Feature-learning in the infinite-width limit with learnable multipliers

Establish whether the use of learnable multipliers alone guarantees maximal feature learning in the infinite-width limit, thereby eliminating the need for manual μP scaling rules.

Background

The paper connects learnable multipliers to μP and observes width-scaling behavior of norms and multipliers. It remains to determine whether multipliers intrinsically enforce the conditions needed for feature learning in the infinite-width limit, or whether additional manual scaling rules remain necessary.

References

Yet, many questions are left open. Or, does application of learnable multipliers automatically ensures maximal feature learning in infinite-width limit without manual scaling rules required in classical μP ?

— Learnable Multipliers: Freeing the Scale of Language Model Matrix Layers  (2601.04890 - Velikanov et al., 8 Jan 2026) in Section 6: Conclusion and discussion