arXiv subjects

Yuhan Peng

Publications and source records attributed to Yuhan Peng.

7 recordsLinked to original sources

arXiv2026

Recovering topological information of light by topological learning

The evolution of modern-day communication networks towards optical solutions with enhanced capacity and robustness is driving interest in topological light waves, exploiting their stability against perturbations through a topological invariant, e.g., the skyrmion number. However, detecting the underlying topology remains a computationally intense process even under ideal conditions, becoming intractable after passing through strongly disordered channels, where the degradation into unrecognisable speckle appears to destroy the topology. Here, we propose and demonstrate a topology-enhanced artificial intelligence (AI) approach to recover and classify such apparently lost topological information by computationally leveraging topological invariants in the data across many length scales. By aligning the topological classification of information with the topology of light, our topology-enhanced learning protocol, termed TOPO$^{2}$, achieves highly efficient recognition of the topological states of light, even from speckle, without the need for any prior learning. Our approach outperforms benchmark tests against standard computational algorithms and has the benefit of requiring just a single intensity pattern as the input, facilitating single-shot operation. To demonstrate this, we leverage the skyrmion number as a robust data carrier of images through a disordered channel, using TOPO$^{2}$ to accurately reconstruct the transmitted images. This work synergises topological photonics and topological AI for unravelling hidden topological signatures in light, opening a pathway towards robust communications even in extreme disordered environments.

physics.optics↗

arXiv2026

Geometric Structures on Graphs: a Holonomy-Based Discretization of Curvature

We propose a holonomy-based framework for discretizing curvature on graphs equipped with local symmetric positive-definite metrics. Each vertex carries a fibre metric $g_i$, and each directed edge carries a reversible metric-compatible transport $F_{ij}$. The ordered product around an oriented triangular loop $\mathcal C$ gives a holonomy $H_{\mathcal C}$, whose normalized logarithm $\Omega_{\mathcal C}=-s_{\mathcal C}^{-1}\operatorname{Log}(H_{\mathcal C})$ is used as a finite-loop curvature observation. Thus the construction discretizes the geometric principle that infinitesimal holonomy is controlled by curvature, rather than treating holonomy as a heuristic feature. Since $\Omega_{\mathcal C}$ lies in the $g_i$-orthogonal Lie algebra, it is not itself a velocity of an SPD metric. We therefore introduce two aggregation mechanisms: a commutator with a symmetric response matrix, producing symmetric Ricci-type metric responses, and an incidence-aware covariant divergence of curvature-induced edge fluxes, reflecting the relation between trace and covariant divergence. The resulting responses are locally orthogonal-gauge equivariant and can drive exponential updates that preserve positive definiteness. We also give a reversible metric-compatible parametrization of edge transports, allowing orthogonal edge factors, loop scales, weights, and response matrices to be learned while respecting the graph geometry. Known-geometry calibrations on the unit sphere test the holonomy--curvature relation, curvature preservation under nontrivial local metric representations, and the empirical recovery of edge transports from local observations.

cs.LG↗

arXiv2026

Demystifying Oversmoothing in Sheaf Neural Networks: An Index-Theoretic Criterion

To combat oversmoothing in Graph Convolutional Networks, Sheaf Neural Networks (SNNs) were proposed as a generalization by equipping the graph with a sheaf structure and replacing the graph Laplacian with a sheaf Laplacian $\mathcal{L}$. Existing analyses connect sheaf diffusion to oversmoothing via the harmonic space ($\ker\mathcal{L}$), taking its absolute dimension as an indicator of anti-oversmoothing capacity. However, absolute dimension alone is not a reliable measure: certain sheaf configurations inflate $\dim \ker \mathcal{L}$ while their harmonic sections remain entirely constant, without enriching discriminative capacity. We instead introduce the first relative, geometric approach, yielding a precise characterisation of anti-oversmoothing capacity. Under natural conditions on stalk transportation and global sheaf structure, we establish an index-theoretic comparison criterion showing that one sheaf's harmonic space genuinely contains another's beyond trivial inflation. We illustrate this with a concrete instance and further introduce \textit{GyroSheaf}, a sheaf with curved gyrovector-space stalks, extending the criterion to the non-linear setting via local tangent-space linearization. Experiments across ten models confirm the theoretical criterion: sheaf models violating the criterion collapse despite possessing index jumps, while compliant models maintain depth-stable representations.

cs.LG↗

arXiv2026

Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule. These second-order representations are naturally captured by points on the symmetric positive definite matrices (SPD) manifold; (2) Standard message passing applies shared transformations across edges. Sheaf neural networks address this via edge-specific transformations, but existing formulations remain confined to vector spaces and therefore cannot propagate matrix-valued features. We address both challenges by developing the first sheaf neural network operates natively on the SPD manifold. Our key insight is that the SPD manifold admits a Lie group structure, enabling well-posed analogs of sheaf operators without projecting to Euclidean space. Theoretically, we prove that SPD-valued sheaves are strictly more expressive than Euclidean sheaves: they admit consistent configurations (global sections) that vector-valued sheaves cannot represent, directly translating to richer learned representations. Empirically, our sheaf convolution transforms effectively rank-1 directional inputs into full-rank matrices encoding local geometric structure. Our dual-stream architecture achieves SOTA on 6/7 MoleculeNet benchmarks, with the sheaf framework providing consistent depth robustness.

cs.LG↗

arXiv2025

Entropy-driven physical amplification in multivalent biosensing

Sensitive detection of low-abundance molecular targets is widely assumed to require enzymatic amplification, such as PCR, to achieve low detection limits. In amplification-free platforms, sensitivity is traditionally constrained by equilibrium binding affinity. Here we show that multivalent linker entropy provides a distinct physical route to exponential sensitivity enhancement in purely equilibrium sensing architectures. Using a statistical-mechanical theory supported by grand canonical Monte Carlo simulations, we demonstrate that redistributing a fixed total interaction strength over increasing linker valency exponentially lowers adsorption thresholds. This scaling emerges not from stronger energetic affinity, but from the rapid growth of combinatorial binding configurations, revealing entropy as an intrinsic amplification mechanism. Consequently, detection limits can be tuned independently of bond strength, enabling ultrasensitive responses without enzymatic replication. Our results establish a general physical design principle for engineering amplification-free detection systems capable of approaching PCR-level sensitivities through entropy-driven collective effects.

cond-mat.soft↗

arXiv2025

3D Medical Imaging Segmentation on Non-Contrast CT

This technical report analyzes non-contrast CT image segmentation in computer vision. It revisits a proposed method, examines the background of non-contrast CT imaging, and highlights the significance of segmentation. The study reviews representative methods, including convolutional-based and CNN-Transformer hybrid approaches, discussing their contributions, advantages, and limitations. The nnUNet stands out as the state-of-the-art method across various segmentation tasks. The report explores the relationship between the proposed method and existing approaches, emphasizing the role of global context modeling in semantic labeling and mask generation. Future directions include addressing the long-tail problem, utilizing pre-trained models for medical imaging, and exploring self-supervised or contrastive pre-training techniques. This report offers insights into non-contrast CT image segmentation and potential advancements in the field.

eess.IV↗

arXiv2024

Designed self-assembly of programmable colloidal atom-electron equivalents

To unlock the potential for assembling complex colloidal "molecules", we investigate a minimal binary system of programmable colloidal atom-electron equivalents (PAE-EE), where electron equivalents (EEs) are multivalent linkers with two distinct types of single-stranded DNA (ssDNA) ends complementary to those ssDNAs on binary programmable atom equivalents (PAEs). We derive a statistical mechanical framework for calculating the effective interaction between PAEs mediated by EEs with arbitrary valency, which quantitatively agrees with simulations that explicitly include EEs. Our analysis reveals an anomalous dependence of PAE-PAE interactions on the EE valency, showing that EE-mediated interactions converge at the large valency limit. Moreover, we identify an optimal EE valency that maximizes the interaction difference between targeted and non-targeted binding pairs of PAEs. These findings offer design principles for targeted self-assembly in PAE-EE systems.

cond-mat.soft↗