# A Step Towards Forgetting: Optimiser History and the Loss of Answer Mass

arXiv: https://arxiv.org/abs/2610.03940 · HTML: https://mlsanity.com/paper/2610.03940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 23 references that are in the map.
- First posted on arXiv 2 Oct 2026.

## Builds on (most cited first, 21 of 21)

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- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
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- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
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- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [SmolLM2: When Smol Goes Big -- Data-Centric Training of a Small Language Model](https://mlsanity.com/paper/2502.02737/) (2025)
- [Revisiting Catastrophic Forgetting in Large Language Model Tuning](https://mlsanity.com/paper/2406.04836/) (2024)
- [The AdEMAMix Optimizer: Better, Faster, Older](https://mlsanity.com/paper/2409.03137/) (2024)
- [Cautious Optimizers: Improving Training with One Line of Code](https://mlsanity.com/paper/2411.16085/) (2024)
- [MoFO: Momentum-Filtered Optimizer for Mitigating Forgetting in LLM Fine-Tuning](https://mlsanity.com/paper/2407.20999/) (2024)
- [How Weight Resampling and Optimizers Shape the Dynamics of Continual Learning and Forgetting in Neural Networks](https://mlsanity.com/paper/2507.01559/) (2025)

## Abstract (arXiv)

During fine-tuning, a language model can assign less probability to previously learned answers even when the current gradient acts to preserve that probability. With momentum, each update also carries gradients computed at earlier model states, and these stored contributions can push the model in the opposite direction. We investigate how this optimiser memory contributes to forgetting by separating old-task loss into confusion among its answers and leakage of probability outside the answer set. Across three language-model families, answer mass consistently declines while discrimination among old answers usually improves: the model becomes less likely to produce answers that it can still distinguish correctly. Decomposing Adam updates reveals opposing contributions to this loss of answer mass. Over training, accumulated history favours leakage, while the current gradient opposes it. Resolving history by age shows that the harmful contributions come mainly from older gradients of the new task, whereas recent gradients tend to protect the old answers. Changes in history's effect are dominated by its orientation relative to the old-task gradient. Interventions that reset momentum while matching the initial update norm establish that stored history affects retention, with state-dependent immediate effects and lower final old-task loss over longer Adam continuations, mainly through recovered answer mass. Finally, integration along finite updates shows that most sampled large loss increases are captured by local projections, while curvature along history amplifies some events. Together, these findings reveal how an optimiser's memory can erode learned behaviour even as its current gradient acts to preserve it.