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SunBURST: Deterministic GPU-Accelerated Bayesian Evidence via Mode-Centric Laplace Integration

Ira Wolfson

TL;DR

SunBURST introduces a deterministic, GPU-accelerated method for Bayesian evidence that leverages mode-centric Laplace integration rather than global volume exploration. By discovering posterior modes via radial rays, refining them with batched L-BFGS, and computing per-mode evidence through the Laplace approximation, SunBURST achieves near-constant or sub-linear wall-clock scaling with dimension and exact results for Gaussian posteriors up to 1024 dimensions. Its GPU-enabled parallelism enables dramatic speedups over traditional nested sampling, delivering machine-precision evidence in seconds for Gaussian-like posteriors and a substantial practical advantage for high-dimensional model comparison. While highly effective for near-Gaussian posteriors common in physics and engineering, SunBURST's accuracy degrades for strongly non-Gaussian posteriors, where it serves best as a fast, geometry-aware estimator or preprocessing step for hybrid workflows. The work demonstrates that high-precision Bayesian evidence can be made tractable in very high dimensions through deterministic, GPU-parallel integration focused on local Gaussian structure around a finite set of modes.

Abstract

Bayesian evidence evaluation becomes computationally prohibitive in high dimensions due to the curse of dimensionality and the sequential nature of sampling-based methods. We introduce SunBURST, a deterministic GPU-native algorithm for Bayesian evidence calculation that replaces global volume exploration with mode-centric geometric integration. The pipeline combines radial mode discovery, batched L-BFGS refinement, and Laplace-based analytic integration, treating modes independently and converting large batches of likelihood evaluations into massively parallel GPU workloads. For Gaussian and near-Gaussian posteriors, where the Laplace approximation is exact or highly accurate, SunBURST achieves numerical agreement at double-precision tolerance in dimensions up to 1024 in our benchmarks, with sub-linear wall-clock scaling across the tested range. In multimodal Gaussian mixtures, conservative configurations yield sub-percent accuracy while maintaining favorable scaling. SunBURST is not intended as a universal replacement for sampling-based inference. Its design targets regimes common in physical parameter estimation and inverse problems, where posterior mass is locally well approximated by Gaussian structure around a finite number of modes. In strongly non-Gaussian settings, the method can serve as a fast geometry-aware evidence estimator or as a preprocessing stage for hybrid workflows. These results show that high-precision Bayesian evidence evaluation can be made computationally tractable in very high dimensions through deterministic integration combined with massive parallelism.

SunBURST: Deterministic GPU-Accelerated Bayesian Evidence via Mode-Centric Laplace Integration

TL;DR

SunBURST introduces a deterministic, GPU-accelerated method for Bayesian evidence that leverages mode-centric Laplace integration rather than global volume exploration. By discovering posterior modes via radial rays, refining them with batched L-BFGS, and computing per-mode evidence through the Laplace approximation, SunBURST achieves near-constant or sub-linear wall-clock scaling with dimension and exact results for Gaussian posteriors up to 1024 dimensions. Its GPU-enabled parallelism enables dramatic speedups over traditional nested sampling, delivering machine-precision evidence in seconds for Gaussian-like posteriors and a substantial practical advantage for high-dimensional model comparison. While highly effective for near-Gaussian posteriors common in physics and engineering, SunBURST's accuracy degrades for strongly non-Gaussian posteriors, where it serves best as a fast, geometry-aware estimator or preprocessing step for hybrid workflows. The work demonstrates that high-precision Bayesian evidence can be made tractable in very high dimensions through deterministic, GPU-parallel integration focused on local Gaussian structure around a finite set of modes.

Abstract

Bayesian evidence evaluation becomes computationally prohibitive in high dimensions due to the curse of dimensionality and the sequential nature of sampling-based methods. We introduce SunBURST, a deterministic GPU-native algorithm for Bayesian evidence calculation that replaces global volume exploration with mode-centric geometric integration. The pipeline combines radial mode discovery, batched L-BFGS refinement, and Laplace-based analytic integration, treating modes independently and converting large batches of likelihood evaluations into massively parallel GPU workloads. For Gaussian and near-Gaussian posteriors, where the Laplace approximation is exact or highly accurate, SunBURST achieves numerical agreement at double-precision tolerance in dimensions up to 1024 in our benchmarks, with sub-linear wall-clock scaling across the tested range. In multimodal Gaussian mixtures, conservative configurations yield sub-percent accuracy while maintaining favorable scaling. SunBURST is not intended as a universal replacement for sampling-based inference. Its design targets regimes common in physical parameter estimation and inverse problems, where posterior mass is locally well approximated by Gaussian structure around a finite number of modes. In strongly non-Gaussian settings, the method can serve as a fast geometry-aware evidence estimator or as a preprocessing stage for hybrid workflows. These results show that high-precision Bayesian evidence evaluation can be made computationally tractable in very high dimensions through deterministic integration combined with massive parallelism.
Paper Structure (103 sections, 47 equations, 1 figure, 10 tables)

This paper contains 103 sections, 47 equations, 1 figure, 10 tables.

Table of Contents

  1. Introduction
  2. Nested Sampling
  3. The GPU Opportunity
  4. Contributions
  5. The Curse of Dimensionality
  6. The Concentration of Measure
  7. The Shell Theorem
  8. The Distance Catastrophe
  9. The $L_\infty$ Metric.
  10. The Sampling Catastrophe
  11. The Evidence Calculation Catastrophe
  12. The Multimodal Catastrophe
  13. Summary: The Five Facets of the Curse
  14. The Geometry of Escape
  15. Theoretical Foundations
  16. ...and 88 more sections

Figures (1)

  • Figure 1: Wall-clock scaling comparison on Gaussian posteriors. SunBURST (dark red circles) maintains near-constant runtime through 64 dimensions before transitioning to $O(d^{1.0})$ scaling. All competitors exhibit exponential growth: dynesty variants timeout beyond 32--64D, UltraNest beyond 8D. Shaded regions indicate dimensions where only SunBURST achieves each accuracy level. SunBURST achieves 1024D in 6.8 seconds.