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Toy Model Results

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Abstract and 1. Introduction

  1. Unfolding

    2.1 Posing the Unfolding Problem

    2.2 Our Unfolding Approach

  2. Denoising Diffusion Probabilistic Models

    3.1 Conditional DDPM

  3. Unfolding with cDDPMs

  4. Results

    5.1 Toy models

    5.2 Physics Results

  5. Discussion, Acknowledgments, and References


Appendices

A. Conditional DDPM Loss Derivation

B. Physics Simulations

C. Detector Simulation and Jet Matching

D. Toy Model Results

E. Complete Physics Results

D Toy Model Results

The full unfolding results of the toy model tests are shown here, including the η, ϕ, and E distributions of the data 4-vectors. In fig. 9 we show the full results of multidimensional unfolding tests as well as the tests on the cDDPM dependence on the training prior when learning the posterior. In fig. 10 the full results for the moments-based unfolding are shown.



Figure 9: Complete unfolding results for the multidimensional toy model tests, demonstrating the cDDPM’s ability to learn the posterior P(x|y) given a dataset of pairs {x, y}. The bottom row shows the unfolding performance when the cDDPM is trained on an alternative dataset with different marginal distributions but the same posterior, confirming that the cDDPM’s sampling is based on the learned posterior without significant dependence on the training prior.


In fig. 10 we present the complete unfolding results for the multidimensional toy model tests using a class of exponential functions. The successful unfolding of all particle properties for the test datasets underscores the cDDPM’s capacity to generalize beyond the specific distributions seen during training.


Authors:

(1) Camila Pazos, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts;

(2) Shuchin Aeron, Department of Electrical and Computer Engineering, Tufts University, Medford, Massachusetts and The NSF AI Institute for Artificial Intelligence and Fundamental Interactions;

(3) Pierre-Hugues Beauchemin, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts and The NSF AI Institute for Artificial Intelligence and Fundamental Interactions;

(4) Vincent Croft, Leiden Institute for Advanced Computer Science LIACS, Leiden University, The Netherlands;

(5) Martin Klassen, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts;

(6) Taritree Wongjirad, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts and The NSF AI Institute for Artificial Intelligence and Fundamental Interactions.


This paper is available on arxiv under CC BY 4.0 DEED license.


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