This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.
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Delay alignment modulation (DAM) is a promising technology for inter-symbol interference (ISI)-free communication without relying on sophisticated channel equalization or multi-carrier transmissions. The key ideas of DAM are delay precompensation and path-based beamforming, so that the multi-path signal components will arrive at the receiver simultaneously and constructively, rather than causing the detrimental ISI. However, the practical implementation of DAM requires channel state information (CSI) at the transmitter side. Therefore, in this letter, we study an efficient channel estimation method for DAM based on block orthogonal matching pursuit (BOMP) algorithm, by exploiting the block sparsity of the channel vector. Based on the imperfectly estimated CSI, the delay pre-compensations and tap-based beamforming are designed for DAM, and the resulting performance is studied. Simulation results demonstrate that with the BOMP-based channel estimation method, the CSI can be effectively acquired with low training overhead, and the performance of DAM based on estimated CSI is comparable to the ideal case with perfect CSI.
This paper addresses the challenge of generating optimal vehicle flow at the macroscopic level. Although several studies have focused on optimizing vehicle flow, little attention has been given to ensuring it can be practically achieved. To overcome this issue, we propose a route-recovery and eco-driving strategy for connected and automated vehicles (CAVs) that guarantees optimal flow generation. Our approach involves identifying the optimal vehicle flow that minimizes total travel time, given the constant travel demands in urban areas. We then develop a heuristic route-recovery algorithm to assign routes to CAVs that satisfy all travel demands while maintaining the optimal flow. Our method lets CAVs arrive at each road segment at their desired arrival time based on their assigned route and desired flow. In addition, we present an efficient coordination framework to minimize the energy consumption of CAVs and prevent collisions while crossing intersections. The proposed method can effectively generate optimal vehicle flow and potentially reduce travel time and energy consumption in urban areas.
Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across $k$ different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising efficient and scalable shared-memory algorithms for all components employed in the best sequential solvers without compromises with regards to solution quality. This work presents the scalable and high-quality hypergraph partitioning framework Mt-KaHyPar. Its most important components are parallel improvement algorithms based on the FM algorithm and maximum flows, as well as a parallel clustering algorithm for coarsening - which are used in a multilevel scheme with $\log(n)$ levels. As additional components, we parallelize the $n$-level partitioning scheme, devise a deterministic version of our algorithm, and present optimizations for plain graphs. We evaluate our solver on more than 800 graphs and hypergraphs, and compare it with 25 different algorithms from the literature. Our fastest configuration outperforms almost all existing hypergraph partitioners with regards to both solution quality and running time. Our highest-quality configuration achieves the same solution quality as the best sequential partitioner KaHyPar, while being an order of magnitude faster with ten threads. Thus, two of our configurations occupy all fronts of the Pareto curve for hypergraph partitioning. Furthermore, our solvers exhibit good speedups, e.g., 29.6x in the geometric mean on 64 cores (deterministic), 22.3x ($\log(n)$-level), and 25.9x ($n$-level).
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.
Data in Knowledge Graphs often represents part of the current state of the real world. Thus, to stay up-to-date the graph data needs to be updated frequently. To utilize information from Knowledge Graphs, many state-of-the-art machine learning approaches use embedding techniques. These techniques typically compute an embedding, i.e., vector representations of the nodes as input for the main machine learning algorithm. If a graph update occurs later on -- specifically when nodes are added or removed -- the training has to be done all over again. This is undesirable, because of the time it takes and also because downstream models which were trained with these embeddings have to be retrained if they change significantly. In this paper, we investigate embedding updates that do not require full retraining and evaluate them in combination with various embedding models on real dynamic Knowledge Graphs covering multiple use cases. We study approaches that place newly appearing nodes optimally according to local information, but notice that this does not work well. However, we find that if we continue the training of the old embedding, interleaved with epochs during which we only optimize for the added and removed parts, we obtain good results in terms of typical metrics used in link prediction. This performance is obtained much faster than with a complete retraining and hence makes it possible to maintain embeddings for dynamic Knowledge Graphs.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Many real-world applications require the prediction of long sequence time-series, such as electricity consumption planning. Long sequence time-series forecasting (LSTF) demands a high prediction capacity of the model, which is the ability to capture precise long-range dependency coupling between output and input efficiently. Recent studies have shown the potential of Transformer to increase the prediction capacity. However, there are several severe issues with Transformer that prevent it from being directly applicable to LSTF, such as quadratic time complexity, high memory usage, and inherent limitation of the encoder-decoder architecture. To address these issues, we design an efficient transformer-based model for LSTF, named Informer, with three distinctive characteristics: (i) a $ProbSparse$ Self-attention mechanism, which achieves $O(L \log L)$ in time complexity and memory usage, and has comparable performance on sequences' dependency alignment. (ii) the self-attention distilling highlights dominating attention by halving cascading layer input, and efficiently handles extreme long input sequences. (iii) the generative style decoder, while conceptually simple, predicts the long time-series sequences at one forward operation rather than a step-by-step way, which drastically improves the inference speed of long-sequence predictions. Extensive experiments on four large-scale datasets demonstrate that Informer significantly outperforms existing methods and provides a new solution to the LSTF problem.
In this paper, we present a comprehensive review of the imbalance problems in object detection. To analyze the problems in a systematic manner, we introduce a problem-based taxonomy. Following this taxonomy, we discuss each problem in depth and present a unifying yet critical perspective on the solutions in the literature. In addition, we identify major open issues regarding the existing imbalance problems as well as imbalance problems that have not been discussed before. Moreover, in order to keep our review up to date, we provide an accompanying webpage which catalogs papers addressing imbalance problems, according to our problem-based taxonomy. Researchers can track newer studies on this webpage available at: //github.com/kemaloksuz/ObjectDetectionImbalance .
This paper introduces an online model for object detection in videos designed to run in real-time on low-powered mobile and embedded devices. Our approach combines fast single-image object detection with convolutional long short term memory (LSTM) layers to create an interweaved recurrent-convolutional architecture. Additionally, we propose an efficient Bottleneck-LSTM layer that significantly reduces computational cost compared to regular LSTMs. Our network achieves temporal awareness by using Bottleneck-LSTMs to refine and propagate feature maps across frames. This approach is substantially faster than existing detection methods in video, outperforming the fastest single-frame models in model size and computational cost while attaining accuracy comparable to much more expensive single-frame models on the Imagenet VID 2015 dataset. Our model reaches a real-time inference speed of up to 15 FPS on a mobile CPU.
Learning similarity functions between image pairs with deep neural networks yields highly correlated activations of embeddings. In this work, we show how to improve the robustness of such embeddings by exploiting the independence within ensembles. To this end, we divide the last embedding layer of a deep network into an embedding ensemble and formulate training this ensemble as an online gradient boosting problem. Each learner receives a reweighted training sample from the previous learners. Further, we propose two loss functions which increase the diversity in our ensemble. These loss functions can be applied either for weight initialization or during training. Together, our contributions leverage large embedding sizes more effectively by significantly reducing correlation of the embedding and consequently increase retrieval accuracy of the embedding. Our method works with any differentiable loss function and does not introduce any additional parameters during test time. We evaluate our metric learning method on image retrieval tasks and show that it improves over state-of-the-art methods on the CUB 200-2011, Cars-196, Stanford Online Products, In-Shop Clothes Retrieval and VehicleID datasets.
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