We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments. The code has been released in //github.com/radarFudan/Curse-of-memory
We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in information-theoretic generalization bounds, it is uncertain if these bounds can provide insight into the exceptional performance of various learning algorithms. Our study of stochastic convex optimization reveals that, for true risk minimization, dimension-dependent mutual information is necessary. This indicates that existing information-theoretic generalization bounds fall short in capturing the generalization capabilities of algorithms like SGD and regularized ERM, which have dimension-independent sample complexity.
Open set recognition (OSR) requires the model to classify samples that belong to closed sets while rejecting unknown samples during test. Currently, generative models often perform better than discriminative models in OSR, but recent studies show that generative models may be computationally infeasible or unstable on complex tasks. In this paper, we provide insights into OSR and find that learning supplementary representations can theoretically reduce the open space risk. Based on the analysis, we propose a new model, namely Multi-Expert Diverse Attention Fusion (MEDAF), that learns diverse representations in a discriminative way. MEDAF consists of multiple experts that are learned with an attention diversity regularization term to ensure the attention maps are mutually different. The logits learned by each expert are adaptively fused and used to identify the unknowns through the score function. We show that the differences in attention maps can lead to diverse representations so that the fused representations can well handle the open space. Extensive experiments are conducted on standard and OSR large-scale benchmarks. Results show that the proposed discriminative method can outperform existing generative models by up to 9.5% on AUROC and achieve new state-of-the-art performance with little computational cost. Our method can also seamlessly integrate existing classification models. Code is available at //github.com/Vanixxz/MEDAF.
Aspect sentiment quad prediction (ASQP) aims to predict the quad sentiment elements for a given sentence, which is a critical task in the field of aspect-based sentiment analysis. However, the data imbalance issue has not received sufficient attention in ASQP task. In this paper, we divide the issue into two-folds, quad-pattern imbalance and aspect-category imbalance, and propose an Adaptive Data Augmentation (ADA) framework to tackle the imbalance issue. Specifically, a data augmentation process with a condition function adaptively enhances the tail quad patterns and aspect categories, alleviating the data imbalance in ASQP. Following previous studies, we also further explore the generative framework for extracting complete quads by introducing the category prior knowledge and syntax-guided decoding target. Experimental results demonstrate that data augmentation for imbalance in ASQP task can improve the performance, and the proposed ADA method is superior to naive data oversampling.
A recurring challenge in the application of redistricting simulation algorithms lies in extracting useful summaries and comparisons from a large ensemble of districting plans. Researchers often compute summary statistics for each district in a plan, and then study their distribution across the plans in the ensemble. This approach discards rich geographic information that is inherent in districting plans. We introduce the projective average, an operation that projects a district-level summary statistic back to the underlying geography and then averages this statistic across plans in the ensemble. Compared to traditional district-level summaries, projective averages are a powerful tool for geographically granular, sub-district analysis of districting plans along a variety of dimensions. However, care must be taken to account for variation within redistricting ensembles, to avoid misleading conclusions. We propose and validate a multiple-testing procedure to control the probability of incorrectly identifying outlier plans or regions when using projective averages.
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.
Benefit from the quick development of deep learning techniques, salient object detection has achieved remarkable progresses recently. However, there still exists following two major challenges that hinder its application in embedded devices, low resolution output and heavy model weight. To this end, this paper presents an accurate yet compact deep network for efficient salient object detection. More specifically, given a coarse saliency prediction in the deepest layer, we first employ residual learning to learn side-output residual features for saliency refinement, which can be achieved with very limited convolutional parameters while keep accuracy. Secondly, we further propose reverse attention to guide such side-output residual learning in a top-down manner. By erasing the current predicted salient regions from side-output features, the network can eventually explore the missing object parts and details which results in high resolution and accuracy. Experiments on six benchmark datasets demonstrate that the proposed approach compares favorably against state-of-the-art methods, and with advantages in terms of simplicity, efficiency (45 FPS) and model size (81 MB).
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.