RiLM: Parameter-Efficient Language Modeling via Geodesic Decoding
Quick summary
arXiv:2609.10305v1 Announce Type: cross Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transformer at embedding width d = 128 still spends roughly one third of its capacity on the output matrix W_out in R^(d x |V|). We propose Riemannian Language Models (RiLM), which remove that layer entirely: context unfolds as a trajectory on a Riemannian manifold, and next-token probabilities arise from squared geodesic distance between the current state and vocabulary embeddings. The same embedding ma
Key takeaways
- arXiv:2609.10305v1 Announce Type: cross Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transformer at embedding width d = 128 still spends roughly one third of its capacity on the output matrix W_out in R^(d x |V|).
- We propose Riemannian Language Models (RiLM), which remove that layer entirely: context unfolds as a trajectory on a Riemannian manifold, and next-token probabilities arise from squared geodesic distance between the current state and vocabulary embeddings.
Why it matters
“RiLM: Parameter-Efficient Language Modeling via Geodesic Decoding” highlights the need for repeatable measurement rather than a single impressive demonstration. Independent validation across datasets and clearly stated limitations determine whether a result can guide product decisions.
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