Organizations: Centre for Disruptive Photonic Technologies, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore · Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Republic of Singapore · School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa · School of Electronic Science and Engineering, Xiamen University, Xiamen 361005, China · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore
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 TOPO2, 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 TOPO2 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.
Figures & tables
Figure 1: Topology-enhanced AI for recovery of topological information. (a) Topological light fields encode information in their skyrmion numbers ( Nsk=2 ), but extracting the topology is expensive in both a measurement and computational sense. (b) The problem becomes intractable after propagation through a strongly scattering disordered medium which scrambles the signal into visually indistinguishable speckle intensity patterns, preventing recovery of the underlying topology using conventional observables and machine learning approaches. (c) Our topology-enhanced AI learning framework (TOPO 2 ) maps these patterns into topology-aware representations, enabling direct recovery of the topological states from single-shot intensity measurements.
Figure 2: Topological representation of information. (a) A k simplex is the convex hull of k+1 vertices: a vertex, edge, filled triangle, and tetrahedron for k=0 – 3 . These are the units from which the geometry of the data is assembled. (b) Betti numbers count the structure features of that geometry: connected components ( β0 ) and independent loops ( β1 ) . Like the skyrmion number, they are unchanged by continuous deformation. (c) These features are extracted across all scales by growing a ball of radius r each data point and linking points whose balls overlap. As r increases, features appear and disappear: here a cycle is born at r=0.52 , filled and died at r=0.72 . How long each feature survives is the main descriptor TOPO 2 uses to recover the topological state from a single-shot speckle pattern.
Figure 3: Dual-mode optical platform for skyrmion generation and topological recovery. (a) Optical skyrmions are generated by coherent superposition of two orthogonally polarized modes on a DMD. A flip mirror switches between (b) Stokes polarimetry for ground-truth characterization and (c) single-shot speckle recording through a disordered medium for TOPO 2 classification, which maps the optical speckle to a point cloud and extracts its persistent topology (here β1=1 ) to recover the skyrmion number. (d) Disordered media consist of liquid crystals, digital amplitude distorting masks, and ground glass.
Figure 4: Topological invariants remain separable under topology-aware representations. (a) Topological data analysis (TDA) extracts multi-scale geometric features from speckle intensity patterns via persistence diagrams, capturing connected components (dim 0) and loop structures (dim 1) across intensity thresholds. (b) Principal component analysis (PCA) projects speckle patterns onto principal components capturing dominant variance. (c) Comparison of the resulting feature spaces shows that the TDA representation exhibits distinct clustering by skyrmion number, whereas the PCA representation shows no clear classwise separation. (d) Quantitative comparison across multiple clustering metrics demonstrates consistent superiority of topology-aware representations over variance-based approaches.
Figure 5: Topology-based optical communication via encoding and decoding of topological states. (a) Topology encoding scheme. Image pixels are mapped to discrete skyrmion numbers, defining a topological alphabet. The resulting fields, upon propagation, generate speckle intensity patterns that retain topological signatures. (b) Topology-aware decoding from speckle. Encoded images are reconstructed from single-shot intensity using the TOPO 2 framework and compared with a ResNet-34 baseline. Confusion matrices reveal that topology-enhanced representations enable superior class discrimination and decoding fidelity across all tested cases.
Many wireless vision applications, such as autonomous driving, require preservation of global structural information rather than only per-pixel fidelity. However, existing Deep joint source-channel coding (DeepJSCC) schemes mainly optimize pixel-wise losses and provide no explicit protection of connectivity or topology. This letter proposes TopoJSCC, a topology-aware DeepJSCC framework that integrates persistent-homology regularizers to end-to-end training. Specifically, we enforce topological consistency by penalizing Wasserstein distances between cubical persistence diagrams of original and reconstructed images, and between Vietoris--Rips persistence of latent features before and after the channel to promote a robust latent manifold. TopoJSCC is based on end-to-end learning and requires no side information. Experiments show improved topology preservation and peak signal-to-noise ratio (PSNR) in low signal-to-noise ratio (SNR) and bandwidth-ratio regimes.
Omar Erak, Omar Alhussein, Fang Fang +1
KU 6G Research Center, College of Computing and Mathematical Sciences, Khalifa University, Abu Dhabi, UAE · Department of Electrical and Computer Engineering, and also with the Department of Computer Science, Western University, London, ON N6A 3K7, Canada
We study the classification task of structured-light beams after propagation through a random turbulent medium. The received speckle patterns are generated by numerical simulation of a stochastic paraxial propagation model, and the classification task is formulated over a finite alphabet of 15 OAM source classes. We benchmark intensity and autocorrelation inputs using SimpleCNN and ResNet-18 as classifiers. We also quantify the effect of training-set size and receiver-window misalignment. Since additional propagated samples may be costly to obtain, we develop a class-conditioned diffusion model for generative augmentation of turbulence-degraded intensity images. The main contribution is a spectrum-aware diffusion objective: a pixel-domain loss combined with a Fourier-domain Bregman regularizer designed to preserve high-frequency speckle statistics. We prove that this hybrid objective is consistent with the posterior-mean regression target of the diffusion model and show that generated samples substantially improve low-data classification.
Aokun Wang, Anjali Nair, Zhongjian Wang +1
Division of Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore · Committee on Computational and Applied Mathematics, University of Chicago, Chicago, IL 60637 USA · Departments of Statistics and Mathematics, University of Chicago, Chicago, IL 60637 USA
Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce quantum topological data encoding (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.
Adam Wesołowski, Dimitrios Thanos, Daniel Leykam +1
Royal Holloway University of London, Department of Computer Science, UK · Leiden Institute of Advanced Computer Science (LIACS), Leiden University, Leiden, The Netherlands · Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, Singapore +1