> For the complete documentation index, see [llms.txt](https://docs.quantaria.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.quantaria.xyz/deep-dives/mpo-mixture-of-experts.md).

# MPO mixture-of-experts

A mixture-of-experts (MoE) layer routes each input to a few expert networks instead of running all of them. This page explains the tensor-network variant used in Hilbert-1 Base, where experts share most of their parameters.

## Standard MoE

A standard MoE layer has many full feed-forward experts. Each expert is a complete set of weights, so adding experts adds parameters in proportion. A router picks a small number of experts per token.

## The MPO variant

The method in [arXiv:2203.01104](https://arxiv.org/abs/2203.01104) writes the experts' weight matrices as matrix product operators. All experts share one central tensor. Each expert adds only a small auxiliary tensor of its own.

The effect is that the shared part is stored once, and each new expert costs only its auxiliary tensors. The paper reports 27× fewer parameters than Switch Transformer. That is the paper's result on its setup.

## Why sharing works

Experts often need similar structure, with differences in a few directions. A shared central tensor captures the common part. The auxiliary tensors capture what is different. This matches how the bond dimension separates shared and expert-specific correlation.

## Trade-offs

* Experts are less independent than in a standard MoE. If the shared part is wrong for a task, every expert inherits the error.
* Routing still adds compute and must be balanced across experts so none is overloaded.

## Quantaria's use

Hilbert-1 Base includes an MPO mixture-of-experts. Nano does not, as listed in [Models](https://github.com/bhavy2908/dataai_docs/tree/main/overview/models.md#hilbert). Expert counts are not published in these docs.

## Related

* [Matrix product operators](/deep-dives/matrix-product-operators.md)
* [Parameter counting](/deep-dives/parameter-counting.md)


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