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  1. ; ; ; (, Foundations of Computational Mathematics)
    Abstract The stein variational gradient descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the Wasserstein gradient flow corresponding to the KL-divergence minimization. In this work, we propose the Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein gradient flow. We establish various theoretical properties of the Regularized Stein Variational Gradient Flow (and its time-discretization) including convergence to equilibrium, existence and uniqueness of weak solutions, and stability of the solutions. We provide preliminary numerical evidence of the improved performance offered by the regularization. 
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  2. ; ; ; (, IEEE Transactions on Information Theory)
    Free, publicly-accessible full text available November 1, 2025
  3. ; ; (, SIAM Journal on Matrix Analysis and Applications)
    Full Text Available 
  4. ; ; (, Communications in Partial Differential Equations)
    Full Text Available 
  5. ; ; ; ; ; (, Proceedings of the 37th International Conference on Neural Information Processing Systems)
    Accepted Manuscript Full Text Available
  6. ; ; (, Numerische Mathematik)
    We introduce a generalization of local density of states which is “windowed” with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual LDOS is recovered in the limit where the position window captures individual sites and the energy window is a delta distribution. We prove that the wLDOS is local in the sense that it can be computed up to arbitrarily small error using spatial truncations of the system Hamiltonian. Using this result we prove that the wLDOS is well-defined and computable for infinite systems satisfying some natural assumptions. We finally present numerical computations of the wLDOS at the edge and in the bulk of a “Fibonacci SSH model”, a one-dimensional non-periodic model with topological edge states. 
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  7. ; ; (, Communications in Mathematical Sciences)
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  8. ; ; ; ; ; (, SIAM Journal on Mathematical Analysis)
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  9. ; ; ; (, Proceedings of the 40th International Conference on Machine Learning)
    Accepted Manuscript Full Text Available
  10. ; ; (, Proceedings of the 40th International Conference on Machine Learning)
    Accepted Manuscript Full Text Available