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Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems, such as the Minimum Linear Arrangement Problem ($\texttt{minLA}$). A linear arrangement is usually defined as a permutation of the $n$ vertices of a graph. An intuitive geometric setting is that of vertices lying on consecutive integer positions in the real line, starting at 1; edges are often drawn as semicircles above the real line. In this paper we study the Maximum Linear Arrangement problem ($\texttt{MaxLA}$), the maximization variant of $\texttt{minLA}$. We devise a new characterization of maximum arrangements of general graphs, and prove that $\texttt{MaxLA}$ can be solved for cycle graphs in constant time, and for $k$-linear trees ($k\le2$) in time $O(n)$. We present two constrained variants of $\texttt{MaxLA}$ we call $\texttt{bipartite MaxLA}$ and $\texttt{1-thistle MaxLA}$. We prove that the former can be solved in time $O(n)$ for any bipartite graph; the latter, by an algorithm that typically runs in time $O(n^4)$ on unlabelled trees. The combination of the two variants has two promising characteristics. First, it solves $\texttt{MaxLA}$ for almost all trees consisting of a few tenths of nodes. Second, we prove that it constitutes a $3/2$-approximation algorithm for $\texttt{MaxLA}$ for trees. Furthermore, we conjecture that $\texttt{bipartite MaxLA}$ solves $\texttt{MaxLA}$ for at least $50\%$ of all free trees.

We propose a new method for cloth digitalization. Deviating from existing methods which learn from data captured under relatively casual settings, we propose to learn from data captured in strictly tested measuring protocols, and find plausible physical parameters of the cloths. However, such data is currently absent, so we first propose a new dataset with accurate cloth measurements. Further, the data size is considerably smaller than the ones in current deep learning, due to the nature of the data capture process. To learn from small data, we propose a new Bayesian differentiable cloth model to estimate the complex material heterogeneity of real cloths. It can provide highly accurate digitalization from very limited data samples. Through exhaustive evaluation and comparison, we show our method is accurate in cloth digitalization, efficient in learning from limited data samples, and general in capturing material variations. Code and data are available //github.com/realcrane/Bayesian-Differentiable-Physics-for-Cloth-Digitalization

As a general method for exploration in deep reinforcement learning (RL), NoisyNet can produce problem-specific exploration strategies. Spiking neural networks (SNNs), due to their binary firing mechanism, have strong robustness to noise, making it difficult to realize efficient exploration with local disturbances. To solve this exploration problem, we propose a noisy spiking actor network (NoisySAN) that introduces time-correlated noise during charging and transmission. Moreover, a noise reduction method is proposed to find a stable policy for the agent. Extensive experimental results demonstrate that our method outperforms the state-of-the-art performance on a wide range of continuous control tasks from OpenAI gym.

Geometric deep learning (GDL), which is based on neural network architectures that incorporate and process symmetry information, has emerged as a recent paradigm in artificial intelligence. GDL bears particular promise in molecular modeling applications, in which various molecular representations with different symmetry properties and levels of abstraction exist. This review provides a structured and harmonized overview of molecular GDL, highlighting its applications in drug discovery, chemical synthesis prediction, and quantum chemistry. Emphasis is placed on the relevance of the learned molecular features and their complementarity to well-established molecular descriptors. This review provides an overview of current challenges and opportunities, and presents a forecast of the future of GDL for molecular sciences.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

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.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.

We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.

Deep learning has yielded state-of-the-art performance on many natural language processing tasks including named entity recognition (NER). However, this typically requires large amounts of labeled data. In this work, we demonstrate that the amount of labeled training data can be drastically reduced when deep learning is combined with active learning. While active learning is sample-efficient, it can be computationally expensive since it requires iterative retraining. To speed this up, we introduce a lightweight architecture for NER, viz., the CNN-CNN-LSTM model consisting of convolutional character and word encoders and a long short term memory (LSTM) tag decoder. The model achieves nearly state-of-the-art performance on standard datasets for the task while being computationally much more efficient than best performing models. We carry out incremental active learning, during the training process, and are able to nearly match state-of-the-art performance with just 25\% of the original training data.