Title: Neuro-Symbolic Embedding for Short and Effective Feature Selection via Autoregressive Generation

Abstract: Feature selection aims to identify the optimal feature subset for enhancing downstream models. Effective feature selection can remove redundant features, save computational resources, accelerate the model learning process, and improve the model overall performance. However, existing works are often time-intensive to identify the effective feature subset within high-dimensional feature spaces. Meanwhile, these methods mainly utilize a single downstream task performance as the selection criterion, leading to the selected subsets that are not only redundant but also lack generalizability. To bridge these gaps, we reformulate feature selection through a neuro-symbolic lens and introduce a novel generative framework aimed at identifying short and effective feature subsets. More specifically, we found that feature ID tokens of the selected subset can be formulated as symbols to reflect the intricate correlations among features. Thus, in this framework, we first create a data collector to automatically collect numerous feature selection samples consisting of feature ID tokens, model performance, and the measurement of feature subset redundancy. Building on the collected data, an encoder-decoder-evaluator learning paradigm is developed to preserve the intelligence of feature selection into a continuous embedding space for efficient search. Within the learned embedding space, we leverage a multi-gradient search algorithm to find more robust and generalized embeddings with the objective of improving model performance and reducing feature subset redundancy. These embeddings are then utilized to reconstruct the feature ID tokens for executing the final feature selection. Ultimately, comprehensive experiments and case studies are conducted to validate the effectiveness of the proposed framework.