Intrinsic-Extrinsic Coupling in Learning Dynamics

Modern language models are likely to be updated throughout their lifetime rather than trained once and frozen. Each update therefore participates in a recurring cycle: decide which experience to learn from, understand what that update changes, and remain capable of learning from what comes next. We show that these challenges are governed by the same evolving update--behavior interaction. We derive a token- and layer-wise decomposition of how learning from one token changes another prediction. By separating the softmax force, shared readout geometry, and residual connections, it exposes two interaction channels and yields a forward-computable approximation. Following this interaction through time reveals a unified picture of continual adaptation. Positive interaction identifies useful experience; negative interaction produces either concentrated collision or accumulated erosion; over longer horizons, updates reshape the shared geometry mediating future learning signals, reducing their transmission. These predictions lead to effective data selection, mechanism-specific controls for interference, and a readout-based diagnostic of future learnability whose degradation predicts the benefit of restoring the readout. Across models and training regimes, the same local interaction thus explains both what an update changes now and how learning today changes what can be learned tomorrow. This view connects data attribution, forgetting, and plasticity loss as distinct regimes of the same evolving learning dynamics.

Critic-free group-based reinforcement learning has become a scalable approach for post-training large language models. However, most existing methods allocate the same number of rollouts to every task and trajectory state, even though some rollouts provide much more useful learning signals than others. Recent work has started to treat rollout generation as an adaptive decision, but two important limitations remain. First, intervention strategies are often based on fixed heuristics and therefore cannot adjust as the policy changes during training. Second, these methods usually decide only how many rollouts to generate, without explicitly controlling where and how to intervene. To address these limitations, we propose Recoverability-Aware Intervention Learning (RAIL), a training-time framework that learns how to generate rollouts based on the improvement produced by each intervention. RAIL models intervention selection as an online contextual-bandit problem and trains a recoverability controller using intervention traces collected through a shadow-to-live procedure. This allows the controller to keep learning while the underlying policy evolves. We evaluate RAIL in terms of effectiveness, adaptivity, expressiveness, and efficiency. Across multiple settings, RAIL consistently improves performance under limited rollout budgets. These results show that recoverability-aware intervention provides a principled way to generate more informative and less redundant rollouts, leading to stronger learning signals during post-training.

World models learn environment dynamics from interaction experience. These dynamics depend on the current state and actions, as well as on properties that persist across interactions. Yet standard predictive training can reduce error using local evidence alone, without organizing persistent information into reusable context. We introduce SPRII, a training principle that uses relations between interactions as weak supervision for persistent context while retaining the learner's native objective. For example, different trajectories of the same system share persistent properties even when their states and actions differ. SPRII uses such relations to guide context learning without numerical property labels. Two composable components encourage contexts from related interactions to agree (Align) and use one interaction's context to predict another's future (Cross). Our analysis distinguishes three linked questions: what persistent information is accessible in the learned context (Formation), how that context influences a fixed predictor (Use), and whether it reduces task error (Value). Success at one stage does not guarantee success at the next. Controlled experiments show that more reliable relations improve representation organization, but adding a shared-property constraint can reduce access to a property that remains shared. Context substitutions change predictions at fixed model weights, while the benefit from history depends on prediction horizon and readout. Evaluations span thirteen settings, including controlled physical systems, public dynamics tasks, robotic and tactile data, and partner interaction, across multiple learner families. Relative to the corresponding baselines, SPRII yields average gains of over 10% in downstream task performance and over 15% in persistent-property readout. The project page is available at https://persistent-learning-review.netlify.app/interactive.html.