mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +00:00
de06a85a83
Lean sorry audit (lake build passes, 3539 jobs): - FixedPointBridge: 10 sorrys quarantined with TODO(lean-port) — all blocked on Float→Q bridge lemmas (Q0_16/Q16_16 round-trip error bounds) - HyperbolicStateSurface: 3 sorrys quarantined — need Q16_16.sqrt error-bound and Q16_16.add_pos_of_pos lemmas - CostEffectiveVerification: 1 sorry quarantined; also fixed pre-existing struct/structure typo, Array.Repr, Real.abs syntax, and Bool/Prop mismatch - MMRFAMMUnification: 1 sorry quarantined — Array.foldl induction lemma missing - WaveformTeleport: constantWaveformAtFixedPoint_base native_decide was numerically false; replaced with sorry + TODO(lean-port) - RcloneIntegration: startTask_pending_non_increasing PROVED — only sorry fully closed, using List.partition_eq_filter_filter + List.filter_sublist - DiffusionSNRBias, GPUVerificationMetaprobe, QFactor, SSMS: already properly quarantined; verified build passes Infrastructure additions: - ene_wiki_body_reingest.py: 5-source priority resolver for ene.wiki_revisions text="" gap (TiddlyWiki → filesystem → Notion → package description → stub) - zfs-pool-setup.sh: stackcache pool (500G sparse vdev) with hot/warm/cold thermal-zone dataset hierarchy; requires reboot to 7.0.9-1-cachyos kernel Docs: - ROADMAP.md: mark Lean→Verilog/FPGA targets as LONG-TERM in Phase 6 - UNIFIED_SIGNAL_ARCHITECTURE.md: add FPGA-column deferral notice Generated with [Devin](https://cli.devin.ai/docs) Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
149 lines
4.9 KiB
Text
149 lines
4.9 KiB
Text
/-
|
|
SemanticRGFlow.lean
|
|
|
|
Formalizes Semantic Renormalization Group (RG) Flow in LLM Latent Spaces.
|
|
Validating implementation against:
|
|
- Li & Wang (2018): "Neural Network Renormalization Group" (arXiv:1802.02840)
|
|
- Zhao et al. (2026): "Application of Deep Neural Networks for Computing RG Flow" (arXiv:2510.06508)
|
|
- Chytas & Singh (2026): "Concept Attractors in LLMs and their Applications" (arXiv:2601.11575)
|
|
|
|
Author: Sovereign Stack Research
|
|
Date: 2026-04-23
|
|
-/
|
|
|
|
import Semantics.FixedPoint
|
|
import Semantics.LocalDerivative
|
|
|
|
namespace Semantics.SemanticRGFlow
|
|
|
|
open Semantics.Q16_16
|
|
open Semantics.LocalDerivative
|
|
|
|
-- ============================================================
|
|
-- 1. RENORMALIZATION GROUP OPERATORS
|
|
-- ============================================================
|
|
|
|
/--
|
|
Decimation Operator (Kadanoff Blocking):
|
|
Maps high-resolution metatypes (UV/microscopic)
|
|
to low-resolution collective variables (IR/macroscopic).
|
|
|
|
Ref: Li & Wang (2018) - Hierarchical change-of-variables.
|
|
-/
|
|
structure DecimationOperator where
|
|
inputSize : Nat
|
|
outputSize : Nat
|
|
weights : List (List Scalar)
|
|
bias : Array Scalar
|
|
/-- Preserves topological invariants during coarse-graining -/
|
|
preservesInvariants : Prop
|
|
|
|
/--
|
|
Disentangler Operator (Unitary/Invertible):
|
|
Transforms the local basis to minimize entanglement between
|
|
slow (relevant) and fast (irrelevant) degrees of freedom.
|
|
|
|
Ref: Li & Wang (2018) - Disentangling local degrees of freedom.
|
|
-/
|
|
structure DisentanglerOperator where
|
|
size : Nat
|
|
matrix : List (List Scalar)
|
|
/-- Disentanglers must be invertible (unitary-like in physical systems) -/
|
|
isInvertible : Prop
|
|
|
|
/--
|
|
The Beta Function β(g) = ∂g/∂ln(s)
|
|
Describes the flow of semantic "coupling constants" across scales.
|
|
|
|
Ref: Zhao et al. (2026) - RGFlow Bijective mapping.
|
|
-/
|
|
structure BetaFunction where
|
|
coupling : Scalar
|
|
flowVel : Scalar -- This is the value of β(g)
|
|
/-- Fixed Points occur where the Beta Function vanishes -/
|
|
isFixedPoint : flowVel = zero
|
|
|
|
/--
|
|
NeuralRG Step: A single layer of the hierarchical mapping.
|
|
Consists of a Disentangling step followed by a Decimating step.
|
|
-/
|
|
structure NeuralRGStep where
|
|
disentangler : DisentanglerOperator
|
|
decimator : DecimationOperator
|
|
/-- The combined step must satisfy the Minimal Mutual Information principle -/
|
|
isMinMI : Prop
|
|
|
|
-- ============================================================
|
|
-- 2. SEMANTIC ATTRACTORS & POTENTIALS
|
|
-- ============================================================
|
|
|
|
/--
|
|
A Semantic Attractor is a fixed point in the latent manifold.
|
|
Layers implement an Iterated Function System (IFS) contractive mapping.
|
|
|
|
Ref: Chytas & Singh (2026) - Concept-specific Attractors.
|
|
-/
|
|
structure SemanticAttractor where
|
|
center : Array Scalar
|
|
basinRadius : Scalar
|
|
potential : Scalar → Scalar -- Semantic potential V(φ)
|
|
isIFSSet : Prop -- Member of the semantic invariant set
|
|
|
|
/--
|
|
Attractor Descent: Implementation of the contractive mapping
|
|
identifying the "Gandalf Attractor" or "Python Attractor".
|
|
-/
|
|
def attractorDescent (point : Array Scalar) (attr : SemanticAttractor) : Array Scalar :=
|
|
-- Layer-wise contractive update toward attractor center
|
|
point -- Simplified model
|
|
|
|
-- ============================================================
|
|
-- 3. MINIMAL MUTUAL INFORMATION PRINCIPLE
|
|
-- ============================================================
|
|
|
|
/--
|
|
Minimal Mutual Information (Information Bottleneck).
|
|
The RG flow minimizes I(X_ir; X_uv) to eliminate irrelevant features.
|
|
|
|
Ref: Zhao et al. (2026) - Information-preserving bijective flow.
|
|
-/
|
|
structure InformationConstraint where
|
|
mutualInfo : Scalar
|
|
threshold : Scalar
|
|
/-- RG Flow is optimized when Mutual Information is minimized across the discard boundary -/
|
|
isOptimized : mutualInfo ≤ threshold
|
|
|
|
/--
|
|
NeuralRG Model: A sequence of RG steps forming a deep generative flow.
|
|
-/
|
|
structure NeuralRGModel where
|
|
steps : List NeuralRGStep
|
|
inputDim : Nat
|
|
latentDim : Nat
|
|
/-- The model defines a flow from microscopic (UV) to macroscopic (IR) -/
|
|
isFlowConserved : Prop
|
|
|
|
/--
|
|
Law: Minimal Mutual Information Principle (MMIP)
|
|
Asserts that when MI(IR; UV) → min, the system converges to a
|
|
critical point where β(g) = 0. Taken as postulate — formal proof
|
|
would require information-theoretic Shannon entropy bounds.
|
|
-/
|
|
structure MMIPHypothesis where
|
|
convergence (info : InformationConstraint) (beta : BetaFunction) :
|
|
info.mutualInfo = zero → beta.flowVel = zero
|
|
|
|
-- ============================================================
|
|
-- 4. MANIFOLD GEOMETRY
|
|
-- ============================================================
|
|
|
|
/--
|
|
Latent Manifold: Riemannian manifold representing LLM latent space.
|
|
Ref: Chytas & Singh (2026) - Iterated layers on Riemannian manifold.
|
|
-/
|
|
structure LatentManifold where
|
|
metric : Array Scalar → List (List Scalar)
|
|
dimension : Nat
|
|
ricciCurvature : Array Scalar → Scalar
|
|
|
|
end Semantics.SemanticRGFlow
|