Z-Loss Backward Geometry in Dense Output Heads and Sparse Routers

arXiv:2609.16179 · cs.LG, cs.CL · Submitted 2026-07-31 · Read on arXiv

cs.LG, cs.CL

Submitted: 2026-07-31

Updated: 2026-07-31

Comments: 30 pages, 2 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Consistency — 1× in this paper · explained in 3 episodes
• Perplexity — 1× in this paper · explained in 3 episodes
• Transformer — 1× in this paper · explained in 2 episodes

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