Reproducing DeepSeek's MHC: When Residual Connections Explode
taylorkolasinski.com
taylorkolasinski.com
Gemma 3n is also using a low-rank projection of the residual stream called LAuReL. Google did not publicize this too much, I noted it when poking around in the model file.
https://arxiv.org/pdf/2411.07501v3
https://old.reddit.com/r/LocalLLaMA/comments/1kuy45r/gemma_3...
Seems to be what they call LAuReL-LR in the paper, with D=2048 and R=64
It feels like we are entering the era of residual stream engineering. For a long time, the standard x + F(x) additive backbone was treated as untouchable. Now, between mHC (weighted scaling) and LAuReL (low-rank projections), labs are finally finding stable ways to make that signal path more dynamic.
I'm curious if the Low-Rank constraint in LAuReL acts as a natural stabilizer against the gradient explosion I saw with unconstrained hyper-connections.
Thanks for the paper link, definitely reading that tonight.
I noted that LAuReL is cited in the mHC paper, but they refer to it as "expanding the width of the residual stream", which is rather odd.
Two key takeaways from the reproduction:
Unconstrained Hyper-Connections really do explode (7x amplification even at 10M scale).
I hit a nasty "stream persistence" bug where my tensors were the right shape, but the architecture was functionally broken.
This is Part 1 (10M scale). Part 2 (scaling to 1B on A100s) is coming later this week. Happy to answer questions about the implementation.
While the sub-modules differ (MHA vs GQA, SwiGLU vs GeLU, Mixture-of-Depths, etc.), the core signal propagation in Llama, Gemini, and Claude relies on that additive residual stream.
My point here is that DeepSeek's mHC challenges that fundamental additive assumption by introducing learnable weighted scaling factors to the residual path itself.
However, transformer-based (which their technical reports confirm they are) implies the standard pre-norm/post-nnorm residual block structure. Without those additive residual connections, training networks of that depth (100+ layers) becomes difficult due to the vanishing gradient problem.
If they had solved deep signal propagation without residual streams, that would likely be a bigger architectural breakthrough than the model itself (akin to Mamba/SSMs). It’s a very high-confidence assumption, but you are right that it is still an assumption.
I suspect your intuition about scale is correct. The theoretical benefit of mHC is that it acts as a sort of relief valve/router for information flow in very deep/wide networks where the standard residual bottleneck becomes an issue. At 8M params, the standard residual stream is likely already perfectly adequate, so mHC might just be adding parameter overhead without solving a real signal propagation problem yet.
Quick question on your run: did you see the signal amplification/instability I saw (values growing during the forward pass)? or was it stable for you, just neutral on loss?
My application has some particularities (important and easy to identify per-token signals) that result in values growing (about 3x to 10x) through layers even in the baseline.
I think your brain may have been taken over by ChatGPT.
I would think that H_post and H_pre could cover the lost expressiveness.
> Not a hack, not a trick. A principled constraint that makes the architecture work at scale.
That being said, I think one could adapt an existing model to add mHC by initializing the routing matrix to the regular residual connection and then post-train the hyper connection matrices. This would let you continue training more efficiently on existing models.
The main risk I see is that the 7x signal amplification happens very aggressively. Even with a gentle initialization, you’d likely need very strict gradient clipping or a tiny learning rate on those new routing matrices to prevent them from blowing up the pre-trained features in the first few steps.
Also, I think there's a mix-up here between mHC (this paper, expressivity) and MLA (latent attention, which provides the massive context efficiency). mHC doesn't save memory, but it might make the model 'smarter' per parameter.
The biggest innovation I think may have been accidental. The doubly stochastic matrix implements conservation on the signal stream.
Treating the signal like the information it is as we do in any other domain is crucial for maintaining its coherence. We don't allow a network router to generate more packets than it receives for the same reason.