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A Deafening Silence: Catastrophic Forgetting Lives in the Output Embeddings of Tokens the Data Never Speaks

Jonghyun Han, Younghoon Song, Jongyoul Park

arXiv:2610.09835v1cs.CLcs.AI

TL;DR

Catastrophic forgetting during continued adaptation is difficult to address when original training data for replay is inaccessible. The paper uses training-time freezing and vocabulary counts to localize forgetting, then recommends output-scoped optimizer damping. It reports that forgetting concentrates in rare-token output embeddings, with corpus vocabulary deficiency providing a pre-retraining risk ranking.

  • Problem

    Continual pre-training and fine-tuning induce catastrophic forgetting, while replay often depends on original pre-training data that is inaccessible.

    Source: §1 · p. 1

  • Method

    The paper uses training-time freezing to measure causal share and token counts to assess vocabulary deficiency and rank pre-retraining risk.

    Source: §3.1 · p. 3, §4.1 · p. 4

  • Results

    Freezing rare-token output embeddings attributes 31–51% of forgetting to them across five stable settings, while the same body band accounts for under 10%.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The practical summary recommends assessing vocabulary deficit before retraining and raising output ϵ when it is high.

    Source: §6 · p. 9

    The pre-retraining diagnostic predicts rank order only; absolute forgetting depends on base capacity and resists cross-tokenizer calibration.

    Source: §6 · p. 9

Abstract

from arXiv · show

Continual pre-training and fine-tuning in Large Language Models (LLMs) inevitably induce catastrophic forgetting, typically mitigated by replay using often-inaccessible original data. In this data-free regime, we analyze where forgetting occurs and why. Systematic parameter freezing across five settings up to 1.4B reveals that forgetting concentrates selectively in the output embeddings of tokens rarely seen in the new corpus, whereas the same sqrt(v-hat) band of the body is inert and new learning resides elsewhere. This localization is governed by the vocabulary deficiency of the corpus rather than the training mode, allowing pre-retraining risk ranking from token counts alone within a fixed base model. Mechanistically, absent tokens receive persistent one-sided softmax gradients that Adam's second-moment (sqrt(v-hat)) normalization amplifies into full-sized updates. We therefore propose an intervention: raising Adam's epsilon exclusively for the output projection during training. Across eight settings spanning 160M to 12B parameters and four model families, this removes 39.4% to 67.9% of forgetting across all seven stable configurations without degrading target learning or requiring per-model tuning. The defense combines additively or better with replay (79.8% on Qwen/Korean) and rescues released-head LoRA from a 23-fold forgetting surge. Because post-hoc editing of the drifted rows recovers under 5% of forgetting, the intervention must operate during training. Our findings indicate that a single-line optimizer adjustment may serve as the primary defense against catastrophic forgetting where the corpus starves the vocabulary.

1 INTRODUCTION

The paper studies data-free adaptation, where replay is often unavailable, and localizes forgetting to under-exposed output embeddings. It proposes raising Adam’s epsilon on that tensor during training to reduce forgetting without sacrificing target learning.

1 INTRODUCTION

  • Replay mitigates forgetting by mixing original pre-training data, but that data is often inaccessible in the data-free regime.The paper frames its localization and intervention as operating without that original data.Source: §1 · p. 1
  • Freezing output embeddings of rare tokens attributes 31–51% of forgetting to them across five stable settings, while the same body band accounts for under 10%.The location is governed by corpus vocabulary deficiency, allowing pre-retraining risk ranking from token counts.Source: §1 · p. 2
  • Absent-token embeddings receive persistent one-sided softmax gradients that Adam’s second-moment normalization amplifies into full-sized updates.Default ϵ fails to curb these updates; raising it only on the output projection suppresses drift without impeding learning.Source: §1 · p. 2
  • Raising ϵ exclusively on the output projection eliminates 39.4–67.9% of forgetting across seven stable settings without degrading target learning.The intervention also composes additively with replay and prevents catastrophic forgetting in released-head LoRA.Source: §1 · p. 2
  • Post-hoc editing of drifted rows recovers under 5% of forgetting, so the intervention must operate during training.When forgetting shifts to the body under in-distribution tuning, damping it costs learning at one of the two measured cells.Source: §1 · p. 2

2 RELATED WORK

Prior data-free defenses constrain aggregate parameter movement, while localization studies disagree about where forgetting resides. This paper connects vocabulary composition to forgetting in output rows and identifies a training-time optimizer intervention.

2 RELATED WORK

  • Data-free defenses constrain aggregate drift through parameter selection, low-rank adapters, or orthogonal projections, potentially sacrificing plasticity for retention.The paper contrasts these approaches with replay, which uses original pre-training data.Source: §2 · p. 2
  • Reported forgetting sites conflict across early attention, lower layers, and FFNs, while correlational weight-displacement metrics leave causal responsibility unresolved.The paper distinguishes continual pre-training from class-incremental learning, where output bias is attributed to task imbalance.Source: §2 · p. 2
  • The paper identifies corpus vocabulary composition as determining where forgetting resides, then names Adam as the drift amplifier and ϵ as its brake.Prior work discusses persistent negative softmax gradients and low-rank dynamics; the paper also contrasts its training-time approach with post-hoc editing.Source: §2 · pp. 2–3

3 PRELIMINARIES

The preliminaries define data-free adaptation, vocabulary deficiency, the output-gradient and AdamW setup, and the experimental comparisons used to assess forgetting and learning.

3.1 PROBLEM SETTING

  • The task adapts a pretrained model to a new corpus without access to its original training data; under-exposed tokens have fewer than 1,000 target occurrences.Vocabulary deficiency is the occurrence-weighted share of old-domain evaluation targets that are under-exposed, computed by tokenizing both corpora with the base tokenizer.Source: §3.1 · p. 3

3.2 BACKGROUND

  • For output embeddings, target tokens are pulled toward the context representation while unselected tokens are pushed along −p_t h; input embeddings update only when they occur.AdamW combines Adam’s adaptive step with decoupled weight decay, and ϵ acts as a floor on the effective step size.Source: §3.2 · p. 3

3.3 EXPERIMENTAL SETUP

  • The grid spans Pythia scaling, tied and untied embeddings, and Korean, code, math, and instruction-tuning targets; training comparisons are budget-matched.Continual pre-training uses 40M tokens, instruction tuning 12.6M, and budget checks extend to 160M and 400M tokens.Source: §3.3 · p. 3
  • Interventions freeze or damp selected parameter groups during training, and results are generally three-seed averages with expanded seeds for disagreements.Learning is judged preserved when its change remains within the reference run’s baseline seed variation.Source: §3.3 · pp. 3–4
  • Forgetting is averaged over held-out old-domain corpora that exclude the adaptation target, while target learning is measured on new-corpus validation loss.Comparisons are made within each old-domain evaluation set, whose corpora vary by adaptation target.Source: §3.3 · p. 4

4 WHERE FORGETTING LIVES, AND WHY THERE

Training-time freezing localizes forgetting to under-exposed output embeddings, while new learning concentrates in upper body bands. The corpus’s vocabulary deficiency, rather than training mode alone, predicts where forgetting concentrates; softmax gradients and Adam explain the output-row drift.

4.1 FREEZING ONE GROUP AT A TIME LOCATES THE FORGETTING

  • Freezing output coordinates with v-hat < 1 × 10^-6 eliminates 31.3–51.0% of forgetting across five settings, while target learning shifts +0.1% to +5.2%.Freezing input embeddings in the same band yields only −1.5% to +1.4% reduction; mass-matched body freezing yields 0.4–12.3% across five stable settings.Source: §4.1 · p. 5
  • Freezing upper body bands eliminates 8.8–40.7% of target learning, whereas freezing output embeddings leaves learning intact.The same v-hat body band holds negligible forgetting share (−1.3% to +2.7%).Source: §4.1 · p. 5

4.2 THE DATA, NOT THE TRAINING MODE, DECIDES THAT LOCATION

  • Baseline forgetting strictly follows vocabulary deficiency across math, code, and Korean within each of three models, but mitigation does not.Tokenizing the corpora beforehand ranks injections within each model, but does not predict cross-model absolute magnitudes; Spearman rank correlation is 0.60.Source: §4.2 · pp. 5–6
  • On KoAlpaca, output-specific epsilon on low-v-hat rows eliminates 29.8–43.3% of forgetting without sacrificing target learning.Freezing MLPs reduces forgetting by 8.2–47.8% but sacrifices 16.3–26.3% of target learning; the attention comparison does not settle whether attention holds an independent share.Source: §4.2 · p. 6

4.3 WHY THOSE EMBEDDINGS MOVE: SOFTMAX AND ADAM

  • Absent output tokens receive one-sided softmax gradients that align along −p_t, and Adam’s second-moment normalization scales down both moments toward full-learning-rate updates.Input embeddings update only on explicit occurrences; across five untied settings, 34.8–51.2% of input parameters retain zero post-training sqrt(v-hat).Source: §4.3 · p. 6
  • Raising epsilon from 10^-8 to 10^-4 damps lowest-band displacement by 48.0–189.2×, versus 1.4–1.8× in the highest band.The bottom band’s directional consistency is 0.67–0.90; default epsilon remains inactive because only 3.5–15.4% of Pythia parameters (5.0% in Qwen) fall below 10^-8.Source: §4.3 · pp. 6–7

5 THE INTERVENTION AND ITS BOUNDARIES

Output-specific epsilon reduces forgetting across model scales and architectures, while the intervention’s value depends on where forgetting resides. Post-hoc edits recover little, and damping body parameters can cost new learning when the body carries both new and prior knowledge.

5.1 THE INTERVENTION AND ITS EQUIVALENTS

  • Set epsilon to 1 × 10^-4 only on the output projection; freezing rare rows or gating their updates produces closely agreeing forgetting reductions.The paper adopts epsilon because it requires no explicit token tracking; scaling embedding learning rate traces the same frontier, while random and count-based masks differ in learning cost.Source: §5.1 · p. 7
  • A high share of old-domain positions with fewer than 1,000 target-corpus occurrences flags output-dominated forgetting; a low share points to body-dominated risk.This ranking heuristic matched empirical forgetting ranks in three models and four earlier checkpoint–corpus comparisons.Source: §5.1 · p. 7

5.2 MAIN RESULT: FREE REDUCTION AT EIGHT SETTINGS

  • 39.4%–67.9% forgetting reduction across seven standard models, with target learning preserved across eight Korean settings from 160M to 12B parameters.The 410M arm is bimodal across seeds, and 160M is evaluated below its peak rate after peak-rate collapse.Source: §5.2 · p. 7, Table 5 · p. 8
  • The defense holds across a low-rate plateau but collapses at excessive rates, so epsilon does not replace learning-rate tuning.The optimal rate is invariant to the intervention, and the method does not require per-model epsilon tuning.Source: §5.2 · p. 8
  • Output-only epsilon works without per-model tuning; replay combines additively on Qwen/Korean and super-additively on OLMo.The Qwen combined reduction is 79.8% versus a 78.0% independence prediction; OLMo reaches 74.4% versus 64.8% predicted.Source: §5.2 · p. 8

5.3 WHY THE REPLAY-FREE BASELINES STOP SHORT

  • Replay-free baselines restrict aggregate parameter drift and either sacrifice target learning or worsen both retention and learning; released-head LoRA shows a 23-fold forgetting surge.Output-scoped epsilon removes 91.1% of that released-head surge at the same rate, while reaching the highest target learning among adapter arms.Source: §5.3 · p. 8

5.4 ACTING AFTER TRAINING FAILS

  • Post-hoc shared-drift edits recover at most 4.6% of forgetting across three settings, while full removal degrades target learning.Earlier editing only raises best recovery from 1.7% to 2.5%; component ablations indicate that the shared direction carries new-domain probability mass and the residual protects legacy capabilities.Source: §5.4 · p. 9

5.5 WHEN THE FORGETTING IS IN THE BODY

  • When new data adds no vocabulary, forgetting shifts into the body; body-scoped epsilon reduces it more than output epsilon but is lossless at only one of two tested cells.Body coordinates mix new representations with prior capabilities, so damping them can suppress acquisition.Source: §5.5 · p. 9

6 DISCUSSION AND LIMITATIONS

The paper frames remedies around vocabulary deficit and advises assessing that deficit before retraining. It also identifies limits in diagnostic scope, in-distribution results, and the coverage of its evaluations.

Discussion

  • Vocabulary deficit unifies the reported remedy patterns: rare-token gating matches output epsilon, while bottom-layer freezing fails under output-dominated forgetting.Uniform weight interpolation degrades more gracefully where selective edits collapse, but still trades learning for retention.Source: §6 · p. 9

Limitations

  • The diagnostic predicts rank order, not absolute forgetting, and does not calibrate across tokenizers; lossless body epsilon holds at only one tested in-distribution cell.Other boundaries include seed disagreement, Pythia-only scaling comparisons, a single adapter rank, and reliance on coordinate-wise adaptive optimizers.Source: §6 · p. 9

Discussion

  • Assess vocabulary deficit before retraining; when it is high, raise output epsilon, use a standard rate sweep, and add replay if available.No tested post-hoc edit recovers what prevention achieves.Source: §6 · p. 9

7 CONCLUSION

The conclusion localizes domain-shift forgetting to under-exposed output embeddings and reports that output-only epsilon reduces forgetting across stable settings. It argues that prevention must occur during training because later edits can strand or destroy compensation for old capabilities.

Conclusion

  • Under-exposed output embeddings are the localized forgetting site, where non-target softmax gradients meet Adam’s scale normalization.Output-only epsilon removes 39.4%–67.9% of forgetting across seven stable settings without original data or lost target learning; post-hoc edits cannot preserve the compensation sharing the drifted tensor.Source: §7 · p. 10

A APPENDIX

The appendix first compiles supplementary tables cited in the main text, then groups deferred details by topic. Its coverage runs from method equivalence and diagnostics through validation, ablations, and post-hoc editing.

Appendix

  • Section A.1 compiles supplementary tables that the main text cites.Source: A APPENDIX · p. 12
  • Subsequent sections cover method equivalence, the pre-retraining readout, learning-rate regime, capability and length validation, and drift geometry.Source: A APPENDIX · p. 12
  • Later sections cover the body dial, low-rank adapters, replay-free baselines, another injected domain, second moments, and post-hoc editing.Source: A APPENDIX · p. 12

A.1 SUPPORTING TABLES

The supporting tables specify learning rates for the domain-varying comparisons and caution against interpreting unmatched-rate comparisons as rate-controlled effects.

A.1 SUPPORTING TABLES

  • Table 3 uses 3×10−5 for math and code except Qwen/math at 1 × 10−5, and 1 × 10−4 for Korean.Source: §A.1 · p. 12
  • Table 4 uses Pythia-410M rates of 3 × 10−5 for Alpaca and 3 × 10−5 for KoAlpaca, while rates differ across the other models.Pythia-1.4B uses 1 × 10−5 and 1 × 10−4; Qwen uses 3 × 10−6 and 3 × 10−5, respectively.Source: §A.1 · p. 12
  • Only Pythia-410M is rate-matched across the two Table 4 corpora, so neither table should be differenced across a row as if rates were matched.Qwen/Korean in Table 3 also gains 0.6% target learning at a rate associated with roughly four times the forgetting of 3×10−5.Source: §A.1 · p. 12

A.2 INSTRUMENT EQUIVALENCE IN DETAIL

The controls distinguish retention from learning: the amount of frozen output parameters affects retention, while which rows remain trainable determines the learning cost.

A.2 INSTRUMENT EQUIVALENCE IN DETAIL

  • At matched 96.6% output-embedding mass, random and count masks remove 66.4% and 68.2% of forgetting, while freezing the whole projection removes 74.4%.The random mask costs −4.4% target learning, compared with −0.2% for the count mask and no cost for ϵ.Source: §A.2 · p. 12
  • Three instruments that stop the same rows achieve equivalent forgetting reduction in the Korean replay-free comparison.Figure A1 plots the three instruments side by side; Pythia-160M has near-zero or noisy metrics because of optimization collapse.Source: §A.2 · p. 12
  • The causal-share table compares freezing by site and √v-hat band, with each column normalized to its own reference run.It distinguishes band-based membership from token-count membership; zero-gradient coordinates receive no update for ϵ to damp.Source: Table A3 · p. 13, Table A4 · p. 13
  • Freezing matched √v-hat bands in the body yields negligible mitigation until the band causes a 41.6% target-learning penalty.This supports the contrast between output embeddings and body coordinates in the tested settings.Source: §A.2 · p. 13
  • A random output-row mask removes 12.1% of forgetting and costs 4.5% target learning, whereas a lowest-√v-hat mask removes 42.7% and gains 1.7%.These arms are not count-matched: they freeze 76.3M and 108.8M parameters, respectively; the lowest-band mask freezes coordinates, not whole rows.Source: §A.2 · p. 13

A.3 READING THE RISK BEFORE RETRAINING

Corpus vocabulary deficiency can rank relative forgetting risk within a fixed base model, but the diagnostic does not predict absolute magnitudes across architectures.

A.3 READING THE RISK BEFORE RETRAINING

  • Vocabulary deficit is the share of held-out old-domain token positions whose target occurs fewer than 1,000 times in the 40M-token new stream.For Pythia, the reported deficits are 63.2% for Korean, 55.9% for code, and 33.9% for math; Qwen values are 61.3%, 52.5%, and 50.6%.Source: §A.3 · p. 13
  • The ϵ-value sweep is reported only for three Pythia checkpoints, so its flatness is not tested on the other three model families.At 1.4B, response is flat across the hundredfold span; at 410M, reduction gives up eleven points at 1 × 10−3, while no value rescues 160M’s collapse regime.Source: Table A5 · p. 14
  • Qwen ties its input and output embeddings, so its output-only ϵ setting acts on one shared table rather than a separable output table.The Qwen/Korean baseline reference was trained at 3 × 10−5, although its reference learns most at 1 × 10−4.Source: Table A6 · p. 14
  • The vocabulary-deficit rank strictly matches observed forgetting ranks across the domain-axis grid for all three models.The rank pattern is also consistent with all four prior checkpoint–corpus comparisons.Source: §A.3 · pp. 13–14
  • Across ten configurations, deficit predicts rank only: its Spearman correlation with absolute forgetting is 0.60, below the preregistered 0.7 threshold.Per-token loss also fails as a correction because tokenization makes cross-tokenizer values incomparable, and byte normalization does not restore predictive power.Source: §A.3 · p. 14

A.4 THE OPERATING REGIME ACROSS LEARNING RATES

Output-only ϵ has a low-rate operating plateau, while excessive learning rates can sharply reduce forgetting mitigation and target learning; ϵ does not replace rate tuning.

A.4 THE OPERATING REGIME ACROSS LEARNING RATES

  • Forgetting reduction holds across the low-rate plateau, then falls sharply at higher rates, where target learning can also collapse.For example, 1.4B reduction is 57.6% at 10−5 and 52.1% at 3 × 10−5, but 6.7% at 10−3; at 410M, target learning drops 49.1% at 10−3.Source: §A.4 · pp. 14–15
  • Disabling weight decay leaves forgetting and reduction unchanged in the Korean replay-free 410M setting.The apparent three-seed advantage reverses with six seeds, indicating the observed gap is noise rather than an effect.Source: Table A7 · p. 15
  • The three instruments achieve equivalent forgetting reduction when stopping the same rows in the Korean replay-free comparison.The figure reports rates in Table A8.Source: Figure A1 · p. 15
  • The ϵ value needs no per-model adjustment in the reported sweep: 1.4B reduction stays within 40.9% to 45.6% across a hundredfold span.At the 10−3 edge, 410M gives up eleven percentage points of reduction.Source: §A.4 · p. 15

A.5 CAPABILITY AND LENGTH CHECKS

This section checks intervention benefits through capability and extended-training evaluations, while examining drift geometry, alternative forgetting sites and methods, and post-hoc repair. It also assesses legacy-capability evidence, which is positive for the embedding residual but does not confirm a role for the body.

A.5 CAPABILITY AND LENGTH CHECKS

  • On Pythia-6.9B, capability-based forgetting reduction is 83.6% versus 73.9% loss-based reduction on the same runs, so loss does not overstate the intervention’s benefit.At Pythia-1.4B the measures agree within 0.2 points (49.0% against 49.1%). In a 400M-token Pythia-410M/code run, output-only ϵ reduces forgetting by 56.2% and improves learning by 10.1%; on Qwen2.5-0.5B, reduction rises from 75.1% at 20M to 84.7% at 400M, though that curve’s levels are not comparable with Table 5.Source: §A.5 · pp. 15–16

A.6 HOW THE DRIFT GEOMETRY IS COMPUTED

  • Absent-row drift is low-rank: the top singular vector captures 66.1% of Qwen, 72.6% of OLMo, and 80.8% of Pythia-1.4B displacement energy, versus 3.2–12.9% in high-exposure controls.The predicted direction aligns with the empirical vector at cosine 0.40 for Qwen/Korean (0.50 with coordinate scaling) and 0.647 for Pythia-1.4B/math, below the preregistered 0.7 threshold. Residual ablation raises forgetting 1.6× to 2.4× while largely preserving learning; shared-component ablation leaves forgetting essentially unchanged but can impair learning substantially.Source: §A.6 · pp. 16–18

A.7 ON THE ATTENTION COLUMN OF THE INSTRUCTION GRID

  • On KoAlpaca at 410M, whole-output freezing yields −3.7% versus +29.8% when ϵ is scoped to low-√v-hat rows, because freezing also pins fed rows that compensate for drift.Target learning remains unharmed at both untied models (+3.0% at 410M and +0.5% at 1.4B).Source: §A.7 · pp. 18–19

A.8 IN-DISTRIBUTION FORGETTING AND THE BODY DIAL

  • For in-distribution Alpaca, the body dial removes 35.6% of forgetting on Qwen with −0.3% target-learning change, but on Pythia-1.4B it imposes a −6.7% learning penalty.At Qwen, body-scoped ϵ = 1 × 10−5 removes 14.5% versus 35.6% at 1 × 10−4, and the appendix treats body-scoped ϵ as preliminary based on the one lossless cell.Source: §A.8 · pp. 19–20

A.9 LOW-RANK ADAPTERS, AND WHERE THEIR RETENTION COMES FROM

  • On Qwen/Korean, releasing the adapter’s output head raises forgetting from 0.1210 to 2.8204 nats, while output-scoped ϵ removes 91.1% of that forgetting and retains the highest target learning among the three arms.TinyLlama reproduces the contrast without tied embeddings: releasing its head multiplies forgetting 16.3-fold, and output-scoped ϵ removes 92.4% at the highest target learning of the three arms. The contrast is within-adapter; the head explains the gap, not all adapter retention.Source: §A.9 · p. 20, Table A17 · p. 21

A.10 THE REPLAY-FREE BASELINE SUITE IN DETAIL; A.11 THE BASELINE SUITE AT A SECOND BASE MODEL

  • On Qwen/Korean, L2-to-base trades 64.3% forgetting reduction for 15.4% less target learning, while KL-to-base and a constant low rate largely halt adaptation and bottom-layer freezing worsens forgetting by 2.5%.At OLMo-2-1B, the ordering transfers: output-scoped ϵ, under-exposed freezing, and step-wise gating again cost nothing; L2 needs λ = 10 to reach two thirds of their reduction and pays for it, while KL and low-rate training trade away nearly all target learning. Input-scoped ϵ again does nothing.Source: §A.10 · p. 21, §A.11 · pp. 21–22, Table A18 · p. 22

A.12 THE SAME INTERVENTION ON A SECOND INJECTED DOMAIN

  • On code injection, the intervention’s forgetting reduction holds across four base checkpoints, a tenfold budget range, and two learning rates on one checkpoint without meaningfully reducing target learning.Code is the next most vocabulary-deficient domain in the reported comparison (55.9% against 63.2% under the Pythia tokenizer); at 160M, old-domain loss falls below the base model’s, yielding a reduction above 100%.Source: §A.12 · p. 22, Table A19 · p. 22

A.13 WHERE THE SECOND MOMENT SITS, SITE BY SITE; A.14 POST-HOC EDITS IN DETAIL

  • At training end, 74–86% of output-embedding coordinates lie below 1 × 10−6 in √v-hat, compared with 0.3–1.4% of body coordinates, while post-hoc drift edits recover at most 4.6% across three replay-free settings.Complete row resets degrade performance, and under 1% replay full restoration worsens recovery from −12.3% at 6.7M to −68.7% at 40M tokens; neither replay regime shows an early viable repair window.Source: §A.13 · p. 22, Table A21 · p. 23, §A.14 · p. 23

A.14 POST-HOC EDITS IN DETAIL

  • Embedding-residual ablation multiplies forgetting while shared-direction ablation does not, but body involvement remains unconfirmed despite cos = +0.248 alignment, eight times random expectation and below the preregistered 0.3.The positive evidence for compensatory adjustments sustaining legacy capabilities resides within the residual of embedding displacement; the authors do not claim the body is uninvolved.Source: §A.14 · p. 24
  • 11.4%, 22.1%, 41.0%, 57.0%, and 81.0% of forgetting was recovered on Qwen/Korean at α = 0.95, 0.9, 0.8, 0.7, and 0.5, respectively.Those recoveries gave up 1.0% to 29.9% of target learning; the corresponding Pythia-1.4B/math sweep recovered 14.0% through 100.5% for +0.5% down to −24.3%. Every point on either frontier paid a cost, while output-scoped ϵ sat above the Qwen/Korean frontier. The sweeps used 1% replay at a single checkpoint per cell; the Pythia cell injected math, and its 0.0364-nat baseline explains the final value above 100%.Source: §A.14 · p. 24
  • Row-level restoration was most destructive, shared-subspace ablation intermediate, and WiSE-FT interpolation (Wortsman et al., 2022) non-catastrophic, matching damage to selective disruption of drift and compensation.Row-level edits replace some rows while leaving neighbors untouched; shared-subspace ablation cuts one direction from every row; WiSE-FT scales every parameter together.Source: §A.14 · p. 24

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