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arXiv:2509.02937v1 Announce Type: cross Abstract: This paper studies the complexity of finding an $epsilon$-stationary point for stochastic bilevel optimization when the upper-level problem is nonconvex and the lower-level problem is strongly convex. Recent work proposed the first-order method, F${}^2$SA, achieving the $tilde{mathcal{O}}(epsilon^{-6})$ upper complexity bound for first-order smooth problems. This is slower than the optimal $Omega(epsilon^{-4})$ complexity lower bound in its single-level counterpart. In this work, we show that faster rates are achievable for higher-order smooth problems. We first reformulate F$^2$SA as approximating the hyper-gradient with a forward difference. Based on this observation, we propose a class of methods F${}^2$SA-$p$ that uses $p$th-order finite difference for hyper-gradient approximation and improves the upper bound to $tilde{mathcal{O}}(p epsilon^{4-p/2})$ for $p$th-order smooth problems. Finally, we demonstrate that the $Omega(epsilon^{-4})$ lower bound also holds for stochastic bilevel problems when the high-order smoothness holds for the lower-level variable, indicating that the upper bound of F${}^2$SA-$p$ is nearly optimal in the highly smooth region $p = Omega( log epsilon^{-1} / log log epsilon^{-1})$.

arXiv:2507.17686v3 Announce Type: replace Abstract: Previous studies have shown that hazard ratios between treatment groups estimated with the Cox model are uninterpretable because the unspecified baseline hazard of the model fails to identify temporal change in the risk set composition due to treatment assignment and unobserved factors among multiple, contradictory scenarios. To alleviate this problem, especially in studies based on observational data with uncontrolled dynamic treatment and real-time measurement of many covariates, we propose abandoning the baseline hazard and using kernel-based machine learning to explicitly model the change in the risk set with or without latent variables. For this framework, we clarify the context in which hazard ratios can be causally interpreted, and then develop a method based on Neyman orthogonality to compute debiased maximum-likelihood estimators of hazard ratios, proving necessary convergence results. Numerical simulations confirm that the proposed method identifies the true hazard ratios with minimal bias. These results lay the foundation for developing a useful, alternative method for causal inference with uncontrolled, observational data in modern epidemiology.

arXiv:2509.03110v1 Announce Type: cross Abstract: While Sharpness-Aware Minimization (SAM) improves generalization in deep neural networks by minimizing both loss and sharpness, it suffers from inefficiency in distributed large-batch training. We present Landscape-Smoothed SAM (LSAM), a novel optimizer that preserves SAM's generalization advantages while offering superior efficiency. LSAM integrates SAM's adversarial steps with an asynchronous distributed sampling strategy, generating an asynchronous distributed sampling scheme, producing a smoothed sharpness-aware loss landscape for optimization. This design eliminates synchronization bottlenecks, accelerates large-batch convergence, and delivers higher final accuracy compared to data-parallel SAM.

arXiv:2509.03151v1 Announce Type: cross Abstract: The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier frequencies. The challenge is to sample the Fourier frequencies well. This work proves convergence of a data adaptive method based on resampling the frequencies asymptotically optimally, as the number of nodes and amount of data tend to infinity. Numerical results based on resampling and adaptive random walk steps together with approximations of the least squares problem by conjugate gradient iterations confirm the analysis for regression and classification problems.

arXiv:2506.05668v4 Announce Type: replace Abstract: Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the density ratio between path distributions, it reveals a fundamental connection between marginal densities and transition kernels, providing a flexible plug-and-play framework that unifies diffusion density estimation, inference-time control, and energy-based diffusion training under a single perspective. Experiments demonstrated that RNE delivers strong results in inference-time control applications, such as annealing and model composition, with promising inference-time scaling performance. Moreover, RNE provides a simple yet efficient regularisation for training energy-based diffusion.

arXiv:2509.02927v1 Announce Type: new Abstract: Ensemble method is considered the gold standard for uncertainty quantification (UQ) for machine learning interatomic potentials (MLIPs). However, their high computational cost can limit its practicality. Alternative techniques, such as Monte Carlo dropout and deep kernel learning, have been proposed to improve computational efficiency; however, some of these methods cannot be applied to already trained models and may affect the prediction accuracy. In this paper, we propose a simple and efficient post-hoc framework for UQ that leverages the descriptor of a trained graph neural network potential to estimate residual errors. We refer to this method as post-hoc descriptor-based residual-based learning (PDRL). PDRL models the discrepancy between MLIP predictions and ground truth values, allowing these residuals to act as proxies for prediction uncertainty. We explore multiple variants of PDRL and benchmark them against established UQ methods, evaluating both their effectiveness and limitations.

arXiv:2508.08005v2 Announce Type: replace Abstract: Extensive experiments and prior studies show that no single maximum clique algorithm consistently performs best across all instances, highlighting the importance of selecting suitable algorithms based on instance features. Through an extensive analysis of relevant studies, it is found that there is a lack of research work concerning algorithm selection oriented toward the Maximum Clique Problem (MCP). In this work, we propose a learning-based framework that integrates both traditional machine learning and graph neural networks to address this gap. We construct a labeled dataset by running four exact MCP algorithms on a diverse collection of graph instances, accompanied by structural and global statistical features extracted from each graph. We first evaluate four conventional classifiers: Support Vector Machine (SVM), Random Forest (RF), Decision Tree (DT), and K-Nearest Neighbors (KNN), across multiple dataset variants. Experimental results show that RF consistently shows strong performance across metrics and dataset variants, making it a reliable baseline. In addition, feature importance analysis indicates that connectivity and topological structure are strong predictors of algorithm performance. Building on these findings, we develop a dual-channel model named GAT-MLP, which combines a Graph Attention Network (GAT) for local structural encoding with a Multilayer Perceptron (MLP) for global feature modeling. The GAT-MLP model shows strong and consistent performance across all metrics. Our results highlight the effectiveness of dual-channel architectures and the promise of graph neural networks in combinatorial algorithm selection.

arXiv:2509.02930v1 Announce Type: new Abstract: In self-supervised reinforcement learning (RL), one of the key challenges is learning a diverse set of skills to prepare agents for unknown future tasks. Despite impressive advances, scalability and evaluation remain prevalent issues. Regarding scalability, the search for meaningful skills can be obscured by high-dimensional feature spaces, where relevant features may vary across downstream task domains. For evaluating skill diversity, defining what constitutes "diversity" typically requires a hard commitment to a specific notion of what it means for skills to be diverse, potentially leading to inconsistencies in how skill diversity is understood, making results across different approaches hard to compare, and leaving many forms of diversity unexplored. To address these issues, we adopt a measure of sample diversity that translates ideas from ecology to machine learning -- the Vendi Score -- allowing the user to specify and evaluate any desired form of diversity. We demonstrate how this metric facilitates skill evaluation and introduce VendiRL, a unified framework for learning diversely diverse sets of skills. Given distinct similarity functions, VendiRL motivates distinct forms of diversity, which could support skill-diversity pretraining in new and richly interactive environments where optimising for various forms of diversity may be desirable.

arXiv:2210.10547v2 Announce Type: replace-cross Abstract: In this era of information explosion, a personalized recommendation system is convenient for users to get information they are interested in. To deal with billions of users and items, large-scale online recommendation services usually consist of three stages: candidate generation, coarse-grained ranking, and fine-grained ranking. The success of each stage depends on whether the model accurately captures the interests of users, which are usually hidden in users' behavior data. Previous research shows that users' interests are diverse, and one vector is not sufficient to capture users' different preferences. Therefore, many methods use multiple vectors to encode users' interests. However, there are two unsolved problems: (1) The similarity of different vectors in existing methods is too high, with too much redundant information. Consequently, the interests of users are not fully represented. (2) Existing methods model the long-term and short-term behaviors together, ignoring the differences between them. This paper proposes a Hierarchical Multi-Interest Co-Network (HCN) to capture users' diverse interests in the coarse-grained ranking stage. Specifically, we design a hierarchical multi-interest extraction layer to update users' diverse interest centers iteratively. The multiple embedded vectors obtained in this way contain more information and represent the interests of users better in various aspects. Furthermore, we develop a Co-Interest Network to integrate users' long-term and short-term interests. Experiments on several real-world datasets and one large-scale industrial dataset show that HCN effectively outperforms the state-of-the-art methods. We deploy HCN into a large-scale real world E-commerce system and achieve extra 2.5% improvements on GMV (Gross Merchandise Value).

arXiv:2509.02967v1 Announce Type: new Abstract: Conventional neural networks frequently face challenges in spectral analysis of signals. To address this challenge, Fourier neural networks (FNNs) and similar approaches integrate components of Fourier series into the structure of neural networks. Nonetheless, a significant hurdle is often overlooked: the superposition of periodic signals does not necessarily result in a periodic signal. For example, when forecasting almost periodic functions composed of signals with incommensurate frequencies, traditional models such as Autoregressive Integrated Moving Average (ARIMA) frequently outperform most neural networks including large language models (LLMs). To tackle this goal, we propose Autoregressive-Weight-Enhanced AR-KAN, a hybrid model that combines the benefits of both methods. Using the Universal Myopic Mapping Theorem, we apply a Kolmogorov-Arnold Network (KAN) for the static nonlinear part and include memory through a pre-trained AR component, which can be explained to retain the most useful information while eliminating redundancy. Experimental data indicates that AR-KAN delivers superior results on $72%$ of real-world datasets.