Image and Video Processing
Guidestar-Free Adaptive Optics with Asymmetric Apertures
Weiyun Jiang, Haiyun Guo, Christopher A. Metzler et al. (+1 more)
This work introduces the first closed-loop adaptive optics (AO) system capable of optically correcting aberrations in real-time without a guidestar or a wavefront sensor. Nearly 40 years ago, Cederquist et al. demonstrated that asymmetric apertures enable phase
retrieval (PR)
algorithms to perform fully computational wavefront sensing, albeit at a high computational cost. More recently, Chimitt et al. extended this approach with machine learning and demonstrated real-time wavefront sensing using only a single (guidestar-based) point-spread-function (PSF) measurement. Inspired by these works, we introduce a guidestar-free AO framework built around asymmetric apertures and machine learning. Our approach combines three key elements: (1) an asymmetric aperture placed at the system's pupil plane that enables PR-based wavefront sensing, (2) a pair of machine learning
algorithms that estimate the PSF from natural scene measurements and reconstruct phase aberrations, and (3) a spatial light modulator that performs optical correction. We experimentally validate this framework on dense natural scenes imaged through unknown obscurants. Our method outperforms state-of-the-art guidestar-free wavefront shaping methods, using an order of magnitude fewer measurements and three orders of magnitude less computation.
Read the full abstract ▾
All authors Weiyun Jiang, Haiyun Guo, Christopher A. Metzler, Ashok Veeraraghavan
Image and Video Processing
Condition Errors Refinement in Autoregressive Image Generation with Diffusion Loss
Yucheng Zhou, Hao Li and Jianbing Shen
Recent studies have explored autoregressive models for image generation, with promising results, and have combined
diffusion models with autoregressive frameworks to optimize image generation via
diffusion losses. In this study, we present a theoretical analysis of
diffusion and autoregressive models with
diffusion loss, highlighting the latter's advantages. We present a theoretical comparison of conditional
diffusion and autoregressive
diffusion with
diffusion loss, demonstrating that patch denoising optimization in autoregressive models effectively mitigates condition errors and leads to a stable condition distribution. Our analysis also reveals that autoregressive condition generation refines the condition, causing the condition error influence to decay exponentially. In addition, we introduce a novel condition refinement approach based on Optimal Transport (OT) theory to address “condition inconsistency”. We theoretically demonstrate that formulating condition refinement as a Wasserstein Gradient Flow ensures convergence toward the ideal condition distribution, effectively mitigating condition inconsistency. Experiments demonstrate the superiority of our method over
diffusion and autoregressive models with
diffusion loss methods.
Read the full abstract ▾
Systems and Control · Cross-listed from cs.DC
Computationally Efficient Laplacian CL-colME
Nikola Stankovic
Decentralized collaborative mean estimation (colME) is a fundamental task in heterogeneous networks. Its graph-based variants B-colME and C-colME achieve high scalability of the problem. This paper evaluates the consensus-based C-colME framework, which relies on doubly
stochastic averaging
matrices to ensure convergence to the oracle solution. We propose CL-colME, a novel variant utilizing
Laplacian-based consensus to avoid the computationally expensive normalization processes. Simulation results show that the proposed CL-colME maintains the convergence behavior and accuracy of C-colME while improving computational efficiency.
Read the full abstract ▾
Systems and Control · Cross-listed from cs.LG
How Does the Lagrangian Guide Safe Reinforcement Learning through Diffusion Models?
Xiaoyuan Cheng, Wenxuan Yuan, Boyang Li et al. (+7 more)
Diffusion policy sampling enables reinforcement learning (RL) to represent
multimodal action distributions beyond suboptimal unimodal Gaussian policies. However, existing
diffusion-based RL methods primarily focus on offline settings for reward maximization, with limited consideration of safety in online settings. To address this gap, we propose Augmented Lagrangian-Guided
Diffusion (ALGD), a novel
algorithm for off-policy safe RL. By revisiting optimization theory and energy-based model, we show that the instability of primal-dual methods arises from the non-convex Lagrangian landscape. In
diffusion-based safe RL, the Lagrangian can be interpreted as an energy function guiding the denoising dynamics. Counterintuitively, direct usage destabilizes both policy generation and training. ALGD resolves this issue by introducing an augmented Lagrangian that locally convexifies the energy landscape, yielding a stabilized policy generation and training process without altering the distribution of the optimal policy. Theoretical analysis and extensive experiments demonstrate that ALGD is both theoretically grounded and empirically effective, achieving strong and stable performance across diverse environments.
Read the full abstract ▾
All authors Xiaoyuan Cheng, Wenxuan Yuan, Boyang Li, Yuanchao Xu, Yiming Yang, Hao Liang, Bei Peng, Robert Loftin, Zhuo Sun, Yukun Hu
Systems and Control · Cross-listed from cs.LG
Spatiotemporal Decision Transformer for Traffic Coordination
Haoran Su, Yandong Sun and Hanxiao Deng
Traffic signal control is a critical challenge in urban transportation, requiring coordination among multiple intersections to optimize network-wide traffic flow. While reinforcement learning has shown promise for adaptive signal control, existing methods struggle with multi-
agent coordination and sample efficiency. We introduce MADT (Multi-
Agent Decision
Transformer), a novel approach that reformulates multi-
agent traffic signal control as a sequence modeling problem. MADT extends the Decision
Transformer paradigm to multi-
agent settings by incorporating: (1) a graph
attention mechanism for modeling spatial dependencies between intersections, (2) a|temporal
transformer encoder for capturing traffic dynamics, and (3) return-to-go conditioning for target performance specification. Our approach enables offline learning from historical traffic data, with architecture design that facilitates potential online fine-tuning. Experiments on synthetic grid networks and real-world traffic scenarios demonstrate that MADT achieves state-of-the-art performance, reducing average travel time by 5-6% compared to the strongest baseline while exhibiting superior coordination among adjacent intersections.
Read the full abstract ▾
Signal Processing
Gridless Full-Space DOA Estimation for STAR-RIS-Assisted Wireless Systems
Ziming Liu, Tao Chen, Muran Guo et al. (+1 more)
Simultaneously transmitting and reflecting reconfigurable intelligent surfaces (
STAR-RIS) enable full-space ($0^\circ$–$360^\circ$) signal coverage, making them a compelling platform for integrated sensing and communication in next-generation wireless networks. In this paper, we investigate gridless direction-of-arrival (DOA) estimation across the full spatial domain in
STAR-RIS-assisted systems operating with a single RF sensing chain. We show that the coupled reflection-transmission mechanism of
STAR-RIS induces a multichannel finite-rate-of-innovation (FRI) structure in the received signal, which enables casting DOA estimation as a structured low-rank recovery problem without angular grid discretization. Building on this observation, we develop a proximal gradient descent
algorithm with alternating projections onto a block-Hankel
matrix set, enabling robust angle
retrieval from limited measurements. Two practically relevant
STAR-RIS configurations are addressed: element-wise uniform and nonuniform energy-splitting designs, each handled through a dedicated lifting strategy that preserves the underlying algebraic structure. A Ziv-Zakai bound is derived for the coupled full-space sensing model as a performance
benchmark across the full SNR range. Numerical results show that the proposed methods consistently outperform grid-based baselines, achieving sub-degree accuracy within $\pm 60^\circ$ of boresight at comparable or lower computational cost.
Read the full abstract ▾
All authors Ziming Liu, Tao Chen, Muran Guo, Francesco Verde
Systems and Control
Estimation of Cell-to-Cell Variation and State of Health for Battery Modules with Parallel-Connected Cells
Qinan Zhou and Jing Sun
Estimating
cell-to-
cell variation (CtCV) and state of health (SoH) for battery modules composed of parallel-connected
cells is challenging when only module-level signals are measurable and individual
cell behaviors remain unobserved. Although progress has been made in SoH estimation, CtCV estimation remains unresolved in the literature. This paper proposes a unified framework that accurately estimates both CtCV and SoH for modules using only module-level information extracted from incremental capacity analysis (ICA) and differential voltage analysis (DVA). With the proposed framework, CtCV and SoH estimations can be decoupled into two separate tasks, allowing each to be solved with dedicated
algorithms without mutual interference and providing greater design flexibility. The framework also exhibits strong versatility in accommodating different CtCV metrics, highlighting its general-purpose nature. Experimental validation on modules with three parallel-connected
cells demonstrates that the proposed framework can systematically select optimal module-level features for CtCV and SoH estimations, deliver accurate CtCV and SoH estimates with high confidence and low computational complexity, remain effective across different C-rates, and be suitable for onboard implementation.
Read the full abstract ▾
Systems and Control · Cross-listed from cs.RO
IMAGINE: Intelligent Multi-Agent Godot-based Indoor Networked Exploration
Tiago Leite, Maria Conceição and António Grilo
The exploration of unknown, Global
Navigation Satellite System (GNSS) denied environments by an autonomous communication-aware and collaborative group of Unmanned Aerial Vehicles (
UAVs) presents significant challenges in coordination, perception, and decentralized decision-making. This paper implements Multi-
Agent Reinforcement Learning (MARL) to address these challenges in a 2D indoor environment, using high-fidelity game-engine simulations (Godot) and continuous action spaces. Policy training aims to achieve emergent collaborative behaviours and decision-making under uncertainty using Network-Distributed Partially Observable Markov Decision Processes (ND-POMDPs). Each
UAV is equipped with a Light Detection and Ranging (
LiDAR) sensor and can share data (sensor measurements and a local occupancy map) with neighbouring
agents. Inter-
agent communication constraints include limited range, bandwidth and latency. Extensive ablation studies evaluated MARL training paradigms, reward function, communication system, neural network (NN) architecture,
memory mechanisms, and POMDP formulations. This work jointly addresses several key limitations in prior research, namely reliance on discrete actions, single-
agent or centralized formulations, assumptions of a priori knowledge and permanent connectivity, inability to handle dynamic obstacles, short planning horizons and architectural complexity in Recurrent NNs/
Transformers. Results show that the scalable training paradigm, combined with a simplified architecture, enables rapid autonomous exploration of an indoor area. The implementation of Curriculum-Learning (five increasingly complex levels) also enabled faster, more robust training. This combination of high-fidelity simulation, MARL formulation, and computational efficiency establishes a strong foundation for deploying learned cooperative strategies in physical robotic systems.
Read the full abstract ▾
Systems and Control · Cross-listed from math.OC
Sub-optimality bounds for certainty equivalent policies in partially observed systems
Berk Bozkurt, Aditya Mahajan, Ashutosh Nayyar et al. (+1 more)
In this paper, we present a generalization of the certainty equivalence principle of
stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as follows: the optimal action at each time is obtained by evaluating the optimal state-feedback policy of the
stochastic linear system at the minimum mean square error (MMSE) estimate of the state. Motivated by this interpretation, we consider certainty equivalent policies for general (non-linear) partially observed
stochastic systems that allow for any state estimate rather than restricting to MMSE estimates. In such settings, the certainty equivalent policy is not optimal. For models where the cost and the dynamics are smooth in an appropriate sense, we derive upper bounds on the sub-optimality of certainty equivalent policies. We present several examples to illustrate the results.
Read the full abstract ▾
All authors Berk Bozkurt, Aditya Mahajan, Ashutosh Nayyar, Yi Ouyang
Image and Video Processing
Real-time topology-aware M-mode OCT segmentation for robotic deep anterior lamellar keratoplasty (DALK) guidance
Rosalinda Xiong, Jinglun Yu, Yaning Wang et al. (+2 more)
Robotic deep anterior lamellar keratoplasty (DALK) requires accurate real time depth feedback to approach Descemet's membrane (DM) without perforation. M-mode intraoperative optical coherence
tomography (OCT) provides high temporal resolution depth traces, but speckle noise, attenuation, and instrument induced shadowing often result in discontinuous or ambiguous layer interfaces that challenge anatomically consistent
segmentation at deployment frame rates. We present a lightweight,
topology aware M-mode
segmentation pipeline based on UNeXt that incorporates anatomical
topology regularization to stabilize boundary continuity and layer ordering under low signal to noise ratio conditions. The proposed system achieves end to end throughput exceeding 80 Hz measured over the complete preprocessing inference overlay pipeline on a single GPU, demonstrating practical real time guidance beyond model only timing. This operating margin provides temporal headroom to reject low quality or dropout frames while maintaining a stable effective depth update rate. Evaluation on a standard rabbit eye M-mode
dataset using an established baseline protocol shows improved qualitative boundary stability compared with
topology agnostic controls, while preserving deployable real time performance.
Read the full abstract ▾
All authors Rosalinda Xiong, Jinglun Yu, Yaning Wang, Ziyi Huang, Jin U. Kang
Image and Video Processing
Super-Resolution and Denoising of Corneal B-Scan OCT Imaging Using Diffusion Model Plug-and-Play Priors
Yaning Wang, Jinglun Yu, Wenhan Guo et al. (+4 more)
Optical coherence
tomography (OCT) is pivotal in corneal imaging for both
surgical planning and diagnosis. However, high-speed acquisitions often degrade spatial resolution and increase speckle noise, posing challenges for accurate interpretation. We propose an advanced super-resolution framework leveraging
diffusion model plug-and-play (PnP) priors to achieve 4x spatial resolution enhancement alongside effective denoising of OCT Bscan images. Our approach formulates reconstruction as a principled
Bayesian inverse problem, combining Markov chain Monte Carlo sampling with pretrained generative priors to enforce anatomical consistency. We comprehensively validate the framework using in vivo fisheye corneal
datasets, to assess robustness and scalability under diverse clinical settings. Comparative experiments against bicubic interpolation, conventional supervised U-Net baselines, and alternative
diffusion priors demonstrate that our method consistently yields more precise anatomical structures, improved delineation of corneal layers, and superior noise suppression. Quantitative results show state-of-the-art performance in peak signal-to-noise ratio, structural similarity index, and perceptual metrics. This work highlights the potential of
diffusion-driven plug-and-play reconstruction to deliver high-fidelity, high-resolution OCT imaging, supporting more reliable clinical assessments and enabling advanced image-guided interventions. Our findings suggest the approach can be extended to other biomedical imaging modalities requiring robust super-resolution and denoising.
Read the full abstract ▾
All authors Yaning Wang, Jinglun Yu, Wenhan Guo, Ziyi Huang, Rosalinda Xiong, Yu Sun, Jin U. Kang
Image and Video Processing
Wide-field high-resolution microscopy via high-speed galvo scanning and real-time mosaicking
Ziyi Huang, Rosalinda Xiong, Yaning Wang et al. (+2 more)
Wide-field high-resolution microscopy requires fast scanning and accurate image mosaicking to cover large fields of view without compromising image quality. However, conventional galvanometric scanning, particularly under sinusoidal driving, can introduce nonuniform spatial sampling, leading to
geometric inconsistencies and brightness variations across the scanned field. To address these challenges, we present an image mosaicking framework for wide-field microscopic imaging that is applicable to both linear and sinusoidal galvanometric scanning strategies. The proposed approach combines a translation-based
geometric mosaicking model with region-of-interest (ROI) based brightness correction and seam-aware feathering to improve radiometric consistency across large fields of view. The method relies on calibrated scan parameters and synchronized scan–camera control, without requiring image-content-based registration. Using the proposed framework, wide-field mosaicked images were successfully reconstructed under both linear and sinusoidal scanning strategies, achieving a field of view of up to $2.5 \times 2.5~\mathrm{cm}^2$ with a total acquisition time of approximately $6~\mathrm{s}$ per
dataset. Quantitative evaluation shows that both scanning strategies demonstrate improved image quality, including enhanced brightness uniformity, increased contrast-to-noise ratio (CNR), and reduced seam-related artifacts after image processing, while preserving a lateral resolution of $7.81~\mu\mathrm{m}$. Overall, the presented framework provides a practical and efficient solution for scan-based wide-field microscopic mosaicking.
Read the full abstract ▾
All authors Ziyi Huang, Rosalinda Xiong, Yaning Wang, Jinglun Yu, Jin U. Kang
Image and Video Processing
Physics-based generation of multilayer corneal OCT data via Gaussian modeling and MCML for AI-driven diagnostic and surgical guidance applications
Jinglun Yu, Yaning Wang, Rosalinda Xiong et al. (+3 more)
Training deep learning models for corneal optical coherence
tomography (OCT) imaging is limited by the availability of large, well-annotated
datasets. We present a configurable Monte Carlo simulation framework that generates synthetic corneal B-scan optical OCT images with pixel-level five-layer
segmentation labels derived directly from the simulation geometry. A five-layer corneal model with Gaussian surfaces captures
curvature and thickness variability in healthy and keratoconic eyes. Each layer is assigned optical properties from the literature and light transport is simulated using Monte Carlo modeling of light transport in multi-layered tissues (MCML), while incorporating system features such as the confocal PSF and sensitivity roll-off. This approach produces over 10,000 high-resolution (1024x1024) image-label pairs and supports customization of geometry,
photon count, noise, and system parameters. The resulting
dataset enables systematic training, validation, and benchmarking of AI models under controlled, ground-truth conditions, providing a reproducible and scalable resource to support the development of diagnostic and
surgical guidance applications in image-guided ophthalmology.
Read the full abstract ▾
All authors Jinglun Yu, Yaning Wang, Rosalinda Xiong, Ziyi Huang, Kristina Irsch, Jin U. Kang
Audio and Speech Processing
Abdoulaye Diack, Perry Nelson, Kwaku Agbesi et al. (+40 more)
The advancement of
speech technology has predominantly favored high-resource
languages, creating a significant digital divide for speakers of most Sub-Saharan African
languages. To address this gap, we introduce WAXAL, a large-scale, openly accessible
speech dataset for 24
languages representing over 100 million speakers. The collection consists of two main components: an Automated
Speech Recognition (ASR)
dataset containing approximately 1,250 hours of transcribed, natural
speech from a diverse range of speakers, and a Text-to-
Speech (TTS)
dataset with around 235 hours of high-quality, single-speaker recordings reading phonetically balanced scripts. This paper details our methodology for data collection, annotation, and quality control, which involved partnerships with four African academic and community organizations. We provide a detailed statistical overview of the
dataset and discuss its potential limitations and ethical considerations. The WAXAL
datasets are released at https://huggingface.co/
datasets/google/WaxalNLP under the permissive CC-BY-4.0 license to catalyze research, enable the development of inclusive technologies, and serve as a vital resource for the digital preservation of these
languages.
Read the full abstract ▾
All authors Abdoulaye Diack, Perry Nelson, Kwaku Agbesi, Angela Nakalembe, MohamedElfatih MohamedKhair, Vusumuzi Dube, Tavonga Siyavora, Subhashini Venugopalan, Jason Hickey, Uche Okonkwo, Abhishek Bapna, Isaac Wiafe, Raynard Dodzi Helegah, Elikem Doe Atsakpo, Charles Nutrokpor, Fiifi Baffoe Payin Winful, Kafui Kwashie Solaga, Jamal-Deen Abdulai, Akon Obu Ekpezu, Audace Niyonkuru, Samuel Rutunda, Boris Ishimwe, Michael Melese, Engineer Bainomugisha, Joyce Nakatumba-Nabende, Andrew Katumba, Claire Babirye, Jonathan Mukiibi, Vincent Kimani, Samuel Kibacia, James Maina, Fridah Emmah, Ahmed Ibrahim Shekarau, Ibrahim Shehu Adamu, Yusuf Abdullahi, Howard Lakougna, Bob MacDonald, Hadar Shemtov, Aisha Walcott-Bryant, Moustapha Cisse, Avinatan Hassidim, Jeff Dean, Yossi Matias
Audio and Speech Processing · Cross-listed from cs.LG
Automated Dysphagia Screening Using Noninvasive Neck Acoustic Sensing
Jade Chng, Rong Xing, Yunfei Luo et al. (+4 more)
Pharyngeal health plays a vital role in essential human functions such as breathing, swallowing, and vocalization. Early detection of swallowing abnormalities, also known as dysphagia, is crucial for timely intervention. However, current diagnostic methods often rely on radiographic imaging or invasive procedures. In this study, we propose an automated framework for detecting dysphagia using portable and noninvasive acoustic sensing coupled with applied machine learning. By capturing subtle acoustic signals from the neck during swallowing tasks, we aim to identify patterns associated with abnormal physiological conditions. Our approach achieves promising test-time abnormality detection performance, with an AUC-ROC of 0.904 under 5 independent train-test splits. This work demonstrates the feasibility of using noninvasive acoustic sensing as a practical and scalable tool for pharyngeal health monitoring.
Read the full abstract ▾
All authors Jade Chng, Rong Xing, Yunfei Luo, Kristen Linnemeyer-Risser, Tauhidur Rahman, Andrew Yousef, Philip A Weissbrod
Signal Processing · Cross-listed from cs.LG
Neural Probabilistic Amplitude Shaping for Nonlinear Fiber Channels
Mohammad Taha Askari, Lutz Lampe and Amirhossein Ghazisaeidi
We introduce neural probabilistic amplitude shaping, a joint-distribution learning framework for coherent fiber systems. The proposed scheme provides a 0.5 dB signal-to-noise ratio gain over sequence selection for dual-polarized 64-QAM transmission across a single-span 205 km link.
Read the full abstract ▾
Image and Video Processing · Cross-listed from physics.med-ph
Perfusion Imaging and Single Material Reconstruction in Polychromatic Photon Counting CT
Namhoon Kim, Ashwin Pananjady, Amir Pourmorteza et al. (+1 more)
Background: Perfusion computed
tomography (CT) images the dynamics of a contrast
agent through the body over time, and is one of the highest X-ray dose scans in medical imaging. Recently, a theoretically justified reconstruction
algorithm based on a monotone variational inequality (VI) was proposed for single material polychromatic
photon-counting CT, and showed promising early results at low-dose imaging. Purpose: We adapt this reconstruction
algorithm for perfusion CT, to reconstruct the concentration map of the contrast
agent while the static background tissue is assumed known; we call our method VI-PRISM (VI-based PeRfusion Imaging and Single Material reconstruction). We evaluate its potential for dose-reduced perfusion CT, using a digital phantom with water and iodine of varying concentration. Methods: Simulated iodine concentrations range from 0.05 to 2.5 mg/ml. The simulated X-ray source emits
photons up to 100 keV, with average intensity ranging from $10^5$ down to $10^2$
photons per detector element. The number of tomographic projections was varied from 984 down to 8 to characterize the tradeoff in
photon allocation between views and intensity. Results: We compare VI-PRISM against filtered back-projection (FBP), and find that VI-PRISM recovers iodine concentration with error below 0.4 mg/ml at all source intensity levels tested. Even with a dose reduction between 10x and 100x compared to FBP, VI-PRISM exhibits reconstruction quality on par with FBP. Conclusion: Across all
photon budgets and angular sampling densities tested, VI-PRISM achieved consistently lower RMSE, reduced noise, and higher SNR compared to filtered back-projection. Even in extremely
photon-limited and sparsely sampled regimes, VI-PRISM recovered iodine concentrations with errors below 0.4 mg/ml, showing that VI-PRISM can support accurate and dose-efficient perfusion imaging in
photon-counting CT.
Read the full abstract ▾
All authors Namhoon Kim, Ashwin Pananjady, Amir Pourmorteza, Sara Fridovich-Keil
Signal Processing
Pilots and Other Predictable Elements of the Starlink Ku-Band Downlink
Wenkai Qin, Mark L. Psiaki, John R. Bowman et al. (+1 more)
We identify and characterize dedicated pilot symbols and other predictable elements embedded within the Starlink Ku-band downlink waveform. Exploitation of these predictable elements enables precise opportunistic positioning,
navigation, and timing using compact, low-gain receivers by maximizing the signal processing gain available for signal acquisition and time-of-arrival (TOA) estimation. We develop an acquisition and demodulation framework to decode Starlink frames and disclose the explicit sequences of the edge pilots – bands of 4QAM symbols located at both edges of each Starlink channel that apparently repeat identically across all frames, beams, channels, and satellites. We further reveal that the great majority of QPSK-modulated symbols do not carry high-
entropy user data but instead follow a regular tessellated structure superimposed on a constant reference template. We demonstrate that exploiting frame-level predictable elements yields a processing gain of approximately 48 dB, thereby enabling low-cost, compact receivers to extract precise TOA measurements even from low-SNR Starlink side beams.
Read the full abstract ▾
All authors Wenkai Qin, Mark L. Psiaki, John R. Bowman, Todd E. Humphreys
Signal Processing · Cross-listed from cs.LG
Learning Consistent Causal Abstraction Networks
Gabriele D'Acunto, Paolo Di Lorenzo and Sergio Barbarossa
Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal knowledge. Pushing in the same direction, we tackle the learning of consistent causal abstraction network (CAN), a sheaf-theoretic framework where (i) SCMs are Gaussian, (ii) restriction maps are transposes of constructive linear causal abstractions (CAs) adhering to the semantic
embedding principle, and (iii) edge stalks correspond–up to permutation–to the node stalks of more detailed SCMs. Our problem formulation separates into edge-specific local Riemannian problems and avoids nonconvex objectives. We propose an efficient search procedure, solving the local problems with SPECTRAL, our iterative method with closed-form updates and suitable for positive definite and semidefinite covariance
matrices. Experiments on synthetic data show competitive performance in the CA learning task, and successful recovery of diverse CAN structures.
Read the full abstract ▾