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University of California, Berkeley

Academic institutionnorthamerica · us
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Research library2,982linked papers
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Selected work

Representative Papers

Possibility Frames and Forcing for Modal Logic

Dec 30, 2015

This paper addresses the semantic divide between classical and intuitionistic modal logic by introducing a novel frame semantics based on partially ordered “possibilities” instead of traditional possible worlds. Methodologically, it constructs possibility frames—interpreting formulas via regular open sets in Alexandrov topologies—and develops a categorical duality theory between such frames and non-atomic CV-Boolean algebraic operators (CV-BAOs). It establishes, for the first time, a duality between full possibility frames and CV-BAOs using filters rather than ultrafilters, thereby avoiding the Axiom of Choice; it also introduces principal possibility frames to characterize V-BAOs. The main contributions are: (i) unifying classical and intuitionistic modal semantics within a single framework; (ii) systematically establishing dualities between possibility frames and various classes of BAOs; (iii) completing definability, correspondence, and strong completeness theories; and (iv) proving that every BAO is fully characterized by a filter-descriptive possibility frame.

46 citations6 influentialRead paper

Causal Panel Analysis under Parallel Trends: Lessons from A Large Reanalysis Study

Sep 27, 2023

The two-way fixed effects (TWFE) estimator is widely used for causal inference in political science but suffers from sensitivity to heterogeneous treatment effects (HTE) and the parallel trends (PT) assumption, undermining result reliability. This study conducts a systematic reanalysis of 49 influential political science papers employing TWFE, marking the first large-scale assessment in the discipline of six HTE-robust estimators’ stability, alongside comprehensive PT diagnostics, sensitivity analyses, and statistical power evaluation. Results show that while HTE-robust estimates are directionally consistent overall, they exhibit substantial variability; explicit PT violations are rare, yet over half the studies suffer severe statistical power deficits under joint HTE and PT constraints. The analysis reveals systematic robustness risks inherent in standard TWFE practice, providing an empirical benchmark and practical guidance for method selection and interpretation in applied political science research.

16 citations1 influentialRead paper

Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee

Oct 23, 2022arXiv.org

For unconstrained convex-concave minimax optimization, this paper proposes a class of inexact regularized Newton-type algorithms that incorporate second-order information into the hypergradient framework while ensuring global convergence under inexact computations. Theoretically, it achieves the first $O(varepsilon^{-2/3})$ iteration complexity—matching the known lower bound—for such problems. Each iteration requires only one Schur decomposition and $O(loglog(1/varepsilon))$ linear solver calls, eliminating the redundant $loglog$ factor present in prior second-order methods. Through analysis based on the restricted gap function, we establish boundedness of iterates and convergence of the averaged sequence to an $varepsilon$-saddle point. Experiments on synthetic and real-world datasets demonstrate that the proposed method significantly outperforms existing second-order minimax optimization algorithms in both accuracy and efficiency.

14 citations6 influentialRead paper

Diffusion Models Learn Low-Dimensional Distributions via Subspace Clustering

Sep 04, 2024arXiv.org

Diffusion models face the curse of dimensionality when modeling high-dimensional image distributions, hindering effective learning of low-dimensional manifold structures underlying images. Method: We reformulate the diffusion training objective as an equivalent subspace clustering problem—establishing, for the first time, a rigorous theoretical equivalence between diffusion models and subspace clustering. Leveraging manifold geometry and the low-rank property of denoising autoencoders, we derive theoretical guarantees showing sample complexity scales linearly with intrinsic dimension. Our framework integrates low-rank Gaussian mixture modeling, score function parameterization, and diffusion loss analysis. Contribution/Results: We prove that learned subspaces admit precise semantic interpretations—corresponding to editable, concept-level image representations. Theoretically, our method ensures exact recovery of low-dimensional distributions even in low-sample regimes. Experiments on synthetic and real-world image data validate both semantic consistency of the recovered subspaces and their strong controllability for image editing.

14 citations1 influentialRead paper

Fast RoPE Attention: Combining the Polynomial Method and Fast Fourier Transform

May 17, 2025

This work addresses the quadratic attention complexity $O(n^2)$ in RoPE-enhanced Transformers. We propose the first near-linear-time approximation algorithm for RoPE attention under a bounded-input assumption. Our core method synergistically integrates polynomial interpolation with the Fast Fourier Transform (FFT), overcoming the fundamental limitation that conventional fast attention techniques fail under RoPE’s rotational positional encoding structure. By constructing a low-rank approximation of RoPE embeddings in the frequency domain, our approach reduces per-layer attention computation to $O(n log n)$—achieving theoretical optimality and matching the known lower bound. Extensive experiments demonstrate that our method significantly accelerates long-sequence inference while preserving model accuracy, establishing a new paradigm for efficient deployment of RoPE-based architectures.

12 citations2 influentialRead paper
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