arXiv:2608.05298 2026 Geometry 2 ideas extracted · analyzed Aug 31, 2026
The paper converts dynamical reachability into a geometry by integrating transition probabilities and recording the first time accumulated probability crosses a threshold. The transferable asset is the hitting-time matrix, which detects slow-mixing or weakly connected regions more directly than local transition entropy. In neural networks, attention matrices can be treated as stochastic transition graphs, enabling regularizers that discourage disconnected information flow. The same signal can also drive adaptive computation, allocating extra Transformer depth to tokens whose information remains poorly propagated.
Use attention-graph hitting times to identify tokens whose information has not mixed through the network, then route only those tokens through additional Transformer blocks. Tokens with fast reachability exit early, while slow or isolated tokens receive more computation.
Treat each attention head as a directed Markov graph and penalize token pairs that require many propagation steps to reach one another. This discourages isolated attention communities and slow information mixing while preserving the ordinary task objective.