α_L
A scalar indicator in position realizability theory, computed solely from the positional encoding and the task, used to determine before training whether length generalization is possible.
Timeline (last 90 days)
The scalar α_L ∈ [0,1] can be read off from (Φ, t_n) alone before any training and serves as a computable witness for the taxonomy derivation.
A sufficiency theorem (Theorem 1) connects α_L to length generalization.
Experiments confirm that in the controlled single-head setting, α_L exactly separates generalizing from non-generalizing (PE, task) cells in the taxonomy, based on measurements from 2625 trained models, stable at vocabulary size 64 and dimension 128.
The single scalar α_L alone suffices to determine, before training, whether a given combination of positional encoding and task can achieve length generalization.
All Facts (4)
The scalar α_L ∈ [0,1] can be read off from (Φ, t_n) alone before any training and serves as a computable witness for the taxonomy derivation.
50%UnverifiedA sufficiency theorem (Theorem 1) connects α_L to length generalization.
50%UnverifiedExperiments confirm that in the controlled single-head setting, α_L exactly separates generalizing from non-generalizing (PE, task) cells in the taxonomy, based on measurements from 2625 trained models, stable at vocabulary size 64 and dimension 128.
50%UnverifiedThe single scalar α_L alone suffices to determine, before training, whether a given combination of positional encoding and task can achieve length generalization.
50%