TurboQuant/TurboVec Retrieval Notes#

TurboQuant/TurboVec is optional retrieval, compression, and audit infrastructure around NFC. It is not the core NeuroTwin model contribution and must not become a required dependency.

Math Summary#

Normalize:

\[r=\|v\|_2,\qquad u=\frac{v}{\|v\|_2}\]

Random rotation:

\[z=Ru\]

High-dimensional coordinate approximation:

\[z_i\approx\mathcal{N}(0,1/d)\]

Quantization map:

\[Q:\mathbb{R}^d\rightarrow\{0,1\}^{bd}\]

MSE objective:

\[\mathbb{E}\|x-\hat{x}\|_2^2\]

Inner-product distortion objective:

\[\mathbb{E}\left[(\langle x,q\rangle-\langle\hat{x},q\rangle)^2\right]\]

Score error bound:

\[|\langle q,z_i\rangle-\langle q,\hat z_i\rangle| \leq \|q\|_2\|z_i-\hat z_i\|_2\]

Retrieval-kNN Baseline#

\[\mathcal{N}_k(q)=\{i_1,\ldots,i_k\}\]
\[\hat y_{\mathrm{test}}= \sum_{i\in \mathcal{N}_k(q)}w_i y_i\]
\[w_i= \frac{\exp(\tau\langle q,z_i\rangle)} {\sum_{j\in\mathcal{N}_k(q)}\exp(\tau\langle q,z_j\rangle)}\]

This baseline may use train labels and test query features. It must never use test targets.

Semantic Near-Duplicate Audit#

\[d_{\min}(x_{\mathrm{test}},\mathcal{D}_{\mathrm{train}}) = \min_{x_i\in\mathcal{D}_{\mathrm{train}}} \|q(x_{\mathrm{test}})-q(x_i)\|\]

This can flag train/test semantic leakage in stimulus features, especially for Algonauts/CNeuroMod.

Why It Could Help#

  • Compress large stimulus-feature stores.

  • Support exact or approximate nearest-neighbor retrieval baselines.

  • Audit semantic near-duplicates between train and test stimuli.

  • Store latent field summaries for memory/debug workflows.

Risks#

  • Low-dimensional vectors can violate high-dimensional approximations.

  • Approximate retrieval can miss duplicates.

  • Quantization distortion can change rankings.

  • Optional dependency friction can break reproducibility.

  • Quantization is not automatically differentiable or claim-relevant.

Implementation Priority#

  1. Numpy exact vector store.

  2. Optional lazy TurboVec adapter.

  3. Retrieval baseline.

  4. Semantic duplicate audit.

No implementation is added in this pass.