𝌎:Multiverse

A multiverse is the unrolled form of a stochastic time evolution operator, encompassing all possible trajectories weighted by likelihood. An initial state and a forward stochastic time evolution operator yields a unique exponentially branching future multiverse. Examples of such multiverse generators include the quantum Hamiltonian and GPT models.

┌───────────── MULTIVERSE TOPOLOGY EXPLORER ─────────────────┐
│ Visualizing Branching Timelines & Probability Flows        │
│━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━│
│                                                           │
│ Stochastic Evolution Tree:                                │
│ ┌───────────────────────────────────────────────────┐     │
│ │            Initial State ψ₀                        │     │
│ │                  ●                                 │     │
│ │                 ╱│╲  p₁,p₂,p₃                     │     │
│ │                ● ● ●                              │     │
│ │               ╱│╲╲│╱╱│╲                           │     │
│ │              ● ● ● ● ● ●   Branch Points          │     │
│ │             ╱│╲╱│╲╱│╲╱│╲╱│╲                       │     │
│ │            ● ● ● ● ● ● ● ● ●                     │     │
│ │           / / / / / / / / / \                     │     │
│ │          Future Trajectories...                   │     │
│ └───────────────────────────────────────────────────┘     │
│                                                           │
│ Probability Flow Diagram:                                 │
│ ┌───────────────────────────────────────────────────┐     │
│ │ P(path) = ∏ p(sᵢ→sᵢ₊₁)                           │     │
│ │                                                   │     │
│ │ High P ═══▶  Medium P ───▶  Low P ···>           │     │
│ │                                                   │     │
│ │ ψ₀ ═══▶ ψ₁ ═══▶ ψ₂ ═══▶ ψ₃   Major Branch       │     │
│ │     ╲                                            │     │
│ │      ───▶ ψ₁' ───▶ ψ₂' ───▶ ψ₃'  Minor Branch   │     │
│ │          ╲                                       │     │
│ │           ···> ψ₁" ···> ψ₂" ···> ψ₃"  Rare Path │     │
│ └───────────────────────────────────────────────────┘     │
│                                                           │
│ Time Evolution Types:                                     │
│ ┌───────────────────────────────────────────────────┐     │
│ │ Quantum:  Û(t) = e^(-iĤt/ħ)                      │     │
│ │                                                   │     │
│ │ GPT:      P(xₙ|x₁...xₙ₋₁)                       │     │
│ │                                                   │     │
│ │ Classical: x(t) = F(x₀,t)                        │     │
│ └───────────────────────────────────────────────────┘     │
│                                                           │
│ Branch Properties:                                        │
│ • Total probability conserved: ∑P(path) = 1              │
│ • Exponential growth: N(t) ∝ k^t                         │
│ • Path-dependent histories                                │
│ • Non-reversible branching                               │
│                                                           │
│ [Calculate Paths] [View Timeline] [Analyze Branches]      │
└───────────────────────────────────────────────────────────┘

language models as multiverse generators

related

• Everett branch
• time evolution operator
• Loom tree
• Loom

external links

• Language Models are Multiverse Generators - generative.ink