ResearchResearch paperTraining & Scaling · Large Language Models · Efficiency & Inference1 source · Oct 20, 2026

Hybrid Momentum Methods for Optimizing Deep Learning Models

We introduce Hybrid Momentum (HyM), which combines a linearly weighted average of past gradients with a geometrically discounted fast momentum.

Key points

  • Momentum is central to stochastic optimization in deep learning, including the training of large language models.
  • In particular, we propose HyMUON, which applies Newton--Schulz orthogonalization to the hybrid direction.
  • Across image classification, machine translation, and language modeling, HyM and HyMUON match or improve upon strong baselines.
  • For LLaMA-1.3B pretraining on C4, HyMUON achieves a final validation loss of 2.777, compared with 2.903 for Muon.

Sources (1)

  • [1]Hybrid Momentum Methods for Optimizing Deep Learning Models
    arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 05:39 AM
    We introduce Hybrid Momentum (HyM), which combines a linearly weighted average of past gradients with a geometrically discounted fast momentum.
    Momentum is central to stochastic optimization in deep learning, including the training of large language models.

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Before this

  1. Oct 19, 2026Introducing Clairic, a new System One class of extraction models
  2. Oct 19, 2026Push-based KV transfer to improve TTFT and TPOT for disaggregated inference in vLLM
  3. Oct 19, 2026LIRQuant: An Efficient Locally Isolated Rotation Quantization Method for Large Language Models
  4. Oct 18, 2026T-MUON: Tensorizing Muon via t-SVD for Large Language Model Pre-training
  5. Oct 18, 2026StopLoss: Teaching Agents to Predict Failure and Stop Early
  6. Oct 17, 2026A Statistical Viewpoint on Adam, Shampoo and Muon

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