arXiv subjects

Liang Geng

Publications and source records attributed to Liang Geng.

5 recordsLinked to original sources

arXiv2026

Discontinuous Prior-Mode Sections and the Geometry of Ambiguity in Intrinsic Image Decomposition

The viral 2015 photograph known as "The Dress" divides observers into two camps because it is ambiguous: the same image colors can be explained either as a blue-black surface under one illuminant or as a white-gold surface under another. We propose a geometric account in which the ambiguity arises from a singularity in intrinsic image decomposition, the inverse problem of separating an observed image into reflectance and illumination. Our central claim is that the prior-mode section, i.e. the prior-preferred decomposition, switches across an ambiguity boundary in image space, and that any smooth learned model can only approximate this discontinuous switch by forming a thin transition layer. This predicts two observable signatures, where $\Delta$ is the jump between branches of the prior-mode section and $\lambda$ is the regularization strength: for inverse decomposers, an albedo Jacobian scaling as $|\Delta|/\sqrt{\lambda}$; and for forward encoders, the Fernet curvature that blows up on a scale of $1/\sqrt{\lambda}$. On CGIntrinsics ($N=1998$ images, $n=2\times 10^7$ pixels), the color-temperature albedo Jacobian of Careaga DPT has partial Spearman correlation $r=0.41$ with dense ground-truth albedo error, compared with $r=0.087$ and $r=0.021$ for brightness and saturation controls. On "The Dress", CLIP ViT-L/14 exhibits a latent curvature peak of $\kappa=73.03$ at $6473\,\mathrm{K}$, one sampled step from D65 daylight, while a control dress image peaks at $\kappa=34.75$ with no comparable feature near D65. The same characteristic appears across architectures (U-Net inverter, diffusion inverter, ViT encoder) and datasets (rendered indoor scenes, web photograph), each measured with the observable appropriate to its model class.

math.DG↗

arXiv2025

The Density of Primes in the Eigensurface of ${\bf S}_3$

The Prime Number Theorem asserts that the density of primes less than or equal to $N$ is asymptotically equal to $1/\log N$. The density of prime triples in coprime triples in $\mathbb{Z}^3_+$ is determined to be $3\zeta (3)/\log N$, where $\zeta$ is the Riemann zeta function. In this paper, we prove that the density of prime triples in coprime triples in the surface $S=\{z_0^{2} - z_1^{2} + z_2^{2} - z_0z_2=0\}$ is greater than $3\zeta (3)/\log N$, meaning that $S$ meets primes more frequently. This surface is the eigensurface of the symmetric group ${\bf S}_3$ with respect to an irreducible representation.

math.NT↗

arXiv2025

A "Wenlu" Brain System for Multimodal Cognition and Embodied Decision-Making: A Secure New Architecture for Deep Integration of Foundation Models and Domain Knowledge

With the rapid penetration of artificial intelligence across industries and scenarios, a key challenge in building the next-generation intelligent core lies in effectively integrating the language understanding capabilities of foundation models with domain-specific knowledge bases in complex real-world applications. This paper proposes a multimodal cognition and embodied decision-making brain system, ``Wenlu", designed to enable secure fusion of private knowledge and public models, unified processing of multimodal data such as images and speech, and closed-loop decision-making from cognition to automatic generation of hardware-level code. The system introduces a brain-inspired memory tagging and replay mechanism, seamlessly integrating user-private data, industry-specific knowledge, and general-purpose language models. It provides precise and efficient multimodal services for enterprise decision support, medical analysis, autonomous driving, robotic control, and more. Compared with existing solutions, ``Wenlu" demonstrates significant advantages in multimodal processing, privacy security, end-to-end hardware control code generation, self-learning, and sustainable updates, thus laying a solid foundation for constructing the next-generation intelligent core.

cs.AI↗

arXiv2024

Improving Apple Object Detection with Occlusion-Enhanced Distillation

Apples growing in natural environments often face severe visual obstructions from leaves and branches. This significantly increases the risk of false detections in object detection tasks, thereby escalating the challenge. Addressing this issue, we introduce a technique called "Occlusion-Enhanced Distillation" (OED). This approach utilizes occlusion information to regularize the learning of semantically aligned features on occluded datasets and employs Exponential Moving Average (EMA) to enhance training stability. Specifically, we first design an occlusion-enhanced dataset that integrates Grounding DINO and SAM methods to extract occluding elements such as leaves and branches from each sample, creating occlusion examples that reflect the natural growth state of fruits. Additionally, we propose a multi-scale knowledge distillation strategy, where the student network uses images with increased occlusions as inputs, while the teacher network employs images without natural occlusions. Through this setup, the strategy guides the student network to learn from the teacher across scales of semantic and local features alignment, effectively narrowing the feature distance between occluded and non-occluded targets and enhancing the robustness of object detection. Lastly, to improve the stability of the student network, we introduce the EMA strategy, which aids the student network in learning more generalized feature expressions that are less affected by the noise of individual image occlusions. Our method significantly outperforms current state-of-the-art techniques through extensive comparative experiments.

cs.CV↗

arXiv2021

Disarranged Zone Learning (DZL): An unsupervised and dynamic automatic stenosis recognition methodology based on coronary angiography

We proposed a novel unsupervised methodology named Disarranged Zone Learning (DZL) to automatically recognize stenosis in coronary angiography. The methodology firstly disarranges the frames in a video, secondly it generates an effective zone and lastly trains an encoder-decoder GRU model to learn the capability to recover disarranged frames. The breakthrough of our study is to discover and validate the Sequence Intensity (Recover Difficulty) is a measure of Coronary Artery Stenosis Status. Hence, the prediction accuracy of DZL is used as an approximator of coronary stenosis indicator. DZL is an unsupervised methodology and no label engineering effort is needed, the sub GRU model in DZL works as a self-supervised approach. So DZL could theoretically utilize infinitely huge amounts of coronary angiographies to learn and improve performance without laborious data labeling. There is no data preprocessing precondition to run DZL as it dynamically utilizes the whole video, hence it is easy to be implemented and generalized to overcome the data heterogeneity of coronary angiography. The overall average precision score achieves 0.93, AUC achieves 0.8 for this pure methodology. The highest segmented average precision score is 0.98 and the highest segmented AUC is 0.87 for coronary occlusion indicator. Finally, we developed a software demo to implement DZL methodology.

eess.IV↗