WhiteMatter: All-to-All Cross-Layer Connections via KV Source Mixing
Wenbo Zhang, Xiang Ren
University of Southern California
Published September 27, 2026 · on the feed September 29, 2026 · ▲ 3 · arXiv 2608.18486
The abstract
When generating text, a Transformer produces representations of past tokens at every layer, but each layer can normally use only representations from the same depth. This restriction prevents the model from fully reusing information it has already computed. We introduce WhiteMatter, which allows every layer to draw on past-token representations from any depth. A learned mixer selects the most useful depths for the current context and combines their representations into shared key-value (KV) cache channels. Sharing these channels across layers can reduce the cache size. Given the same number of training tokens, WhiteMatter with a full-size cache performs comparably to a standard Transformer with 50% more layers. With half the KV cache, WhiteMatter outperforms matched standard Transformers at two model scales, up to 1.3B parameters. Cross-layer connections, however, introduce dependencies that slow training and prompt processing. We address this problem with cyclic iteration, which updates interleaved groups of tokens in turn while processing the tokens within each group in parallel. On a reference model trained with exact autoregressive execution, cyclic iteration converges 12.5x faster than standard Jacobi iteration.
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Transcript
WhiteMatter. All-to-All Cross-Layer Connections via KV Source Mixing. By Wenbo Zhang and one other, from the University of Southern California. Published on the twenty-seventh of September. Its code repository is worked out: about one hundred and eighty source files, with a readme and a licence.
A Transformer generating text builds a representation of every past token at every layer. Yet each layer can normally read only the representations from its own depth. A middle layer attends to what that same layer produced, and nothing else. The authors see a loss in this: the model has already computed information at other depths, and the restriction stops it from fully reusing what it has.
WhiteMatter lifts the restriction. Every layer is allowed to draw on past-token representations from any depth. A learned mixer decides, for the current context, which depths are most useful, and combines their representations into shared key-value cache channels. The mixing happens at the source of the keys and values. In effect the cache is no longer a private record per layer but a common pool that any layer can consult. And because those channels are shared across layers, the cache itself can shrink, so the same idea that widens what a layer can see also narrows what has to be stored.
Connecting layers across depth has a cost, and the paper names it. The new connections introduce dependencies that slow down training and prompt processing. The answer is cyclic iteration. Tokens are split into interleaved groups, the groups are updated in turn, and the tokens inside each group are processed in parallel. On a reference model trained with exact autoregressive execution, cyclic iteration converges twelve point five times faster than standard Jacobi iteration.
Two comparisons carry the case for the architecture itself. At the same number of training tokens, WhiteMatter with a full-size cache performs comparably to a standard Transformer with fifty percent more layers. And with half the key-value cache, it outperforms matched standard Transformers at two model scales, reaching up to one point three billion parameters. So a smaller cache does not have to mean a weaker model here.
One way to hear WhiteMatter is as a trade between resources. Memory is saved because depths share a cache, and quality holds because any layer can reach any depth. The price is sequential dependency between layers, and cyclic iteration is the authors' way of paying it down.
Paper Quest · 7 chapters · about 41 min
Play this paper
Learn it by doing: make the calls the authors made, guess the result before you see it, and defend it in a viva graded on your own words. Chapter 1 is right here.
Chapter 1 🧩 · The problem
Every quest starts with a wall. Here it is a model that forgets what its own deeper layers already worked out.
You are generating text with a Transformer. For every past token it has built a representation at every layer, and stored keys and values for each.
The road ahead
- 1 · The problem ~7 min A Transformer computes every past token at every layer, yet each layer can only read the stored keys and values from its own depth.
- 2 · What came before ~3 min
- 3 · The key idea ~9 min A learned mixer blends each past token's states from all depths into a few shared key-value channels that any layer can read.
- 4 · Choose your own research ~3 min
- 5 · Build the method ~8 min Run the layers, mix every layer's state into shared channels with a router, store them, and let each layer read one channel.
- 6 · The experiment ~6 min You’ll guess: With only half the KV cache, how did WhiteMatter, whose layers read past-token representations from any depth, compare with matched standard Transformers?
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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