LatentKV: Preserving Reasoning Ability in Continual Latent Reasoning

Latent reasoning carries intermediate computation in continuous hidden states rather than generating an explicit chain of thought, solving problems with a few continuous thoughts and far fewer reasoning tokens. Continually adapting such models to new tasks while preserving previously acquired reasoning abilities poses a further challenge: because the states carry the computation, the final output does not directly reveal how internal reasoning changes as the model is updated. Answer-based replay shapes these states only through the answer loss and does not distinguish how different state changes affect it; matching historical states constrains every state component to its historical value and may over-restrict adaptation to the new task. The key question is therefore which state perturbations affect the old-task answer loss locally. Through local perturbation analysis, we find that (i) projecting KV-state changes onto the sensitivity direction of the answer loss yields a signal correlated with the change in old-task loss, and (ii) sensitivity computed on the current model predicts this change more accurately than sensitivity inherited from the historical model. We propose LatentKV, a continual-learning method for latent reasoning that combines historical-KV replay with answer-sensitive state constraints using a single LoRA adapter and a fixed replay budget. For replay, LatentKV guides old samples with a surrogate gradient conditioned on stored historical KV. For constraint, it periodically refreshes both the reference KV and the answer-loss sensitivity, and applies a symmetric projection penalty that limits state change along answer-sensitive directions. When continually adapting from GSM8K to SVAMP, LatentKV raises old-task latent accuracy from 26.80% to 52.13% over sequential fine-tuning, while achieving 69.09% accuracy on the new task, a decrease of 3.89 percentage points. Code is available at https://anonymous.4open.science/r/latentkv/.