Reproducing DeepSeek's MHC: When Residual Connections Explode

https://taylorkolasinski.com/notes/mhc-reproduction/

by taykolasinski • 6 months ago

121 30 6 months ago

taylorkolasinski.com

taykolasinski7• 6 months ago

OP here. I spent the last few days reproducing the mHC architecture from the recent DeepSeek paper (2512.24880).

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.

WiSaGaN2• 6 months ago

How do you know "GPT-5, Claude, Llama, Gemini. Under the hood, they all do the same thing: x+F(x)."?

taykolasinski7• 6 months ago

I’m referring specifically to the fundamental residual connection backbone that defines the transformer architecture (x_{l+1} = x_l + F(x_l)).

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.

solarkraft3• 6 months ago

I’ve been wondering for a while: Why isn’t this architecture more common in other LLMs? The context efficiency is amazing, after all - doesn’t that translate to a lot of money at scale?

kevmo314• 6 months ago

It's an incremental improvement, not really a revolutionary step.

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.

taykolasinski7• 6 months ago

That initialization strategy (effectively starting as identity to match the standard residual stream) is clever. It would let you surgery an existing model like Llama-3 and fine-tune it into an mHC architecture.

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.

yorwba• 6 months ago

https://arxiv.org/abs/2512.24880 was published less than two weeks ago, which should explain why it's not more common yet. And it's not that amazing either. It's a slight quality improvement for a slight increase in cost. It's not even clear to me whether it pays for itself.

solarkraft3• 6 months ago

My bad, I took this as something Multi-head Latent Attention (MLA) related.

graemefawcett• 6 months ago

I think the biggest benefit is bandwidth more so than efficiency. This gives you multiple streams to mux which and a means to control their mixing.

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.

sbondaryev• 6 months ago

Nice visualization of the residual connections. Is the animated svg manually created or programmatically generated? What tools did you use?

taykolasinski7• 6 months ago

Thanks! Manually created Astro components with inline SVG and CSS animations.

cpldcpu2• 6 months ago

May be worth pointing out, that this is not the first residual connection innovation to be in production.

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

taykolasinski7• 6 months ago

This is a fantastic catch. I hadn't realized Gemma 3n was already shipping with a variant of this in production.

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.

cpldcpu2• 6 months ago

Thanks! Would be quite interesting to see how this fares compared to mHC.

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.

Scene_Cast22• 6 months ago

I implemented this for a toy 8M ViT-style model. Got neutral results. This is just an anecdote and is not representative - I think mHC will help with larger parameter sizes and larger token counts.

taykolasinski7• 6 months ago

That's interesting.

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?

Scene_Cast22• 6 months ago

My baseline was non-HC "vanilla" residuals; I didn't do a meaningful HC run to compare.

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.

astrange• 6 months ago

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?

I think your brain may have been taken over by ChatGPT.

theschwa• 6 months ago

Between the clear writing and the diagrams, this was a great write up. I had actually skipped reading up on mHC as it sounded like it was going to take some time to grok, but this made it immediately approachable. I hope you do more write ups like this in the future.

roywiggins2• 6 months ago

imho the prose is very ChatGPT unfortunately

E-Reverance• 6 months ago

Residual connections are more than a trick to help gradients flow. They’re a conservation law.
Not a hack, not a trick. A principled constraint that makes the architecture work at scale.

in-silico• 6 months ago

Why can't you just leave H_res as the identity matrix (or just not use it at all)? In that case, the model is basically a ResNet again and you don't need to worry about exploding/vanishing gradients from H_res.

I would think that H_post and H_pre could cover the lost expressiveness.

john-titor• 6 months ago

great write up. it's been a while since I had the pleasure to read a straightforward blog post about ML tricks that feel genuinely applicable to many use cases.

AlexCoventry• 6 months ago

What's the advantage of having multiple channels with separate residual connections? Why not just concatenate those channels, and do residual connections on the concatenated channel?

Reproducing DeepSeek's MHC: When Residual Connections Explode

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