Large language models (LLMs) have achieved impressive results on complex reasoning tasks, but their high inference cost remains a major barrier to real-world deployment. A promising solution is to use cascaded inference, where small, cheap models handle easy queries, and only the hardest examples are escalated to more powerful models. However, existing cascade methods typically rely on supervised training with labeled data, offer no theoretical generalization guarantees, and provide limited control over test-time computational cost. We introduce **C3PO** (*Cost Controlled Cascaded Prediction Optimization*), a self-supervised framework for optimizing LLM cascades under probabilistic cost constraints. By focusing on minimizing regret with respect to the most powerful model (MPM), C3PO avoids the need for labeled data by constructing a cascade using only unlabeled model outputs. It leverages conformal prediction to bound the probability that inference cost exceeds a user-specified budget. We provide theoretical guarantees on both cost control and generalization error, and show that our optimization procedure is effective even with small calibration sets. Empirically, C3PO achieves state-of-the-art performance across a diverse set of reasoning benchmarks including GSM8K, MATH-500, BigBench-Hard and AIME, outperforming strong LLM cascading baselines in both accuracy and cost-efficiency. Our results demonstrate that principled, label-free cascade optimization can enable scalable LLM deployment.

The performance of transformers for time-series forecasting has improved significantly. Recent architectures learn complex temporal patterns by segmenting a time-series into patches and using the patches as tokens. The patch size controls the ability of transformers to learn the temporal patterns at different frequencies: shorter patches are effective for learning localized, high-frequency patterns, whereas mining long-term seasonalities and trends requires longer patches. Inspired by this observation, we propose a novel framework, Multi-resolution Time-Series Transformer (MTST), which consists of a multi-branch architecture for simultaneous modeling of diverse temporal patterns at different resolutions. In contrast to many existing time-series transformers, we employ relative positional encoding, which is better suited for extracting periodic components at different scales. Extensive experiments on several real-world datasets demonstrate the effectiveness of MTST in comparison to state-of-the-art forecasting techniques.

The existing definitions of graph convolution, either from spatial or spectral perspectives, are inflexible and not unified. Defining a general convolution operator in the graph domain is challenging due to the lack of canonical coordinates, the presence of irregular structures, and the properties of graph symmetries. In this work, we propose a novel and general graph convolution framework by parameterizing the kernels as continuous functions of pseudo-coordinates derived via graph positional encoding. We name this Continuous Kernel Graph Convolution (CKGConv). Theoretically, we demonstrate that CKGConv is flexible and expressive. CKGConv encompasses many existing graph convolutions, and exhibits a stronger expressiveness, as powerful as graph transformers in terms of distinguishing non-isomorphic graphs. Empirically, we show that CKGConv-based Networks outperform existing graph convolutional networks and perform comparably to the best graph transformers across a variety of graph datasets. The code and models are publicly available at https://github.com/networkslab/CKGConv.

Adaptive importance sampling (AIS) methods provide a useful alternative to Markov Chain Monte Carlo (MCMC) algorithms for performing inference of intractable distributions. Population Monte Carlo (PMC) algorithms constitute a family of AIS approaches which adapt the proposal distributions iteratively to improve the approximation of the target distribution. Recent work in this area primarily focuses on ameliorating the proposal adaptation procedure for high-dimensional applications. However, most of the AIS algorithms use simple proposal distributions for sampling, which might be inadequate in exploring target distributions with intricate geometries. In this work, we construct expressive proposal distributions in the AIS framework using normalizing flow, an appealing approach for modeling complex distributions. We use an iterative parameter update rule to enhance the approximation of the target distribution. Numerical experiments show that in high-dimensional settings, the proposed algorithm offers significantly improved performance compared to the existing techniques.

Multiple Instance Learning (MIL) is a weakly supervised learning problem where the aim is to assign labels to sets or bags of instances, as opposed to traditional supervised learning where each instance is assumed to be independent and identically distributed (IID) and is to be labeled individually. Recent work has shown promising results for neural network models in the MIL setting. Instead of focusing on each instance, these models are trained in an end-to-end fashion to learn effective bag-level representations by suitably combining permutation invariant pooling techniques with neural architectures. In this paper, we consider modelling the interactions between bags using a graph and employ Graph Neural Networks (GNNs) to facilitate end-to-end learning. Since a meaningful graph representing dependencies between bags is rarely available, we propose to use a Bayesian GNN framework that can generate a likely graph structure for scenarios where there is uncertainty in the graph or when no graph is available. Empirical results demonstrate the efficacy of the proposed technique for several MIL benchmark tasks and a distribution regression task.

Graph neural network (GNN) models achieve superior performance when classifying nodes in graph-structured data. Given that state-of-the-art GNNs share many similarities with their CNN cousins and that CNNs suffer adversarial vulnerabilities, there has also been interest in exploring analogous vulnerabilities in GNNs. Indeed, recent work has demonstrated that node classification performance of several graph models, including the popular graph convolution network (GCN) model, can be severely degraded through adversarial perturbations to the graph structure and the node features. In this work, we take a first step towards detecting adversarial attacks against graph models. We first propose a straightforward single node threshold test for detecting nodes subject to targeted attacks. Subsequently, we describe a kernel-based two-sample test for detecting whether a given subset of nodes within a graph has been maliciously corrupted. The efficacy of our algorithms is established via thorough experiments using commonly used node classification benchmark datasets. We also illustrate the potential practical benefit of our detection method by demonstrating its application to a real-world Bitcoin transaction network.

Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference of the hidden states for probabilistic forecasting. We use particle flow as the tool for approximating the posterior distribution of the states, as it is shown to be highly effective in complex, high-dimensional settings. Thorough experimentation on several real world time-series datasets demonstrates that our approach provides better characterization of uncertainty while maintaining comparable accuracy to the state-of-the-art point forecasting methods.

Node classification in attributed graphs is an important task in multiple practical settings, but it can often be difficult or expensive to obtain labels. Active learning can improve the achieved classification performance for a given budget on the number of queried labels. The best existing methods are based on graph neural networks, but they often perform poorly unless a sizeable validation set of labelled nodes is available in order to choose good hyperparameters. We propose a novel graph-based active learning algorithm for the task of node classification in attributed graphs; our algorithm uses graph cognizant logistic regression, equivalent to a linearized graph-convolutional neural network (GCN), for the prediction phase and maximizes the expected error reduction in the query phase. To reduce the delay experienced by a labeller interacting with the system, we derive a preemptive querying system that calculates a new query during the labelling process, and to address the setting where learning starts with almost no labelled data, we also develop a hybrid algorithm that performs adaptive model averaging of label propagation and linearized GCN inference. We conduct experiments on five public benchmark datasets, demonstrating a significant improvement over state-of-the-art approaches and illustrate the practical value of the method by applying it to a private microwave link network dataset.

Graphs are ubiquitous in modelling relationalstructures. Recent endeavours in machine learningfor graph structured data have led to manyarchitectures and learning algorithms. However,the graph used by these algorithms is oftenconstructed based on inaccurate modellingassumptions and/or noisy data. As a result, itfails to represent the true relationships betweennodes. A Bayesian framework which targetsposterior inference of the graph by consideringit as a random quantity can be beneficial. Inthis paper, we propose a novel non-parametricgraph model for constructing the posterior distributionof graph adjacency matrices. The proposedmodel is flexible in the sense that it caneffectively take into account the output of graphbased learning algorithms that target specifictasks. In addition, model inference scales wellto large graphs. We demonstrate the advantagesof this model in three different problem settings:node classification, link prediction andrecommendation.

Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the performance has been impressive, the current implementations have limited capability to incorporate uncertainty in the graph structure. Almost all GCNNs process a graph as though it is a ground-truth depiction of the relationship between nodes, but often the graphs employed in applications are themselves derived from noisy data or modelling assumptions. Spurious edges may be included; other edges may be missing between nodes that have very strong relationships. In this paper we adopt a Bayesian approach, viewing the observed graph as a realization from a parametric family of random graphs. We then target inference of the joint posterior of the random graph parameters and the node (or graph) labels. We present the Bayesian GCNN framework and develop an iterative learning procedure for the case of assortative mixed-membership stochastic block models. We present the results of experiments that demonstrate that the Bayesian formulation can provide better performance when there are very few labels available during the training process.

Community detection from graphs has many applications in machine learning, biological and social sciences. While there is a broad spectrum of literature based on various approaches, recently there has been a significant focus on inference algorithms for statistical models of community structure. These algorithms strive to solve an inference problem based on a generative model of the network. Recent advances in stochastic gradient MCMC have played a crucial role in improving the scalability of these techniques. In this paper, we propose a version of a degree corrected stochastic block model and present an MCMC based inference algorithm. Experimental results on several real world networks demonstrate the effectiveness of the proposed approach.

Particle filters has become a standard tool for state estimation in nonlinear systems. However, their performance usually deteriorates if the dimension of state space is high or the measurements are highly informative. A major challenge is to construct a proposal density that is well matched to the posterior distribution. Particle flow methods are a promising option for addressing this task. In this paper, we develop a particle flow particle filter algorithm to address the case where both the process noise and the measurement noise are distributed as mixtures of Gaussians. Numerical experiments are performed to explore when the proposed method offers advantages compared to existing techniques.