# Hierarchical and Permutation-Invariant Feature Transformation Learning via Policy-Guided Embedding Search

arXiv: https://arxiv.org/abs/2609.10225 · HTML: https://mlsanity.com/paper/2609.10225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 33 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Feature Engineering for Predictive Modeling using Reinforcement Learning](https://mlsanity.com/paper/1709.07150/) (2017)
- [The autofeat Python Library for Automated Feature Engineering and Selection](https://mlsanity.com/paper/1901.07329/) (2019)
- [AutoML to Date and Beyond: Challenges and Opportunities](https://mlsanity.com/paper/2010.10777/) (2020)
- [Automated Machine Learning on Graphs: A Survey](https://mlsanity.com/paper/2103.00742/) (2021)
- [Group-wise Reinforcement Feature Generation for Optimal and Explainable Representation Space Reconstruction](https://mlsanity.com/paper/2205.14526/) (2022)
- [One button machine for automating feature engineering in relational databases](https://mlsanity.com/paper/1706.00327/) (2017)
- [AutoDS: Towards Human-Centered Automation of Data Science](https://mlsanity.com/paper/2101.05273/) (2021)
- [Reinforcement-Enhanced Autoregressive Feature Transformation: Gradient-steered Search in Continuous Space for Postfix Expressions](https://mlsanity.com/paper/2309.13618/) (2023)
- [Feature Selection as Deep Sequential Generative Learning](https://mlsanity.com/paper/2403.03838/) (2024)
- [Unsupervised Generative Feature Transformation via Graph Contrastive Pre-training and Multi-objective Fine-tuning](https://mlsanity.com/paper/2405.16879/) (2024)
- [Techniques for Automated Machine Learning](https://mlsanity.com/paper/1907.08908/) (2019)
- [Continuous Optimization for Feature Selection with Permutation-Invariant Embedding and Policy-Guided Search](https://mlsanity.com/paper/2505.11601/) (2025)
- [Permutation-Invariant Representation Learning for Robust and Privacy-Preserving Feature Selection](https://mlsanity.com/paper/2510.05535/) (2025)

## Built on by (most cited first, 2 of 2)

- [Flat-Consensus Diffusion for Robust Data Reshaping under Noisy Evaluator](https://mlsanity.com/paper/2609.32696/) (2026)
- [Rethinking Data Augmentation under Covariate Shift: Invariant-Guided Diffusion and Prototype Reweighting](https://mlsanity.com/paper/2610.00873/) (2026)

## Abstract (arXiv)

Feature transformation improves predictive performance on tabular data by constructing informative abstractions from raw features. Recent generative approaches encode transformation knowledge into continuous embedding spaces for efficient exploration of candidate strategies, but face three key limitations: (1) overlooking hierarchical relationships between low-level features, operations, and high-level abstractions; (2) enforcing order-sensitive embeddings on inherently permutation-invariant transformation sequences, thereby introducing systematic bias; and (3) relying on gradient-based search, which is ill-suited to non-convex transformation spaces. We propose a framework with two complementary components. First, a permutation-invariant hierarchical module captures interactions across features, operations, and abstraction levels, with a self-attention pooling mechanism that maps semantically equivalent structures to consistent embeddings aligned with downstream performance. Second, a policy-guided multi-objective reinforcement learning strategy initializes the search from empirically strong seeds and jointly optimizes predictive accuracy and transformation efficiency. Extensive experiments on diverse tabular benchmarks demonstrate the effectiveness and robustness of our framework against strong baselines. Our code and data are publicly available at: https://github.com/RayLiu1103/PHER.