Output Latent Spaces in Multihead Attention

2025-07-28 · Source: Chris McCormick · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Software Development & Engineering, Data Science & Analytics · Depth: Advanced, extended

Summary

This analysis explores the potential benefits and drawbacks of introducing a shared output latent space in Multihead Attention (MHA) models, mirroring existing shared input latent spaces for queries, keys, and values. Models like DeepSeek-V3 and Moonshot's Kimi-K2 already employ Multihead Latent Attention (MLA), compressing input token vectors (e.g., 7,168 dimensions) to smaller latent spaces (e.g., 512 for keys/values, 1,536 for queries). The proposed shared output projection would constrain where attention heads write to the residual stream, potentially reducing parameter count and FLOPs. For DeepSeek-V3, a shared output space of 3,072 dimensions could reduce output head parameters by 38% (from 112M to 69M). Singular Value Decomposition (SVD) analysis of DeepSeek-V3's WO matrices reveals significant compression opportunities in early layers and when fusing Value (WV) and Output (WO) matrices, but less so in middle layers of pre-trained models.

Key takeaway

For AI Scientists and Research Scientists designing or optimizing transformer architectures, consider integrating a shared output latent space into your Multihead Attention layers, especially during new model pre-training. While direct application to existing pre-trained models like DeepSeek-V3 may yield limited gains in middle layers, the approach offers significant parameter and FLOPs reduction, particularly in early layers and when fusing Value and Output projections. Experiment with this constraint to potentially improve model quality and interpretability, as suggested by DeepSeek's MLA performance.

Key insights

Shared output latent spaces in Multihead Attention can enhance efficiency and structure, complementing existing input latent spaces.

Principles

• Shared subspaces promote parameter reuse and generalization.
• Fusing matrices can uncover additional low-rank structure.
• Gradients always update shared projections, fostering learning.

Method

Propose a shared output latent space by factoring the WO matrix into a per-head projection WOAi and a shared projection WOB, then analyze compressibility using SVD on WO and fused WVO matrices.

In practice

• Consider shared output latent spaces for new model pre-training.
• Apply SVD analysis to identify compression opportunities in early layers.
• Explore fusing WV and WO matrices to enhance rank reduction.

Topics

• Multihead Latent Attention
• Latent Spaces
• Model Compression
• Singular Value Decomposition
• DeepSeek-V3

Code references

• chrisjmccormick/shared-subspaces

Best for: AI Scientist, Research Scientist, AI Researcher, Deep Learning Engineer, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by Chris McCormick.