Higher Order Derivatives in Costa's Entropy Power Inequality

Let $X$ be an arbitrary continuous random variable and $Z$ be an independent Gaussian random variable with zero mean and unit variance. For $t~>~0$, Costa proved that $e^{2h(X+\sqrt{t}Z)}$ is concave in $t$, where the proof hinged on the first and second order derivatives of $h(X+\sqrt{t}Z)$. Specifically, these two derivatives are signed, i.e., $\frac{\partial}{\partial t}h(X+\sqrt{t}Z) \geq 0$ and $\frac{\partial^2}{\partial t^2}h(X+\sqrt{t}Z) \leq 0$. In this paper, we show that the third order derivative of $h(X+\sqrt{t}Z)$ is nonnegative, which implies that the Fisher information $J(X+\sqrt{t}Z)$ is convex in $t$. We further show that the fourth order derivative of $h(X+\sqrt{t}Z)$ is nonpositive. Following the first four derivatives, we make two conjectures on $h(X+\sqrt{t}Z)$: the first is that $\frac{\partial^n}{\partial t^n} h(X+\sqrt{t}Z)$ is nonnegative in $t$ if $n$ is odd, and nonpositive otherwise; the second is that $\log J(X+\sqrt{t}Z)$ is convex in $t$. The first conjecture can be rephrased in the context of completely monotone functions: $J(X+\sqrt{t}Z)$ is completely monotone in $t$. The history of the first conjecture may date back to a problem in mathematical physics studied by McKean in 1966. Apart from these results, we provide a geometrical interpretation to the covariance-preserving transformation and study the concavity of $h(\sqrt{t}X+\sqrt{1-t}Z)$, revealing its connection with Costa's EPI.Comment: Second version submitted. https://sites.google.com/site/chengfancuhk

Split, Encode and Aggregate for Long Code Search

Code search with natural language plays a crucial role in reusing existing code snippets and accelerating software development. Thanks to the Transformer-based pretraining models, the performance of code search has been improved significantly compared to traditional information retrieval (IR) based models. However, due to the quadratic complexity of multi-head self-attention, there is a limit on the input token length. For efficient training on standard GPUs like V100, existing pretrained code models, including GraphCodeBERT, CodeBERT, RoBERTa (code), take the first 256 tokens by default, which makes them unable to represent the complete information of long code that is greater than 256 tokens. Unlike long text paragraph that can be regarded as a whole with complete semantics, the semantics of long code is discontinuous as a piece of long code may contain different code modules. Therefore, it is unreasonable to directly apply the long text processing methods to long code. To tackle the long code problem, we propose SEA (Split, Encode and Aggregate for Long Code Search), which splits long code into code blocks, encodes these blocks into embeddings, and aggregates them to obtain a comprehensive long code representation. With SEA, we could directly use Transformer-based pretraining models to model long code without changing their internal structure and repretraining. Leveraging abstract syntax tree (AST) based splitting and attention-based aggregation methods, SEA achieves significant improvements in long code search performance. We also compare SEA with two sparse Trasnformer methods. With GraphCodeBERT as the encoder, SEA achieves an overall mean reciprocal ranking score of 0.785, which is 10.1% higher than GraphCodeBERT on the CodeSearchNet benchmark.Comment: 9 page

To Explain or Not to Explain: A Study on the Necessity of Explanations for Autonomous Vehicles

Explainable AI, in the context of autonomous systems, like self driving cars, has drawn broad interests from researchers. Recent studies have found that providing explanations for an autonomous vehicle actions has many benefits, e.g., increase trust and acceptance, but put little emphasis on when an explanation is needed and how the content of explanation changes with context. In this work, we investigate which scenarios people need explanations and how the critical degree of explanation shifts with situations and driver types. Through a user experiment, we ask participants to evaluate how necessary an explanation is and measure the impact on their trust in the self driving cars in different contexts. We also present a self driving explanation dataset with first person explanations and associated measure of the necessity for 1103 video clips, augmenting the Berkeley Deep Drive Attention dataset. Additionally, we propose a learning based model that predicts how necessary an explanation for a given situation in real time, using camera data inputs. Our research reveals that driver types and context dictates whether or not an explanation is necessary and what is helpful for improved interaction and understanding.Comment: 9.5 pages, 7 figures, submitted to UIST202

Fault diagnosis of a mixed-flow pump under cavitation condition based on deep learning techniques

Deep learning technique is an effective mean of processing complex data that has emerged in recent years, which has been applied to fault diagnosis of a wide range of equipment. In the present study, three types of deep learning techniques, namely, stacked autoencoder (SAE) network, long short term memory (LSTM) network, and convolutional neural network (CNN) are applied to fault diagnosis of a mixed-flow pump under cavitation conditions. Vibration signals of the mixed-flowed pump are collected from experiment measurements, and then employed as input datasets for deep learning networks. The operation status is clarified into normal, minor cavitation, and severe cavitation conditions according to visualized bubble density. The techniques of FFT and dropout algorithms are also applied to improve diagnosis accuracy. The results show that the diagnosis accuracy based on SAE and LSTM networks is lower than 50%, while is higher than 68% when using CNN. The maximum accuracy can reach 87.2% by mean of a combination of CNN, BN, MLP, and using frequency domain data by FFT as inputs, which validates the feasibility of applying CNN in mixed-flow pumps

OnUVS: Online Feature Decoupling Framework for High-Fidelity Ultrasound Video Synthesis

Ultrasound (US) imaging is indispensable in clinical practice. To diagnose certain diseases, sonographers must observe corresponding dynamic anatomic structures to gather comprehensive information. However, the limited availability of specific US video cases causes teaching difficulties in identifying corresponding diseases, which potentially impacts the detection rate of such cases. The synthesis of US videos may represent a promising solution to this issue. Nevertheless, it is challenging to accurately animate the intricate motion of dynamic anatomic structures while preserving image fidelity. To address this, we present a novel online feature-decoupling framework called OnUVS for high-fidelity US video synthesis. Our highlights can be summarized by four aspects. First, we introduced anatomic information into keypoint learning through a weakly-supervised training strategy, resulting in improved preservation of anatomical integrity and motion while minimizing the labeling burden. Second, to better preserve the integrity and textural information of US images, we implemented a dual-decoder that decouples the content and textural features in the generator. Third, we adopted a multiple-feature discriminator to extract a comprehensive range of visual cues, thereby enhancing the sharpness and fine details of the generated videos. Fourth, we constrained the motion trajectories of keypoints during online learning to enhance the fluidity of generated videos. Our validation and user studies on in-house echocardiographic and pelvic floor US videos showed that OnUVS synthesizes US videos with high fidelity.Comment: 14 pages, 13 figures and 6 table