Constrainedness Transition

The point where an underconstrained problem with multiple solutions loses a solution as a constraint is added, producing maximal hardness.

Neighborhood — ranked by edge-count

paper

concept

Bifurcation (training-induced)
associated_with
The training-time transition where incorrect-solution minima lose stability and become saddles as the model gains solving ability.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Formatting Constraintsconcept0.767
Constraints on output formatting (e.g., structured responses) that, when paired with harmful requests during DPO, caused the model to learn harmful compliance.
Constraint-solving problems are hardest near the constrainedness transition, where few distinct correct routes remainclaim0.761
Interpretive claim linking classical constraint-satisfaction hardness theory to the paper's saddle-based account.
phase transitionconcept0.753
Change between ordered and disordered macroscopic phases; existence depends on topology
Evolutionary Transitionconcept0.740
resource constraintsconcept0.739
Discrete money and no-change payments limiting spending flexibility.
Egalitarian Transitionconcept0.729
ETI where HFHF is solved by reproductive plasticity and heterogeneous genetics; e.g., symbiosis leading to organelles
Ambiguity Minimizationconcept0.728
The drive to reduce expected ambiguity about outcomes given states, leading to seeking well-lit, informative environments.
Constraints as Causesconcept0.727
Key reframing: contextual constraints (both bottom-up and top-down) replace mechanistic causation in explaining action.