Phase-transition thresholds for curriculum scheduling

Структурный скелет

The source paper studies a system whose macroscopic behavior changes when local magnetic polarons become connected enough to support a new transport regime. The reusable skeleton is a thresholded connectivity process with a measurable order parameter.

The editorial test is whether the scheduler has a measurable state variable that behaves like connectivity, not whether the training curve merely looks nonlinear. For ISOM this matters because the transferable object is the transition rule: local components become globally coordinated only after enough cross-component evidence exists. The source paper therefore functions as a disciplined template for asking when a learning system has built enough internal linkage to justify changing the optimization regime.

Физическая концепция / Математический объект

The transferable object is percolation near a regime boundary: sparse local clusters become a system-wide pathway once connectivity crosses a critical point.

Проблема целевого объекта ИИ

Target a curriculum scheduler for sparse or modular models. Instead of advancing phases by wall-clock time, advance when a representation-level connectivity statistic crosses a threshold.

Сопоставление переменных / операторов / цели

• Local polaron cluster -> locally useful feature islands or specialist subnetworks
• Connectivity/percolation threshold -> criterion for switching from isolated skill learning to coordinated optimization
• Macroscopic transport change -> measurable improvement in transfer, routing efficiency, or cross-task generalization

Почему это может сработать

Curricula often fail because they change phases too early or too late. A percolation view suggests waiting until the learned substructures become sufficiently connected, which is closer to a state-based control policy than a schedule heuristic.

A useful implementation would treat router co-activation, feature reuse, or module-to-module dependency as a graph that evolves during training. If curriculum switches are triggered by that graph rather than by epoch count, the policy becomes responsive to the model's learned state. That is the core ISOM claim: the transfer is not the word 'phase transition', but a falsifiable control rule based on a threshold statistic.

Почему это может не получиться

The analogy breaks if the monitored connectivity statistic is not causally related to the downstream regime change. It also fails when training dynamics are smooth enough that there is no meaningful threshold to exploit.

Наименьший опровержимый эксперимент

Train a sparse MoE or modular sequence model on a staged task suite. Compare fixed-step curriculum switches against switches triggered by a graph connectivity statistic measured over router co-activation. Reject the hypothesis if threshold-triggered switching shows no benefit in stability or transfer under matched compute.

The smallest clean experiment should pre-register the connectivity statistic before training, then compare three conditions: fixed schedule, validation-loss schedule, and connectivity-threshold schedule. Use identical compute, seeds, architecture, and data order except for the switching rule. The hypothesis survives only if the threshold rule improves transfer to held-out task combinations or reduces collapse during phase changes without simply delaying training.