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1. Slice Sampling Reparameterization Gradients

   Zoltowski, David; Cai, Diana; Adams, Ryan P. (January 2021, Advances in neural information processing systems)

   Many probabilistic modeling problems in machine learning use gradient-based optimization in which the objective takes the form of an expectation. These problems can be challenging when the parameters to be optimized determine the probability distribution under which the expectation is being taken, as the na\"ive Monte Carlo procedure is not differentiable. Reparameterization gradients make it possible to efficiently perform optimization of these Monte Carlo objectives by transforming the expectation to be differentiable, but the approach is typically limited to distributions with simple forms and tractable normalization constants. Here we describe how to differentiate samples from slice sampling to compute \textit{slice sampling reparameterization gradients}, enabling a richer class of Monte Carlo objective functions to be optimized. Slice sampling is a Markov chain Monte Carlo algorithm for simulating samples from probability distributions; it only requires a density function that can be evaluated point-wise up to a normalization constant, making it applicable to a variety of inference problems and unnormalized models. Our approach is based on the observation that when the slice endpoints are known, the sampling path is a deterministic and differentiable function of the pseudo-random variables, since the algorithm is rejection-free. We evaluate the method on synthetic examples and apply it to a variety of applications with reparameterization of unnormalized probability distributions. 

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2. Approximation properties of slice-matching operators

   https://doi.org/10.1007/s43670-024-00089-7  

   Li, Shiying; Moosmüller, Caroline (June 2024, Sampling Theory, Signal Processing, and Data Analysis)
3. A note on rationally slice knots

   Levine, Adam Simon (December 2023, New York journal of mathematics)

   Kawauchi proved that every strongly negative amphichiral knot K in S^3 bounds a smoothly embedded disk in some rational homology ball V_K, whose construction a priori depends on K. We show that V_K is independent of K up to diffeomorphism. Thus, a single 4-manifold, along with connected sums thereof, accounts for all known examples of knots that are rationally slice but not slice. 

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4. Single-Shot Fourier-Slice Dual-Comb Spectroscopy

   https://doi.org/10.1109/LPT.2023.3325799  

   Lomsadze, Bachana; Weight, Skyler; Clark, Peyton (October 2023, IEEE Photonics Technology Letters)
5. Distinguishing slice disks using knot Floer homology

   https://doi.org/10.1007/s00029-019-0531-6  

   Juhász, András; Zemke, Ian (February 2020, Selecta Mathematica)