COBRA belief filter#

A robot’s belief about a person as a density matrix whose measurement basis is rotated by the previous sensor frame, so what a reading means depends on what came before it. The equations are on the mathematics page.

Legend: blue inputs, violet internal steps, green outputs, coral people, dashed grey classical baselines. Each entry is labelled by origin: Unique to Quantum Mind designed in this library; it builds on the methods cited with it, Published model, extended implements the cited model as published; Quantum Mind adds the capabilities listed, Published method implements the cited method as published, Software tool infrastructure rather than a model; and by category: Quantum-like quantum probability used to model people; runs on an ordinary computer, Quantum computing quantum circuits; run on the simulator or sent to quantum hardware, Classical classical statistics, decision theory or baselines, Mixed combines parts from more than one of these categories.

Context-rotated belief filter (COBRA)#

Unique to Quantum Mind Quantum-like

Density-matrix belief updated by a generalised measurement whose basis is rotated by the previous frame, then partially dephased. Contains the Bayes filter (no rotation) and an incoherent context filter (full dephasing) as special cases.

        flowchart LR
    accTitle: Block diagram of Context-rotated belief filter (COBRA)
    accDescr: Density-matrix belief updated by a generalised measurement whose basis is rotated by the previous frame, then partially dephased. Contains the Bayes filter (no rotation) and an incoherent context filter (full dephasing) as special cases.
    prev["previous frame x₍t−1₎"]:::in --> U["rotation U(x₍t−1₎)<br/>learned Hermitian generators"]:::op
    x["frame xₜ"]:::in --> w["evidence weights<br/>exp(½(Wxₜ+b))"]:::op
    U --> M["measurement M = U·diag(w)·U†"]:::op
    w --> M
    rho["belief ρ"]:::hum --> upd["ρ → MρM / tr"]:::op
    M --> upd --> deph["dephasing g"]:::op --> rho2["ρ₍t₎<br/>P(z) = ρ_zz"]:::out
    bayes["Bayes filter (H = 0)"]:::base -.-> rho2
    inc["incoherent context filter (g = 1)"]:::base -.-> rho2
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    classDef op fill:#2a1b3d,stroke:#d2a8ff,color:#e6edf3
    classDef out fill:#0f2e1a,stroke:#7ee787,color:#e6edf3
    classDef hum fill:#3d1414,stroke:#ff7b72,color:#e6edf3
    classDef base fill:#262626,stroke:#8b949e,color:#e6edf3,stroke-dasharray:4 3

  • API: COBRA

  • Compared with: Gaussian Bayes filter; incoherent context filter (g = 1); logistic regression and MLP on the flattened sequence

  • Origin: Unique to Quantum Mind: designed in this library; it builds on the methods cited with it.

  • Category: Quantum-like: quantum probability used to model people; runs on an ordinary computer.

  • Reference: Busemeyer, J. R., & Bruza, P. D. (2012). Quantum Models of Cognition and Decision. Cambridge University Press; Kraus, K. (1983). States, Effects and Operations: Fundamental Notions of Quantum Theory. Springer.

Online belief#

Unique to Quantum Mind Quantum-like

The same filter run one frame at a time, as a robot would: update with each sensor frame, read the probabilities and the coherence.

        flowchart LR
    accTitle: Block diagram of Online belief
    accDescr: The same filter run one frame at a time, as a robot would: update with each sensor frame, read the probabilities and the coherence.
    s["sensor stream"]:::in --> u["update(frame)"]:::op --> p["P(intent)"]:::out
    u --> c["l1 coherence"]:::out
    p --> d["min_cost_action<br/>hand over · wait · ask"]:::out
    classDef in fill:#0b2a4a,stroke:#79c0ff,color:#e6edf3
    classDef op fill:#2a1b3d,stroke:#d2a8ff,color:#e6edf3
    classDef out fill:#0f2e1a,stroke:#7ee787,color:#e6edf3
    classDef hum fill:#3d1414,stroke:#ff7b72,color:#e6edf3
    classDef base fill:#262626,stroke:#8b949e,color:#e6edf3,stroke-dasharray:4 3

  • API: OnlineBelief

  • Origin: Unique to Quantum Mind: designed in this library; it builds on the methods cited with it.

  • Category: Quantum-like: quantum probability used to model people; runs on an ordinary computer.

  • Reference: Busemeyer, J. R., & Bruza, P. D. (2012). Quantum Models of Cognition and Decision. Cambridge University Press.

Gaussian Bayes filter#

Published method Classical

The commutative classical reference: independent Gaussian features per hypothesis, so reordering the frames cannot change the belief.

        flowchart LR
    accTitle: Block diagram of Gaussian Bayes filter
    accDescr: The commutative classical reference: independent Gaussian features per hypothesis, so reordering the frames cannot change the belief.
    f["frames"]:::in --> g["per-class Gaussians"]:::op --> post["product of likelihoods × prior"]:::op --> p["P(hypothesis)"]:::out
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    classDef out fill:#0f2e1a,stroke:#7ee787,color:#e6edf3
    classDef hum fill:#3d1414,stroke:#ff7b72,color:#e6edf3
    classDef base fill:#262626,stroke:#8b949e,color:#e6edf3,stroke-dasharray:4 3

  • API: GaussianBayesFilter

  • Origin: Published method: implements the cited method as published.

  • Category: Classical: classical statistics, decision theory or baselines.

  • Reference: Maron, M. E. (1961). Automatic indexing: an experimental inquiry. Journal of the ACM, 8(3), 404-417.

Minimum-cost action#

Published method Classical

Choose the action with the lowest expected cost under a belief; an “ask” row lets the robot hedge when the belief is spread out.

        flowchart LR
    accTitle: Block diagram of Minimum-cost action
    accDescr: Choose the action with the lowest expected cost under a belief; an "ask" row lets the robot hedge when the belief is spread out.
    p["belief P(z)"]:::in --> e["expected cost Σ_z C[a,z]·P(z)"]:::op --> a["argmin over actions"]:::out
    C[("cost matrix")]:::in --> e
    classDef in fill:#0b2a4a,stroke:#79c0ff,color:#e6edf3
    classDef op fill:#2a1b3d,stroke:#d2a8ff,color:#e6edf3
    classDef out fill:#0f2e1a,stroke:#7ee787,color:#e6edf3
    classDef hum fill:#3d1414,stroke:#ff7b72,color:#e6edf3
    classDef base fill:#262626,stroke:#8b949e,color:#e6edf3,stroke-dasharray:4 3

  • API: min_cost_action()

  • Origin: Published method: implements the cited method as published.

  • Category: Classical: classical statistics, decision theory or baselines.

  • Reference: Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer.