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We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems -- including matrix-vector product, matrix inversion, matrix multiplication and powering -- existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms. For example, for almost all matrices $A$, including the discrete Fourier transform (DFT) matrix, we prove that quantum circuits with at most $T$ input queries and $S$ qubits of memory require $T=\Omega(n^2/S)$ to compute matrix-vector product $Ax$ for $x \in \{0,1\}^n$. We similarly prove that matrix multiplication for $n\times n$ binary matrices requires $T=\Omega(n^3 / \sqrt{S})$. Because many of our lower bounds match deterministic algorithms with the same time and space complexity, we show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity -- the sum of the space per layer of a circuit. We also consider Boolean (i.e. AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for $n\times n$ Boolean matrix multiplication to $T=\Omega(n^{2.5}/S^{1/3})$ from $T=\Omega(n^{2.5}/S^{1/2})$. Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem used in prior work. Our tight lower bounds for linear algebra problems require adding a new bucketing method to the recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.

Underwater target localization uses real-time sensory measurements to estimate the position of underwater objects of interest, providing critical feedback information for underwater robots. While acoustic sensing is the most acknowledged method in underwater robots and possibly the only effective approach for long-range underwater target localization, such a sensing modality generally suffers from low resolution, high cost and high energy consumption, thus leading to a mediocre performance when applied to close-range underwater target localization. On the other hand, optical sensing has attracted increasing attention in the underwater robotics community for its advantages of high resolution and low cost, holding a great potential particularly in close-range underwater target localization. However, most existing studies in underwater optical sensing are restricted to specific types of targets due to the limited training data available. In addition, these studies typically focus on the design of estimation algorithms and ignore the influence of illumination conditions on the sensing performance, thus hindering wider applications in the real world. To address the aforementioned issues, this paper proposes a novel target localization method that assimilates both optical and acoustic sensory measurements to estimate the 3D positions of close-range underwater targets. A test platform with controllable illumination conditions is designed and developed to experimentally investigate the proposed multi-modal sensing approach. A large vision model is applied to process the optical imaging measurements, eliminating the requirement for training data acquisition, thus significantly expanding the scope of potential applications. Extensive experiments are conducted, the results of which validate the effectiveness of the proposed underwater target localization method.

The importance of proper data normalization for deep neural networks is well known. However, in continuous-time state-space model estimation, it has been observed that improper normalization of either the hidden state or hidden state derivative of the model estimate, or even of the time interval can lead to numerical and optimization challenges with deep learning based methods. This results in a reduced model quality. In this contribution, we show that these three normalization tasks are inherently coupled. Due to the existence of this coupling, we propose a solution to all three normalization challenges by introducing a normalization constant at the state derivative level. We show that the appropriate choice of the normalization constant is related to the dynamics of the to-be-identified system and we derive multiple methods of obtaining an effective normalization constant. We compare and discuss all the normalization strategies on a benchmark problem based on experimental data from a cascaded tanks system and compare our results with other methods of the identification literature.

The designing of efficient signal detectors is important and yet challenge for orthogonal time frequency space (OTFS) systems in high-mobility scenarios. In this letter, we develop an efficient message feedback interference cancellation aided unitary approximate message passing (denoted as UAMPMFIC) iterative detector, where the latest feedback messages from variable nodes are utilized for more reliable interference cancellation and performance improvement. A fast recursive scheme is leveraged in the proposed UAMP-MFIC detector to prevent complexity increasing. To further alleviate the error-propagation and improve the receiver performance, we also develop the bidirectional symbol detection structures, where Turbo UAMP-MFIC detector and iterative weight UAMP-MFIC detector are proposed to efficiently fuse the estimation results of forward and backward UAMP-MFIC detectors. The simulation results are finally provided to demonstrate performance improvement of our proposed detectors over existing detectors.

The integration of a near-space information network (NSIN) with the reconfigurable intelligent surface (RIS) is envisioned to significantly enhance the communication performance of future wireless communication systems by proactively altering wireless channels. This paper investigates the problem of deploying a RIS-integrated NSIN to provide energy-efficient, ultra-reliable and low-latency communications (URLLC) services. We mathematically formulate this problem as a resource optimization problem, aiming to maximize the effective throughput and minimize the system power consumption, subject to URLLC and physical resource constraints. The formulated problem is challenging in terms of accurate channel estimation, RIS phase alignment, theoretical analysis, and effective solution. We propose a joint resource allocation algorithm to handle these challenges. In this algorithm, we develop an accurate channel estimation approach by exploring message passing and optimize phase shifts of RIS reflecting elements to further increase the channel gain. Besides, we derive an analysis-friend expression of decoding error probability and decompose the problem into two-layered optimization problems by analyzing the monotonicity, which makes the formulated problem analytically tractable. Extensive simulations have been conducted to verify the performance of the proposed algorithm. Simulation results show that the proposed algorithm can achieve outstanding channel estimation performance and is more energy-efficient than diverse benchmark algorithms.

The accelerating deployment of spacecraft in orbit have generated interest in on-orbit servicing (OOS), inspection of spacecraft, and active debris removal (ADR). Such missions require precise rendezvous and proximity operations in the vicinity of non-cooperative, possible unknown, resident space objects. Safety concerns with manned missions and lag times with ground-based control necessitate complete autonomy. This requires robust characterization of the target's geometry. In this article, we present an approach for mapping geometries of satellites on orbit based on 3D Gaussian Splatting that can run on computing resources available on current spaceflight hardware. We demonstrate model training and 3D rendering performance on a hardware-in-the-loop satellite mock-up under several realistic lighting and motion conditions. Our model is shown to be capable of training on-board and rendering higher quality novel views of an unknown satellite nearly 2 orders of magnitude faster than previous NeRF-based algorithms. Such on-board capabilities are critical to enable downstream machine intelligence tasks necessary for autonomous guidance, navigation, and control tasks.

Triangle counting in networks under LDP (Local Differential Privacy) is a fundamental task for analyzing connection patterns or calculating a clustering coefficient while strongly protecting sensitive friendships from a central server. In particular, a recent study proposes an algorithm for this task that uses two rounds of interaction between users and the server to significantly reduce estimation error. However, this algorithm suffers from a prohibitively high communication cost due to a large noisy graph each user needs to download. In this work, we propose triangle counting algorithms under LDP with a small estimation error and communication cost. We first propose two-rounds algorithms consisting of edge sampling and carefully selecting edges each user downloads so that the estimation error is small. Then we propose a double clipping technique, which clips the number of edges and then the number of noisy triangles, to significantly reduce the sensitivity of each user's query. Through comprehensive evaluation, we show that our algorithms dramatically reduce the communication cost of the existing algorithm, e.g., from 6 hours to 8 seconds or less at a 20 Mbps download rate, while keeping a small estimation error.

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.

Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.

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.