Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control
该研究通过几何监督的潜模型和局部-全局度量铰链方法，解决了非线性确定系统在有限样本下的控制问题，确保了度量保真度和均匀受控动力学。
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Selected work
Representative Papers
Wasserstein gradient flows for Coulomb discrepancies
This study investigates the long-time convergence behavior of the squared Maximum Mean Discrepancy (MMD) with a Coulomb kernel under Wasserstein gradient flows, with particular attention to challenges arising in vacuum regions and unbounded domains. By introducing a defective Polyak–Łojasiewicz inequality and leveraging the variational structure of MMD together with hypercontractivity estimates and Hölder regularity analysis, the authors establish the existence of global-in-time weak solutions emanating from arbitrary Borel probability measures and prove that these solutions instantaneously belong to \(L^\infty\) for any positive time. Key contributions include demonstrating exponential decay of MMD for positive target measures on the torus and uncovering fundamental obstructions to convergence in the whole space \(\mathbb{R}^d\), while establishing an exponential convergence mechanism under radial symmetry.
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The role of neuromorphic principles in the future of biomedicine and healthcare
This study addresses the challenges of applying neuromorphic engineering in biomedical and healthcare domains by convening, for the first time, a diverse coalition of stakeholders—including academia, industry, clinicians, and funding agencies—to systematically assess the current state and critical bottlenecks of the technology through interdisciplinary expert workshops. By integrating insights from neuroscience, biomedical engineering, and brain-inspired computing, the project delineates key development pathways and collaborative strategies, establishing a community-wide consensus. The outcomes—including workshop recordings, presentations, and strategic recommendations—have been publicly released to provide a clear roadmap and guiding framework for future research and development in the field.
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Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle
This work addresses the challenge of selecting regularization hyperparameters in conditional moment models when the smoothness of the unknown perturbation function is unavailable. We propose the first adaptive framework based on the bias principle, which automatically balances bias and variance without requiring prior knowledge of the smoothness level. The method is applicable to both Regularized DeepIV (RDIV) and Tikhonov-regularized Adversarial Estimators (TRAE), yielding a fully adaptive doubly robust estimator. Theoretical analysis demonstrates that the proposed approach achieves the same optimal convergence rates—both in weak and strong norms—as if the smoothness were known a priori, thereby establishing the first instance of adaptive optimal inference for linear functionals in this setting.
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Obstruction theory and the complexity of counting group homomorphisms
This study investigates the computational complexity of counting homomorphisms from an input group Γ to a finite group G. The problem is shown to be #P-hard when G is non-abelian and Γ is given by a finite presentation. In contrast, a polynomial-time algorithm exists when G is a 2-step nilpotent group and Γ is either the fundamental group of a 3-manifold or a finite group. By integrating techniques from computational group theory, group cohomology, obstruction theory, and triangulations of 3-manifolds, this work establishes—for the first time—a connection between the approximability of Eilenberg–MacLane spaces and the existence of efficient algorithms, thereby highlighting the profound influence of topological structure on computational complexity.
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Finite-Sample Metric Non-Collapse for Geometrically Supervised Latent World Models in Control
该研究通过几何监督的潜模型和局部-全局度量铰链方法，解决了非线性确定系统在有限样本下的控制问题，确保了度量保真度和均匀受控动力学。
0 citationsRead paper
Wasserstein gradient flows for Coulomb discrepancies
This study investigates the long-time convergence behavior of the squared Maximum Mean Discrepancy (MMD) with a Coulomb kernel under Wasserstein gradient flows, with particular attention to challenges arising in vacuum regions and unbounded domains. By introducing a defective Polyak–Łojasiewicz inequality and leveraging the variational structure of MMD together with hypercontractivity estimates and Hölder regularity analysis, the authors establish the existence of global-in-time weak solutions emanating from arbitrary Borel probability measures and prove that these solutions instantaneously belong to \(L^\infty\) for any positive time. Key contributions include demonstrating exponential decay of MMD for positive target measures on the torus and uncovering fundamental obstructions to convergence in the whole space \(\mathbb{R}^d\), while establishing an exponential convergence mechanism under radial symmetry.
0 citationsRead paper
The role of neuromorphic principles in the future of biomedicine and healthcare
This study addresses the challenges of applying neuromorphic engineering in biomedical and healthcare domains by convening, for the first time, a diverse coalition of stakeholders—including academia, industry, clinicians, and funding agencies—to systematically assess the current state and critical bottlenecks of the technology through interdisciplinary expert workshops. By integrating insights from neuroscience, biomedical engineering, and brain-inspired computing, the project delineates key development pathways and collaborative strategies, establishing a community-wide consensus. The outcomes—including workshop recordings, presentations, and strategic recommendations—have been publicly released to provide a clear roadmap and guiding framework for future research and development in the field.
0 citationsRead paper
Adaptive Estimation and Inference in Conditional Moment Models via the Discrepancy Principle
This work addresses the challenge of selecting regularization hyperparameters in conditional moment models when the smoothness of the unknown perturbation function is unavailable. We propose the first adaptive framework based on the bias principle, which automatically balances bias and variance without requiring prior knowledge of the smoothness level. The method is applicable to both Regularized DeepIV (RDIV) and Tikhonov-regularized Adversarial Estimators (TRAE), yielding a fully adaptive doubly robust estimator. Theoretical analysis demonstrates that the proposed approach achieves the same optimal convergence rates—both in weak and strong norms—as if the smoothness were known a priori, thereby establishing the first instance of adaptive optimal inference for linear functionals in this setting.
0 citationsRead paper
Obstruction theory and the complexity of counting group homomorphisms
This study investigates the computational complexity of counting homomorphisms from an input group Γ to a finite group G. The problem is shown to be #P-hard when G is non-abelian and Γ is given by a finite presentation. In contrast, a polynomial-time algorithm exists when G is a 2-step nilpotent group and Γ is either the fundamental group of a 3-manifold or a finite group. By integrating techniques from computational group theory, group cohomology, obstruction theory, and triangulations of 3-manifolds, this work establishes—for the first time—a connection between the approximability of Eilenberg–MacLane spaces and the existence of efficient algorithms, thereby highlighting the profound influence of topological structure on computational complexity.
0 citationsRead paper