Recent works have shown that imposing tensor structures on the coefficient tensor in regression problems can lead to more reliable parameter estimation and lower sample complexity compared to vector-based methods. This work investigates a new low-rank tensor model, called Low Separation Rank (LSR), in Generalized Linear Model (GLM) problems. The LSR model -- which generalizes the well-known Tucker and CANDECOMP/PARAFAC (CP) models, and is a special case of the Block Tensor Decomposition (BTD) model -- is imposed onto the coefficient tensor in the GLM model. This work proposes a block coordinate descent algorithm for parameter estimation in LSR-structured tensor GLMs. Most importantly, it derives a minimax lower bound on the error threshold on estimating the coefficient tensor in LSR tensor GLM problems. The minimax bound is proportional to the intrinsic degrees of freedom in the LSR tensor GLM problem, suggesting that its sample complexity may be significantly lower than that of vectorized GLMs. This result can also be specialised to lower bound the estimation error in CP and Tucker-structured GLMs. The derived bounds are comparable to tight bounds in the literature for Tucker linear regression, and the tightness of the minimax lower bound is further assessed numerically. Finally, numerical experiments on synthetic datasets demonstrate the efficacy of the proposed LSR tensor model for three regression types (linear, logistic and Poisson). Experiments on a collection of medical imaging datasets demonstrate the usefulness of the LSR model over other tensor models (Tucker and CP) on real, imbalanced data with limited available samples.
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Pilot contamination is a critical issue in distributed massive MIMO networks, where the reuse of pilot sequences due to limited availability of orthogonal pilots for channel estimation leads to performance degradation. In this work, we propose a novel distributed pilot assignment scheme to effectively mitigate the impact of pilot contamination. Our proposed scheme not only reduces signaling overhead, but it also enhances fault-tolerance. Extensive numerical simulations are conducted to evaluate the performance of the proposed scheme. Our results establish that the proposed scheme outperforms existing centralized and distributed schemes in terms of mitigating pilot contamination and significantly enhancing network throughput.
Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper provides a new modeling framework to accomplish this task via autoregression (AR). By considering a low-rank Tucker decomposition for the transition tensor, the proposed tensor AR can flexibly capture the underlying low-dimensional tensor dynamics, providing both substantial dimension reduction and meaningful multi-dimensional dynamic factor interpretations. For this model, we first study several nuclear-norm-regularized estimation methods and derive their non-asymptotic properties under the approximate low-rank setting. In particular, by leveraging the special balanced structure of the transition tensor, a novel convex regularization approach based on the sum of nuclear norms of square matricizations is proposed to efficiently encourage low-rankness of the coefficient tensor. To further improve the estimation efficiency under exact low-rankness, a non-convex estimator is proposed with a gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation studies and an empirical analysis of tensor-valued time series data from multi-category import-export networks demonstrate the advantages of the proposed approach.
We consider the problem of distilling efficient network topologies for collective communications. We provide an algorithmic framework for constructing direct-connect topologies optimized for the latency vs. bandwidth trade-off associated with the workload. Our approach synthesizes many different topologies and schedules for a given cluster size and degree and then identifies the appropriate topology and schedule for a given workload. Our algorithms start from small, optimal base topologies and associated communication schedules and use a set of techniques that can be iteratively applied to derive much larger topologies and schedules. Additionally, we incorporate well-studied large-scale graph topologies into our algorithmic framework by producing efficient collective schedules for them using a novel polynomial-time algorithm. Our evaluation uses multiple testbeds and large-scale simulations to demonstrate significant performance benefits from our derived topologies and schedules.
The flexibility of Simultaneous Localization and Mapping (SLAM) algorithms in various environments has consistently been a significant challenge. To address the issue of LiDAR odometry drift in high-noise settings, integrating clustering methods to filter out unstable features has become an effective module of SLAM frameworks. However, reducing the amount of point cloud data can lead to potential loss of information and possible degeneration. As a result, this research proposes a LiDAR odometry that can dynamically assess the point cloud's reliability. The algorithm aims to improve adaptability in diverse settings by selecting important feature points with sensitivity to the level of environmental degeneration. Firstly, a fast adaptive Euclidean clustering algorithm based on range image is proposed, which, combined with depth clustering, extracts the primary structural points of the environment defined as ambient skeleton points. Then, the environmental degeneration level is computed through the dense normal features of the skeleton points, and the point cloud cleaning is dynamically adjusted accordingly. The algorithm is validated on the KITTI benchmark and real environments, demonstrating higher accuracy and robustness in different environments.
Reinforcement learning (RL) for bipedal locomotion has recently demonstrated robust gaits over moderate terrains using only proprioceptive sensing. However, such blind controllers will fail in environments where robots must anticipate and adapt to local terrain, which requires visual perception. In this paper, we propose a fully-learned system that allows bipedal robots to react to local terrain while maintaining commanded travel speed and direction. Our approach first trains a controller in simulation using a heightmap expressed in the robot's local frame. Next, data is collected in simulation to train a heightmap predictor, whose input is the history of depth images and robot states. We demonstrate that with appropriate domain randomization, this approach allows for successful sim-to-real transfer with no explicit pose estimation and no fine-tuning using real-world data. To the best of our knowledge, this is the first example of sim-to-real learning for vision-based bipedal locomotion over challenging terrains.
Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in $\textbf{calf}$, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all correctness invariants are intrinsically maintained. Then, we describe and verify precise cost bounds on the operations, making use of the red-black tree invariants. Finally, we implement standard algorithms on sequences using the simple join-based signature and bound their cost in the case that red-black trees are used as the underlying implementation. All proofs are formally mechanized using the embedding of $\textbf{calf}$ in the Agda theorem prover.
Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.
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.
Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).
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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