Neural Networks Dec 2025 · #85 most cited · 65 citations

mHC: Manifold-Constrained Hyper-Connections

Zhenda Xie et al.

arXiv:2512.24880

In short

Hyper-connections widen the residual stream to boost performance but break the identity shortcut that keeps deep networks stable. mHC projects those connections onto a constrained set that restores the identity property, with infrastructure work to keep it efficient at scale.

Why it matters

The residual connection hadn’t changed in a decade; this is a stable way to go beyond it.

Read first

The 3 Field Guide ideas this paper leans on.

Starting from scratch? The full route 16 ideas · basics first
  1. Machine Learning ✓ understood

    Building systems that learn patterns from data instead of following hand-written rules, getting better at a task as they see more examples.

  2. Neural Network ✓ understood

    A computational model inspired by biological neural networks, consisting of interconnected nodes (neurons) organized in layers that process information through weighted connections.

  3. Activation Function ✓ understood

    A non-linear function applied to neuron outputs that introduces non-linearity, enabling networks to learn complex patterns.

  4. Dataset ✓ understood

    A collection of data examples used for training, validating, or testing machine learning models.

  5. Training · read first ✓ understood

    The process of fitting a model to data by repeatedly measuring how wrong its outputs are and adjusting its parameters to reduce that error.

  6. Loss Function ✓ understood

    A function that scores how wrong a model's prediction is as a single number, which training then works to make as small as possible.

  7. Gradient Descent ✓ understood

    An optimization method that repeatedly moves a model's parameters a small step in the direction that most reduces the loss.

  8. Backpropagation ✓ understood

    The algorithm for computing gradients of the loss with respect to network weights, enabling training through gradient descent.

  9. Vanishing Gradient ✓ understood

    A problem where gradients become extremely small during backpropagation, preventing deep networks from learning effectively.

  10. Residual Connection · read first ✓ understood

    Skip connections that allow gradients to flow directly through a network, enabling training of very deep networks (ResNet).

  11. Feature ✓ understood

    A single measurable property of an example, such as a house's floor area or how many links an email contains, used as an input to a model.

  12. Deep Learning ✓ understood

    A subset of machine learning that uses neural networks with multiple layers (deep neural networks) to learn hierarchical representations of data.

  13. Representation Learning ✓ understood

    Learning useful features or representations of data automatically, rather than hand-crafting them.

  14. Embedding ✓ understood

    A list of numbers (a vector) that represents a word, sentence, image or other item, learned so that similar items end up close together.

  15. Attention Mechanism ✓ understood

    A technique that lets a neural network weigh every part of its input when producing each output, focusing on the parts most relevant at that step.

  16. Transformer · read first ✓ understood

    A neural network architecture, introduced in 2017, built from stacked self-attention and feed-forward layers; the basis of nearly every modern large language model.

In the frontier

Rank
#85 of 100
Citations
65
as of Aug 9, 2026
Published
Dec 2025

Topics: Model architecture , Efficiency and serving

Selection: 1kpapers.com by Together AI, most-cited as of Aug 9, 2026

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