TAPES: Terminal Adjoint-Propagated Error Scheduling for Financial Diffusion Samplers

Paper: arXiv 2611.16484

Authors: Yilie Huang

Abstract

Financial diffusion samplers are often reused with a small number of function evaluations (NFE) inside scenario and risk pipelines, where numerical time-grid error can distort terminal quantities such as covariances, tails, and drawdown proxies. We study offline grid construction for a frozen probability-flow ODE: the score network, conditioning, Euler solver, report normalization, and deployment NFE remain fixed. TAPES (Terminal Adjoint-Propagated Error Scheduling) estimates signed local defects by Richardson comparisons, transports them through the remaining discrete flow and a terminal-report adjoint, and optimizes the squared norm of their sum before a capped direct refinement. We show that this transported signed sum is the first-order terminal-report error and quantify, under an aligned-defect model, the inefficiency of diagonal criteria. Across six budgets on a regime-switching simulation and chronologically held-out Mag7 contexts, TAPES gives the lowest design- and audit-report errors in all 24 dataset–budget–report rows within the reported five-pipeline panel. Cross-budget mean relative audit-error reductions are about 10–11% on Regime-SV and about 1% on Mag7, with Bonferroni intervals excluding zero; all displayed winners persist under a doubled-resolution reference, and a small Regime-SV Heun probe preserves the TAPES-first audit ordering. TAPES changes only the offline schedule and retains the prescribed deployment NFE; claims concern numerical fidelity to frozen generators.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly mathematical approach to optimizing time-step scheduling for financial diffusion samplers, backed by rigorous empirical validation on both simulated and real-world datasets. The novel adjoint-propagated error scheduling method demonstrates significant improvements in numerical fidelity for terminal financial reports.

Research Flowchart

  flowchart TD
    A[Research Goal: Mitigate Numerical Time-Grid Error in Financial Diffusion Samplers' Terminal Quantities] --> B{Key Methodology: TAPES (Terminal Adjoint-Propagated Error Scheduling)};
    B --> C[Methodology Details: Estimate Signed Local Defects via Richardson Comparisons];
    C --> D[Computational Process: Transport Defects through Discrete Flow & Terminal-Report Adjoint];
    D --> E[Computational Process: Optimize Squared Norm of Sum of Defects for Grid Refinement];
    E --> F{Data/Inputs: Regime-Switching Simulation & Chronologically Held-Out Mag7 Contexts};
    F --> G[Key Findings: TAPES Achieves Lowest Design- & Audit-Report Errors Across All 24 Dataset-Budget-Report Rows];
    G --> H[Outcome: Cross-Budget Mean Relative Audit-Error Reductions (10-11% on Regime-SV, ~1% on Mag7)];

Cited References (46)

1. Score-Based Generative Modeling through Stochastic Differential Equations (2021) — link
2. Denoising Diffusion Probabilistic Models (2020)
3. Elucidating the Design Space of Diffusion-Based Generative Models (2022)
4. DPM-Solver : A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps (2022)
5. Align Your Steps: Optimizing Sampling Schedules in Diffusion Models (2024) — link
6. An Optimal Control Approach to A Posteriori Error Estimation in Finite Element Methods (2001) — link
7. Adjoint Methods for PDEs : A Posteriori Error Analysis and Postprocessing by Duality (2002) — link
8. Solving Ordinary Differential Equations I: Nonstiff Problems (1993) — link

3 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2570 linked papers.