Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation

For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\'e II, Painlev\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutions can be obtained by solving linear ordinary differential equations.Comment: 14 pages. The original model (1) in previous version is generalized to a more extensive form and the incorrect equations (35) and (36) in previous version are correcte

Min-Max Similarity: A Contrastive Learning Based Semi-Supervised Learning Network for Surgical Tools Segmentation

Segmentation of images is a popular topic in medical AI. This is mainly due to the difficulty to obtain a significant number of pixel-level annotated data to train a neural network. To address this issue, we proposed a semi-supervised segmentation network based on contrastive learning. In contrast to the previous state-of-the-art, we introduce a contrastive learning form of dual-view training by employing classifiers and projectors to build all-negative, and positive and negative feature pairs respectively to formulate the learning problem as solving min-max similarity problem. The all-negative pairs are used to supervise the networks learning from different views and make sure to capture general features, and the consistency of unlabeled predictions is measured by pixel-wise contrastive loss between positive and negative pairs. To quantitative and qualitative evaluate our proposed method, we test it on two public endoscopy surgical tool segmentation datasets and one cochlear implant surgery dataset which we manually annotate the cochlear implant in surgical videos. The segmentation performance (dice coefficients) indicates that our proposed method outperforms state-of-the-art semi-supervised and fully supervised segmentation algorithms consistently. The code is publicly available at: https://github.com/AngeLouCN/Min_Max_Similarit

PromptCARE: Prompt Copyright Protection by Watermark Injection and Verification

Large language models (LLMs) have witnessed a meteoric rise in popularity among the general public users over the past few months, facilitating diverse downstream tasks with human-level accuracy and proficiency. Prompts play an essential role in this success, which efficiently adapt pre-trained LLMs to task-specific applications by simply prepending a sequence of tokens to the query texts. However, designing and selecting an optimal prompt can be both expensive and demanding, leading to the emergence of Prompt-as-a-Service providers who profit by providing well-designed prompts for authorized use. With the growing popularity of prompts and their indispensable role in LLM-based services, there is an urgent need to protect the copyright of prompts against unauthorized use. In this paper, we propose PromptCARE, the first framework for prompt copyright protection through watermark injection and verification. Prompt watermarking presents unique challenges that render existing watermarking techniques developed for model and dataset copyright verification ineffective. PromptCARE overcomes these hurdles by proposing watermark injection and verification schemes tailor-made for prompts and NLP characteristics. Extensive experiments on six well-known benchmark datasets, using three prevalent pre-trained LLMs (BERT, RoBERTa, and Facebook OPT-1.3b), demonstrate the effectiveness, harmlessness, robustness, and stealthiness of PromptCARE.Comment: To Appear in the 45th IEEE Symposium on Security and Privacy 2024, code is available at: https://github.com/grasses/PromptCAR

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

RMT: Rule-based Metamorphic Testing for Autonomous Driving Models

Deep neural network models are widely used for perception and control in autonomous driving. Recent work uses metamorphic testing but is limited to using equality-based metamorphic relations and does not provide expressiveness for defining inequality-based metamorphic relations. To encode real world traffic rules, domain experts must be able to express higher order relations e.g., a vehicle should decrease speed in certain ratio, when there is a vehicle x meters ahead and compositionality e.g., a vehicle must have a larger deceleration, when there is a vehicle ahead and when the weather is rainy and proportional compounding effect to the test outcome. We design RMT, a declarative rule-based metamorphic testing framework. It provides three components that work in concert:(1) a domain specific language that enables an expert to express higher-order, compositional metamorphic relations, (2) pluggable transformation engines built on a variety of image and graphics processing techniques, and (3) automated test generation that translates a human-written rule to a corresponding executable, metamorphic relation and synthesizes meaningful inputs.Our evaluation using three driving models shows that RMT can generate meaningful test cases on which 89% of erroneous predictions are found by enabling higher-order metamorphic relations. Compositionality provides further aids for generating meaningful, synthesized inputs-3012 new images are generated by compositional rules. These detected erroneous predictions are manually examined and confirmed by six human judges as meaningful traffic rule violations. RMT is the first to expand automated testing capability for autonomous vehicles by enabling easy mapping of traffic regulations to executable metamorphic relations and to demonstrate the benefits of expressivity, customization, and pluggability