What Quantum Mind adds to published models#

Most models in this library were published by other researchers, and each model atlas entry cites its source. The atlas labels every entry by origin: Unique to Quantum Mind, Published model, extended, Published method or Software tool.

The papers report a model as point estimates fitted once to a group of people. A robot works with one person at a time, needs to know how sure it is, and has to choose what to ask next. Three tools in quantum_mind.core give every people model those abilities, quantum-like or classical, which is what the “extended” label refers to. The equations are on the core mathematics page.

Tool	What it gives	Works with
`bootstrap()`	Intervals for parameters and for predicted answer probabilities	every model
`OnlinePersonModel`	A per-person posterior, updated after every answer, starting from the population fit	models fitted by likelihood
`rank_conditions()`, `model_posterior()`	The question, order or display that best tells competing models apart, and the model probabilities after each answer	models fitted by likelihood

Example: one person, live#

import numpy as np
from quantum_mind import fit, bootstrap, OnlinePersonModel
from quantum_mind.core import rank_conditions, model_posterior
from quantum_mind.families.order_effects import QuantumOrderModel4D, BayesOrderModel

group = {'AB': [40, 10, 20, 30], 'BA': [30, 20, 10, 40]}     # answers from earlier participants
q = fit(QuantumOrderModel4D, group)
b = fit(BayesOrderModel, group)
print(bootstrap(q, group, n_boot=50).predictive_interval()['AB'])   # how sure the robot is

person = OnlinePersonModel(QuantumOrderModel4D, prior=q, prior_scale=0.5)
print(rank_conditions([q.model, b.model], ['AB', 'BA']))      # which order to ask in
person.update('AB', 0)                                        # the person said yes, yes
print(model_posterior([q.model, b.model], {'AB': [1, 0, 0, 0]}))
print(person.predict()['BA'])                                 # this person's predicted answers

The bootstrap needs repeated fits, so it belongs before or between interactions. The online model and the design functions cost a fraction of a second per answer and can run during one.

For robots#

Four published robotics methods are extended in the same spirit, and one method is new to this library.

Published method	Quantum Mind’s extension
Split conformal prediction	`AdaptiveConformalSets`: sets for a person’s next answer that keep their long-run coverage while the person changes, with a guaranteed bound; the robot asks when the set holds more than one answer
Partial pooling	`PersonalisedHumanModel(method='online')`: a full per-person posterior from the population prior, with credible intervals
Task allocation QUBO	`trust_aware_allocation()`: expected failures of robot-assisted steps from each person’s trust in the robot, plus workload; solved exactly or exported as an Ising model
Reinforcement learning against a fixed simulated person	`sample_people()` and the `people=` option of the environments: a new simulated person every episode, drawn from a fitted model’s uncertainty
(new) Bayes filtering of sensor frames	`COBRA`: a density-matrix belief whose measurement basis is rotated by the previous frame, with the Bayes filter and an incoherent filter as built-in limits

What was measured: the adaptive conformal sets keep their coverage while the robot learns a new person, and the trust-aware allocation changes the plan whenever a person’s trust in the robot is low (both on simulated people). COBRA’s gain over a Bayes filter is shown on a synthetic task built to contain a context effect, with a control task, ablations and paired tests (benchmarks/context_intent_benchmark.py); it has not been tested on human data.