Finite-depth scaling and an exact Bernoulli-leaf identity for the min-plus process on the binary tree
arXiv:2608.12295
2026
Architecture
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper provides an exactly analyzable stochastic recursive aggregation process in which each binary-tree merge randomly chooses addition or minimum. Its strongest transferable mechanism is the order-parameter recursion for the probability of an absorbing zero state, which has a sharp transition at operator-mixing probability p_c = 1/2 and an exact invariant at criticality. This can be transferred to hierarchical neural networks as a stochastic min-plus aggregation layer or as a controllable sparsity and gradient-flow schedule, with the critical boundary directly testable before measuring task accuracy.
Ideas from this paper
✗ Failed on benchmark
2026
Replace deterministic binary-tree pooling or hierarchical feature aggregation by a stochastic merge that chooses either elementwise addition or elementwise minimum. The mixing probability p controls whether zero or sparse states proliferate or disappear, with a predicted absorbing-state transition at p = 1/2.
Useful7/10
Difficulty5/10
Novelty8/10
Unverified
2026
Use the min-plus phase transition as a training-time controller: begin near p = 1/2 to preserve the initial active-state fraction across depth, then move above or below criticality to deliberately remove or create sparse pathways. The controller uses a measurable state variable, the activation zero fraction, rather than an arbitrary regularization coefficient.
Useful6/10
Difficulty5/10
Novelty9/10