arXiv subjects

Simeng Li

Publications and source records attributed to Simeng Li.

2 recordsLinked to original sources

arXiv2025

Exact CHY Integrand Construction Using Combinatorial Neural Networks and Discrete Optimization

Constructing a rational CHY integrand that realizes prescribed physical pole constraints is a discrete inverse problem whose combinatorial complexity grows with multiplicity. We encode the pole hierarchy through generalized pole degrees $K(A)$ (channels $s_A$), defined as signed internal-edge counts associated with particle subsets in a colored integrand graph. Additivity under integrand multiplication together with the elementary face recursion on the subset lattice expresses all higher-channel $K(A)$ as linear functions of the two-particle data $\{K(s_{ij})\}$ and reduces the inverse step to a mixed-integer linear feasibility problem. The subset lattice provides a fixed dependency graph for deterministic message passing with forward evaluation and backward residual propagation; this computation is parameter-free and involves no training. In factorial-rescaled variables $\widetilde K(A)=(|A|-2)!\,K(A)$, every local update is integral, so propagation is exact in the rescaled recursion variables and does not rely on numerical reconstruction. We further organize generalized integrand graphs by an $n$-regular grading under multiplication, where degree-zero (0-regular) factors act as M\"obius-invariant insertions that can be decomposed into four-point cross ratios. We illustrate the construction at six and eight points, including pick-pole selection and higher-order pole reduction.

hep-th↗

arXiv2020

A New Modal Autoencoder for Functionally Independent Feature Extraction

Autoencoders have been widely used for dimensional reduction and feature extraction. Various types of autoencoders have been proposed by introducing regularization terms. Most of these regularizations improve representation learning by constraining the weights in the encoder part, which maps input into hidden nodes and affects the generation of features. In this study, we show that a constraint to the decoder can also significantly improve its performance because the decoder determines how the latent variables contribute to the reconstruction of input. Inspired by the structural modal analysis method in mechanical engineering, a new modal autoencoder (MAE) is proposed by othogonalising the columns of the readout weight matrix. The new regularization helps to disentangle explanatory factors of variation and forces the MAE to extract fundamental modes in data. The learned representations are functionally independent in the reconstruction of input and perform better in consecutive classification tasks. The results were validated on the MNIST variations and USPS classification benchmark suite. Comparative experiments clearly show that the new algorithm has a surprising advantage. The new MAE introduces a very simple training principle for autoencoders and could be promising for the pre-training of deep neural networks.

cs.LG↗