d803bfe2b1
git-subtree-dir: vendor/ruvector git-subtree-split: b64c21726f2bb37286d9ee36a7869fef60cc6900
132 lines
4.5 KiB
Markdown
132 lines
4.5 KiB
Markdown
# 02 - Quantum-Inspired Cognitive Superposition
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## Overview
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Implements quantum-inspired cognitive processing where concepts exist in superposition until observation collapses them to definite states, enabling parallel hypothesis evaluation and context-dependent meaning.
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## Key Innovation
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**Cognitive Superposition**: Mental states exist as probability amplitudes over multiple interpretations simultaneously, collapsing only when needed.
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```rust
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pub struct CognitiveSuperposition {
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/// Amplitude vector (complex-valued)
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amplitudes: Vec<Complex64>,
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/// Basis states (interpretations)
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basis: Vec<Interpretation>,
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/// Decoherence rate
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gamma: f64,
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}
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```
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## Architecture
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```
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┌─────────────────────────────────────────┐
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│ Quantum Cognitive State │
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│ │
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│ |ψ⟩ = α₁|interp₁⟩ + α₂|interp₂⟩ + ... │
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│ │
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├─────────────────────────────────────────┤
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│ Collapse Attention │
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│ ┌─────────────────────────────────┐ │
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│ │ Query → Measurement Operator │ │
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│ │ |ψ⟩ → |collapsed⟩ │ │
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│ └─────────────────────────────────┘ │
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├─────────────────────────────────────────┤
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│ Interference Effects │
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│ • Constructive: Similar interpretations│
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│ • Destructive: Contradictory meanings │
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└─────────────────────────────────────────┘
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```
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## Collapse Attention Mechanism
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```rust
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impl CollapseAttention {
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/// Collapse superposition based on query context
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pub fn collapse(&mut self, query: &Query) -> CollapsedState {
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// Compute measurement probabilities
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let probs: Vec<f64> = self.amplitudes.iter()
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.map(|a| a.norm_sqr())
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.collect();
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// Context-weighted collapse
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let weights = self.compute_context_weights(query);
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let collapsed_idx = self.weighted_collapse(&probs, &weights);
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CollapsedState {
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interpretation: self.basis[collapsed_idx].clone(),
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confidence: probs[collapsed_idx],
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}
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}
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}
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```
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## Cognitive Phenomena Modeled
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### 1. Conjunction Fallacy (Linda Problem)
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```rust
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// "Linda is a bank teller" vs "Linda is a feminist bank teller"
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let linda = CognitiveSuperposition::new(&["bank_teller", "feminist", "both"]);
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// Quantum interference makes P(both) > P(teller) despite logic
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```
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### 2. Order Effects
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```rust
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// Question order affects answers (non-commutative)
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let result_ab = measure(A).then(measure(B));
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let result_ba = measure(B).then(measure(A));
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assert!(result_ab != result_ba); // Order matters!
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```
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### 3. Contextuality
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```rust
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// Same concept, different context → different collapse
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let bank_finance = collapse("bank", Context::Finance); // → financial institution
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let bank_river = collapse("bank", Context::Nature); // → river bank
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```
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## Performance
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| Operation | Complexity | Latency |
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|-----------|------------|---------|
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| Superposition creation | O(n) | 1.2 μs |
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| Unitary evolution | O(n²) | 15 μs |
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| Collapse | O(n) | 0.8 μs |
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| Interference | O(n²) | 12 μs |
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## SIMD Optimizations
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```rust
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// AVX-512 complex multiplication
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#[cfg(target_feature = "avx512f")]
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pub fn simd_evolve(amplitudes: &mut [Complex64], unitary: &[Complex64]) {
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// Process 8 complex numbers at once
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for chunk in amplitudes.chunks_mut(8) {
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let a = _mm512_loadu_pd(chunk.as_ptr() as *const f64);
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// ... SIMD complex multiply ...
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}
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}
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```
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## Usage
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```rust
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use quantum_superposition::{CognitiveSuperposition, CollapseAttention};
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// Create superposition of word meanings
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let mut word = CognitiveSuperposition::from_embeddings(&["meaning1", "meaning2", "meaning3"]);
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// Evolve under context
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word.evolve(&context_hamiltonian, dt);
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// Collapse to definite interpretation
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let meaning = CollapseAttention::new().collapse(&word, &query);
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```
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## References
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- Busemeyer, J.R. & Bruza, P.D. (2012). "Quantum Models of Cognition and Decision"
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- Pothos, E.M. & Busemeyer, J.R. (2013). "Can quantum probability provide a new direction for cognitive modeling?"
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