The rate-distortion curve captures the fundamental tradeoff between compression length and resolution in lossy data compression. However, it conceals the underlying dynamics of optimal source encodings or test channels. We argue that these typically follow a piecewise smooth trajectory as the source information is compressed. These smooth dynamics are interrupted at bifurcations, where solutions change qualitatively. Sub-optimal test channels may collide or exchange optimality there, for example. There is typically a plethora of sub-optimal solutions, which stems from restrictions of the reproduction alphabet. We devise a family of algorithms that exploits the underlying dynamics to track a given test channel along the rate-distortion curve. To that end, we express implicit derivatives at the roots of a non-linear operator by higher derivative tensors. Providing closed-form formulae for the derivative tensors of Blahut's algorithm thus yields implicit derivatives of arbitrary order at a given test channel, thereby approximating others in its vicinity. Finally, our understanding of bifurcations guarantees the optimality of the root being traced, under mild assumptions, while allowing us to detect when our assumptions fail. Beyond the interest in rate distortion, this is an example of how understanding a problem's bifurcations can be translated to a numerical algorithm.
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Fast and precise beam alignment is crucial for high-quality data transmission in millimeter-wave (mmWave) communication systems, where large-scale antenna arrays are utilized to overcome the severe propagation loss. To tackle the challenging problem, we propose a novel deep learning-based hierarchical beam alignment method for both multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) systems, which learns two tiers of probing codebooks (PCs) and uses their measurements to predict the optimal beam in a coarse-to-fine search manner. Specifically, a hierarchical beam alignment network (HBAN) is developed for MISO systems, which first performs coarse channel measurement using a tier-1 PC, then selects a tier-2 PC for fine channel measurement, and finally predicts the optimal beam based on both coarse and fine measurements. The propounded HBAN is trained in two steps: the tier-1 PC and the tier-2 PC selector are first trained jointly, followed by the joint training of all the tier-2 PCs and beam predictors. Furthermore, an HBAN for MIMO systems is proposed to directly predict the optimal beam pair without performing beam alignment individually at the transmitter and receiver. Numerical results demonstrate that the proposed HBANs are superior to the state-of-art methods in both alignment accuracy and signaling overhead reduction.
Maintaining high efficiency and high precision are two fundamental challenges in UAV tracking due to the constraints of computing resources, battery capacity, and UAV maximum load. Discriminative correlation filters (DCF)-based trackers can yield high efficiency on a single CPU but with inferior precision. Lightweight Deep learning (DL)-based trackers can achieve a good balance between efficiency and precision but performance gains are limited by the compression rate. High compression rate often leads to poor discriminative representations. To this end, this paper aims to enhance the discriminative power of feature representations from a new feature-learning perspective. Specifically, we attempt to learn more disciminative representations with contrastive instances for UAV tracking in a simple yet effective manner, which not only requires no manual annotations but also allows for developing and deploying a lightweight model. We are the first to explore contrastive learning for UAV tracking. Extensive experiments on four UAV benchmarks, including UAV123@10fps, DTB70, UAVDT and VisDrone2018, show that the proposed DRCI tracker significantly outperforms state-of-the-art UAV tracking methods.
The rise in popularity of ChatGPT and GPT-4 has significantly accelerated the development of large models, leading to the creation of numerous impressive large language models(LLMs) and multimodal large language models (MLLMs). These cutting-edge models owe their remarkable performance to high-quality data. However, the details of the training data used in leading paradigms are often kept confidential. This lack of transparency, coupled with the scarcity of open-source data, impedes further developments within the community. As a response, this paper presents "Wan Juan", a large-scale multimodal dataset composed of both Chinese and English data, collected from a wide range of web sources. The dataset incorporates text, image-text, and video modalities, with a total volume exceeding 2TB. It was utilized in the training of InternLM, a model that demonstrated significant advantages in multi-dimensional evaluations when compared to models of a similar scale. All data can be accessed at //opendatalab.org.cn/WanJuan1.0.
Counting and sampling directed acyclic graphs from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper we show that these tasks can be performed in polynomial time, solving a long-standing open problem in this area. Our algorithms are effective and easily implementable. As we show in experiments, these breakthroughs make thought-to-be-infeasible strategies in active learning of causal structures and causal effect identification with regard to a Markov equivalence class practically applicable.
Graph-based kNN algorithms have garnered widespread popularity for machine learning tasks due to their simplicity and effectiveness. However, as factual data often inherit complex distributions, the conventional kNN graph's reliance on a unified k-value can hinder its performance. A crucial factor behind this challenge is the presence of ambiguous samples along decision boundaries that are inevitably more prone to incorrect classifications. To address the situation, we propose the Preferential Attached k-Nearest Neighbors Graph (paNNG), which adopts distribution-aware adaptive-k into graph construction. By incorporating distribution information as a cohesive entity, paNNG can significantly improve performance on ambiguous samples by "pulling" them towards their original classes and hence enhance overall generalization capability. Through rigorous evaluations on diverse datasets, paNNG outperforms state-of-the-art algorithms, showcasing its adaptability and efficacy across various real-world scenarios.
Spatial Manifestations of Order Reduction in Runge-Kutta Methods for Initial Boundary Value Problems
This paper studies the spatial manifestations of order reduction that occur when time-stepping initial-boundary-value problems (IBVPs) with high-order Runge-Kutta methods. For such IBVPs, geometric structures arise that do not have an analog in ODE IVPs: boundary layers appear, induced by a mismatch between the approximation error in the interior and at the boundaries. To understand those boundary layers, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers persist over many time steps. Based on this, two remedies to order reduction are studied: first, a new condition on the Butcher tableau, called weak stage order, that is compatible with diagonally implicit Runge-Kutta schemes; and second, the impact of modified boundary conditions on the boundary layer theory is analyzed.
Large Language Models (LLMs) hold immense potential to generate synthetic data of high quality and utility, which has numerous applications from downstream model training to practical data utilisation. However, contemporary models, despite their impressive capacities, consistently struggle to produce both coherent and diverse data. To address the coherency issue, we introduce contrastive expert guidance, where the difference between the logit distributions of fine-tuned and base language models is emphasised to ensure domain adherence. In order to ensure diversity, we utilise existing real and synthetic examples as negative prompts to the model. We deem this dual-pronged approach to logit reshaping as STEER: Semantic Text Enhancement via Embedding Repositioning. STEER operates at inference-time and systematically guides the LLMs to strike a balance between adherence to the data distribution (ensuring semantic fidelity) and deviation from prior synthetic examples or existing real datasets (ensuring diversity and authenticity). This delicate balancing act is achieved by dynamically moving towards or away from chosen representations in the latent space. STEER demonstrates improved performance over previous synthetic data generation techniques, exhibiting better balance between data diversity and coherency across three distinct tasks: hypothesis generation, toxic and non-toxic comment generation, and commonsense reasoning task generation. We demonstrate how STEER allows for fine-tuned control over the diversity-coherency trade-off via its hyperparameters, highlighting its versatility.
Conventional beamforming with fixed-position antenna (FPA) arrays has a fundamental trade-off between maximizing the signal power (array gain) over a desired direction and simultaneously minimizing the interference power over undesired directions. To overcome this limitation, this letter investigates the movable antenna (MA) array enhanced beamforming by exploiting the new degree of freedom (DoF) via antenna position optimization, in addition to the design of antenna weights. We show that by jointly optimizing the antenna positions vector (APV) and antenna weights vector (AWV) of a linear MA array, the full array gain can be achieved over the desired direction while null steering can be realized over all undesired directions, under certain numbers of MAs and null-steering directions. The optimal solutions for AWV and APV are derived in closed form, which reveal that the optimal AWV for MA arrays requires only the signal phase adjustment with a fixed amplitude. Numerical results validate our analytical solutions for MA array beamforming and show their superior performance to the conventional beamforming techniques with FPA arrays.
Linkage analysis has provided valuable insights to the GWAS studies, particularly in revealing that SNPs in linkage disequilibrium (LD) can jointly influence disease phenotypes. However, the potential of LD network data has often been overlooked or underutilized in the literature. In this paper, we propose a locally adaptive structure learning algorithm (LASLA) that provides a principled and generic framework for incorporating network data or multiple samples of auxiliary data from related source domains; possibly in different dimensions/structures and from diverse populations. LASLA employs a $p$-value weighting approach, utilizing structural insights to assign data-driven weights to individual test points. Theoretical analysis shows that LASLA can asymptotically control FDR with independent or weakly dependent primary statistics, and achieve higher power when the network data is informative. Efficiency again of LASLA is illustrated through various synthetic experiments and an application to T2D-associated SNP identification.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
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