Cosmological Parameter Inference from Filtered Merger Tree Motifs via Quantum Tensor Train Decomposition

Abstract: Inferring cosmological parameters from the complex structure of dark matter halo merger trees is a challenging problem. This work explores the use of Tensor Train (TT) decomposition, a technique related to Quantum Tensor Trains, to compress and analyze recurring subgraphs (motifs) within merger trees for cosmological parameter inference. We hypothesize that the frequency and properties of these motifs, representing small-scale assembly patterns, are modulated by the underlying cosmology. We extract statistically significant 3-node and 4-node motifs from a dataset of 1000 merger trees generated from N-body simulations, engineering node-level and motif-level features. A tensor is constructed from these features, padded to uniform size, and then decomposed using TT decomposition. Finally, a gradient boosting regressor is trained to predict cosmological parameters ($\Omega$\_m, $\sigma$\_8) from the TT cores. Our results show that the TT-compressed motif features are predictive of $\Omega$\_m, achieving an R² score of approximately 0.36, but perform poorly in predicting $\sigma$\_8 (R² ≈ -0.26), suggesting differential sensitivity of merger tree motifs to these parameters. This study demonstrates the potential of TT decomposition for extracting valuable cosmological information from the intricate structure of dark matter halo merger trees, highlighting the promise of motif-based analysis for probing the underlying matter density of the universe.

Subjects:	gr-qc; hep-th; astro-ph.CO
Cite as:	PX:2508.00078