# Hidden not Deleted: How Networks Suppress Entangled Features

arXiv: https://arxiv.org/abs/2609.27593 · HTML: https://mlsanity.com/paper/2609.27593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings](https://mlsanity.com/paper/1607.06520/) (2016)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [The WMDP Benchmark: Measuring and Reducing Malicious Use With Unlearning](https://mlsanity.com/paper/2403.03218/) (2024)
- [Null It Out: Guarding Protected Attributes by Iterative Nullspace Projection](https://mlsanity.com/paper/2004.07667/) (2020)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Bias in Bios: A Case Study of Semantic Representation Bias in a High-Stakes Setting](https://mlsanity.com/paper/1901.09451/) (2019)
- [LEACE: Perfect linear concept erasure in closed form](https://mlsanity.com/paper/2306.03819/) (2023)
- [Hidden Progress in Deep Learning: SGD Learns Parities Near the Computational Limit](https://mlsanity.com/paper/2207.08799/) (2022)
- [Linear Adversarial Concept Erasure](https://mlsanity.com/paper/2201.12091/) (2022)
- [Kernelized Concept Erasure](https://mlsanity.com/paper/2201.12191/) (2022)
- [Unlearning Isn't Deletion: Investigating Reversibility of Machine Unlearning in LLMs](https://mlsanity.com/paper/2505.16831/) (2025)
- [Robust Concept Erasure via Kernelized Rate-Distortion Maximization](https://mlsanity.com/paper/2312.00194/) (2023)
- [Erase or Hide? Suppressing Spurious Unlearning Neurons for Robust Unlearning](https://mlsanity.com/paper/2509.22263/) (2025)

## Abstract (arXiv)

Concept erasure methods that operate via linear projection assume that features occupy separable subspaces. We show this assumption fails under dense superposition: when two features are forced into an antipodal pair sharing a single subspace, state-of-the-art linear erasure destroys both, not just the target. Networks trained with gradient descent instead solve this problem non-linearly, but not uniformly: they converge to one of two distinct circuit-level solutions depending on initialization, which we call mirror and shadow solutions. We map this bifurcation as a function of feature entanglement, show it reflects a stable attractor structure rather than an artifact of our setup, and use targeted causal interventions to demonstrate that both solutions leave a substantial, measurable trace of the erased feature's representation intact, recoverable through a single scalar patch rather than requiring any further training. This mirrors a failure mode recently observed empirically in LLM unlearning, where suppression rather than deletion allows forgotten knowledge to resurface; our results offer a mechanistic, causally-validated account of why that failure mode occurs.