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Ohio State University

Academic institutionnorthamerica · us
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Research library894linked papers
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Selected work

Representative Papers

Understanding Deep Representation Learning via Layerwise Feature Compression and Discrimination

Nov 06, 2023arXiv.org

This work investigates the fundamental mechanisms underlying hierarchical representation learning in deep neural networks. Addressing the central question—“how do features evolve across layers”—we propose a joint quantification framework for inter-layer feature compression ratio and discriminability. We theoretically uncover, for the first time, a geometric–linear dual-rate pattern of feature evolution in deep linear networks: intra-class features contract geometrically, while inter-class discriminability increases linearly. This pattern is rigorously established under minimal norm, weight balancing, and near-low-rank assumptions, and extended to nonlinear networks via intermediate-feature modeling for multi-class classification. Numerical experiments validate its robustness across architectures and datasets. Our results provide an interpretable theoretical foundation for representation learning and yield quantitative guidance for layer selection in transfer learning and knowledge distillation.

18 citations2 influentialRead paper

Quantum Ruzsa Divergence to Quantify Magic

Jan 25, 2024

This work addresses the fundamental challenge of quantifying quantum state “magic.” Methodologically, it introduces a novel theoretical framework grounded in quantum convolution and quantum entropy: (i) adapts the classical Ruzsa inequality to quantum information by defining the quantum Ruzsa divergence; (ii) establishes an entropy convergence theory under quantum convolution and proposes the convolutional strong subadditivity conjecture; and (iii) extends inverse sumset theory to the quantum regime, integrating stabilizer formalism and magic theory to develop new analytical tools. Key contributions include: (1) two axiomatically compliant magic measures—the quantum Ruzsa magic measure and quantum doubling constant; (2) proof that the quantum Ruzsa divergence satisfies the triangle inequality; (3) a quantum central limit theorem with explicit magic-gap control; and (4) a computable, robust quantification scheme applicable to arbitrary pure and mixed states.

6 citationsRead paper

Identification and Estimation of Continuous-Time Dynamic Discrete Choice Games

Nov 04, 2025

This paper addresses identification and estimation in continuous-time dynamic discrete-choice games, focusing on the previously overlooked challenges of endogeneity and heterogeneity in decision arrival rates (i.e., timing of actions). Under the realistic constraint of fixed-interval discrete observations, we are the first to model the arrival rate as an estimable parameter and allow it to vary across agents. Within a Markov perfect equilibrium framework, we derive sufficient conditions for nonparametric identification of the underlying continuous-time primitives—including policy functions, the discount factor, and the distribution of heterogeneous arrival rates—using only discrete-time data. Monte Carlo simulations and empirical application to Rust’s (1987) bus engine replacement data demonstrate the method’s estimation accuracy, robustness, and computational feasibility across sampling frequencies. Results show that neglecting arrival-rate heterogeneity systematically biases behavioral inference, underscoring the model’s significant contribution to structural econometrics and empirical industrial organization.

5 citationsRead paper

On the Global Convergence of Risk-Averse Policy Gradient Methods with Expected Conditional Risk Measures

Jan 26, 2023International Conference on Machine Learning

This work investigates the global convergence of policy gradient (PG) and natural policy gradient (NPG) methods for risk-sensitive reinforcement learning under expectation-based conditional risk measures (ECRMs). For time-consistent ECRMs, we develop a unified PG/NPG algorithmic framework covering four practical parameterizations: constrained direct parameterization, log-barrier regularized softmax, entropy-regularized softmax, and approximate NPG. We establish, for the first time, a rigorous global optimality guarantee and iteration complexity analysis—achieving $O(1/varepsilon^2)$ for PG and $O(1/varepsilon)$ for NPG—for ECRM-based risk optimization, thereby filling a critical theoretical gap in globally convergent risk-sensitive RL. Empirical evaluation on a stochastic Cliffwalk environment demonstrates that the proposed algorithms effectively mitigate risk while maintaining stability and convergence.

5 citationsRead paper

Uniquely optimal codes of low complexity are symmetric

Aug 28, 2020arXiv.org

This study addresses the fundamental question of whether optimal codes in compact metric spaces necessarily exhibit symmetry, focusing on low-complexity uniquely optimal encodings. Method: Integrating tools from metric geometry, extremal combinatorics, and group action theory, we develop constructive coding design techniques, symmetry detection algorithms, and rigorous optimality proofs. Contribution/Results: We formulate and systematically verify the universal conjecture that every low-complexity uniquely optimal code admits a nontrivial symmetry. Through comprehensive case studies on canonical spaces—including the sphere and torus—we empirically and theoretically confirm that symmetry is a necessary condition for uniqueness and optimality under low complexity constraints. Our work establishes, for the first time, a deep structural connection between the geometry of the underlying metric space and the symmetry properties of its optimal codes. This yields novel principled guidance for efficient encoding design, advancing both theoretical understanding and practical construction of optimal codes in geometric settings.

3 citationsRead paper
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