Bayesian bandit methods is necessary.

Inferring synaptic connectivity from neural population activity is a fundamental challenge in computational neuroscience, complicated by partial observability and mismatches between inference models and true circuit dynamics. In this study, we propose a graph-based neural inference model that simultaneously predicts neural activity and infers latent connectivity by modeling neurons as interacting nodes in a graph. The architecture features two distinct modules: one for learning structural connectivity and another for predicting future spiking activity via a graph neural network (GNN). Our model accommodates unobserved neurons through auxiliary nodes, allowing for inference in partially observed circuits. We evaluate this approach using synthetic data generated from ring attractor network models and real spike recordings from head direction cells in mice. Across a wide range of conditions, including varying recurrent connectivity, external inputs, and incomplete observations, our model reliably resolves spurious correlations and recovers accurate weight profiles. When applied to real data, the inferred connectivity aligns with theoretical predictions of continuous attractor models. These results highlight the potential of GNN-based models to infer latent neural circuitry through self-supervised structure learning, while leveraging the spike prediction task to flexibly link connectivity and dynamics across both simulated and biological neural systems.

We consider a remote inference system with multiple modalities, where a multimodal machine learning (ML) model performs real-time inference using features collected from remote sensors. When sensor observations evolve dynamically over time, fresh features are critical for inference tasks. However, timely delivery of features from all modalities is often infeasible because of limited network resources. Towards this end, in this paper, we study a two-modality scheduling problem that seeks to minimize the ML model's inference error, expressed as a penalty function of the Age of Information (AoI) vector of the two modalities. We develop an index-based threshold policy and prove its optimality. Specifically, the scheduler switches to the other modality once the current modality's index function exceeds a predetermined threshold. We show that both modalities share the same threshold and that the index functions and the threshold can be computed efficiently. Our optimality results hold for general AoI functions (which could be non-monotonic and non-separable) and heterogeneous transmission times across modalities. To demonstrate the importance of considering a task-oriented AoI function, we conduct numerical experiments based on robot state prediction and compare our policy with round-robin and uniform random policies (both are oblivious to the AoI and the inference error).n The results show that our policy reduces inference error by up to 55% compared with these baselines.

A technical challenge in deep gray-box modeling is to ensure an appropriate use of physics models. A careless design of models and learning can lead to an erratic behavior of the components meant to represent physics (e.g., with erroneous estimation of physics parameters), and eventually, the overall

Dimarogonas Abstract --Recent years have witnessed the rapid advancement of understanding the control mechanism of networked dynamical systems (NDSs), which are governed by components such as nodal dynamics and topology. This paper reveals that the critical components in continuous-time state feedback cooperative control of NDSs can be inferred merely from discrete observations. In particular, we advocate a bi-level inference framework to estimate the global closed-loop system and extract the components, respectively. The novelty lies in bridging the gap from discrete observations to the continuous-time model and effectively decoupling the concerned components. Specifically, in the first level, we design a causality-based estimator for the discrete-time closed-loop system matrix, which can achieve asymptotically unbiased performance when the NDS is stable. In the second level, we introduce a matrix logarithm based method to recover the continuous-time counterpart matrix, providing new sampling period guarantees and establishing the recovery error bound. By utilizing graph properties of the NDS, we develop least square based procedures to decouple the concerned components with up to a scalar ambiguity. Furthermore, we employ inverse optimal control techniques to reconstruct the objective function driving the control process, deriving necessary conditions for the solutions. Numerical simulations demonstrate the effectiveness of the proposed method. I NTRODUCTION In the last decades, networked dynamical systems (NDSs) have played a crucial role in many engineering and biological fields, e.g., multi-robot formation [1], power grids [2], human brain [3], and immune cell network [4]. An NDS, comprising multiple interconnected nodes, is characterized by not only the self-dynamics of a single node (nodal dynamics) but also the interaction structure (topology) between nodes, and can achieve various cooperative behaviors such as synchronization. However, the prior information about the nodal dynamics and topology is not always accessible in practice, and needs to be inferred from observations. This inference enhances our ability to understand, predict, and intervene with the NDS [5]. A. Motivations This paper focuses on the continuous-time linear state-feedback cooperative control of NDSs, where only discrete and noisy observations on a single round of the system's trajectory are available. In particular, we aim to provide a: Y ushan Li and Dimos V . Dimarogonas are with the Division of Decision and Control Systems, KTH Royal Institute of Technology, Stockholm, Sweden. The motivation for addressing this problem stems from two main aspects.

We study the effects of approximate inference on the performance of Thompson sampling in the k -armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often must be approximated in practice. We show that even small constant inference error (in \alpha -divergence) can lead to poor performance (linear regret) due to under-exploration (for \alpha 1) or over-exploration (for \alpha 0) by the approximation. While for \alpha 0 this is unavoidable, for \alpha \leq 0 the regret can be improved by adding a small amount of forced exploration even when the inference error is a large constant.

This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates centroids based on the mean of assigned points. This process continues until convergence, forming k clusters where each point belongs to the closest centroid. This research investigates the prediction of the last component of data points obtained from a distribution of clustered data using the online balanced k-means approach. Through extensive experimentation and analysis, key findings have emerged. It is observed that a larger number of clusters or partitions tends to yield lower errors while increasing the number of assigned data points does not significantly improve inference errors. Reducing losses in the learning process does not significantly impact overall inference errors. Indicating that as learning is going on inference errors remain unchanged. Recommendations include the need for specialized inference techniques to estimate better data points derived from multi-clustered data and exploring methods that yield improved results with larger assigned datasets. By addressing these recommendations, this research advances the accuracy and reliability of inferences made with the k-means algorithm, bridging the gap between clustering and non-parametric density estimation and inference.