Transductive Maximum Margin Classifier for Few-Shot Learning

Few-shot learning aims to train a classifier that can generalize well when just a small number of labeled samples per class are given. We introduce Transductive Maximum Margin Classifier (TMMC) for few-shot learning. The basic idea of the classical maximum margin classifier is to solve an optimal prediction function that the corresponding separating hyperplane can correctly divide the training data and the resulting classifier has the largest geometric margin. In few-shot learning scenarios, the training samples are scarce, not enough to find a separating hyperplane with good generalization ability on unseen data. TMMC is constructed using a mixture of the labeled support set and the unlabeled query set in a given task. The unlabeled samples in the query set can adjust the separating hyperplane so that the prediction function is optimal on both the labeled and unlabeled samples. Furthermore, we leverage an efficient and effective quasi-Newton algorithm, the L-BFGS method to optimize TMMC. Experimental results on three standard few-shot learning benchmarks including miniImagenet, tieredImagenet and CUB suggest that our TMMC achieves state-of-the-art accuracies.

Temporal Alignment Prediction for Few-Shot Video Classification

The goal of few-shot video classification is to learn a classification model with good generalization ability when trained with only a few labeled videos. However, it is difficult to learn discriminative feature representations for videos in such a setting. In this paper, we propose Temporal Alignment Prediction (TAP) based on sequence similarity learning for few-shot video classification. In order to obtain the similarity of a pair of videos, we predict the alignment scores between all pairs of temporal positions in the two videos with the temporal alignment prediction function. Besides, the inputs to this function are also equipped with the context information in the temporal domain. We evaluate TAP on two video classification benchmarks including Kinetics and Something-Something V2. The experimental results verify the effectiveness of TAP and show its superiority over state-of-the-art methods.

CLTR: An End-to-End, Transformer-Based System for Cell Level Table Retrieval and Table Question Answering

We present the first end-to-end, transformer-based table question answering (QA) system that takes natural language questions and massive table corpus as inputs to retrieve the most relevant tables and locate the correct table cells to answer the question. Our system, CLTR, extends the current state-of-the-art QA over tables model to build an end-to-end table QA architecture. This system has successfully tackled many real-world table QA problems with a simple, unified pipeline. Our proposed system can also generate a heatmap of candidate columns and rows over complex tables and allow users to quickly identify the correct cells to answer questions. In addition, we introduce two new open-domain benchmarks, E2E_WTQ and E2E_GNQ, consisting of 2,005 natural language questions over 76,242 tables. The benchmarks are designed to validate CLTR as well as accommodate future table retrieval and end-to-end table QA research and experiments. Our experiments demonstrate that our system is the current state-of-the-art model on the table retrieval task and produces promising results for end-to-end table QA.

Learning Structures for Deep Neural Networks

In this paper, we focus on the unsupervised setting for structure learning of deep neural networks and propose to adopt the efficient coding principle, rooted in information theory and developed in computational neuroscience, to guide the procedure of structure learning without label information. This principle suggests that a good network structure should maximize the mutual information between inputs and outputs, or equivalently maximize the entropy of outputs under mild assumptions. We further establish connections between this principle and the theory of Bayesian optimal classification, and empirically verify that larger entropy of the outputs of a deep neural network indeed corresponds to a better classification accuracy. Then as an implementation of the principle, we show that sparse coding can effectively maximize the entropy of the output signals, and accordingly design an algorithm based on global group sparse coding to automatically learn the inter-layer connection and determine the depth of a neural network. Our experiments on a public image classification dataset demonstrate that using the structure learned from scratch by our proposed algorithm, one can achieve a classification accuracy comparable to the best expert-designed structure (i.e., convolutional neural networks (CNN)). In addition, our proposed algorithm successfully discovers the local connectivity (corresponding to local receptive fields in CNN) and invariance structure (corresponding to pulling in CNN), as well as achieves a good tradeoff between marginal performance gain and network depth.

$L^2$ estimate for polynomials of the Laplace operator with Gaussian measure

Let $P(Delta)$ be a polynomial of the Laplace operator $Delta=sum_{j=1}^nfrac{partial^2}{partial x^2_j}$ on $mathbb{R}^n$. We prove the existence of weak solutions of the equation $P(Delta)u=f$ and the existence of a bounded right inverse of the differential operator $P(Delta)$ in the weighted Hilbert space with Gaussian measure, i.e., $L^2(mathbb{R}^n,e^{-|x|^2})$.

Two-phase Pseudo Label Densification for Self-training based Domain Adaptation

Recently, deep self-training approaches emerged as a powerful solution to the unsupervised domain adaptation. The self-training scheme involves iterative processing of target data; it generates target pseudo labels and retrains the network. However, since only the confident predictions are taken as pseudo labels, existing self-training approaches inevitably produce sparse pseudo labels in practice. We see this is critical because the resulting insufficient training-signals lead to a suboptimal, error-prone model. In order to tackle this problem, we propose a novel Two-phase Pseudo Label Densification framework, referred to as TPLD. In the first phase, we use sliding window voting to propagate the confident predictions, utilizing intrinsic spatial-correlations in the images. In the second phase, we perform a confidence-based easy-hard classification. For the easy samples, we now employ their full pseudo labels. For the hard ones, we instead adopt adversarial learning to enforce hard-to-easy feature alignment. To ease the training process and avoid noisy predictions, we introduce the bootstrapping mechanism to the original self-training loss. We show the proposed TPLD can be easily integrated into existing self-training based approaches and improves the performance significantly. Combined with the recently proposed CRST self-training framework, we achieve new state-of-the-art results on two standard UDA benchmarks.

Uniform estimates for the canonical solution to the $barpartial$-equation on product domains

We obtain uniform estimates for the canonical solution to $barpartial u=f$ on the Cartesian product of smoothly bounded planar domains, when $f$ is continuous up to the boundary. This generalizes Landuccis result for the bidisc toward higher dimensional product domains.

Unsupervised Intra-domain Adaptation for Semantic Segmentation through Self-Supervision

Convolutional neural network-based approaches have achieved remarkable progress in semantic segmentation. However, these approaches heavily rely on annotated data which are labor intensive. To cope with this limitation, automatically annotated data generated from graphic engines are used to train segmentation models. However, the models trained from synthetic data are difficult to transfer to real images. To tackle this issue, previous works have considered directly adapting models from the source data to the unlabeled target data (to reduce the inter-domain gap). Nonetheless, these techniques do not consider the large distribution gap among the target data itself (intra-domain gap). In this work, we propose a two-step self-supervised domain adaptation approach to minimize the inter-domain and intra-domain gap together. First, we conduct the inter-domain adaptation of the model; from this adaptation, we separate the target domain into an easy and hard split using an entropy-based ranking function. Finally, to decrease the intra-domain gap, we propose to employ a self-supervised adaptation technique from the easy to the hard split. Experimental results on numerous benchmark datasets highlight the effectiveness of our method against existing state-of-the-art approaches. The source code is available at https://github.com/feipan664/IntraDA.git.

Anomalous relation between in-plane and out-of-plane stiffnesses in 2D networked materials

For thin networked materials, which are spatial discrete structures constructed by continuum components, a paradox on the effective thickness defined by the in-plane and out-of-plane stiffnesses is found, i.e. the effective thickness is not a constant but varies with loading modes. To reveal the mechanism underneath the paradox, we have established a micromechanical framework to investigate the deformation mechanism and predict the stiffness matrix of the networked materials. It is revealed that the networked materials can carry in-plane loads by axial stretching/compression of the components in the networks and resist out-of-plane loading by bending and torsion of the components. The bending deformation of components has a corresponding relation to the axial stretching/compression through the effective thickness, as the continuum plates do, while the torsion deformation has no relation to the axial stretching/compression. The isolated torsion deformation breaks the classical stiffness relation between the in-plane stiffness and the out-of-plane stiffness, which can even be further distorted by the stiffness threshold effect in randomly networked materials. Accordingly, a new formula is summarized to describe the anomalous stiffness relation. This network model can also apply in atomic scale 2D nanomaterials when combining with the molecular structural mechanics model. This work gives an insight into the understanding of the mechanical properties of discrete materials/structures ranging from atomic scale to macro scale.

fPINNs: Fractional Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly encoded into the NN using automatic differentiation, while the sum of the mean-squared PDE-residuals and the mean-squared error in initial/boundary conditions is minimized with respect to the NN parameters. We extend PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and we demonstrate their accuracy and effectiveness in solving multi-dimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box forcing terms). A novel element of the fPINNs is the hybrid approach that we introduce for constructing the residual in the loss function using both automatic differentiation for the integer-order operators and numerical discretization for the fractional operators. We consider 1D time-dependent fractional ADEs and compare white-box (WB) and black-box (BB) forcing. We observe that for the BB forcing fPINNs outperform FDM. Subsequently, we consider multi-dimensional time-, space-, and space-time-fractional ADEs using the directional fractional Laplacian and we observe relative errors of $10^{-4}$. Finally, we solve several inverse problems in 1D, 2D, and 3D to identify the fractional orders, diffusion coefficients, and transport velocities and obtain accurate results even in the presence of significant noise.