IRAM-Ω-QAdaptive uncertainty regulation
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IRAM-Ω-Q / Inside the simulation

Regulating
uncertainty.

How the simulation works

An agent regulates its internal uncertainty while the world keeps changing. Step inside the loop—and see what its state and regulatory effort reveal.

Explore the simulation
An illustrated guide · 2026
An illuminated human-like agent adjusts a dial while a translucent barrier separates it from a field of disturbance.
A research question

What does it take for an adaptive system to remain organized under uncertainty?

01 / The model

State is only part of the story.

Look beyond
the stable surface.

Two agents may reach similar internal states while one needs substantially more corrective control. IRAM-Ω-Q makes that difference visible by tracking both the regulated state and the adaptive gain recruited to maintain it.

The framework models uncertainty regulation under stochastic disturbance. Its central comparison is simple: can regulation act before disturbance enters, or only after?

The five mathematical objects behind the model
State ψ or ρ
The mathematical representation of the agent’s current internal state.
Hamiltonian H
The generator of its coherent internal evolution.
Controller μ
The adaptive gain controlling how much regulation is recruited.
Noise η
The disturbance applied to the state.
Target S*
The desired entropy level against which the state is evaluated.

An everyday analogy

Think of a thermostat for uncertainty. The controller compares the current uncertainty with a target and adjusts its response. The aim is a workable internal state—not the elimination of all uncertainty.

Explore the causal order

Same challenge. Different timing.

  1. 1Read the state

    Estimate the current internal uncertainty.

  2. 2Regulate

    Use adaptive control to attenuate incoming exposure.

  3. 3Receive disturbance

    The current-cycle disturbance enters with regulation available.

Anticipatory regulation (RF). In the foundational and memory studies, regulation before exposure generally requires lower adaptive gain than reactive recovery.

A conceptual comparison: a protective barrier before incoming disturbance on the left, and recovery after disturbance on the right.

Both orderings share the underlying model and then undergo coherent evolution; the timing of regulation differs. See the full model on page 5.

Inside each run

Measure. Adjust. Observe. Repeat.

  1. 01

    Set conditions

    Choose the target, disturbance, and experimental schedule.

  2. 02

    Apply changes

    Introduce scheduled interventions or resets, if the experiment calls for them.

  3. 03

    Step the agent

    Execute the regulation-first or disturbance-first sequence.

  4. 04

    Measure

    Read entropy, coherence gap, gain, and controller change.

  5. 05

    Record

    Keep measurements aligned with the same time and conditions.

Open the model diagram in a new tab

Reading the model

State and effort.
Read them together.

A vector state represents multiple internal alternatives; its density matrix supports entropy and coherence-gap measurements. This “quantum-like” mathematics is a representational tool.

S(ρ) Entropy
The internal uncertainty signal used by the controller.
ΔC Coherence gap
A state-structure observable comparing diagonal spread with full-state entropy.
μ Adaptive gain
The amount of regulation recruited. A larger value can signal a greater control burden.
An abstract landscape of luminous peaks and interconnected paths in blue, gold, and violet.

03 / Reading the results

Original plots from the research papers.

Similar state.
Different effort.

Read the two measurements side by side. A state trajectory can look broadly similar even when the controller works harder to sustain it.

Blue and orange coherence-gap trajectories broadly overlap over the analyzed interval.
The state

The RF and DF coherence-gap trajectories overlap substantially at the reference setting.

Disturbance-first adaptive gain stays above regulation-first adaptive gain as both decline over time.
The effort

Adaptive gain separates: DF generally recruits more regulation in this comparison.

Finding the sensitive regions

Where do fluctuations rise?

Susceptibility measures temporal variability in the coherence gap after burn-in. Sweeping disturbance and initial gain reveals a ridge where the state becomes especially fluctuation-prone. This is an estimate on the tested grid, not a universal safe threshold.

Regulation-first susceptibility heat map with its estimated critical initial-gain curve.
Regulation first

Where coherence-gap fluctuations are greatest under anticipatory regulation.

Disturbance-first susceptibility heat map with its estimated critical initial-gain curve.
Disturbance first

The same measurement under reactive recovery.

The disturbance-first critical initial-gain curve is shifted above regulation-first across several disturbance intervals.
Compare the ridges

DF shifts parts of the critical ridge toward higher initial gain.

Hysteresis

The path matters.

Move the uncertainty target outward, then reverse it without resetting the agent. Entering and leaving the same target need not trace the same route. This is how the model tests history dependence.

Adaptive gain forms separate increasing-target and decreasing-target branches for both causal orderings.
Regulatory carryover

The same target can require different gain depending on the direction of travel.

Coherence-gap branches also show path dependence, with less consistent separation between causal orderings.
State-level response

The state also carries history, but the ordering effect is clearer in regulatory gain.

The robustness check

Does the burden difference persist?

The memory study repeats matched RF/DF comparisons across nine combinations of disturbance and initial gain, with 30 matched pairs at each point.

The clearest consistent ordering effect is in the controller variable μ. Coherence-gap effects are not universal in sign, so the result does not mean one ordering always produces a better state.

Heat maps show positive average disturbance-first minus regulation-first regulatory burden throughout the tested nine-condition grid.
Checking the neighborhood

Positive DF-minus-RF gain means that reactive ordering recruited more regulation across the ramp.

04 / When access comes and goes

Intermittent anticipatory regulation

Switching is more
than an average.

An agent may repeatedly lose and regain anticipatory control. Does that simply average the two fixed modes—or change the later regulatory burden?

Switching schedules

RF · Regulation firstDF · Disturbance first
PeriodicEqual dwell times
  1. RF
  2. DF
  3. RF
  4. DF
  5. RF
  6. DF
  7. RF
  8. DF
StochasticVariable dwell times
  1. RF
  2. DF
  3. RF
  4. DF
  5. RF
  6. DF
State and controller history continue across switches. Box widths illustrate time spent in each ordering.
At the reference operating point, all 13 mean switching penalties and their 95 percent confidence intervals lie below the zero-mixture baseline.
Below the simple-mixture prediction

At the reference operating point, every tested periodic and stochastic schedule has a negative mean switching penalty in the high-statistics experiment.

How to read the plot

Below zero means less burden than the mixture predicts.

The baseline combines matched fixed-RF and fixed-DF trajectories according to the time spent in each mode. The switching penalty is the observed mean gain minus that baseline.

13tested schedules
1,000 matched replicates each

At the reference operating point, all tested schedule means lie below zero in the high-statistics result. The effect is small—approximately half a percent of mean gain.

This does not establish that switching outperforms continuous anticipatory control, or that every individual run benefits.

The boundary check

Where does the advantage weaken?

The scan asks whether switching relief persists beyond the reference setting. No tested cell combines a resolved fixed-RF advantage with a resolved positive switching penalty. As the fixed-mode advantage fades, relief can weaken or become statistically unresolved.

Blue, amber, and gray map cells classify the relation between fixed-ordering advantage and switching relief; there are no red cells.
Where relief persists

Blue: resolved RF advantage and switching relief. Amber: resolved RF advantage, with attenuated or unresolved switching relief. Gray: no resolved fixed RF advantage.

As target uncertainty increases, fixed-ordering separation falls toward zero and switching relief becomes smaller.
Where relief weakens

Increasing the target reduces fixed RF/DF separation; switching relief also attenuates toward zero.

05 / A small laboratory

What the workflow makes testable

Change the conditions.
Watch the response.

The same loop supports controlled experiments on regulation, recovery, and the carryover of earlier experience.

01

Interventions

Temporarily change disturbance, target, or learning scale.

02

Resets

Reset state, gain, or controller memory to test recovery.

03

Ramps

Move the target gradually and reverse it to expose history dependence.

04

Switching

Alternate access to anticipatory regulation while retaining history.

Extending the workflow: where does disturbance come from?

The source matters, too.

In the induced-cost condition, positive controller updates generate immediate disturbance. The response is nonmonotonic: exposure initially rises, variability increases over an intermediate range, and higher costs can suppress corrective activity.

These findings apply within the tested model and grid; they do not establish a general instability law.

Four plots show effective disturbance initially rising, with adaptive gain and controller changes declining as induced cost grows.
When correction adds disturbance

The fourth study extends the workflow to distinguish external, internal, and control-generated disturbance.

06 / The takeaway

The dynamics
behind stability.

IRAM-Ω-Q is a controlled laboratory for adaptive uncertainty regulation.

The agent senses uncertainty, adjusts its regulatory gain, and reveals how its state responds—whether it settles, fluctuates, recovers, or carries history forward.

What is supported

In the foundational and memory experiments, anticipatory ordering can maintain comparable state-level behavior with lower recruited regulation.

What the numbers mean

Gain is modeled regulatory demand—not energy, compute cost, or task performance. “Stable” describes the narrative framing, not a formal stability theorem.

What is not claimed

The model does not show conscious software, a quantum brain, or universal superiority of regulation-first control.