> 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/index.md).

# Tech Deep Dives

These pages explain the mathematics and engineering behind Quantaria's models, one technique at a time. They are for readers who want more than the overview, such as ML engineers, quantum researchers, and anyone evaluating the approach.

Each page separates two things:

* **The technique.** Background from linear algebra, tensor networks, quantum information, or machine learning. These parts do not depend on Quantaria.
* **Quantaria's use.** How Hilbert-1, Schmidt, Dirac, Born, or Bond applies the technique, and what is planned, in research, or live.

Numbers quoted from papers are labelled as such and are not Quantaria results. See [Research Foundations](https://github.com/bhavy2908/dataai_docs/tree/main/architecture/research-foundations.md) for the full list.

## Tensor networks

1. [Matrix product states from scratch](/deep-dives/matrix-product-states.md)
2. [Matrix product operators as weight matrices](/deep-dives/matrix-product-operators.md)
3. [Singular value decomposition and truncation](/deep-dives/svd-and-truncation.md)
4. [Bond dimension and entanglement entropy](/deep-dives/bond-dimension-and-entanglement.md)
5. [Schmidt decomposition](/deep-dives/schmidt-decomposition.md)
6. [Canonical forms and sweeps](/deep-dives/canonical-forms-and-sweeps.md)
7. [Tensor-train decomposition of a weight matrix](/deep-dives/tensor-train-decomposition.md)
8. [Parameter counting for tensor-network layers](/deep-dives/parameter-counting.md)
9. [Rank-adaptive training](/deep-dives/rank-adaptive-training.md)
10. [MERA and disentanglers](/deep-dives/mera-and-disentanglers.md)

## Models and training

11. [Tensor Product Attention](/deep-dives/tensor-product-attention.md)
12. [The KV cache and why it limits context](/deep-dives/kv-cache.md)
13. [MPO mixture-of-experts](/deep-dives/mpo-mixture-of-experts.md)
14. [Transfusion: text and images in one model](/deep-dives/transfusion-objective.md)
15. [Diffusion on image patches](/deep-dives/diffusion-on-patches.md)

## Quantum path and sampling

16. [Staircase circuits: preparing an MPS on qubits](/deep-dives/staircase-circuits.md)
17. [The Cayley transform and unitary adapters](/deep-dives/cayley-unitary-adapters.md)
18. [Born machines: sampling from |ψ|²](/deep-dives/born-machines.md)
19. [DMRG-style sweeps](/deep-dives/dmrg-sweeps.md)

## Evaluation

20. [Evaluating against matched dense baselines](/deep-dives/evaluation-methodology.md)

## Related

* [Tensor-Network Weights](https://github.com/bhavy2908/dataai_docs/tree/main/architecture/tensor-network-weights.md): the terms used on these pages
* [Quantum Path](https://github.com/bhavy2908/dataai_docs/tree/main/architecture/quantum-path.md): what runs where today


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