Back to docs

Cognitive Optimal Transport

The mathematical foundation behind CBrowser's persona system.

CBrowser treats cognitive personas as probability measures in Wasserstein space. This enables distance computation, persona interpolation, adversarial generation, and attention modeling. It is the first application of optimal transport theory to UX persona simulation.

The Core Principle

Transport cost = cognitive processing cost.

This is empirically validated across 40+ papers:

  • Taylor & Fiebach (2025): Wasserstein distance between letter shapes predicts EEG neural activity at <225ms
  • Dabney et al. (Nature 2020): The brain maintains reward distributions, not point estimates
  • Galeotti et al. (2022): Visual cortex V1 performs image deformation along Wasserstein geodesics

When a user views a web page, the effort to process it relates to the Wasserstein distance. That distance measures the gap between what the user expects and what the page shows.

Four Layers of OT in CBrowser

1. Persona Distance (cognitive_distance)

26 cognitive traits are normalized to a probability measure (simplex). The W₁ distance between any two personas gives their true cognitive distance.

Applications:

  • Clustering personas by cognitive similarity
  • Selecting the N most different personas for maximum test coverage
  • Quantifying how "far apart" two user types are

2. Perceptual Transport (empathy_audit)

Screenshot-based Wasserstein analysis. Apply the persona's visual filter (blur, color shift, or contrast reduction). Then compute the W distance from the original. This measures actual visual information loss.

Applications:

  • Color-blind: how much color information is lost?
  • Low-vision: which elements disappear after blur?
  • Motor-impaired: which elements are too far to reach?

3. Cognitive Load Estimation (cognitive_load_estimate)

8-dimensional transport cost across: information density, visual complexity, interactive element count, text density, animation level, choice count, navigation depth, and patience.

Applications:

  • Predict which persona will be overwhelmed by a page
  • Identify the bottleneck dimension (too many choices? too much text?)
  • Compare the same page across all personas

4. Attention Transport (attention_analysis)

W₂ saliency on CIE-Lab color distributions with persona-specific attention filters. Shows where each persona's attention goes.

v18.54.0: Value-Driven Saliency. Schwartz motivational values now shape the attention filter via 4 parameters (exponent, center bias, global bias, threshold). Two personas with identical traits but different values produce different heatmaps.

A security-driven user scans for trust badges. A stimulation-driven user notices novel visual elements.

Based on motivated attention research (Pessoa 2009, Anderson 2013, Balcetis & Dunning 2006).

Applications:

  • ADHD: Is the animation stealing attention from the CTA?
  • Elderly: Are the important elements visible enough?
  • Motor-impaired: Is attention narrowing to avoid misclicks?
  • Builder vs trust-seeker: Does social proof capture the right audience's attention?
  • Custom personas: Does your specific user's value profile change what they see on your specific page?

Mathematical Foundations

All operations are O(d³) or better for d=26 traits. Sub-millisecond. No GPU required.

Operation Method Complexity
Cognitive distance W₁ with ground metric + Bures-Wasserstein W₂ O(d²)
Barycenter Weighted CDF averaging (exact for 1D marginals) O(K×d²)
Geodesic McCann displacement interpolation O(N×d)
Adversarial DRO with Wasserstein ball (Esfahani & Kuhn 2018) O(N×d²)
Saliency Center-surround W₂ on CIE-Lab Gaussians O(cells²)
Cognitive load Per-dimension capacity vs demand O(d)

MCP Tools

Tool What It Does
cognitive_distance W₁/W₂ distance between two personas
cognitive_coverage Select N most different personas
cognitive_interpolate Geodesic persona blending
cognitive_load_estimate 8-dimensional page complexity per persona
attention_analysis W₂ CIE-Lab saliency with persona filter
attention_compare Compare attention between two personas

Research References

Neuroscience

  • Taylor & Fiebach (2025) — OT for sub-letter orthographic processing
  • Galeotti et al. (2022) — Cortically based optimal transport
  • Dabney et al. (Nature 2020) — Distributional code for value in dopamine neurons
  • Thual et al. (NeurIPS 2022) — Fused unbalanced Gromov-Wasserstein brain alignment

HCI / UX

  • Klein & Frintrop (DAGM 2012) — W₂ saliency on multivariate normals
  • Bylinskii et al. (IEEE TPAMI 2019) — EMD for saliency evaluation
  • Plonsky et al. (2022) — Wasserstein distance in human decision-making
  • Grossman & Balakrishnan (ACM TOCHI 2005) — Probabilistic pointing models

Mathematics

  • Agueh & Carlier (SIAM 2011) — Barycenters in Wasserstein space
  • Esfahani & Kuhn (Math Programming 2018) — DRO with Wasserstein metric
  • Nadjahi et al. (NeurIPS 2020) — Sliced Wasserstein properties

Full research synthesis: GitHub — research/

From the Blog