BetaEdit: Null-Space Constrained Sequential Model Editing

Fang et al. (2025) introduced a null-space constrained projection, named AlphaEdit, for locate-then-edit knowledge editing methods, theoretically guaranteeing that edits do not disrupt previously preserved knowledge, and reports substantial gains over existing editing methods on LLaMA3, GPT2-XL, and GPT-J. In this work, we present a reproducibility study of AlphaEdit, reproducing its reported results under the original experimental setup and extending the evaluation along three axes: new model architectures, additional downstream benchmarks, and substantially longer sequential editing horizons. We successfully reproduce AlphaEdit's reported metrics across the original models, though we identify a discrepancy in the reported fluency and consistency metric. Extending AlphaEdit to newer model families, we find that its advantage does not generalize uniformly, which we trace to architectural assumptions in the locate-then-edit paradigm that are violated by these newer models. We further stress-test AlphaEdit's central sequential-editing claim by extending the number of edits well beyond those evaluated in the original paper, and find that performance, which is stable at the originally reported scale, degrades as edits reach a much higher count, indicating that the null-space projection's protection against catastrophic forgetting is bounded rather than unconditional. Finally, we extend evaluation of edited models on three extra benchmarks, namely, BoolQ, HellaSwag, and XSTest, and we find that large-scale sequential editing degrades both general downstream task competence and safety-relevant refusal behavior. Our results confirm that AlphaEdit performs as reported within its original scope, while showing that its core theoretical guarantees are sensitive to model architecture and editing scale in ways that have practical implications for its deployment.

Sequential editing of structured knowledge in large language models allows targeted factual updates without retraining, yet existing methods often rely on complex regularization or constraint mechanisms whose necessity remains unclear. In this work, we systematically investigate the mechanisms underlying effective and stable sequential editing. Specifically, we first analyze the empirical success of AlphaEdit and establish, via a rigorous optimization analysis, the formal equivalence between one-time and sequential editing. Building on this insight, we generalize the equivalence to a broader class of editing objectives, demonstrating that stability emerges naturally from properly accounting for accumulated editing constraints, rather than from specialized regularization or null-space operations. We empirically confirm that many commonly used regularization strategies are unnecessary for reliable sequential updates. Furthermore, we extend our framework to handle conflicting edits, ensuring robust and consistent behavior under contradictory updates. Ultimately, our work provides Ariadne's thread through the labyrinth of sequential editing, charting a path toward simpler, more interpretable, and dependable knowledge updates. Our code is available at https://github.com/Wangzzzzzzzz/OTE-SE-Alignment.

Large language models encode vast factual knowledge that can become outdated or incorrect after deployment, yet retraining is prohibitively costly. This motivates lifelong model editing, which updates targeted behavior while preserving the rest of the model. Existing editors, both parameter-modifying and parameter-preserving, degrade severely as edits accumulate and struggle to generalize across paraphrases. We propose HoReN, a codebook-based parameter-preserving editor that wraps a single MLP layer with a discrete key-value memory. HoReN treats each codebook entry as both a knowledge key and a Hopfield stored pattern, retrieves edits by angular similarity on the unit hypersphere, and refines queries through damped Hopfield dynamics so paraphrases converge to the correct memory basin while unrelated inputs remain stable. HoReN achieves strong editing performance with consistent gains across diverse benchmarks spanning standard ZsRE, structured WikiBigEdit, and unstructured UnKE evaluations. Moreover, HoReN scales to 50K sequential edits on ZsRE with stable overall performance above 0.93, while prior editors collapse or degrade severely before reaching 10K. Our code is available at https://github.com/ha11ucin8/HoReN.