# Continual Learning as Shared-Manifold Continuation Under Compatible Shift

Source: [Continual Learning as Shared-Manifold Continuation Under Compatible Shift](<https://www.sota2.com/research/paper/69c0c8f00636e5bf4afc3adb>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-03-24T05:00:03.763Z

Authors: Henry J. Kobs

Published: 2026-03-20T15:21:19.000Z

## Abstract

Continual learning methods usually preserve old behavior by regularizing parameters, matching old outputs, or replaying previous examples. These strategies can reduce forgetting, but they do not directly specify how the latent representation should evolve. We study a narrower geometric alternative for the regime where old and new data should remain on the same latent support: continual learning as continuation of a shared manifold. We instantiate this view within Support-Preserving Manifold Assimilation (SPMA) and evaluate a geometry-preserving variant, SPMA-OG, that combines sparse replay, output distillation, relational geometry preservation, local smoothing, and chart-assignment regularization on old anchors. On representative compatible-shift CIFAR10 and Tiny-ImageNet runs, SPMA-OG improves over sparse replay baselines in old-task retention and representation-preservation metrics while remaining competitive on new-task accuracy. On a controlled synthetic atlas-manifold benchmark, it achieves near-perfect anchor-geometry preservation while also improving new-task accuracy over replay. These results provide evidence that geometry-aware anchor regularization is a useful inductive bias when continual learning should preserve a shared latent support rather than create a new one.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Continual Learning on CIFAR10 compatible-shift](<https://www.sota2.com/research/sota/continual-learning-on-cifar10-compatible-shift.md>): Continual Learning; CIFAR10 compatible-shift; Old-task Accuracy: 81.95.

- [Continual Learning on Tiny-ImageNet compatible-shift](<https://www.sota2.com/research/sota/continual-learning-on-tiny-imagenet-compatible-shift.md>): Continual Learning; Tiny-ImageNet compatible-shift; Old-task Accuracy: 30.59.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2603.20036>)

[PDF](<https://arxiv.org/pdf/2603.20036.pdf>)