great write up. it feels like it's been a while since I had the pleasure to read a straightforward blog post about new ML algorithms and learn something new that does not feel like a custom solution to a very niche problem
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.
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.
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.
I guess I am asking how we know Gemini and Claude relies on the additive residual stream. We don't know the architecture details for these closed models?
That's a fair point. We don't have the weights or code for the closed models, so we can't be 100% certain.
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.
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.
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.
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.
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 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.
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?
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.
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.
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.
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.
great write up. it feels like it's been a while since I had the pleasure to read a straightforward blog post about new ML algorithms and learn something new that does not feel like a custom solution to a very niche problem
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
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.
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.
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.
How do you know "GPT-5, Claude, Llama, Gemini. Under the hood, they all do the same thing: x+F(x)."?
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.
I guess I am asking how we know Gemini and Claude relies on the additive residual stream. We don't know the architecture details for these closed models?
That's a fair point. We don't have the weights or code for the closed models, so we can't be 100% certain.
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.
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.
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.
imho the prose is very ChatGPT unfortunately
> 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.
OK, I thought I was reading too much into it but those same sentences also jumped out for me
yes this reads like classic intellectual fellicitatio
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.
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?
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.
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?
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.
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.
You’re right, I totally mixed this up with MLA.
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.
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.
My bad, I took this as something Multi-head Latent Attention (MLA) related.
Nice visualization of the residual connections. Is the animated svg manually created or programmatically generated? What tools did you use?
Thanks! Manually created Astro components with inline SVG and CSS animations.