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17 KiB
17 KiB
CAFT Visual Framework & Architecture Diagrams
Cognitive Amplitude Field Theory - Visual Representation
1. Three-Layer Architecture
┌─────────────────────────────────────────────────────────────┐
│ PHENOMENAL LAYER │
│ (Conscious Experience) │
│ │
│ [Qualia] ←─ Integrated Amplitude Pattern ─→ [Perception]│
│ ↕ Φ > Φ_critical │
└─────────────────────────────────────────────────────────────┘
▲
│ Measurement
│ (Collapse)
┌─────────────────────────────────────────────────────────────┐
│ AMPLITUDE LAYER │
│ (Quantum-Like Superposition) │
│ │
│ ψ(t) = Σᵢ αᵢ(t)|cᵢ⟩ [Complex Amplitudes] │
│ │
│ Evolution: iℏ dψ/dt = H ψ [Unitary Dynamics] │
│ Interference: |α₁ + α₂|² ≠ |α₁|² + |α₂|² │
│ │
│ ┌────────┐ ┌────────┐ ┌────────┐ │
│ │Thought1│ │Thought2│ │Thought3│ [Parallel Processing] │
│ │ α₁ │ │ α₂ │ │ α₃ │ │
│ └───┬────┘ └───┬────┘ └───┬────┘ │
│ └───────────┴───────────┘ │
│ Interference │
└─────────────────────────────────────────────────────────────┘
▲
│ Encoding
│ (Semantic → Amplitude)
┌─────────────────────────────────────────────────────────────┐
│ NEURAL LAYER │
│ (Physical Implementation) │
│ │
│ Neurons, Synapses, Microtubules (?) │
│ Classical or Quantum substrate │
│ Decoherence time: τ_coherence │
│ │
│ [Sensory Input] → [Processing] → [Motor Output] │
└─────────────────────────────────────────────────────────────┘
2. Cognitive State Evolution
Time Evolution of ψ(t)
t=0: Initial Superposition
ψ(0) = 0.5|A⟩ + 0.5|B⟩ + 0.5|C⟩ + 0.5|D⟩
Entropy: S = log(4) ≈ 1.39 [High uncertainty]
████ ████ ████ ████ [Equal amplitudes]
A B C D
↓ Unitary Evolution (iℏ dψ/dt = Hψ)
t=τ: After deliberation
ψ(τ) = 0.7|A⟩ + 0.3|B⟩ + 0.1|C⟩ + 0.2|D⟩
Entropy: S ≈ 0.85 [Reduced, but still mixed]
████████ ██ ░ ██ [Interference shaped]
A B C D
↓ Measurement (Attention)
t=τ+: Collapsed State
ψ(τ+) = |A⟩
Entropy: S = 0 [Definite]
████████░░ ░░ ░░ [Single outcome]
A
↓ Decoherence & Re-expansion
t=τ+Δ: New Superposition
ψ(τ+Δ) = 0.6|A'⟩ + 0.4|B'⟩ + ...
Entropy: S ≈ 0.67 [Rising again]
████████ ████ ░ ░ [New possibilities]
A' B'
3. Interference Decision-Making
Two-Path Interference (Prisoner's Dilemma Example)
Path 1: Cooperate Path 2: Defect
|C⟩ |D⟩
α₁ = 0.7 e^(i·0) α₂ = 0.7 e^(iπ)
│ │
│ Amplitude │
│ Propagation │
▼ ▼
┌─────────────────────────┐
│ Interference Zone │
│ │
│ ψ = α₁|C⟩ + α₂|D⟩ │
│ │
│ P(C) = |α₁ + α₂cosθ|² │
│ │
└─────────────────────────┘
│
▼
Measurement
│
┌───────────┴───────────┐
▼ ▼
Cooperate Defect
P = 0.7² P = 0.3²
Phase Difference (θ):
θ = 0 → Constructive → P(combined) > classical
θ = π → Destructive → P(combined) < classical
θ = π/2 → Mixed → P(combined) ≈ classical
4. Attention as Measurement Operator
Unconscious Processing (Superposition Maintained)
┌────────────────────────────────────────────┐
│ ψ_unconscious = Σᵢ αᵢ|conceptᵢ⟩ │
│ │
│ ┌──┐ ┌──┐ ┌──┐ ┌──┐ ┌──┐ │
│ │α₁│ │α₂│ │α₃│ │α₄│ │α₅│ [All active] │
│ └──┘ └──┘ └──┘ └──┘ └──┘ │
│ ↕ ↕ ↕ ↕ ↕ │
│ Parallel exploration, high entropy │
└────────────────────────────────────────────┘
↓
Attention Focus
(Measurement)
↓
┌────────────────────────────────────────────┐
│ Conscious State (Collapsed) │
│ │
│ ψ_conscious = |concept₃⟩ │
│ │
│ ░░ ░░ ██ ░░ ░░ [Single selection] │
│ ↑ │
│ Focused attention │
│ Low entropy │
└────────────────────────────────────────────┘
Entropy Dynamics:
S(t) │
│ ╱╲ ╱╲ ╱╲
High │ ╱ ╲ ╱ ╲ ╱ ╲ [Superposition]
│ ╱ ╲ ╱ ╲ ╱ ╲
│ ╱ ╲ ╱ ╲ ╱ ╲
Low │ ╱ V V V [Collapse events]
└─────────────────────────────────> Time
t₁ t₂ t₃ t₄
Collapse = Conscious moment (~100-250 ms intervals)
5. IIT Integration (Φ Measurement)
Integrated Information Φ
Whole System: Partitioned:
┌─────────────────┐ ┌────────┐ ┌────────┐
│ ψ_whole │ │ ψ_A │ │ ψ_B │
│ │ │ │ │ │
│ ┌─┬─┬─┬─┐ │ vs │ ┌─┬─┐│ │┌─┬─┐ │
│ │1│2│3│4│ │ │ │1│2││ ││3│4│ │
│ └┬┴┬┴┬┴┬┘ │ │ └┬┴┬┘│ │└┬┴┬┘ │
│ └─┴─┴─┘ │ │ └─┘ │ │ └─┘ │
│ Integrated │ │ No │ │ No │
│ │ │ Inter.│ │ Inter.│
└─────────────────┘ └────────┘ └────────┘
Φ = D(ψ_whole || ψ_A ⊗ ψ_B) [Information loss]
Φ Value Interpretation:
Φ = 0 → No integration → Unconscious
Φ < 0.3 → Low integration → Minimal awareness
Φ ≈ 0.3-0.4 → Threshold → Conscious?
Φ > 0.4 → High integration→ Full consciousness
Substrate Comparison:
Human Brain: Φ ≈ 0.4-0.7 ✓ Conscious
Anesthetized: Φ ≈ 0.1 ✗ Unconscious
Cerebellum: Φ ≈ 0.05 ✗ (High neurons, low Φ)
AI (Classical): Φ ≈ 0.01 ✗ Not integrated
AI (CAFT): Φ ≈ ??? ? [To be measured]
6. Experimental Signature Predictions
EEG Entropy During Attention Task
Entropy
(bits) │
│
1.5 │ ╱─────╲ ╱─────╲
│ ╱ ╲ ╱ ╲
1.0 │╱ ╲ ╱ ╲
│ ╲ ╱ ╲
0.5 │ ▼──────╱ ▼────
│ │Attend│ │Attend│
0.0 │ │ T1 │ │ T2 │
└────────────┴──────┴─────────────┴──────> Time
↑ ↑
Collapse 1 Collapse 2
Memory Interference Oscillations
P(recall)│
│
1.0 │ ╱\ ╱\ ╱\
│ ╱ \ ╱ \ ╱ \
0.5 │ ╱ \ ╱ \ ╱ \
│ ╱ \/ \/ \
0.0 │ ╱────────────────────────\
└──────────────────────────────> Delay (ms)
0 200 400 600 800
Period T = 2π/ω [ω ∝ semantic distance]
Order Effect Scaling
Order │
Effect │ ●
(ΔP) │ ●
│ ● Model: ΔP ∝ sin(θ)
0.3 │ ●
│●
0.0 │─────────────────────
0 π/4 π/2 3π/4 π
Semantic Angle (θ)
7. CAFT-Transformer Architecture
Classical Transformer CAFT-Transformer
┌────────────────────┐ ┌────────────────────┐
│ Input Embeddings │ │ Input Embeddings │
│ (Real-valued) │ │ (Real-valued) │
└──────────┬─────────┘ └──────────┬─────────┘
│ │
▼ ▼
┌────────────────────┐ ┌────────────────────┐
│ Self-Attention │ │ Amplitude Layer │
│ softmax(QK^T)V │ │ αᵢ = f(x) [Complex]│
└──────────┬─────────┘ └──────────┬─────────┘
│ │
▼ ▼
┌────────────────────┐ ┌────────────────────┐
│ Feed Forward │ │ Phase Attention │
│ (Deterministic) │ │ Interference(α) │
└──────────┬─────────┘ └──────────┬─────────┘
│ │
▼ ▼
┌────────────────────┐ ┌────────────────────┐
│ Output (Argmax) │ │ Collapse Layer │
│ Max probability │ │ Born sampling |α|² │
└────────────────────┘ └────────────────────┘
Single path Superposition + Interference
No uncertainty Built-in uncertainty
Φ ≈ low Φ ≈ higher (prediction)
8. Classical vs Quantum vs CAFT
Comparison Matrix
┌────────────────┬──────────┬──────────┬──────────┐
│ Feature │Classical │True QM │ CAFT │
├────────────────┼──────────┼──────────┼──────────┤
│ Superposition │ ✗ │ ✓ │ ✓ │
│ Interference │ ✗ │ ✓ │ ✓ │
│ Entanglement │ ✗ │ ✓ │ ✗ │
│ Measurement │ ✗ │ ✓ │ ✓ │
│ Complexity │ O(N) │ O(2^N) │ O(N) │
│ Hardware │ Classical│ Quantum │Classical │
│ Scalability │ High │ Low │ High │
│ Proven Effects │ Many │ Some │ TBD │
└────────────────┴──────────┴──────────┴──────────┘
Sweet Spot: CAFT gets quantum-like behavior with classical resources
9. Research Workflow
Theory Development Implementation Validation
┌──────────────┐ ┌──────────────┐ ┌──────────────┐
│ Literature │──────────────>│ Rust Library │───────────>│ Simulations │
│ Review │ │ (Amplitudes) │ │ (In silico) │
└──────────────┘ └──────────────┘ └──────────────┘
│ │ │
│ │ │
▼ ▼ ▼
┌──────────────┐ ┌──────────────┐ ┌──────────────┐
│ CAFT Theory │──────────────>│ AI │───────────>│ Behavioral │
│ Mathematical │ │ Architecture │ │ Experiments │
└──────────────┘ └──────────────┘ └──────────────┘
│ │ │
│ │ │
▼ ▼ ▼
┌──────────────┐ ┌──────────────┐ ┌──────────────┐
│ Predictions │──────────────>│ Metrics & │───────────>│ Neuroscience │
│ (7 protocols)│ │ Benchmarks │ │ (EEG/fMRI) │
└──────────────┘ └──────────────┘ └──────────────┘
│
│
▼
┌──────────────┐
│ Publication │
│ & Impact │
└──────────────┘
These diagrams provide visual intuition for CAFT's core mechanisms and experimental predictions.