Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir Computing strategies, such as the ESN, require high-order networks, i.e., many neurons, resulting in a large number of states that are magnitudes higher than the number of model inputs and outputs. A large number of states not only makes the time-step computation more costly but also may pose robustness issues, especially when applying ESNs to problems such as Model Predictive Control (MPC) and other optimal control problems. One way to circumvent this complexity issue is through Model Order Reduction strategies such as the Proper Orthogonal Decomposition (POD) and its variants (POD-DEIM), whereby we find an equivalent lower order representation to an already trained high dimension ESN. To this end, this work aims to investigate and analyze the performance of POD methods in Echo State Networks, evaluating their effectiveness through the Memory Capacity (MC) of the POD-reduced network compared to the original (full-order) ESN. We also perform experiments on two numerical case studies: a NARMA10 difference equation and an oil platform containing two wells and one riser. The results show that there is little loss of performance comparing the original ESN to a POD-reduced counterpart and that the performance of a POD-reduced ESN tends to be superior to a normal ESN of the same size. Also, the POD-reduced network achieves speedups of around $80\%$ compared to the original ESN.
The spoken language serves as an accessible and efficient interface, enabling non-experts and disabled users to interact with complex assistant robots. However, accurately grounding language utterances gives a significant challenge due to the acoustic variability in speakers' voices and environmental noise. In this work, we propose a novel speech-scene graph grounding network (SGGNet$^2$) that robustly grounds spoken utterances by leveraging the acoustic similarity between correctly recognized and misrecognized words obtained from automatic speech recognition (ASR) systems. To incorporate the acoustic similarity, we extend our previous grounding model, the scene-graph-based grounding network (SGGNet), with the ASR model from NVIDIA NeMo. We accomplish this by feeding the latent vector of speech pronunciations into the BERT-based grounding network within SGGNet. We evaluate the effectiveness of using latent vectors of speech commands in grounding through qualitative and quantitative studies. We also demonstrate the capability of SGGNet$^2$ in a speech-based navigation task using a real quadruped robot, RBQ-3, from Rainbow Robotics.
Given a set of squares and a strip of bounded width and infinite height, we consider a square strip packaging problem, which we call the square independent packing problem (SIPP), to minimize the strip height so that all the squares are packed into independent cells separated by horizontal and vertical partitions. For the SIPP, we first investigate efficient solution representations and propose a compact representation that reduces the search space from $\Omega(n!)$ to $O(2^n)$, with $n$ the number of given squares, while guaranteeing that there exists a solution representation that corresponds to an optimal solution. Based on the solution representation, we show that the problem is NP-hard, and then we propose a fully polynomial-time approximation scheme (FPTAS) to solve it. We also propose three mathematical programming formulations based on different solution representations and confirm the performance of these algorithms through computational experiments. Finally, we discuss several extensions that are relevant to practical applications.
Online polarization research currently focuses on studying single-issue opinion distributions or computing distance metrics of interaction network structures. Limited data availability often restricts studies to positive interaction data, which can misrepresent the reality of a discussion. We introduce a novel framework that aims at combining these three aspects, content and interactions, as well as their nature (positive or negative), while challenging the prevailing notion of polarization as an umbrella term for all forms of online conflict or opposing opinions. In our approach, built on the concepts of cleavage structures and structural balance of signed social networks, we factorize polarization into two distinct metrics: Antagonism and Alignment. Antagonism quantifies hostility in online discussions, based on the reactions of users to content. Alignment uses signed structural information encoded in long-term user-user relations on the platform to describe how well user interactions fit the global and/or traditional sides of discussion. We can analyse the change of these metrics through time, localizing both relevant trends but also sudden changes that can be mapped to specific contexts or events. We apply our methods to two distinct platforms: Birdwatch, a US crowd-based fact-checking extension of Twitter, and DerStandard, an Austrian online newspaper with discussion forums. In these two use cases, we find that our framework is capable of describing the global status of the groups of users (identification of cleavages) while also providing relevant findings on specific issues or in specific time frames. Furthermore, we show that our four metrics describe distinct phenomena, emphasizing their independent consideration for unpacking polarization complexities.
Car pooling is expected to significantly help in reducing traffic congestion and pollution in cities by enabling drivers to share their cars with travellers with similar itineraries and time schedules. A number of car pooling matching services have been designed in order to efficiently find successful ride matches in a given pool of drivers and potential passengers. However, it is now recognised that many non-monetary aspects and social considerations, besides simple mobility needs, may influence the individual willingness of sharing a ride, which are difficult to predict. To address this problem, in this study we propose GoTogether, a recommender system for car pooling services that leverages on learning-to-rank techniques to automatically derive the personalised ranking model of each user from the history of her choices (i.e., the type of accepted or rejected shared rides). Then, GoTogether builds the list of recommended rides in order to maximise the success rate of the offered matches. To test the performance of our scheme we use real data from Twitter and Foursquare sources in order to generate a dataset of plausible mobility patterns and ride requests in a metropolitan area. The results show that the proposed solution quickly obtain an accurate prediction of the personalised user's choice model both in static and dynamic conditions.
Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.
Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.
Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.
Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.
Link prediction for knowledge graphs is the task of predicting missing relationships between entities. Previous work on link prediction has focused on shallow, fast models which can scale to large knowledge graphs. However, these models learn less expressive features than deep, multi-layer models -- which potentially limits performance. In this work, we introduce ConvE, a multi-layer convolutional network model for link prediction, and report state-of-the-art results for several established datasets. We also show that the model is highly parameter efficient, yielding the same performance as DistMult and R-GCN with 8x and 17x fewer parameters. Analysis of our model suggests that it is particularly effective at modelling nodes with high indegree -- which are common in highly-connected, complex knowledge graphs such as Freebase and YAGO3. In addition, it has been noted that the WN18 and FB15k datasets suffer from test set leakage, due to inverse relations from the training set being present in the test set -- however, the extent of this issue has so far not been quantified. We find this problem to be severe: a simple rule-based model can achieve state-of-the-art results on both WN18 and FB15k. To ensure that models are evaluated on datasets where simply exploiting inverse relations cannot yield competitive results, we investigate and validate several commonly used datasets -- deriving robust variants where necessary. We then perform experiments on these robust datasets for our own and several previously proposed models, and find that ConvE achieves state-of-the-art Mean Reciprocal Rank across all datasets.
To address the sparsity and cold start problem of collaborative filtering, researchers usually make use of side information, such as social networks or item attributes, to improve recommendation performance. This paper considers the knowledge graph as the source of side information. To address the limitations of existing embedding-based and path-based methods for knowledge-graph-aware recommendation, we propose Ripple Network, an end-to-end framework that naturally incorporates the knowledge graph into recommender systems. Similar to actual ripples propagating on the surface of water, Ripple Network stimulates the propagation of user preferences over the set of knowledge entities by automatically and iteratively extending a user's potential interests along links in the knowledge graph. The multiple "ripples" activated by a user's historically clicked items are thus superposed to form the preference distribution of the user with respect to a candidate item, which could be used for predicting the final clicking probability. Through extensive experiments on real-world datasets, we demonstrate that Ripple Network achieves substantial gains in a variety of scenarios, including movie, book and news recommendation, over several state-of-the-art baselines.