This short paper is a fast proof-of-concept that the 3-order B-splines used in Kolmogorov-Arnold Networks (KANs) can be well approximated by Gaussian radial basis functions. Doing so leads to FastKAN, a much faster implementation of KAN which is also a radial basis function (RBF) network.

In the realm of time series analysis, accurately measuring similarity is crucial for applications such as forecasting, anomaly detection, and clustering. However, existing metrics often fail to capture the complex, multidimensional nature of time series data, limiting their effectiveness and application. This paper introduces the Structured Similarity Index Measure for Time Series (TS3IM), a novel approach inspired by the success of the Structural Similarity Index Measure (SSIM) in image analysis, tailored to address these limitations by assessing structural similarity in time series. TS3IM evaluates multiple dimensions of similarity-trend, variability, and structural integrity-offering a more nuanced and comprehensive measure. This metric represents a significant leap forward, providing a robust tool for analyzing temporal data and offering more accurate and comprehensive sequence analysis and decision support in fields such as monitoring power consumption, analyzing traffic flow, and adversarial recognition. Our extensive experimental results also show that compared with traditional methods that rely heavily on computational correlation, TS3IM is 1.87 times more similar to Dynamic Time Warping (DTW) in evaluation results and improves by more than 50% in adversarial recognition.

Federated learning (FL) offers a privacy-centric distributed learning framework, enabling model training on individual clients and central aggregation without necessitating data exchange. Nonetheless, FL implementations often suffer from non-i.i.d. and long-tailed class distributions across mobile applications, e.g., autonomous vehicles, which leads models to overfitting as local training may converge to sub-optimal. In our study, we explore the impact of data heterogeneity on model bias and introduce an innovative personalized FL framework, Multi-level Personalized Federated Learning (MuPFL), which leverages the hierarchical architecture of FL to fully harness computational resources at various levels. This framework integrates three pivotal modules: Biased Activation Value Dropout (BAVD) to mitigate overfitting and accelerate training; Adaptive Cluster-based Model Update (ACMU) to refine local models ensuring coherent global aggregation; and Prior Knowledge-assisted Classifier Fine-tuning (PKCF) to bolster classification and personalize models in accord with skewed local data with shared knowledge. Extensive experiments on diverse real-world datasets for image classification and semantic segmentation validate that MuPFL consistently outperforms state-of-the-art baselines, even under extreme non-i.i.d. and long-tail conditions, which enhances accuracy by as much as 7.39% and accelerates training by up to 80% at most, marking significant advancements in both efficiency and effectiveness.

In this work, we develop and analyze a Gradient Descent (GD) based solution, called Alternating GD and Minimization (AltGDmin), for efficiently solving the low rank matrix completion (LRMC) in a federated setting. LRMC involves recovering an $n \times q$ rank-$r$ matrix $\Xstar$ from a subset of its entries when $r \ll \min(n,q)$. Our theoretical guarantees (iteration and sample complexity bounds) imply that AltGDmin is the most communication-efficient solution in a federated setting, is one of the fastest, and has the second best sample complexity among all iterative solutions to LRMC. In addition, we also prove two important corollaries. (a) We provide a guarantee for AltGDmin for solving the noisy LRMC problem. (b) We show how our lemmas can be used to provide an improved sample complexity guarantee for AltMin, which is the fastest centralized solution.

The Universal Similarity Metric (USM) has been demonstrated to give practically useful measures of "similarity" between sequence data. Here we have used the USM as an alternative distance metric in a K-Nearest Neighbours (K-NN) learner to allow effective pattern recognition of variable length sequence data. We compare this USM approach with the commonly used string-to-word vector approach. Our experiments have used two data sets of divergent domains: (1) spam email filtering and (2) protein subcellular localisation. Our results with this data reveal that the USM based K-NN learner (1) gives predictions with higher classification accuracy than those output by techniques that use the string to word vector approach, and (2) can be used to generate reliable probability forecasts.

In recent years, genetic programming (GP)-based evolutionary feature construction has achieved significant success. However, a primary challenge with evolutionary feature construction is its tendency to overfit the training data, resulting in poor generalization on unseen data. In this research, we draw inspiration from PAC-Bayesian theory and propose using sharpness-aware minimization in function space to discover symbolic features that exhibit robust performance within a smooth loss landscape in the semantic space. By optimizing sharpness in conjunction with cross-validation loss, as well as designing a sharpness reduction layer, the proposed method effectively mitigates the overfitting problem of GP, especially when dealing with a limited number of instances or in the presence of label noise. Experimental results on 58 real-world regression datasets show that our approach outperforms standard GP as well as six state-of-the-art complexity measurement methods for GP in controlling overfitting. Furthermore, the ensemble version of GP with sharpness-aware minimization demonstrates superior performance compared to nine fine-tuned machine learning and symbolic regression algorithms, including XGBoost and LightGBM.

Vision graph neural networks (ViG) offer a new avenue for exploration in computer vision. A major bottleneck in ViGs is the inefficient k-nearest neighbor (KNN) operation used for graph construction. To solve this issue, we propose a new method for designing ViGs, Dynamic Axial Graph Construction (DAGC), which is more efficient than KNN as it limits the number of considered graph connections made within an image. Additionally, we propose a novel CNN-GNN architecture, GreedyViG, which uses DAGC. Extensive experiments show that GreedyViG beats existing ViG, CNN, and ViT architectures in terms of accuracy, GMACs, and parameters on image classification, object detection, instance segmentation, and semantic segmentation tasks. Our smallest model, GreedyViG-S, achieves 81.1% top-1 accuracy on ImageNet-1K, 2.9% higher than Vision GNN and 2.2% higher than Vision HyperGraph Neural Network (ViHGNN), with less GMACs and a similar number of parameters. Our largest model, GreedyViG-B obtains 83.9% top-1 accuracy, 0.2% higher than Vision GNN, with a 66.6% decrease in parameters and a 69% decrease in GMACs. GreedyViG-B also obtains the same accuracy as ViHGNN with a 67.3% decrease in parameters and a 71.3% decrease in GMACs. Our work shows that hybrid CNN-GNN architectures not only provide a new avenue for designing efficient models, but that they can also exceed the performance of current state-of-the-art models.

We consider the problem of learning an $\varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Given access to a generative model, we achieve rate-optimal sample complexity by performing a simple, \emph{perturbed} version of least-squares value iteration with orthogonal trigonometric polynomials as features. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our~$\widetilde{\mathcal{O}}(\epsilon^{-2-d/(\nu+1)})$ sample complexity, where $d$ is the dimension of the state-action space and $\nu$ the order of smoothness, recovers the state-of-the-art result of discretization approaches for the special case of Lipschitz MDPs $(\nu=0)$. At the same time, for $\nu\to\infty$, it recovers and greatly generalizes the $\mathcal{O}(\epsilon^{-2})$ rate of low-rank MDPs, which are more amenable to regression approaches. In this sense, our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.

Honeyfiles are a particularly useful type of honeypot: fake files deployed to detect and infer information from malicious behaviour. This paper considers the challenge of naming honeyfiles so they are camouflaged when placed amongst real files in a file system. Based on cosine distances in semantic vector spaces, we develop two metrics for filename camouflage: one based on simple averaging and one on clustering with mixture fitting. We evaluate and compare the metrics, showing that both perform well on a publicly available GitHub software repository dataset.

Traffic flow forecasting is a crucial task in transportation management and planning. The main challenges for traffic flow forecasting are that (1) as the length of prediction time increases, the accuracy of prediction will decrease; (2) the predicted results greatly rely on the extraction of temporal and spatial dependencies from the road networks. To overcome the challenges mentioned above, we propose a multi-channel spatial-temporal transformer model for traffic flow forecasting, which improves the accuracy of the prediction by fusing results from different channels of traffic data. Our approach leverages graph convolutional network to extract spatial features from each channel while using a transformer-based architecture to capture temporal dependencies across channels. We introduce an adaptive adjacency matrix to overcome limitations in feature extraction from fixed topological structures. Experimental results on six real-world datasets demonstrate that introducing a multi-channel mechanism into the temporal model enhances performance and our proposed model outperforms state-of-the-art models in terms of accuracy.