| name | quantum-probability-flow-hebbian-learning |
| category | ai_collection |
| description | Quantum probability-flow principle for deriving local Hebbian learning rules in associative memory networks using quantum annealer validation. arXiv:2606.02098 |
| created | 2026-06-19T00:00:00.000Z |
| version | 1.0 |
| tags | ["quantum","hebbian-learning","associative-memory","quantum-annealing","probability-flow","attention","D-Wave"] |
| source | arXiv:2606.02098 |
| trigger | quantum probability flow, Hebbian learning, associative memory, transverse field, survival loss, quantum annealer, D-Wave, softmax Hebbian, attention mechanism |
Attention-Like Hebbian Learning from Quantum Probability Flow
Overview
A quantum probability-flow principle for deriving local learning rules in associative memory networks. Transverse field defines leakage channels from data states, and minimizing measured survival loss gives stability-driven updates. Validated on D-Wave quantum annealer.
Core Methodology
1. Quantum Probability Flow Principle
- Transverse field defines leakage channels from data states
- Survival loss: Measure probability leakage from target states
- Minimize survival loss: Derives local learning updates
2. Imaginary-Time Dephased Dynamics
For imaginary-time, dephased dynamics:
- Local leakage free energy = log-sum-exp of energy gaps
- Gradient = softmax-weighted Hebbian rule
- Attention-like weighting emerges naturally from quantum dynamics
3. Real-Time Dynamics
- Real-time stability yields power-law weighting
- Contrasts with softmax from imaginary-time dynamics
4. Experimental Validation
D-Wave standard- and fast-anneal tests of one-hot attention forward map:
- Better fitted by effective softmax than Lorentzian power law
- Confirms imaginary-time dynamics as better model
Implementation Pattern
1. Define transverse field Hamiltonian H = H_data + Γ·H_transverse
2. Measure survival probability of data states under evolution
3. Compute survival loss L = 1 - P_survival
4. Derive learning rule: Δw ∝ -∂L/∂w
5. For imaginary-time: softmax-weighted Hebbian update
6. For real-time: power-law weighted update
7. Validate on quantum annealer hardware
Applications
- Associative memory network design
- Quantum-inspired learning rules
- Attention mechanism derivation
- Quantum annealer validation
- Biologically plausible learning algorithms
Key Equations
- Leakage free energy: F_leak = log-sum-exp(ΔE_i)
- Imaginary-time gradient: ∂F_leak/∂w = softmax(ΔE) · Hebbian
- Real-time weighting: power-law(ΔE) · Hebbian
Pitfalls
- Imaginary-time vs real-time dynamics give qualitatively different learning rules
- D-Wave annealing approximates imaginary-time but not perfectly
- One-hot attention map is a simplified test case; general networks may differ
