Noise-Resilient Symbolic Regression with Dynamic Gating Reinforcement Learning

Symbolic regression (SR) has emerged as a pivotal technique for uncovering the intrinsic information within data and enhancing the interpretability of AI models. However, current state-of-the-art (sota) SR methods struggle to perform correct recovery of symbolic expressions from high-noise data. To address this issue, we introduce a novel noise-resilient SR (NRSR) method capable of recovering expressions from high-noise data. Our method leverages a novel reinforcement learning (RL) approach in conjunction with a designed noise-resilient gating module (NGM) to learn symbolic selection policies. The gating module can dynamically filter the meaningless information from high-noise data, thereby demonstrating a high noise-resilient capability for the SR process. And we also design a mixed path entropy (MPE) bonus term in the RL process to increase the exploration capabilities of the policy. Experimental results demonstrate that our method significantly outperforms several popular baselines on benchmarks with high-noise data. Furthermore, our method also can achieve sota performance on benchmarks with clean data, showcasing its robustness and efficacy in SR tasks.

Deep Recursive Embedding for High-Dimensional Data

Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data embedding. We introduce a generic deep embedding network (DEN) framework, which is able to learn a parametric mapping from high-dimensional space to low-dimensional space, guided by well-established objectives such as Kullback-Leibler (KL) divergence minimization. We further propose a recursive strategy, called deep recursive embedding (DRE), to make use of the latent data representations for boosted embedding performance. We exemplify the flexibility of DRE by different architectures and loss functions, and benchmarked our method against the two most popular embedding methods, namely, t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP). The proposed DRE method can map out-of-sample data and scale to extremely large datasets. Experiments on a range of public datasets demonstrated improved embedding performance in terms of local and global structure preservation, compared with other state-of-the-art embedding methods.