be aligned with the downstream decision-making. We propose a decision-oriented learning framework that incorporates the downstream task performance in the prediction phase via a differentiable optimization layer. The main computational challenge in such a framework is to make the combinatorial optimization, i.e., non-monotone submodular maximization, differentiable. This function is not naturally differentiable. We propose the Differentiable Cost Scaled Greedy algorithm (D-CSG), which is a continuous and differentiable relaxation of CSG. We demonstrate the efficacy of the proposed framework through numerical simulations. The results show that the proposed framework can result in better performance than the traditional two-stage approach.
Variational quantum algorithms are gaining attention as an early application of Noisy Intermediate-Scale Quantum (NISQ) devices. One of the main problems of variational methods lies in the phenomenon of Barren Plateaus, present in the optimization of variational parameters. Adding geometric inductive bias to the quantum models has been proposed as a potential solution to mitigate this problem, leading to a new field called Geometric Quantum Machine Learning. In this work, an equivariant architecture for variational quantum classifiers is introduced to create a label-invariant model for image classification with $C_4$ rotational label symmetry. The equivariant circuit is benchmarked against two different architectures, and it is experimentally observed that the geometric approach boosts the model's performance. Finally, a classical equivariant convolution operation is proposed to extend the quantum model for the processing of larger images, employing the resources available in NISQ devices.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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