ADNet: Leveraging Error-Bias Towards Normal Direction in Face Alignment

The recent progress of CNN has dramatically improved face alignment performance. However, few works have paid attention to the error-bias with respect to error distribution of facial landmarks. In this paper, we investigate the error-bias issue in face alignment, where the distributions of landmark errors tend to spread along the tangent line to landmark curves. This error-bias is not trivial since it is closely connected to the ambiguous landmark labeling task. Inspired by this observation, we seek a way to leverage the error-bias property for better convergence of CNN model. To this end, we propose anisotropic direction loss (ADL) and anisotropic attention module (AAM) for coordinate and heatmap regression, respectively. ADL imposes strong binding force in normal direction for each landmark point on facial boundaries. On the other hand, AAM is an attention module which can get anisotropic attention mask focusing on the region of point and its local edge connected by adjacent points, it has a stronger response in tangent than in normal, which means relaxed constraints in the tangent. These two methods work in a complementary manner to learn both facial structures and texture details. Finally, we integrate them into an optimized end-to-end training pipeline named ADNet. Our ADNet achieves state-of-the-art results on 300W, WFLW and COFW datasets, which demonstrates the effectiveness and robustness.

A C`adl`ag Rough Path Foundation for Robust Finance

Using rough path theory, we provide a pathwise foundation for stochastic It^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called Property (RIE) for c`adl`ag paths, which is shown to imply the existence of a c`adl`ag rough path and of quadratic variation in the sense of Follmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type, and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Covers universal portfolio are admissible integrands, and that Property (RIE) is satisfied by both (Young) semimartingales and typical price paths.

Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time. By conditioning the process on its filtration, we introduce a family of higher order kernel mean embeddings (KMEs) that generalizes the notion of KME and captures additional information related to the filtration. We derive empirical estimators for the associated higher order maximum mean discrepancies (MMDs) and prove consistency. We then construct a filtration-sensitive kernel two-sample test able to pick up information that gets missed by the standard MMD test. In addition, leveraging our higher order MMDs we construct a family of universal kernels on stochastic processes that allows to solve real-world calibration and optimal stopping problems in quantitative finance (such as the pricing of American options) via classical kernel-based regression methods. Finally, adapting existing tests for conditional independence to the case of stochastic processes, we design a causal-discovery algorithm to recover the causal graph of structural dependencies among interacting bodies solely from observations of their multidimensional trajectories.

Model-free Portfolio Theory: A Rough Path Approach

Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Follmer integration. Without the assumption of any underlying probabilistic model, we prove pathwise Master formulae analogous to those of classical SPT, describing the growth of wealth processes associated to functionally generated portfolios relative to the market portfolio. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Covers universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by considering (non-functionally generated) log-optimal portfolios in an ergodic It^o diffusion setting.

The discovery of the largest gas filament in our Galaxy, or a new spiral arm?

Using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we detect a giant HI filamentary structure in the sky region of 307$.!!^{circ}$7 $<$ $alpha$ $<$ 311$.!!^{circ}$0 and 40$.!!^{circ}$9 $<$ $delta$ $<$ 43$.!!^{circ}$4. The structure has a velocity range of $-$170 km s$^{-1}$ to $-$130 km s$^{-1}$, and a mean velocity of $-$150 km s$^{-1}$, putting it to a Galactocentric distance of 22 kpc. The HI structure has a length of 1.1 kpc, which appears to be so far the furthest and largest giant filament in the Galaxy and we name it Cattail. Its mass is calculated to be 6.5 $times$ 10$^4$ M$_{odot}$ and the linear mass density is 60 M$_{odot}$ pc$^{-1}$. Its width is 207 pc, corresponding to an aspect ratio of 5:1. Cattail possesses a small velocity gradient (0.02 km s$^{-1}$ pc$^{-1}$) along its major axis. Together with the HI4PI data, we find that Cattail could have an even larger length, up to 5 kpc. We also identify another new elongated structure to be the extension into the Galactic first quadrant of the Outer Scutum-Centaurus (OSC) arm, and Cattail appears to be located far behind the OSC. The question about how such a huge filament is produced at the extreme Galactic location remains open. Alternatively, Cattail might be part of a new arm beyond the OSC, though it is puzzling that the structure does not fully follow the warp of the Galactic disk.

Graph Convolution for Re-ranking in Person Re-identification

Nowadays, deep learning is widely applied to extract features for similarity computation in person re-identification (re-ID) and have achieved great success. However, due to the non-overlapping between training and testing IDs, the difference between the data used for model training and the testing data makes the performance of learned feature degraded during testing. Hence, re-ranking is proposed to mitigate this issue and various algorithms have been developed. However, most of existing re-ranking methods focus on replacing the Euclidean distance with sophisticated distance metrics, which are not friendly to downstream tasks and hard to be used for fast retrieval of massive data in real applications. In this work, we propose a graph-based re-ranking method to improve learned features while still keeping Euclidean distance as the similarity metric. Inspired by graph convolution networks, we develop an operator to propagate features over an appropriate graph. Since graph is the essential key for the propagation, two important criteria are considered for designing the graph, and three different graphs are explored accordingly. Furthermore, a simple yet effective method is proposed to generate a profile vector for each tracklet in videos, which helps extend our method to video re-ID. Extensive experiments on three benchmark data sets, e.g., Market-1501, Duke, and MARS, demonstrate the effectiveness of our proposed approach.

The three-year shear catalog of the Subaru Hyper Suprime-Cam SSP Survey

We present the galaxy shear catalog that will be used for the three-year cosmological weak gravitational lensing analyses using data from the Wide layer of the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) Survey. The galaxy shapes are measured from the $i$-band imaging data acquired from 2014 to 2019 and calibrated with image simulations that resemble the observing conditions of the survey based on training galaxy images from the Hubble Space Telescope in the COSMOS region. The catalog covers an area of 433.48 deg$^2$ of the northern sky, split into six fields. The mean $i$-band seeing is 0.59 arcsec. With conservative galaxy selection criteria (e.g., $i$-band magnitude brighter than 24.5), the observed raw galaxy number density is 22.9 arcmin$^{-2}$, and the effective galaxy number density is 19.9 arcmin$^{-2}$. The calibration removes the galaxy property-dependent shear estimation bias to a level: $|delta m|<9times 10^{-3}$. The bias residual $delta m$ shows no dependence on redshift in the range $0<zleq 3$. We define the requirements for cosmological weak lensing science for this shear catalog, and quantify potential systematics in the catalog using a series of internal null tests for systematics related to point-spread function modelling and shear estimation. A variety of the null tests are statistically consistent with zero or within requirements, but (i) there is evidence for PSF model shape residual correlations; and (ii) star-galaxy shape correlations reveal additive systematics. Both effects become significant on $>1$ degree scales and will require mitigation during the inference of cosmological parameters using cosmic shear measurements.

Vision-Language Navigation with Random Environmental Mixup

Vision-language Navigation (VLN) tasks require an agent to navigate step-by-step while perceiving the visual observations and comprehending a natural language instruction. Large data bias, which is caused by the disparity ratio between the small data scale and large navigation space, makes the VLN task challenging. Previous works have proposed various data augmentation methods to reduce data bias. However, these works do not explicitly reduce the data bias across different house scenes. Therefore, the agent would overfit to the seen scenes and achieve poor navigation performance in the unseen scenes. To tackle this problem, we propose the Random Environmental Mixup (REM) method, which generates cross-connected house scenes as augmented data via mixuping environment. Specifically, we first select key viewpoints according to the room connection graph for each scene. Then, we cross-connect the key views of different scenes to construct augmented scenes. Finally, we generate augmented instruction-path pairs in the cross-connected scenes. The experimental results on benchmark datasets demonstrate that our augmentation data via REM help the agent reduce its performance gap between the seen and unseen environment and improve the overall performance, making our model the best existing approach on the standard VLN benchmark.

Exploration and Exploitation: Two Ways to Improve Chinese Spelling Correction Models

A sequence-to-sequence learning with neural networks has empirically proven to be an effective framework for Chinese Spelling Correction (CSC), which takes a sentence with some spelling errors as input and outputs the corrected one. However, CSC models may fail to correct spelling errors covered by the confusion sets, and also will encounter unseen ones. We propose a method, which continually identifies the weak spots of a model to generate more valuable training instances, and apply a task-specific pre-training strategy to enhance the model. The generated adversarial examples are gradually added to the training set. Experimental results show that such an adversarial training method combined with the pretraining strategy can improve both the generalization and robustness of multiple CSC models across three different datasets, achieving stateof-the-art performance for CSC task.

Phase-field modeling of rock fractures with roughness

Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the existing phase-field models, however, incorporates the impact of surface roughness on the mechanical response of fractures -- such as elastic deformability and shear-induced dilation -- despite the importance of this behavior for subsurface systems. To fill this gap, here we introduce the first framework for phase-field modeling of rough rock fractures. The framework transforms a displacement-jump-based discrete constitutive model for discontinuities into a strain-based continuous model, and then casts it into a phase-field formulation for frictional interfaces. We illustrate the framework by constructing a particular phase-field form employing a rock joint model originally formulated for discrete modeling. The results obtained by the new formulation show excellent agreement with those of a well-established discrete method for a variety of problems ranging from shearing of a single discontinuity to compression of fractured rocks. Consequently, our phase-field framework provides an unprecedented bridge between a discrete constitutive model for rough discontinuities -- common in rock mechanics -- and the continuous finite element method -- standard in computational mechanics -- without any algorithm to explicitly represent discontinuity geometry.