This paper presents an approach to learning (deep) $n$D features equivariant under orthogonal transformations, utilizing hyperspheres and regular $n$-simplexes. Our main contributions are theoretical and tackle major challenges in geometric deep learning such as equivariance and invariance under geometric transformations. Namely, we enrich the recently developed theory of steerable 3D spherical neurons -- SO(3)-equivariant filter banks based on neurons with spherical decision surfaces -- by extending said neurons to $n$D, which we call deep equivariant hyperspheres, and enabling their multi-layer construction. Using synthetic and real-world data in $n$D, we experimentally verify our theoretical contributions and find that our approach is superior to the competing methods for benchmark datasets in all but one case, additionally demonstrating a better speed/performance trade-off in all but one other case.
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We present VOICE, a novel approach to science communication that connects large language models' (LLM) conversational capabilities with interactive exploratory visualization. VOICE introduces several innovative technical contributions that drive our conversational visualization framework. Our foundation is a pack-of-bots that can perform specific tasks, such as assigning tasks, extracting instructions, and generating coherent content. We employ fine-tuning and prompt engineering techniques to tailor bots' performance to their specific roles and accurately respond to user queries. Our interactive text-to-visualization method generates a flythrough sequence matching the content explanation. Besides, natural language interaction provides capabilities to navigate and manipulate the 3D models in real-time. The VOICE framework can receive arbitrary voice commands from the user and respond verbally, tightly coupled with corresponding visual representation with low latency and high accuracy. We demonstrate the effectiveness of our approach by applying it to the molecular visualization domain: analyzing three 3D molecular models with multi-scale and multi-instance attributes. We finally evaluate VOICE with the identified educational experts to show the potential of our approach. All supplemental materials are available at //osf.io/g7fbr.
This paper addresses the challenges of real-time, large-scale, and near-optimal multi-agent pathfinding (MAPF) through enhancements to the recently proposed LaCAM* algorithm. LaCAM* is a scalable search-based algorithm that guarantees the eventual finding of optimal solutions for cumulative transition costs. While it has demonstrated remarkable planning success rates, surpassing various state-of-the-art MAPF methods, its initial solution quality is far from optimal, and its convergence speed to the optimum is slow. To overcome these limitations, this paper introduces several improvement techniques, partly drawing inspiration from other MAPF methods. We provide empirical evidence that the fusion of these techniques significantly improves the solution quality of LaCAM*, thus further pushing the boundaries of MAPF algorithms.
Covariate shift is a common transfer learning scenario where the marginal distributions of input variables vary between source and target data while the conditional distribution of the output variable remains consistent. The existing notions describing differences between marginal distributions face limitations in handling scenarios with unbounded support, particularly when the target distribution has a heavier tail. To overcome these challenges, we introduce a new concept called density ratio exponent to quantify the relative decay rates of marginal distributions' tails under covariate shift. Furthermore, we propose the local k-nearest neighbour regressor for transfer learning, which adapts the number of nearest neighbours based on the marginal likelihood of each test sample. From a theoretical perspective, convergence rates with and without supervision information on the target domain are established. Those rates indicate that our estimator achieves faster convergence rates when the density ratio exponent satisfies certain conditions, highlighting the benefits of using density estimation for determining different numbers of nearest neighbours for each test sample. Our contributions enhance the understanding and applicability of transfer learning under covariate shift, especially in scenarios with unbounded support and heavy-tailed distributions.
Recent years have seen a surge of interest in the algorithmic estimation of stochastic entropy production (EP) from trajectory data via machine learning. A crucial element of such algorithms is the identification of a loss function whose minimization guarantees the accurate EP estimation. In this study, we show that there exists a host of loss functions, namely those implementing a variational representation of the $\alpha$-divergence, which can be used for the EP estimation. By fixing $\alpha$ to a value between $-1$ and $0$, the $\alpha$-NEEP (Neural Estimator for Entropy Production) exhibits a much more robust performance against strong nonequilibrium driving or slow dynamics, which adversely affects the existing method based on the Kullback-Leibler divergence ($\alpha = 0$). In particular, the choice of $\alpha = -0.5$ tends to yield the optimal results. To corroborate our findings, we present an exactly solvable simplification of the EP estimation problem, whose loss function landscape and stochastic properties give deeper intuition into the robustness of the $\alpha$-NEEP.
This paper introduces LogLead, a tool designed for efficient log analysis benchmarking. LogLead combines three essential steps in log processing: loading, enhancing, and anomaly detection. The tool leverages Polars, a high-speed DataFrame library. We currently have Loaders for eight systems that are publicly available (HDFS, Hadoop, BGL, Thunderbird, Spirit, Liberty, TrainTicket, and GC Webshop). We have multiple enhancers with three parsers (Drain, Spell, LenMa), Bert embedding creation and other log representation techniques like bag-of-words. LogLead integrates to five supervised and four unsupervised machine learning algorithms for anomaly detection from SKLearn. By integrating diverse datasets, log representation methods and anomaly detectors, LogLead facilitates comprehensive benchmarking in log analysis research. We show that log loading from raw file to dataframe is over 10x faster with LogLead compared to past solutions. We demonstrate roughly 2x improvement in Drain parsing speed by off-loading log message normalization to LogLead. Our brief benchmarking on HDFS indicates that log representations extending beyond the bag-of-words approach offer limited additional benefits. Tool URL: //github.com/EvoTestOps/LogLead
This paper presents exact formulas for the probability distribution function (PDF) and moment generating function (MGF) of the sum-product of statistically independent but not necessarily identically distributed (i.n.i.d.) Nakagami-$m$ random variables (RVs) in terms of Meijer's G-function. Additionally, exact series representations are also derived for the sum of double-Nakagami RVs, providing useful insights on the trade-off between accuracy and computational cost. Simple asymptotic analytical expressions are provided to gain further insight into the derived formula, and the achievable diversity order is obtained. The suggested statistical properties are proved to be a highly useful tool for modeling parallel cascaded Nakagami-$m$ fading channels. The application of these new results is illustrated by deriving exact expressions and simple tight upper bounds for the outage probability (OP) and average symbol error rate (ASER) of several binary and multilevel modulation signals in intelligent reflecting surfaces (IRSs)-assisted communication systems operating over Nakagami-$m$ fading channels. It is demonstrated that the new asymptotic expression is highly accurate and can be extended to encompass a wider range of scenarios. To validate the theoretical frameworks and formulations, Monte-Carlo simulation results are presented. Additionally, supplementary simulations are provided to compare the derived results with two common types of approximations available in the literature, namely the central limit theorem (CLT) and gamma distribution.
Graph learning architectures based on the k-dimensional Weisfeiler-Leman (k-WL) hierarchy offer a theoretically well-understood expressive power. However, such architectures often fail to deliver solid predictive performance on real-world tasks, limiting their practical impact. In contrast, global attention-based models such as graph transformers demonstrate strong performance in practice, but comparing their expressive power with the k-WL hierarchy remains challenging, particularly since these architectures rely on positional or structural encodings for their expressivity and predictive performance. To address this, we show that the recently proposed Edge Transformer, a global attention model operating on node pairs instead of nodes, has at least 3-WL expressive power. Empirically, we demonstrate that the Edge Transformer surpasses other theoretically aligned architectures regarding predictive performance while not relying on positional or structural encodings.
Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.
This paper explores meta-learning in sequential recommendation to alleviate the item cold-start problem. Sequential recommendation aims to capture user's dynamic preferences based on historical behavior sequences and acts as a key component of most online recommendation scenarios. However, most previous methods have trouble recommending cold-start items, which are prevalent in those scenarios. As there is generally no side information in the setting of sequential recommendation task, previous cold-start methods could not be applied when only user-item interactions are available. Thus, we propose a Meta-learning-based Cold-Start Sequential Recommendation Framework, namely Mecos, to mitigate the item cold-start problem in sequential recommendation. This task is non-trivial as it targets at an important problem in a novel and challenging context. Mecos effectively extracts user preference from limited interactions and learns to match the target cold-start item with the potential user. Besides, our framework can be painlessly integrated with neural network-based models. Extensive experiments conducted on three real-world datasets verify the superiority of Mecos, with the average improvement up to 99%, 91%, and 70% in HR@10 over state-of-the-art baseline methods.
Network representation learning in low dimensional vector space has attracted considerable attention in both academic and industrial domains. Most real-world networks are dynamic with addition/deletion of nodes and edges. The existing graph embedding methods are designed for static networks and they cannot capture evolving patterns in a large dynamic network. In this paper, we propose a dynamic embedding method, dynnode2vec, based on the well-known graph embedding method node2vec. Node2vec is a random walk based embedding method for static networks. Applying static network embedding in dynamic settings has two crucial problems: 1) Generating random walks for every time step is time consuming 2) Embedding vector spaces in each timestamp are different. In order to tackle these challenges, dynnode2vec uses evolving random walks and initializes the current graph embedding with previous embedding vectors. We demonstrate the advantages of the proposed dynamic network embedding by conducting empirical evaluations on several large dynamic network datasets.
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