Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
Performing integration-by-parts reductions using NeatIBP 1.1 + Kira
9 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce a new version v1.1 of NeatIBP. In this new version, a Kira interface is included. It allows the user to reduce the integration-by-parts (IBP) identity systems generated by NeatIBP using Kira in a highly automated way. This new version also implements the so-called spanning cuts method. It helps to reduce the total computational complexity of IBP reduction for certain hard problems. Another important feature of this new version is an algorithm to simplify the solution module of the syzygy equations hinted by the idea of maximal cuts.
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2026 9representative citing papers
Syzygy solutions for IBP reduction are systematically constructed as maximal minors of certificate matrices derived from the leading Landau singularities of Feynman diagrams.
Derives gravitational Compton amplitude at O(G^4) and N-matrix element for scattering phase shift, verified by agreement with black-hole perturbation theory.
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
citing papers explorer
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Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding
Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
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Compact Syzygies for Feynman Integrals from Landau Singularities
Syzygy solutions for IBP reduction are systematically constructed as maximal minors of certificate matrices derived from the leading Landau singularities of Feynman diagrams.
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Gravitational Compton scattering at the fourth post-Minkowskian order
Derives gravitational Compton amplitude at O(G^4) and N-matrix element for scattering phase shift, verified by agreement with black-hole perturbation theory.
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Magic Relations and Critical Varieties of Feynman Integrals
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
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Discrete symmetries of Feynman integrals
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
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Chebyshev Approximations of Feynman Integrals for Collider Physics
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
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On the spanning cuts consistency problem in the IBP reductions of Feynman integrals
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
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All-order structure of static gravitational interactions and the seventh post-Newtonian potential
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
-
AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.