We study identification and inference in nonlinear dynamic systems defined on unknown interaction networks. The system evolves through an unobserved dependence matrix governing cross-sectional shock propagation via a nonlinear operator. We show that the network structure is not generically identified, and that identification requires sufficient spectral heterogeneity. In particular, identification arises when the network induces non-exchangeable covariance patterns through heterogeneous amplification of eigenmodes. When the spectrum is concentrated, dependence becomes observationally equivalent to common shocks or scalar heterogeneity, leading to non-identification. We provide necessary and sufficient conditions for identification, characterize observational equivalence classes, and propose a semiparametric estimator with asymptotic theory. We also develop tests for network dependence whose power depends on spectral properties of the interaction matrix. The results apply to a broad class of economic models, including production networks, contagion models, and dynamic interaction systems.

We consider the problem of estimating Ising models over $n$ variables in Total Variation (TV) distance, given $l$ independent samples from the model. While the statistical complexity of the problem is well-understood [DMR20], identifying computationally and statistically efficient algorithms has been challenging. In particular, remarkable progress has occurred in several settings, such as when the underlying graph is a tree [DP21, BGPV21], when the entries of the interaction matrix follow a Gaussian distribution [GM24, CK24], or when the bulk of its eigenvalues lie in a small interval [AJK+24, KLV24], but no unified framework for polynomial-time estimation in TV exists so far. Our main contribution is a unified analysis of the Maximum Pseudo-Likelihood Estimator (MPLE) for two general classes of Ising models. The first class includes models that have bounded operator norm and satisfy the Modified Log-Sobolev Inequality (MLSI), a functional inequality that was introduced to study the convergence of the associated Glauber dynamics to stationarity. In the second class of models, the interaction matrix has bounded infinity norm (or bounded width), which is the most common assumption in the literature for structure learning of Ising models. We show how our general results for these classes yield polynomial-time algorithms and optimal or near-optimal sample complexity guarantees in a variety of settings. Our proofs employ a variety of tools from tensorization inequalities to measure decompositions and concentration bounds.

Abstract--Although the collaborative filtering (CF) algorithm has achieved remarkable performance in recommendation systems, it suffers from suboptimal recommendation performance due to noise in the user-item interaction matrix. Numerous noise-removal studies have improved recommendation models, but most existing approaches conduct denoising on a single graph. This may cause attenuation of collaborative signals: removing edges between two nodes can interrupt paths between other nodes, weakening path-dependent collaborative information. T o address these limitations, this study proposes a novel GNN-based CF model called DRCSD for denoising unstable interactions. DRCSD includes two core modules: a collaborative signal decoupling module (decomposes signals into distinct orders by structural characteristics) and an order-wise denoising module (performs targeted denoising on each order). Additionally, the information aggregation mechanism of traditional GNN-based CF models is modified to avoid cross-order signal interference until the final pooling operation. Extensive experiments on three public real-world datasets show that DRCSD has superior robustness against unstable interactions and achieves statistically significant performance improvements in recommendation accuracy metrics compared to state-of-the-art baseline models.

Accurately predicting magnetic behavior across diverse materials systems remains a longstanding challenge due to the complex interplay of structural and electronic factors and is pivotal for the accelerated discovery and design of next-generation magnetic materials. In this work, a refined descriptor is proposed that significantly improves the prediction of two critical magnetic properties -- magnetic ordering (Ferromagnetic vs. Ferrimagnetic) and magnetic moment per atom -- using only the structural information of materials. Unlike previous models limited to Mn-based or lanthanide-transition metal compounds, the present approach generalizes across a diverse dataset of 5741 stable, binary and ternary, ferromagnetic and ferrimagnetic compounds sourced from the Materials Project. Leveraging an enriched elemental vector representation and advanced feature engineering, including nonlinear terms and reduced matrix sparsity, the LightGBM-based model achieves an accuracy of 82.4% for magnetic ordering classification and balanced recall across FM and FiM classes, addressing a key limitation in prior studies. The model predicts magnetic moment per atom with a correlation coefficient of 0.93, surpassing the Hund's matrix and orbital field matrix descriptors. Additionally, it accurately estimates formation energy per atom, enabling assessment of both magnetic behavior and material stability. This generalized and computationally efficient framework offers a robust tool for high-throughput screening of magnetic materials with tailored properties.

While classical formulations of multi-armed bandit problems assume that each arm's reward is independent and stationary, real-world applications often involve non-stationary environments and interdependencies between arms. In particular, selecting one arm may influence the future rewards of other arms, a scenario not adequately captured by existing models such as rotting bandits or restless bandits. To address this limitation, we propose the influential bandit problem, which models inter-arm interactions through an unknown, symmetric, positive semi-definite interaction matrix that governs the dynamics of arm losses. We formally define this problem and establish two regret lower bounds, including a superlinear $Ω(T^2 / \log^2 T)$ bound for the standard LCB algorithm (loss minimization version of UCB) and an algorithm-independent $Ω(T)$ bound, which highlight the inherent difficulty of the setting. We then introduce a new algorithm based on a lower confidence bound (LCB) estimator tailored to the structure of the loss dynamics. Under mild assumptions, our algorithm achieves a regret of $O(KT \log T)$, which is nearly optimal in terms of its dependence on the time horizon. The algorithm is simple to implement and computationally efficient. Empirical evaluations on both synthetic and real-world datasets demonstrate the presence of inter-arm influence and confirm the superior performance of our method compared to conventional bandit algorithms.

Spatio-temporal forecasting is critical in applications such as traffic prediction, energy demand modeling, and weather monitoring. While Graph Attention Networks (GATs) are popular for modeling spatial dependencies, they rely on predefined adjacency structures and dynamic attention scores, introducing inductive biases and computational overhead that can obscure interpretability. We propose InterGAT, a simplified alternative to GAT that replaces masked attention with a fully learnable, symmetric node interaction matrix, capturing latent spatial relationships without relying on fixed graph topologies. Our framework, InterGAT-GRU, which incorporates a GRU-based temporal decoder, outperforms the baseline GAT-GRU in forecasting accuracy, achieving at least a 21% improvement on the SZ-Taxi dataset and a 6% improvement on the Los-Loop dataset across all forecasting horizons (15 to 60 minutes). Additionally, we observed reduction in training time by 60-70% compared to GAT-GRU baseline. Crucially, the learned interaction matrix reveals interpretable structure: it recovers sparse, topology-aware attention patterns that align with community structure. Spectral and clustering analyses show that the model captures both localized and global dynamics, offering insights into the functional topology driving predictions. This highlights how structure learning can simultaneously support prediction, computational efficiency, and topological interpretabil-ity in dynamic graph-based domains.

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. We uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention nor fixed connectivity is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: \href{https://github.com/millioniron/LLM_exploration}{LLM4Exploration}

The problem of image-based visual servoing (IBVS) of an aerial robot using deep-learning-based keypoint detection is addressed in this article. A monocular RGB camera mounted on the platform is utilized to collect the visual data. A convolutional neural network (CNN) is then employed to extract the features serving as the visual data for the servoing task. This paper contributes to the field by circumventing not only the challenge stemming from the need for man-made marker detection in conventional visual servoing techniques, but also enhancing the robustness against undesirable factors including occlusion, varying illumination, clutter, and background changes, thereby broadening the applicability of perception-guided motion control tasks in aerial robots. Additionally, extensive physics-based ROS Gazebo simulations are conducted to assess the effectiveness of this method, in contrast to many existing studies that rely solely on physics-less simulations. A demonstration video is available at https://youtu.be/Dd2Her8Ly-E.