Geometry Conflict: Explaining and Controlling Forgetting in LLM Continual Post-Training

Large language models (LLMs) often suffer from catastrophic forgetting in continual learning: after learning new tasks sequentially, they perform worse on earlier tasks. Existing methods mitigate catastrophic forgetting by data replay, parameter freezing, or regularization. However, these methods lack understanding of LLM mechanisms and cannot distinguish which parameters store important knowledge from previous tasks and which parameters can be updated for new tasks. To address this, we propose the attribution-guided continual fine-tuning framework that leverages Layer-wise Relevance Propagation (LRP) to estimate parameter importance based on the internal computational process of LLMs. During continual learning, parameters critical to previous tasks are constrained to receive smaller updates, while less relevant parameters remain available for learning new tasks. Extensive experiments show that, compared with baseline methods, our approach reduces catastrophic forgetting while preserving adaptability to new tasks, highlighting the value of mechanistic attribution for continual fine-tuning of LLMs.

Large language models (LLMs) can acquire new capabilities through fine-tuning, but continual adaptation often leads to catastrophic forgetting. We propose CRAFT, a continual learning framework that avoids updating model weights by instead learning low-rank interventions on hidden representations. CRAFT proceeds in three stages: it first routes each task to a group of similar tasks based on output-distribution divergence; it then fine-tunes the model using a Kullback-Leibler (KL) divergence against the group's prior state, which directly controls forgetting and determines convergence; finally, it merges interventions for the updated task into the shared representation using the same KL signal. This design unifies routing, regularization, and merging through a single KL-based objective. CRAFT improves overall performance and reduces forgetting compared to strong LoRA-based approaches across multiple benchmarks and model scales, while remaining robust to task ordering. These results suggest that controlling adaptation in representation space, guided by output-space divergence, provides a scalable and principled approach to continual learning in LLMs.

As large language models (LLMs) become increasingly capable, the next question is how can we enable models to continually learn? Today, the field largely frames this as a problem of context management and mitigating forgetting. We argue this framing is incomplete: continual learning is fundamentally about increasing model competence as the world changes. We disentangle this change along two axes -- space, where the model encounters new domains, and time, where the underlying data drifts under a fixed task. This framing lets us study continual learning under realistic conditions: new domains arrive over time, facts drift past their training cutoff, and agentic interactions accumulate state across episodes. To evaluate methods under this setting, we recast widely used LLM benchmarks as sequential problems and introduce a single mechanism-agnostic protocol that compares prompt-based methods (GEPA, ACE), supervised learning (SFT, SDFT), reinforcement learning (GRPO, SDPO), and context compression (Cartridges, In-place TTT). Prompt-based methods fit each new stage quickly but degrade on future tasks. Distillation-based methods accumulate knowledge stably but struggle to update outdated facts. Context compression improves efficiency without substantially improving the ability to learn new tasks. Online reinforcement learning adapts most effectively to knowledge updates but remains sensitive to noisy reward signals. Overall, our results suggest that continual learning is not a single capability: different patterns of environmental change require fundamentally different update behaviors, determining when adaptation must be learned inside model weights and when it can be achieved through external scaffolding. We hope that understanding where each method succeeds and fails will guide the design of stronger continual learning systems.