Theory¶

Self from Coupled Predictive Loops Hypothesis

1. Problem Definition¶

This theory aims to explain the following phenomena:

Why consciousness appears as a unified experience
Why there exists a stable and unique “self”
Why we experience “I am thinking” and “I am acting”
Why the self exhibits temporal continuity

This model does not attempt to answer:

Why subjective experience exists (the metaphysical “hard problem”)

Instead, it focuses on:

Under what structural and dynamical conditions a system will necessarily exhibit a unified self and coherent subjective reports.

2. Basic Structure (Revised Minimal Structure)¶

This model does not assume fixed functional modules. Instead, it proposes the following minimal structural constraint:

The system can generate multiple predictive trajectories and, under temporal continuity constraints, selects and maintains one of them over time.

This structure consists of three coupled processes (functional distinctions rather than modular separations):

2.1 Multi-Prediction¶

At any given moment, the system generates multiple possible future state trajectories.

Sources include:

Internal uncertainty (probabilistic distributions / sampling)
Modeling of potential changes
Parallel expansion of multiple actions or strategies
External or internal perturbations (not required)

Thus:

Multi-prediction is an intrinsic property of the system, not dependent on a specific mechanism.

2.2 Trajectory Compression and Representation¶

The system compresses historical states into an encoded structure, forming comparable trajectories.

Functions:

Provide cross-temporal continuity constraints
Reduce noise and redundancy
Construct a trajectory space

Thus:

Compression defines the set of trajectories that can be matched and selected.

2.3 Matching and Selection¶

The system continuously compares:

Actual state evolution
Multiple predicted trajectories

and tends to:

Select the trajectory with minimal continuity error.

This trajectory becomes:

→ the dominant trajectory

3. Temporal Continuity and Trajectory Selection¶

3.1 Definition of Continuity¶

Continuity is not instantaneous agreement but a cross-temporal constraint:

Continuity = temporal sequence consistency between actual and predicted trajectories

3.2 Continuity Error¶

Formally:

E = D(trajectory_actual || trajectory_predicted)

Or locally:

E_t = d(x_t, \hat{x}_t)

This variable serves as:

The core basis for trajectory selection
A measure of self-stability

3.3 Self as a Result of Trajectory Selection¶

Definition:

Self = argmin (continuity error over trajectories)

That is:

The self is the dominant trajectory continuously selected within trajectory space.

This selection exhibits:

Temporal persistence
History dependence
Stability under constraints

4. Indistinguishability Principle¶

When multiple internal signals satisfy:

High temporal synchronization
Reference to the same state variables
Shared representational space
Lack of independent channels or external references

then:

The system cannot distinguish their sources, and these signals collapse into a single internal representation.

This manifests subjectively as:

→ a unified experience

5. Subjective Experience¶

Definition:

Subjective experience = the indistinguishable coupling of multiple signals along the dominant trajectory

These signals include:

Predictive signals
Matching signals
State integration signals

The unity of experience arises from:

Indistinguishability, rather than a single generating source

6. Agency¶

Agency is not the result of a single successful prediction, but:

A process of selection and attribution among multiple predictive trajectories

Specifically:

The system generates multiple predictive trajectories
Actual evolution matches one of them
This match persists over time

Then:

→ The current state is attributed to the dominant trajectory → Experienced as “generated by me”

If:

Predictions fail
Or continuity is disrupted

Then:

→ Attribution may shift → Experienced as externally generated

7. Unified Self and Stability¶

The system tends to maintain:

A single dominant trajectory

Reasons:

Coexisting trajectories create prediction conflicts
Continuity error cannot be minimized simultaneously across multiple trajectories
The system converges toward stable solutions (analogous to attractors)

This gives rise to:

Uniqueness of the self
Temporal continuity
Stable attribution structure

8. No External Reference and Unified Interpretation¶

Internal processes (prediction, matching, integration):

Operate within the same state space
Lack independent labels or external markers

Thus:

The system cannot distinguish signal origins and can only form a unified interpretation

This unified interpretation manifests as:

The self
Subjective experience

9. Emergence of the First-Person Perspective¶

Generation pathway:

Multi-prediction and multi-signal coupling
→ Indistinguishability
→ Formation of dominant trajectory
→ Single internal representation
→ Unified output interface
→ Linguistic expression as “I”

Thus:

The first-person perspective is not an independent mechanism, but a structural output.

10. Boundary Conditions (Conditions for Self)¶

The self may fail to stably form under the following conditions:

Inability to maintain temporal continuity
Absence of multi-prediction structure
Lack of trajectory compression (no basis for comparison)
Failure of signal coupling

This implies:

The self is a product of structural conditions, not a necessary feature of all systems

11. Minimal Self-System Definition¶

A minimal self-system requires at least:

State representation
+ Multi-prediction generation
+ Trajectory compression
+ Continuity evaluation
+ Selection & attribution mechanism

Not required:

Explicit perturbation modules
A dedicated “self unit”

12. Core Expressions (Compressed Form)¶

Self = trajectory with minimal continuity error  

Experience = indistinguishable coupled signals on the selected trajectory  

Agency = attribution based on sustained prediction–evolution matching

13. Nature of the Theory¶

This model is:

An information-structural model
A dynamical process model
A non-ontological model

Characteristics:

Does not introduce additional conscious entities
Emphasizes constraints and selection mechanisms
Amenable to formalization (information theory / dynamical systems)
Amenable to simulation (multi-trajectory systems)

14. Current Limitations¶

Continuity error is not yet rigorously formalized
The trajectory selection mechanism lacks a complete dynamical model
The attribution mechanism is not fully mathematized
No experimental validation yet
Does not address the ontological nature of experience

15. Future Work¶

Formal definition of continuity error
Dynamical systems modeling of trajectory selection and attribution
Minimal simulations of multi-prediction systems (toy models)
Development of observable metrics and experimental designs