In this paper, we employ Bayesian optimization to concurrently explore the optimal values for both the shape parameter and the radius in the partition of unity interpolation using radial basis functions. Bayesian optimization is a probabilistic, iterative approach that models the error function through a progressively self-updated Gaussian process. Meanwhile, the partition of unity approach harnesses a meshfree method, allowing us to significantly reduce computational expenses, particularly when considering a substantial number of scattered data points. This reduction in computational cost is achieved by decomposing the entire domain into several smaller subdomains, each of them with a variable radius. We provide an estimation of the complexity of our algorithm and carry out numerical experiments to illustrate the effectiveness of our approach, dealing with test and real-world datasets.
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We consider the optimization problem associated with fitting two-layer ReLU networks with respect to the squared loss, where labels are assumed to be generated by a target network. Focusing first on standard Gaussian inputs, we show that the structure of spurious local minima detected by stochastic gradient descent (SGD) is, in a well-defined sense, the \emph{least loss of symmetry} with respect to the target weights. A closer look at the analysis indicates that this principle of least symmetry breaking may apply to a broader range of settings. Motivated by this, we conduct a series of experiments which corroborate this hypothesis for different classes of non-isotropic non-product distributions, smooth activation functions and networks with a few layers.
Recent research has extended beyond assessing the performance of Large Language Models (LLMs) to examining their characteristics from a psychological standpoint, acknowledging the necessity of understanding their behavioral characteristics. The administration of personality tests to LLMs has emerged as a noteworthy area in this context. However, the suitability of employing psychological scales, initially devised for humans, on LLMs is a matter of ongoing debate. Our study aims to determine the reliability of applying personality assessments to LLMs, explicitly investigating whether LLMs demonstrate consistent personality traits. Analyzing responses under 2,500 settings reveals that gpt-3.5-turbo shows consistency in responses to the Big Five Inventory, indicating a high degree of reliability. Furthermore, our research explores the potential of gpt-3.5-turbo to emulate diverse personalities and represent various groups, which is a capability increasingly sought after in social sciences for substituting human participants with LLMs to reduce costs. Our findings reveal that LLMs have the potential to represent different personalities with specific prompt instructions. By shedding light on the personalization of LLMs, our study endeavors to pave the way for future explorations in this field. We have made our experimental results and the corresponding code openly accessible via //github.com/CUHK-ARISE/LLMPersonality.
The challenge of producing accurate statistics while respecting the privacy of the individuals in a sample is an important area of research. We study minimax lower bounds for classes of differentially private estimators. In particular, we show how to characterize the power of a statistical test under differential privacy in a plug-and-play fashion by solving an appropriate transport problem. With specific coupling constructions, this observation allows us to derive Le Cam-type and Fano-type inequalities not only for regular definitions of differential privacy but also for those based on Renyi divergence. We then proceed to illustrate our results on three simple, fully worked out examples. In particular, we show that the problem class has a huge importance on the provable degradation of utility due to privacy. In certain scenarios, we show that maintaining privacy results in a noticeable reduction in performance only when the level of privacy protection is very high. Conversely, for other problems, even a modest level of privacy protection can lead to a significant decrease in performance. Finally, we demonstrate that the DP-SGLD algorithm, a private convex solver, can be employed for maximum likelihood estimation with a high degree of confidence, as it provides near-optimal results with respect to both the size of the sample and the level of privacy protection. This algorithm is applicable to a broad range of parametric estimation procedures, including exponential families.
In this paper, we consider enumeration of geodesics on a polyhedron, where a geodesic means locally-shortest path between two points. Particularly, we consider the following preprocessing problem: given a point $s$ on a polyhedral surface and a positive real number $r$, to build a data structure that enables, for any point $t$ on the surface, to enumerate all geodesics from $s$ to $t$ whose length is less than $r$. First, we present a naive algorithm by removing the trimming process from the MMP algorithm (1987). Next, we present an improved algorithm which is practically more efficient on a non-convex polyhedron, in terms of preprocessing time and memory consumption. Moreover, we introduce a single-pair geodesic graph to succinctly encode a result of geodesic query. Lastly, we compare these naive and improved algorithms by some computer experiments.
In this paper, we propose a transmission mechanism for fluid antennas (FAs) enabled multiple-input multiple-output (MIMO) communication systems based on index modulation (IM), named FA-IM, which incorporates the principle of IM into FAs-assisted MIMO system to improve the spectral efficiency (SE) without increasing the hardware complexity. In FA-IM, the information bits are mapped not only to the modulation symbols, but also the index of FA position patterns. Additionally, the FA position pattern codebook is carefully designed to further enhance the system performance by maximizing the effective channel gains. Then, a low-complexity detector, referred to efficient sparse Bayesian detector, is proposed by exploiting the inherent sparsity of the transmitted FA-IM signal vectors. Finally, a closed-form expression for the upper bound on the average bit error probability (ABEP) is derived under the finite-path and infinite-path channel condition. Simulation results show that the proposed scheme is capable of improving the SE performance compared to the existing FAs-assisted MIMO and the fixed position antennas (FPAs)-assisted MIMO systems while obviating any additional hardware costs. It has also been shown that the proposed scheme outperforms the conventional FA-assisted MIMO scheme in terms of error performance under the same transmission rate.
In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and demonstrating their properties. We establish the uniqueness of derivations, drawing upon Rosens 1975 research, and verify the Church-Rosser theorem using Ehrigs and Kreowskis 1976 proof, thereby demonstrating the effectiveness of our formalisation approach. The paper details our methodology in employing Isabelle/HOL, including key design decisions that shaped the current iteration. We explore the technical complexities involved in applying higher-order logic, aiming to give readers an insightful perspective into the engaging aspects of working with an Interactive Theorem Prover. This work emphasizes the increasing importance of formal verification tools in clarifying complex mathematical concepts.
This paper proposes an iterative detection and decoding (IDD) scheme and an approach to improve the selection of access points (APs) in uplink cell-free massive multiple-antenna systems. A cost-effective scheme for selection of APs based on local log-likelihood ratios (LLRs) is developed that provides sufficient statistics to the central processing unit and selects which APs should be considered for each user. {Numerical results show that the proposed IDD scheme works very well and the proposed LLRs-based approach to select APs outperforms the existing techniques in terms of bit error rate and spectral efficiency while requiring a comparable fronthaul load.
In this paper, we present our finding that prepending a Task-Agnostic Prefix Prompt (TAPP) to the input improves the instruction-following ability of various Large Language Models (LLMs) during inference. TAPP is different from canonical prompts for LLMs in that it is a fixed prompt prepended to the beginning of every input regardless of the target task for zero-shot generalization. We observe that both base LLMs (i.e. not fine-tuned to follow instructions) and instruction-tuned models benefit from TAPP, resulting in 34.58% and 12.26% improvement on average, respectively. This implies that the instruction-following ability of LLMs can be improved during inference time with a fixed prompt constructed with simple heuristics. We hypothesize that TAPP assists language models to better estimate the output distribution by focusing more on the instruction of the target task during inference. In other words, such ability does not seem to be sufficiently activated in not only base LLMs but also many instruction-fine-tuned LLMs. All experiments are reproducible from //github.com/seonghyeonye/TAPP.
This paper aims to propose the quality of experience (QoE) models based on the expectation and/or the perception of 5G users to evaluate for mean opinion score (MOS) for real-time or interactive services/applications with high reliability. Therefore, Based on the fundamental QoE concept, the analytic hierarchy process (AHP) decision making technique has been applied.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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