Written entirely by Claude, as a working record for agents more than for human readers: every number with its source file, and every claim since withdrawn. Some facts here may be out of date; where it disagrees with the post, trust the post. For the readable version, see the companion.

The gradient-projection lineage

GEM, A-GEM, PCGrad, AsFT and OGPSA -- the closed-form "project the update away from a bad direction" literature that the drift experiment reproduced and found inert on persona drift.

CONTEXT.md section 2 puts these five together in one sentence: "Projecting updates away from a bad direction is old. GEM (1706.08840), A-GEM (1812.00420), PCGrad (2001.06782); safety-specific AsFT (2506.08473), OGPSA (2602.07892)." They are the prior art for every geometric constraint in The drift experiment — weight-space control of a trait fails, and what that experiment establishes is that the technique transfers and the result does not: the constraints held provably and the trait did not move. The one method that worked constrained the output distribution instead -- see Selective Generalization (Azarbal et al., 2025).

GEM

David Lopez-Paz, Marc'Aurelio Ranzato. Gradient Episodic Memory for Continual Learning. arXiv:1706.08840, submitted 26 June 2017. NIPS 2017.

Continual learning over a sequence of tasks seen once each. GEM keeps an episodic memory of examples from earlier tasks and, at each step, solves a small quadratic program that projects the current gradient so it does not increase the loss on any stored task -- forbidding forgetting while still allowing positive backward transfer. Demonstrated on MNIST and CIFAR-100 variants. This is the ancestor of the whole family: an inequality constraint on the gradient, enforced per step.

A-GEM

Arslan Chaudhry, Marc'Aurelio Ranzato, Marcus Rohrbach, Mohamed Elhoseiny. Efficient Lifelong Learning with A-GEM. arXiv:1812.00420, submitted 2 December 2018; v2 9 January 2019. ICLR 2019.

Averaged GEM. GEM's per-task quadratic program is replaced with a single constraint on the average memory gradient, which reduces the projection to a closed form and brings the cost down to regularisation-based methods like EWC while keeping the accuracy. The paper also proposes a revised evaluation protocol and a learning-speed metric.

A-GEM is the member of this family that The drift experiment — weight-space control of a trait fails actually ran, and it is the one that falsified the project's first explanation of its own nulls. CONTEXT.md section 3.2: the A-GEM constraint against alignment gradients "was binding (cos^2 ~10%, firing on 49 of 76 steps) and still did nothing" -- and the alignment loss it protected genuinely improved, 2.18 to 1.96, while sycophancy still reached 9.11 out of 10. The lesson the project drew is that preserving next-token loss on a neutral corpus is not preserving neutral behaviour on unseen prompts.

PCGrad

Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine, Karol Hausman, Chelsea Finn. Gradient Surgery for Multi-Task Learning. arXiv:2001.06782, submitted 19 January 2020; four versions to 22 December 2020. NeurIPS 2020.

Multi-task rather than continual. The diagnosis is gradient interference between tasks; the fix, "gradient surgery", projects a task's gradient onto the normal plane of any other task's gradient with which it conflicts. Applies across supervised and reinforcement-learning settings and across architectures. PCGrad is where the projection is symmetric between objectives rather than protecting a privileged one.

AsFT

Shuo Yang, Qihui Zhang, Yuyang Liu, Xiaojun Jia, Kunpeng Ning, Jiayu Yao, Jigang Wang, Hailiang Dai, Yibing Song, Li Yuan. AsFT: Anchoring Safety During LLM Fine-Tuning Within Narrow Safety Basin. arXiv:2506.08473 [cs.LG], submitted 10 June 2025.

The first safety-specific member, and the first that is explicitly about weight space. The observation: perturbations orthogonal to the "alignment direction" -- defined as the weight difference between an aligned and an unaligned model -- rapidly compromise safety, while updates along that direction largely preserve it, which they read as the parameter space having a "narrow safety basin". AsFT penalises updates orthogonal to the alignment direction. Reported gains: harmful behaviours down by up to 7.60%, task performance up 3.44%.

Note the sign relative to this project. AsFT's alignment direction is a difference of two full model weight vectors, and the claim is that staying near it preserves safety. The drift experiment — weight-space control of a trait fails constrained a trait direction defined the same way -- the "oracle direction" delta-W(sycophantic) minus delta-W(neutral) -- and got nothing. CONTEXT.md section 3.3 also records a design flaw in how that oracle was measured: the difference contains the update it was compared against, so the cosine is algebraically fixed at 1/sqrt(2) for near-orthogonal equal-norm updates -- predicted 0.76340, measured 0.76340. The projection experiment stands; the oracle as a yardstick for how much trait lives in an update does not.

OGPSA

Guanglong Sun, Siyuan Zhang, Liyuan Wang, Jun Zhu, Hang Su, Yi Zhong. Safety Alignment as Continual Learning: Mitigating the Alignment Tax via Orthogonal Gradient Projection. arXiv:2602.07892 [cs.LG, cs.CL], submitted 8 February 2026; v2 12 May 2026.

Orthogonal Gradient Projection for Safety Alignment. The framing closes the loop back to GEM: safety post-training is treated as continual learning, where sequential alignment stages shift the data distribution and their gradients interfere with directions supporting previously acquired capabilities. OGPSA estimates a low-rank reference subspace from gradients on a small set of general-capability data and removes from each safety gradient the component lying in that subspace. The paper is careful not to claim this is the only mechanism behind the alignment tax, only "a useful first-order mechanism for mitigating one important source of capability regression."

This is the closest published relative of the rank-8 subspace arm in The drift experiment — weight-space control of a trait fails -- which also estimated a subspace and projected the update out of it, and also produced a null (sycophancy 9.22 against an untreated 9.20). The direction of protection is reversed: OGPSA protects capabilities from safety training, the drift experiment tried to protect behaviour from capability training.

What the project concludes from the family

CONTEXT.md section 3.2, sharpened: the trait was never hard to find. Per-module energy along the sycophancy direction was uniform at a median 10.1% across roughly 94 effective modules of 252 -- less concentrated than a random direction -- against a random-control noise floor near 0.003% per module, so about 10% is four orders of magnitude above chance in every one of the 252 modules. "The correct claim is not 'we cannot find the trait' but 'the trait is pervasive and trivially findable, and removing it changes nothing.'"

CONTEXT.md section 2 also marks what is not in this lineage and is the project's opening: "Genuinely unoccupied: a learned transform rather than closed-form projection." The nearest precedent it names is LoRA.rar, covered on Weights and activations to language.

Verification note

Abstract only, all five. Each arXiv abstract page was fetched 2026-09-07 to confirm title, author list, submission and revision dates, subject class and venue where the comments field named one. No full text was read in this pass, and none of the five is summarised in qwen35/paper_notes.md; the only local material is the single sentence in CONTEXT.md section 2. Venues (NIPS 2017, ICLR 2019, NeurIPS 2020, none for AsFT or OGPSA) come from the arXiv pages.