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Shiyu Yan

Shiyu Yan contributes to research discovery and scholarly infrastructure.

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Machine Learning Software Engineering Computer Vision Logic in Computer Science

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preprint2026arXiv

A semantic mutation metric for metamorphic relation adequacy in scientific computing programs

Context. Metamorphic Testing addresses the test-oracle problem in scientific computing, but classical Mutation Score operates on syntactic AST mutations and misses domain semantics. Objective. We propose the Semantic Mutation Score (SMS), built on five domain-semantic operators (Conservation Erosion, Operator Substitution, Hyperparameter, Trajectory Flip, Structural Injection). SMS degenerates almost everywhere to MS in a characterised limit, so any SMS-based conclusion remains consistent with prior mutation-testing literature in the classical regime. Method. A 12-PUT x 5-MP design over four single-output float-to-float classes (numeric, probabilistic, surrogate, machine-learning) is paired with a three-layer attribution classifier separating true semantic faults from tolerance, OOD, statistical, and artefact categories. A same-source / cross-source ablation under an identical prompt isolates the LLM-source-diversity contribution. LLM-generated mutants are compared against a default-configuration cosmic-ray syntactic pool at the AST-normalised level. Results. The pre-registered large-effect threshold for Cliff's delta is not met under the point-estimate criterion; the observed effect lies in the medium-effect range. Cross-source pooling under an identical prompt does not appreciably shift delta, indicating that LLM identity is not the lever within this design. AST-level overlap between LLM-generated and default cosmic-ray syntactic mutants is small; the Hyperparameter, Structural Injection, and Trajectory Flip classes are unreachable under default first-order syntactic configurations. Conclusion. SMS is a backward-compatible adequacy metric for domain-semantic metamorphic-relation sets in scientific computing. The first-order unreachability evidence is independent of the effect-size question.

preprint2026arXiv

NOETHER: A Constructive Framework for Metamorphic Pattern Discovery from Operator Algebras

Context. Metamorphic Testing is recognised in IEEE/ISO software-testing standards and increasingly recommended for AI systems, but its progress is bottlenecked by metamorphic relation (MR) identification: existing approaches (structured frameworks, mining and evolutionary pipelines, LLM-assisted methods, MetaPattern catalogues) share an inductive grounding that leaves three foundational questions open: origin, closure, and transferability. Objective. We propose a framework whose downstream step from program-induced operator algebra to MetaPattern set is mechanical and provable, while the upstream curation of the algebra is a stated empirical hypothesis with explicit scope precondition. Method. NOETHER is a two-layer framework. The upstream layer is an eight-block decomposition over recurrent mathematical structures (symmetry, order, self-adjoint, time-reversal, limit, qualitative-dynamics, method-comparison, relational equivalence). The downstream CONSTRUCT-MP algorithm produces a MetaPattern set with algebraic-closure (Theorem 1) and polynomial-time decidability (Theorem 2) guarantees. We test the framework on three operator-algebraic domains. Results. On Boltzmann reactor physics NOETHER systematises a prior inductive catalogue; on equivariant ML it derives executable MRs for rotation invariance, adjoint duality, and training-trajectory reversibility; on relational query optimisers it exercises the relational-equivalence block. The central falsifiable prediction (L*-blindness on homogeneity-preserving mutators) holds on the in-scope substrate. The absolute-completeness conjecture (Theorem 1') is falsified on PWR core diffusion via two pairwise-independent counterexamples that identify five Translate-extension dimensions. Conclusion. Induction is relocated from per-program MR sampling to a per-domain algebraic layer; the downstream step is deductive and mechanical.

preprint2021arXiv

Self-supervised Low Light Image Enhancement and Denoising

This paper proposes a self-supervised low light image enhancement method based on deep learning, which can improve the image contrast and reduce noise at the same time to avoid the blur caused by pre-/post-denoising. The method contains two deep sub-networks, an Image Contrast Enhancement Network (ICE-Net) and a Re-Enhancement and Denoising Network (RED-Net). The ICE-Net takes the low light image as input and produces a contrast enhanced image. The RED-Net takes the result of ICE-Net and the low light image as input, and can re-enhance the low light image and denoise at the same time. Both of the networks can be trained with low light images only, which is achieved by a Maximum Entropy based Retinex (ME-Retinex) model and an assumption that noises are independently distributed. In the ME-Retinex model, a new constraint on the reflectance image is introduced that the maximum channel of the reflectance image conforms to the maximum channel of the low light image and its entropy should be the largest, which converts the decomposition of reflectance and illumination in Retinex model to a non-ill-conditioned problem and allows the ICE-Net to be trained with a self-supervised way. The loss functions of RED-Net are carefully formulated to separate the noises and details during training, and they are based on the idea that, if noises are independently distributed, after the processing of smoothing filters (\eg mean filter), the gradient of the noise part should be smaller than the gradient of the detail part. It can be proved qualitatively and quantitatively through experiments that the proposed method is efficient.

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