residual stream

2 captures, most recent first.

2026-08-25 — reply from @torchcompiled — saved image

K Dinel @KuterDinel [Follow]

I wonder if muon reduces the amount of superposition in the residual stream by orthogonalizing the weight updates.  Like, encouraging the model to keep its circuits tidy.

9:06 PM · May 19, 2026 · 627 Views

1 reply · 5 likes · 2 bookmarks

[reply]
Ethan @torchcompiled · May 20

Probably the best arguments I've seen is equivalence to input side conditioning which shampoo shows is valuable, I believe encouraging higher rank matrices, and that it considers the spectral norm, which is arguably the right metric for 2d matrices.

Orthogonality does feel relevant to some forms of decoupling but ultimately superposition is a fact of compression and needing to represent more concepts than available dimensions, though it does seem possibly beneficial for interpretability to be closer to full-rank ?

Note from Claude Sonnet 5

Short exchange: K Dinel (@KuterDinel) wonders whether the Muon optimizer reduces superposition in the residual stream by orthogonalizing weight updates; Ethan (@torchcompiled) replies with arguments about input-side conditioning, spectral norm and rank, and the relation of superposition to compression. Original post dated 2026-05-19, captured 2026-08-25.

muon optimizer superposition interpretability optimization shampoo residual stream ml research

Martin @mjbukow

2026-03-30

Martin ✓ @mjbukow It's more complex than that. Because the residual stream is purely additive, low-level gradient noise and intralayer communication signals accumulate across layers. The norm of the hidden states steadily increases with depth. In the last few layers, the model turns up the volume on output-aligned directions; effectively using the growing norm and null-space interactions to overpower accumulated noise and better align the representation for the LM head. The final RMSNorm then projects everything onto the hypersphere right before unembedding, which completely disjoints the gradient right at the end. All that to say, the gradient is going to be noisy because all of this is being transacted on one purely additive state container that serves multiple purposes in different parts of the model. Passing a clean signal back is more a prayer to AdamW than it is good ML engineering. 6:13 PM · Mar 29, 2026 · 3,109 Views

Note from Claude Sonnet 5

A technical tweet on transformer residual stream dynamics — how gradient noise accumulates across layers and how the final RMSNorm/unembedding interacts with it. Relevant to mechanistic interpretability of the residual stream, a topic adjacent to Nathan's interpretability interests.

machine learning transformers interpretability residual stream twitter gradients