arXiv subjects

Haotian Tian

Publications and source records attributed to Haotian Tian.

5 recordsLinked to original sources

arXiv2026

Crossed products by compact group actions with the weak tracial Rokhlin property

In this paper, we introduce compact group actions with the weak tracial Rokhlin property. This concept simultaneously generalizes finite group actions with the weak tracial Rokhlin property and compact group actions with the tracial Rokhlin property (in the sense of the Elliott program). Under this framework, we prove that simplicity, pure infiniteness, tracial $\mathcal{Z}$-stability and the combination of nuclearity and $\mathcal{Z}$-stability can be transferred from the original algebra to the crossed product. We also show that the radius of comparison of the fixed point algebra does not exceed that of the original algebra. Furthermore, we discuss the relationship between our definition and natural generalization of the finite group case in non-Elliott program settings. Finally, we provide a nontrivial example of a compact group action with the weak tracial Rokhlin property with comparison: an action of $(S_2)^\mathbb{N}$ on the Jiang-Su algebra $\mathcal{Z}$. Since $\mathcal{Z}$ contains no nontrivial projections, this action does not possess the tracial Rokhlin property.

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arXiv2025

Unsupervised Deep Equilibrium Model Learning for Large-Scale Channel Estimation with Performance Guarantees

Supervised deep learning methods have shown promise for large-scale channel estimation (LCE), but their reliance on ground-truth channel labels greatly limits their practicality in real-world systems. In this paper, we propose an unsupervised learning framework for LCE that does not require ground-truth channels. The proposed approach leverages Generalized Stein's Unbiased Risk Estimate (GSURE) as a principled unsupervised loss function, which provides an unbiased estimate of the projected mean-squared error (PMSE) from compressed noisy measurements. To ensure a guaranteed performance, we integrate a deep equilibrium (DEQ) model, which implicitly represents an infinite-depth network by directly learning the fixed point of a parameterized iterative process. We theoretically prove that, under mild conditions, the proposed GSURE-based unsupervised DEQ learning can achieve oracle-level supervised performance. In particular, we show that the DEQ architecture inherently enforces a compressible solution. We then demonstrate that DEQ-induced compressibility ensures that optimizing the projected error via GSURE suffices to guarantee a good MSE performance, enabling a rigorous performance guarantee. Extensive simulations validate the theoretical findings and demonstrate that the proposed framework significantly outperforms various baselines when ground-truth channel is unavailable.

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arXiv2025

Information-Preserving CSI Feedback: Invertible Networks with Endogenous Quantization and Channel Error Mitigation

Deep learning has emerged as a promising solution for efficient channel state information (CSI) feedback in frequency division duplex (FDD) massive MIMO systems. Conventional deep learning-based methods typically rely on a deep autoencoder to compress the CSI, which leads to irreversible information loss and degrades reconstruction accuracy. This paper introduces InvCSINet, an information-preserving CSI feedback framework based on invertible neural networks (INNs). By leveraging the bijective nature of INNs, the model ensures information-preserving compression and reconstruction with shared model parameters. To address practical challenges such as quantization and channel-induced errors, we endogenously integrate an adaptive quantization module, a differentiable bit-channel distortion module and an information compensation module into the INN architecture. This design enables the network to learn and compensate the information loss during CSI compression, quantization, and noisy transmission, thereby preserving the CSI integrity throughout the feedback process. Simulation results validate the effectiveness of the proposed scheme, demonstrating superior CSI recovery performance and robustness to practical impairments with a lightweight architecture.

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arXiv2025

Uniform property $Γ$ for Crossed products by group actions with the Rokhlin-type properties

In this paper, let $A$ be a unital separable simple infinite dimensional C*-algebra which has uniform property $Γ$. Let $α\colon G\to \mathrm{Aut}(A)$ be an action of a finite group which has the weak tracial Rokhlin property. Then we prove that the crossed product $A\rtimes_αG$ and fixed point algebra $A^α$ have uniform property $Γ$. Let $α\colon G\to \mathrm{Aut}(A)$ be an action of a second-countable compact group which has the tracial Rokhlin property with comparison. Then we prove that the crossed product $A\rtimes_αG$ and fixed point algebra $A^α$ have uniform property $Γ$.

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arXiv2023

Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property

In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with comparison that could be deduced from the properties of its original algebra: (1) stable rank one; (2) real rank zero; (3) $β$-comparison; (4) Winter's $n$-comparison; (5) $m$-almost divisible; (6) weakly ($m$,$n$)-divisible.

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