Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea
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Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries. However, such a segmentation strategy cannot take into account the connectivity of the image edge features, increasing the risk of shortcut problem, especially in the case of complicated scenario. In this work, we introduce a new image segmentation model based on the minimal geodesic framework in conjunction with an adaptive cut-based circular optimal path computation scheme and a graph-based boundary proposals grouping scheme. Specifically, the adaptive cut can disconnect the image domain such that the target contours are imposed to pass through this cut only once. The boundary proposals are comprised of precomputed image edge segments, providing the connectivity information for our segmentation model. These boundary proposals are then incorporated into the proposed image segmentation model, such that the target segmentation contours are made up of a set of selected boundary proposals and the corresponding geodesic paths linking them. Experimental results show that the proposed model indeed outperforms state-of-the-art minimal paths-based image segmentation approaches.
Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on the variational approximation family. In this work, we introduce a general computational framework to implement MF variational inference for Bayesian models, with or without latent variables, using the Wasserstein gradient flow (WGF), a modern mathematical technique for realizing a gradient flow over the space of probability measures. Theoretically, we analyze the algorithmic convergence of the proposed approaches, providing an explicit expression for the contraction factor. We also strengthen existing results on MF variational posterior concentration from a polynomial to an exponential contraction, by utilizing the fixed point equation of the time-discretized WGF. Computationally, we propose a new constraint-free function approximation method using neural networks to numerically realize our algorithm. This method is shown to be more precise and efficient than traditional particle approximation methods based on Langevin dynamics.
Current machine learning methods struggle to solve Bongard problems, which are a type of IQ test that requires deriving an abstract "concept" from a set of positive and negative "support" images, and then classifying whether or not a new query image depicts the key concept. On Bongard-HOI, a benchmark for natural-image Bongard problems, existing methods have only reached 66% accuracy (where chance is 50%). Low accuracy is often attributed to neural nets' lack of ability to find human-like symbolic rules. In this work, we point out that many existing methods are forfeiting accuracy due to a much simpler problem: they do not incorporate information contained in the support set as a whole, and rely instead on information extracted from individual supports. This is a critical issue, because unlike in few-shot learning tasks concerning object classification, the "key concept" in a typical Bongard problem can only be distinguished using multiple positives and multiple negatives. We explore a variety of simple methods to take this cross-image context into account, and demonstrate substantial gains over prior methods, leading to new state-of-the-art performance on Bongard-LOGO (75.3%) and Bongard-HOI (72.45%) and strong performance on the original Bongard problem set (60.84%).
Ising machines have emerged as a promising solution for rapidly solving NP-complete combinatorial optimization problems, surpassing the capabilities of traditional computing methods. By efficiently determining the ground state of the Hamiltonian during the annealing process, Ising machines can effectively complement CPUs in tackling optimization challenges. To realize these Ising machines, a bi-stable oscillator is essential to emulate the atomic spins and interactions of the Ising model. This study introduces a Josephson parametric oscillator (JPO)-based tile structure, serving as a fundamental unit for scalable superconductor-based Ising machines. Leveraging the bi-stable nature of JPOs, which are superconductor-based oscillators, the proposed machine can operate at frequencies of 7.5GHz while consuming significantly less power (by three orders of magnitude) than CMOS-based systems. Furthermore, the compatibility of the proposed tile structure with the Lechner-Hauke-Zoller (LHZ) architecture ensures its viability for large-scale integration. We conducted simulations of the tile in a noisy environment to validate its functionality. We verified its operational characteristics by comparing the results with the analytical solution of its Hamiltonian model. This verification demonstrates the feasibility and effectiveness of the JPO-based tile in implementing Ising machines, opening new avenues for efficient and scalable combinatorial optimization in quantum computing.
We propose a novel method for 3D object reconstruction from a sparse set of views captured from a 360-degree calibrated camera rig. We represent the object surface through a hybrid model that uses both an MLP-based neural representation and a triangle mesh. A key contribution in our work is a novel object-centric sampling scheme of the neural representation, where rays are shared among all views. This efficiently concentrates and reduces the number of samples used to update the neural model at each iteration. This sampling scheme relies on the mesh representation to ensure also that samples are well-distributed along its normals. The rendering is then performed efficiently by a differentiable renderer. We demonstrate that this sampling scheme results in a more effective training of the neural representation, does not require the additional supervision of segmentation masks, yields state of the art 3D reconstructions, and works with sparse views on the Google's Scanned Objects, Tank and Temples and MVMC Car datasets.
Based on the signals received across its antennas, a multi-antenna base station (BS) can apply the classic multiple signal classification (MUSIC) algorithm for estimating the angle of arrivals (AOAs) of its incident signals. This method can be leveraged to localize the users if their line-of-sight (LOS) paths to the BS are available. In this paper, we consider a more challenging AOA estimation setup in the intelligent reflecting surface (IRS) assisted integrated sensing and communication (ISAC) system, where LOS paths do not exist between the BS and the users, while the users' signals can be transmitted to the BS merely via their LOS paths to the IRS as well as the LOS path from the IRS to the BS. Specifically, we treat the IRS as the anchor and are interested in estimating the AOAs of the incident signals from the users to the IRS. Note that we have to achieve the above goal based on the signals received by the BS, because the passive IRS cannot process its received signals. However, the signals received across different antennas of the BS only contain AOA information of its incident signals via the LOS path from the IRS to the BS. To tackle this challenge arising from the spatial-domain received signals, we propose an innovative approach to create temporal-domain multi-dimension received signals for estimating the AOAs of the paths from the users to the IRS. Specifically, via a proper design of the user message pattern and the IRS reflecting pattern, we manage to show that our designed temporal-domain multi-dimension signals can be surprisingly expressed as a function of the virtual steering vectors of the IRS towards the users. This amazing result implies that the classic MUSIC algorithm can be applied to our designed temporal-domain multi-dimension signals for accurately estimating the AOAs of the signals from the users to the IRS.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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