How Does mHC Use Its Residual Streams? Selective Routing and Near-Identity Mixing
Analysis of DeepSeek-V4-Flash shows four-stream mHC residual blocks use only about two streams effectively, with late-layer mixing providing little benefit.
The study examines the four-stream residual pathway of DeepSeek-V4-Flash, finding typical attention or FFN sites effectively use about two streams and that residual mixing is modest, occurring primarily in early layers. Replacing late mixers with identity increases C4 perplexity by only 1.9% while replacing early mixers raises it by 41%. Retaining the three largest routing weights per token increases perplexity by at most 2.7%, showing the model uses only part of the flexibility afforded by the four-stream design.
- Typical blocks use ~2 of 4 streams; dominant stream shifts across depth
- Late-layer mixers replaceable by identity with only 1.9% perplexity increase
- Early mixer structure matters more than token-wise variation
- Routing weights can be pruned to top-3 per token with minimal impact
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Hyper-Connections and their manifold-constrained variant mHC widen a residual pathway from one stream to n, yet how trained models use this capacity remains unclear: how broadly blocks read and write, how strongly the residual pathway mixes streams, and whether the streams carry distinct representations. We examine these properties in the four-stream residual pathway of DeepSeek-V4-Flash using effective stream counts, cross-stream residual weights, and inter-stream cosine similarity. Read/write routing is concentrated but varies across depth: a typical attention or FFN site effectively uses about two streams, while the dominant stream changes across layers and the representations remain directionally distinct. Residual mixing is modest and occurs primarily in early layers; in layers 22-42, the pathway mostly carries each stream forward separately. Targeted interventions establish the functional significance of these patterns. Replacing the late mixers by identity increases C4 perplexity by only 1.9% and preserves the six-task average score, whereas replacing the early mixers increases perplexity by 41%. Fixing each early mixer to its C4 diagnostic mean increases perplexity by only 0.2% and reduces the average score by 0.25 percentage points, showing that its site-specific structure matters more than its token-wise variation on the evaluated metrics. Likewise, retaining the three largest routing weights per token at every site increases perplexity by at most 2.7% and changes the average score by at most 0.4 points. Thus, the studied model realizes only part of the flexibility afforded by four-stream mHC: individual blocks rarely require all four streams, and late residual mixing provides little measured benefit.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.05309