Many electronic devices spend most of their time waiting for a wake-up event: pacemakers waiting for an anomalous heartbeat, security systems on alert to detect an intruder, smartphones listening for the user to say a wake-up phrase. These devices continuously convert physical signals into electrical currents that are then analyzed on a digital computer -- leading to power consumption even when no event is taking place. Solving this problem requires the ability to passively distinguish relevant from irrelevant events (e.g. tell a wake-up phrase from a regular conversation). Here, we experimentally demonstrate an elastic metastructure, consisting of a network of coupled silicon resonators, that passively discriminates between pairs of spoken words -- solving the wake-up problem for scenarios where only two classes of events are possible. This passive speech recognition is demonstrated on a dataset from speakers with significant gender and accent diversity. The geometry of the metastructure is determined during the design process, in which the network of resonators ('mechanical neurones') learns to selectively respond to spoken words. Training is facilitated by a machine learning model that reduces the number of computationally expensive three-dimensional elastic wave simulations. By embedding event detection in the structural dynamics, mechanical neural networks thus enable novel classes of always-on smart devices with no standby power consumption.
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It is well-known that the dimension of optimal anticodes in the rank-metric is divisible by the maximum m between the number of rows and columns of the matrices. Moreover, for a fixed k divisible by m, optimal rank-metric anticodes are the codes with least maximum rank, among those of dimension k. In this paper, we study the family of rank-metric codes whose dimension is not divisible by m and whose maximum rank is the least possible for codes of that dimension, according to the Anticode bound. As these are not optimal anticodes, we call them quasi optimal anticodes (qOACs). In addition, we call dually qOAC a qOAC whose dual is also a qOAC. We describe explicitly the structure of dually qOACs and compute their weight distributions, generalized weights, and associated q-polymatroids.
Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems. Such models typically exhibit a second-order structure and their material properties as well as their excitation may be depending on the driving frequency. We show and compare the effectiveness of all considered methods by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic problems.
Pattern matching on graphs has been widely studied lately due to its importance in genomics applications. Unfortunately, even the simplest problem of deciding if a string appears as a subpath of a graph admits a quadratic lower bound under the Orthogonal Vectors Hypothesis (Equi et al. ICALP 2019, SOFSEM 2021). To avoid this bottleneck, the research has shifted towards more specific graph classes, e.g. those induced from multiple sequence alignments (MSAs). Consider segmenting $\mathsf{MSA}[1..m,1..n]$ into $b$ blocks $\mathsf{MSA}[1..m,1..j_1]$, $\mathsf{MSA}[1..m,j_1+1..j_2]$, $\ldots$, $\mathsf{MSA}[1..m,j_{b-1}+1..n]$. The distinct strings in the rows of the blocks, after the removal of gap symbols, form the nodes of an elastic founder graph (EFG) where the edges represent the original connections observed in the MSA. An EFG is called indexable if a node label occurs as a prefix of only those paths that start from a node of the same block. Equi et al. (ISAAC 2021) showed that such EFGs support fast pattern matching and gave an $O(mn \log m)$-time algorithm for preprocessing the MSA in a way that allows the construction of indexable EFGs maximizing the number of blocks and, alternatively, minimizing the maximum length of a block, in $O(n)$ and $O(n \log\log n)$ time respectively. Using the suffix tree and solving a novel ancestor problem on trees, we improve the preprocessing to $O(mn)$ time and the $O(n \log \log n)$-time EFG construction to $O(n)$ time, thus showing that both types of indexable EFGs can be constructed in time linear in the input size.
Stochastic PDE eigenvalue problems often arise in the field of uncertainty quantification, whereby one seeks to quantify the uncertainty in an eigenvalue, or its eigenfunction. In this paper we present an efficient multilevel quasi-Monte Carlo (MLQMC) algorithm for computing the expectation of the smallest eigenvalue of an elliptic eigenvalue problem with stochastic coefficients. Each sample evaluation requires the solution of a PDE eigenvalue problem, and so tackling this problem in practice is notoriously computationally difficult. We speed up the approximation of this expectation in four ways: we use a multilevel variance reduction scheme to spread the work over a hierarchy of FE meshes and truncation dimensions; we use QMC methods to efficiently compute the expectations on each level; we exploit the smoothness in parameter space and reuse the eigenvector from a nearby QMC point to reduce the number of iterations of the eigensolver; and we utilise a two-grid discretisation scheme to obtain the eigenvalue on the fine mesh with a single linear solve. The full error analysis of a basic MLQMC algorithm is given in the companion paper [Gilbert and Scheichl, 2022], and so in this paper we focus on how to further improve the efficiency and provide theoretical justification for using nearby QMC points and two-grid methods. Numerical results are presented that show the efficiency of our algorithm, and also show that the four strategies we employ are complementary.
We present an expanded version of our previously released Kazakh text-to-speech (KazakhTTS) synthesis corpus. In the new KazakhTTS2 corpus, the overall size is increased from 93 hours to 271 hours, the number of speakers has risen from two to five (three females and two males), and the topic coverage is diversified with the help of new sources, including a book and Wikipedia articles. This corpus is necessary for building high-quality TTS systems for Kazakh, a Central Asian agglutinative language from the Turkic family, which presents several linguistic challenges. We describe the corpus construction process and provide the details of the training and evaluation procedures for the TTS system. Our experimental results indicate that the constructed corpus is sufficient to build robust TTS models for real-world applications, with a subjective mean opinion score of above 4.0 for all the five speakers. We believe that our corpus will facilitate speech and language research for Kazakh and other Turkic languages, which are widely considered to be low-resource due to the limited availability of free linguistic data. The constructed corpus, code, and pretrained models are publicly available in our GitHub repository.
Temporal receptive fields of models play an important role in action segmentation. Large receptive fields facilitate the long-term relations among video clips while small receptive fields help capture the local details. Existing methods construct models with hand-designed receptive fields in layers. Can we effectively search for receptive field combinations to replace hand-designed patterns? To answer this question, we propose to find better receptive field combinations through a global-to-local search scheme. Our search scheme exploits both global search to find the coarse combinations and local search to get the refined receptive field combination patterns further. The global search finds possible coarse combinations other than human-designed patterns. On top of the global search, we propose an expectation guided iterative local search scheme to refine combinations effectively. Our global-to-local search can be plugged into existing action segmentation methods to achieve state-of-the-art performance.
Learning structural representations of node sets from graph-structured data is crucial for applications ranging from node-role discovery to link prediction and molecule classification. Graph Neural Networks (GNNs) have achieved great success in structural representation learning. However, most GNNs are limited by the 1-Weisfeiler-Lehman (WL) test and thus possible to generate identical representation for structures and graphs that are actually different. More powerful GNNs, proposed recently by mimicking higher-order-WL tests, only focus on entire-graph representations and cannot utilize sparsity of the graph structure to be computationally efficient. Here we propose a general class of structure-related features, termed Distance Encoding (DE), to assist GNNs in representing node sets with arbitrary sizes with strictly more expressive power than the 1-WL test. DE essentially captures the distance between the node set whose representation is to be learnt and each node in the graph, which includes important graph-related measures such as shortest-path-distance and generalized PageRank scores. We propose two general frameworks for GNNs to use DEs (1) as extra node attributes and (2) further as controllers of message aggregation in GNNs. Both frameworks may still utilize the sparse structure to keep scalability to process large graphs. In theory, we prove that these two frameworks can distinguish node sets embedded in almost all regular graphs where traditional GNNs always fail. We also rigorously analyze their limitations. Empirically, we evaluate these two frameworks on node structural roles prediction, link prediction and triangle prediction over six real networks. The results show that our models outperform GNNs without DEs by up-to 15% improvement in average accuracy and AUC. Our models also significantly outperform other SOTA baselines particularly designed for those tasks.
An attributed network enriches a pure network by encoding a part of widely accessible node auxiliary information into node attributes. Learning vector representation of each node a.k.a. Network Embedding (NE) for such an attributed network by considering both structure and attribute information has recently attracted considerable attention, since each node embedding is simply a unified low-dimension vector representation that makes downstream tasks e.g. link prediction more efficient and much easier to realize. Most of previous works have not considered the significant case of a network with incomplete structure information, which however, would often appear in our real-world scenarios e.g. the abnormal users in a social network who intentionally hide their friendships. And different networks obviously have different levels of incomplete structure information, which imposes more challenges to balance two sources of information. To tackle that, we propose a robust NE method called Attributed Biased Random Walks (ABRW) to employ attribute information for compensating incomplete structure information by using transition matrices. The experiments of link prediction and node classification tasks on real-world datasets confirm the robustness and effectiveness of our method to the different levels of the incomplete structure information.
Network embedding has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accelerated by distributed computing schemes. To address these problems, we propose RandNE, a novel and simple billion-scale network embedding method. Specifically, we propose a Gaussian random projection approach to map the network into a low-dimensional embedding space while preserving the high-order proximities between nodes. To reduce the time complexity, we design an iterative projection procedure to avoid the explicit calculation of the high-order proximities. Theoretical analysis shows that our method is extremely efficient, and friendly to distributed computing schemes without any communication cost in the calculation. We demonstrate the efficacy of RandNE over state-of-the-art methods in network reconstruction and link prediction tasks on multiple datasets with different scales, ranging from thousands to billions of nodes and edges.
Model compression is significant for the wide adoption of Recurrent Neural Networks (RNNs) in both user devices possessing limited resources and business clusters requiring quick responses to large-scale service requests. This work aims to learn structurally-sparse Long Short-Term Memory (LSTM) by reducing the sizes of basic structures within LSTM units, including input updates, gates, hidden states, cell states and outputs. Independently reducing the sizes of basic structures can result in inconsistent dimensions among them, and consequently, end up with invalid LSTM units. To overcome the problem, we propose Intrinsic Sparse Structures (ISS) in LSTMs. Removing a component of ISS will simultaneously decrease the sizes of all basic structures by one and thereby always maintain the dimension consistency. By learning ISS within LSTM units, the obtained LSTMs remain regular while having much smaller basic structures. Based on group Lasso regularization, our method achieves 10.59x speedup without losing any perplexity of a language modeling of Penn TreeBank dataset. It is also successfully evaluated through a compact model with only 2.69M weights for machine Question Answering of SQuAD dataset. Our approach is successfully extended to non- LSTM RNNs, like Recurrent Highway Networks (RHNs). Our source code is publicly available at //github.com/wenwei202/iss-rnns
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