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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.18686 |
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| _version_ | 1866918457738526720 |
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| author | Ghosh, Kausik Kumar, Sidhaarth Niarchos, Vasilis Stergiou, Andreas |
| author_facet | Ghosh, Kausik Kumar, Sidhaarth Niarchos, Vasilis Stergiou, Andreas |
| contents | We demonstrate that simple feed-forward neural networks (NNs) can accurately compute correlation functions of conformal field theories (CFTs) on a line. Strikingly, by optimising a NN solely on crossing symmetry and providing only the scaling dimension of the leading non-trivial operator and the correlator's value at a single "anchor point", we can reconstruct target physical correlators to within a few percent. We establish the robustness of this minimal-data approach across a broad class of theories and dimensions, including generalised free fields, contact and one-loop Witten diagrams in AdS$_2$, unitary and non-unitary 2d minimal models, the 3d Ising model, and half-BPS correlators in 4d $\mathcal{N}=4$ super-Yang-Mills theory, together with several thermal two-point functions, notably including those of the 3d Ising model. We argue that this remarkable alignment between NNs and CFTs stems from the spectral bias of gradient-based training, which heavily favours smooth functions. To ground this connection, we analyse the smoothness of conformal correlators using fractional Sobolev semi-norms, Chebyshev spectral decompositions, and a measure based on curvature. Finally, we establish the broader reconstructive power of this technique by extending it beyond the diagonal kinematics of the line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural Spectral Bias and Conformal Correlators I: Introduction and Applications Ghosh, Kausik Kumar, Sidhaarth Niarchos, Vasilis Stergiou, Andreas High Energy Physics - Theory We demonstrate that simple feed-forward neural networks (NNs) can accurately compute correlation functions of conformal field theories (CFTs) on a line. Strikingly, by optimising a NN solely on crossing symmetry and providing only the scaling dimension of the leading non-trivial operator and the correlator's value at a single "anchor point", we can reconstruct target physical correlators to within a few percent. We establish the robustness of this minimal-data approach across a broad class of theories and dimensions, including generalised free fields, contact and one-loop Witten diagrams in AdS$_2$, unitary and non-unitary 2d minimal models, the 3d Ising model, and half-BPS correlators in 4d $\mathcal{N}=4$ super-Yang-Mills theory, together with several thermal two-point functions, notably including those of the 3d Ising model. We argue that this remarkable alignment between NNs and CFTs stems from the spectral bias of gradient-based training, which heavily favours smooth functions. To ground this connection, we analyse the smoothness of conformal correlators using fractional Sobolev semi-norms, Chebyshev spectral decompositions, and a measure based on curvature. Finally, we establish the broader reconstructive power of this technique by extending it beyond the diagonal kinematics of the line. |
| title | Neural Spectral Bias and Conformal Correlators I: Introduction and Applications |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.18686 |