Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature robust optimal transport (FROT) for high-dimensional data, which jointly solves feature selection and OT problems. Specifically, we formulate the FROT problem as a min--max optimization problem. Then, we propose a convex formulation of FROT and solve it with the Frank--Wolfe-based optimization algorithm, where the sub-problem can be efficiently solved using the Sinkhorn algorithm. A key advantage of FROT is that important features can be analytically determined by simply solving the convex optimization problem. Furthermore, we propose using the FROT algorithm for the layer selection problem in deep neural networks for semantic correspondence. By conducting synthetic and benchmark experiments, we demonstrate that the proposed method can determine important features. Additionally, we show that the FROT algorithm achieves a state-of-the-art performance in real-world semantic correspondence datasets.
Since its inception, the neural estimation of mutual information (MI) has demonstrated the empirical success of modeling expected dependency between high-dimensional random variables. However, MI is an aggregate statistic and cannot be used to measure point-wise dependency between different events. In this work, instead of estimating the expected dependency, we focus on estimating point-wise dependency (PD), which quantitatively measures how likely two outcomes co-occur. We show that we can naturally obtain PD when we are optimizing MI neural variational bounds. However, optimizing these bounds is challenging due to its large variance in practice. To address this issue, we develop two methods (free of optimizing MI variational bounds): Probabilistic Classifier and Density-Ratio Fitting. We demonstrate the effectiveness of our approaches in 1) MI estimation, 2) self-supervised representation learning, and 3) cross-modal retrieval task.
Self-supervised representation learning adopts self-defined signals as supervision and uses the learned representation for downstream tasks, such as masked language modeling (e.g., BERT) for natural language processing and contrastive visual representation learning (e.g., SimCLR) for computer vision applications. In this paper, we present a theoretical framework explaining that self-supervised learning is likely to work under the assumption that only the shared information (e.g., contextual information or content) between the input (e.g., non-masked words or original images) and self-supervised signals (e.g., masked-words or augmented images) contributes to downstream tasks. Under this assumption, we demonstrate that self-supervisedly learned representation can extract task-relevant and discard task-irrelevant information. We further connect our theoretical analysis to popular contrastive and predictive (self-supervised) learning objectives. In the experimental section, we provide controlled experiments on two popular tasks: 1) visual representation learning with various self-supervised learning objectives to empirically support our analysis; and 2) visual-textual representation learning to challenge that input and self-supervised signal lie in different modalities.
The human language has heterogeneous sources of information, including tones of voice, facial gestures, and spoken language. Recent advances introduced computational models to combine these multimodal sources and yielded strong performance on human-centric tasks. Nevertheless, most of the models are often black-box, which comes with the price of lacking interpretability. In this paper, we propose Multimodal Routing to separate the contributions to the prediction from each modality and the interactions between modalities. At the heart of our method is a routing mechanism that represents each prediction as a concept, i.e., a vector in a Euclidean space. The concept assumes a linear aggregation from the contributions of multimodal features. Then, the routing procedure iteratively 1) associates a feature and a concept by checking how this concept agrees with this feature and 2) updates the concept based on the associations. In our experiments, we provide both global and local interpretation using Multimodal Routing on sentiment analysis and emotion prediction, without loss of performance compared to state-of-the-art methods. For example, we observe that our model relies mostly on the text modality for neutral sentiment predictions, the acoustic modality for extremely negative predictions, and the text-acoustic bimodal interaction for extremely positive predictions.
We introduce a new routing algorithm for capsule networks, in which a child capsule is routed to a parent based only on agreement between the parent's state and the child's vote. The new mechanism 1) designs routing via inverted dot-product attention; 2) imposes Layer Normalization as normalization; and 3) replaces sequential iterative routing with concurrent iterative routing. When compared to previously proposed routing algorithms, our method improves performance on benchmark datasets such as CIFAR-10 and CIFAR-100, and it performs at-par with a powerful CNN (ResNet-18) with 4x fewer parameters. On a different task of recognizing digits from overlayed digit images, the proposed capsule model performs favorably against CNNs given the same number of layers and neurons per layer. We believe that our work raises the possibility of applying capsule networks to complex real-world tasks. Our code is publicly available at: https://github.com/apple/ml-capsules-inverted-attention-routing An alternative implementation is available at: https://github.com/yaohungt/Capsules-Inverted-Attention-Routing/blob/master/README.md
While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform, and studies have shown a potentially richer representation of complex nets. In this paper, we propose a Complex Transformer, which incorporates the transformer model as a backbone for sequence modeling; we also develop attention and encoder-decoder network operating for complex input. The model achieves state-of-the-art performance on the MusicNet dataset and an In-phase Quadrature (IQ) signal dataset.
Estimating mutual information is an important machine learning and statistics problem. To estimate the mutual information from data, a common practice is preparing a set of paired samples. However, in some cases, it is difficult to obtain a large number of data pairs. To address this problem, we propose squared-loss mutual information (SMI) estimation using a small number of paired samples and the available unpaired ones. We first represent SMI through the density ratio function, where the expectation is approximated by the samples from marginals and its assignment parameters. The objective is formulated using the optimal transport problem and quadratic programming. Then, we introduce the least-square mutual information-Sinkhorn algorithm (LSMI-Sinkhorn) for efficient optimization. Through experiments, we first demonstrate that the proposed method can estimate the SMI without a large number of paired samples. We also evaluate and show the effectiveness of the proposed LSMI-Sinkhorn on various types of machine learning problems such as image matching and photo album summarization.