Compositionality is at the heart of computer science and several other areas of applied category theory such as computational linguistics, categorical quantum mechanics, interpretable AI, dynamical systems, compositional game theory, and Petri nets. However, the meaning of the term seems to vary across the many different applications. This work contributes to understanding, and in particular qualifying, different kinds of compositionality. Formally, we introduce invariants of categories that we call zeroth and first homotopy posets, generalising in a precise sense the $\pi_0$ and $\pi_1$ of a groupoid. These posets can be used to obtain a qualitative description of how far an object is from being terminal and a morphism is from being iso. In the context of applied category theory, this formal machinery gives us a way to qualitatively describe the "failures of compositionality", seen as failures of certain (op)lax functors to be strong, by classifying obstructions to the (op)laxators being isomorphisms. Failure of compositionality, for example for the interpretation of a categorical syntax in a semantic universe, can both be a bad thing and a good thing, which we illustrate by respective examples in graph theory and quantum theory.
The rise of datathons, also known as data or data science hackathons, has provided a platform to collaborate, learn, and innovate in a short timeframe. Despite their significant potential benefits, organizations often struggle to effectively work with data due to a lack of clear guidelines and best practices for potential issues that might arise. Drawing on our own experiences and insights from organizing >80 datathon challenges with >60 partnership organizations since 2016, we provide guidelines and recommendations that serve as a resource for organizers to navigate the data-related complexities of datathons. We apply our proposed framework to 10 case studies.
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output changes can result in costly decisions, reduced user trust, potential security concerns, and lack of replicability. In this study, we consider the Lipschitz continuity of algorithms as a stability measure and initiate a systematic study of the Lipschitz continuity of algorithms for (weighted) graph problems. Depending on how we embed the output solution to a metric space, we can think of several Lipschitzness notions. We mainly consider the one that is invariant under scaling of weights, and we provide Lipschitz continuous algorithms and lower bounds for the minimum spanning tree problem, the shortest path problem, and the maximum weight matching problem. In particular, our shortest path algorithm is obtained by first designing an algorithm for unweighted graphs that are robust against edge contractions and then applying it to the unweighted graph constructed from the original weighted graph. Then, we consider another Lipschitzness notion induced by a natural mapping that maps the output solution to its characteristic vector. It turns out that no Lipschitz continuous algorithm exists for this Lipschitz notion, and we instead design algorithms with bounded pointwise Lipschitz constants for the minimum spanning tree problem and the maximum weight bipartite matching problem. Our algorithm for the latter problem is based on an LP relaxation with entropy regularization.
This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.
Transformer is a new kind of neural architecture which encodes the input data as powerful features via the attention mechanism. Basically, the visual transformers first divide the input images into several local patches and then calculate both representations and their relationship. Since natural images are of high complexity with abundant detail and color information, the granularity of the patch dividing is not fine enough for excavating features of objects in different scales and locations. In this paper, we point out that the attention inside these local patches are also essential for building visual transformers with high performance and we explore a new architecture, namely, Transformer iN Transformer (TNT). Specifically, we regard the local patches (e.g., 16$\times$16) as "visual sentences" and present to further divide them into smaller patches (e.g., 4$\times$4) as "visual words". The attention of each word will be calculated with other words in the given visual sentence with negligible computational costs. Features of both words and sentences will be aggregated to enhance the representation ability. Experiments on several benchmarks demonstrate the effectiveness of the proposed TNT architecture, e.g., we achieve an 81.5% top-1 accuracy on the ImageNet, which is about 1.7% higher than that of the state-of-the-art visual transformer with similar computational cost. The PyTorch code is available at //github.com/huawei-noah/CV-Backbones, and the MindSpore code is available at //gitee.com/mindspore/models/tree/master/research/cv/TNT.
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.
Transformers have become one of the most important architectural innovations in deep learning and have enabled many breakthroughs over the past few years. Here we propose a simple attention-free network architecture, gMLP, based solely on MLPs with gating, and show that it can perform as well as Transformers in key language and vision applications. Our comparisons show that self-attention is not critical for Vision Transformers, as gMLP can achieve the same accuracy. For BERT, our model achieves parity with Transformers on pretraining perplexity and is better on some downstream tasks. On finetuning tasks where gMLP performs worse, making the gMLP model substantially larger can close the gap with Transformers. In general, our experiments show that gMLP can scale as well as Transformers over increased data and compute.
Transformer is a type of deep neural network mainly based on self-attention mechanism which is originally applied in natural language processing field. Inspired by the strong representation ability of transformer, researchers propose to extend transformer for computer vision tasks. Transformer-based models show competitive and even better performance on various visual benchmarks compared to other network types such as convolutional networks and recurrent networks. In this paper we provide a literature review of these visual transformer models by categorizing them in different tasks and analyze the advantages and disadvantages of these methods. In particular, the main categories include the basic image classification, high-level vision, low-level vision and video processing. Self-attention in computer vision is also briefly revisited as self-attention is the base component in transformer. Efficient transformer methods are included for pushing transformer into real applications. Finally, we give a discussion about the further research directions for visual transformer.
Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit the given data to reveal the underlying cluster structure. Some types of losses---such as k-means, or its non-linear version: kernelized k-means (centroid based), and DBSCAN (density based)---are popular choices due to their good empirical performance on a range of applications. Although every so often the clustering output using these standard losses fails to reveal the underlying structure, and the practitioner has to custom-design their own variation. In this work we take an intrinsically different approach to clustering: rather than fitting a dataset to a specific clustering loss, we train a recurrent model that learns how to cluster. The model uses as training pairs examples of datasets (as input) and its corresponding cluster identities (as output). By providing multiple types of training datasets as inputs, our model has the ability to generalize well on unseen datasets (new clustering tasks). Our experiments reveal that by training on simple synthetically generated datasets or on existing real datasets, we can achieve better clustering performance on unseen real-world datasets when compared with standard benchmark clustering techniques. Our meta clustering model works well even for small datasets where the usual deep learning models tend to perform worse.
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.