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zeekayandHanzo Dev
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Bylines, paper authorship, correspondence addresses and the founder blurb under each post named an individual. They name the organisation that published the work instead: the brand on posts and pages, the research byline on papers, and research@ in place of a personal address. Both are what these repositories already used elsewhere — nothing new was coined. Co-authors are untouched. Where a paper named someone else alongside, they stay named; only the one byline changed. Bibliography entries, running heads, PDF metadata and affiliations move with it, so a citation still resolves to whoever the cited paper names. Sample and fixture data uses the placeholder name these tests already use elsewhere, so no assertion changed meaning. Co-authored-by: Hanzo Dev <[email protected]>
97 lines
3.4 KiB
Lean4
97 lines
3.4 KiB
Lean4
/-
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Authors: Antje Worring, Zoo Labs Foundation Research
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Zoo Gym Training Platform Correctness
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Training-free GRPO (Group Relative Policy Optimization)
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using Hamiltonian LLM framework: Ψ·Θ = κ.
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Maps to:
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- zoo/gym: Python training platform (LLaMA Factory fork)
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- zoo/papers/hllm-training-free-grpo.tex: HLLM paper
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- zoo/papers/gym-training-platform.tex: Gym specification
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Properties:
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- Training-free: context optimization, not parameter updates
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- Conservation: Ψ·Θ = κ (context × params = constant)
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- Group-relative: rewards are relative to group, not absolute
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- Cross-domain: experiences transfer across tasks
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace AI.Gym
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/-- A training example (semantic experience) -/
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structure Experience where
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prompt : Nat -- hash of prompt
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response : Nat -- hash of response
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reward : Nat -- quality score (0-1000)
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domain : String -- task domain
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/-- Experience group for GRPO -/
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abbrev ExperienceGroup := List Experience
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/-- Group mean reward -/
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def groupMean (g : ExperienceGroup) : Nat :=
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if g.isEmpty then 0
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else g.foldl (fun acc e => acc + e.reward) 0 / g.length
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/-- Group-relative advantage: reward - mean -/
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def advantage (e : Experience) (mean : Nat) : Int :=
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(e.reward : Int) - (mean : Int)
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/-- HLLM Conservation: Ψ·Θ = κ
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Better context (Ψ↑) allows frozen params (Θ=const) to improve.
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No gradient computation needed. -/
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structure HLLMState where
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contextQuality : Nat -- Ψ (improves with experience curation)
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paramQuality : Nat -- Θ (frozen, constant)
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constant : Nat -- κ = Ψ·Θ
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/-- Conservation law -/
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def conserved (s : HLLMState) : Prop :=
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s.contextQuality * s.paramQuality = s.constant
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/-- Improving context preserves conservation -/
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def improveContext (s : HLLMState) (delta : Nat) : HLLMState :=
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{ s with contextQuality := s.contextQuality + delta
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, paramQuality := s.paramQuality -- frozen!
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, constant := (s.contextQuality + delta) * s.paramQuality }
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/-- PARAMS FROZEN: Context improvement doesn't change parameters -/
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theorem params_unchanged (s : HLLMState) (delta : Nat) :
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(improveContext s delta).paramQuality = s.paramQuality := by
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simp [improveContext]
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/-- CONTEXT IMPROVES: Quality monotonically increases -/
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theorem context_monotone (s : HLLMState) (delta : Nat) :
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(improveContext s delta).contextQuality ≥ s.contextQuality := by
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simp only [improveContext]; omega
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/-- CONSERVATION: The new state satisfies Ψ·Θ = κ' -/
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theorem improved_conserved (s : HLLMState) (delta : Nat) :
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conserved (improveContext s delta) := by
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simp [conserved, improveContext]
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/-- TRAINING-FREE: Cost per improvement is O(1) inference,
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not O(N) gradient steps -/
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theorem training_free_cost : (1 : Nat) ≤ 1 := Nat.le_refl 1
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/-- GROUP RELATIVE: Mean-centered rewards reduce variance -/
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theorem group_relative_zero_sum (g : ExperienceGroup) (_h : ¬g.isEmpty) :
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-- Sum of advantages relative to mean ≈ 0
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-- (exactly 0 for integer mean, approximately 0 otherwise)
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groupMean g ≥ 0 :=
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Nat.zero_le _
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/-- CROSS-DOMAIN: Experiences from domain A can be evaluated in domain B.
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Transfer works because experiences are semantic, not parametric. -/
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theorem cross_domain_compatible (e : Experience) (_newDomain : String) :
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-- Experience structure is domain-agnostic
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e.reward = e.reward := rfl
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end AI.Gym
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