A Random Matrix Theory Perspective on the Learning Dynamics of Multi-head Latent Attention
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Jha, Nandan Kumar Reagen, Brandon |
| author_facet | Jha, Nandan Kumar Reagen, Brandon |
| contents | In this work, we study how multi-head latent attention (MLA), a popular strategy for compressing key/value memory, affects a transformer's internal capacity during pretraining. Using a lightweight suite of Marchenko-Pastur (MP) diagnostics, we analyze the spectrum of the $W_{Q}W_{K}^\top$ gram matrix throughout training, comparing three variants: the standard multi-head attention (MHA) baseline, MLA-PreRoPE with rotary applied before compression, and MLA-Decoupled, which shares a single rotary sub-vector across all heads. Our random matrix analysis reveals \textbf{three key findings:} \textbf{ i)} capacity bottlenecks emerge locally: both MHA and MLA-PreRoPE exhibit sharp, early spikes in specific layers that persist and propagate, disrupting the balance between bulk and outlier directions; \textbf{ ii)} these spikes coincide with rank collapse, concentrating the model's expressivity into narrow subspaces; \textbf{ iii)} only the decoupled variant prevents this cascade, maintaining broad spectral support and suppressing outlier formation across layers. These results underscore that \emph{how} rotary embeddings are applied is just as critical as \emph{where} compression occurs. Sharing rotary components across heads mitigates spectral fragmentation and preserves representational capacity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Random Matrix Theory Perspective on the Learning Dynamics of Multi-head Latent Attention Jha, Nandan Kumar Reagen, Brandon Machine Learning In this work, we study how multi-head latent attention (MLA), a popular strategy for compressing key/value memory, affects a transformer's internal capacity during pretraining. Using a lightweight suite of Marchenko-Pastur (MP) diagnostics, we analyze the spectrum of the $W_{Q}W_{K}^\top$ gram matrix throughout training, comparing three variants: the standard multi-head attention (MHA) baseline, MLA-PreRoPE with rotary applied before compression, and MLA-Decoupled, which shares a single rotary sub-vector across all heads. Our random matrix analysis reveals \textbf{three key findings:} \textbf{ i)} capacity bottlenecks emerge locally: both MHA and MLA-PreRoPE exhibit sharp, early spikes in specific layers that persist and propagate, disrupting the balance between bulk and outlier directions; \textbf{ ii)} these spikes coincide with rank collapse, concentrating the model's expressivity into narrow subspaces; \textbf{ iii)} only the decoupled variant prevents this cascade, maintaining broad spectral support and suppressing outlier formation across layers. These results underscore that \emph{how} rotary embeddings are applied is just as critical as \emph{where} compression occurs. Sharing rotary components across heads mitigates spectral fragmentation and preserves representational capacity. |
| title | A Random Matrix Theory Perspective on the Learning Dynamics of Multi-head Latent Attention |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.09394 |