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249 lines
10 KiB
Text
249 lines
10 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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VirtualGPUTopology.lean — Virtual GPU on Topological Manifold
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Replaces scripts/virtual_gpu_topology_loader.py with a formal Lean module
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that defines virtual GPU structures and topology-aware model placement.
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Per AGENTS.md:
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- Q16_16 for scoring (§1.4)
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- PascalCase types, camelCase functions (§2)
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- Theorems for correctness (§4)
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- No proof placeholders in committed code (§1.6)
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.List.Basic
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namespace Semantics.VirtualGPUTopology
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Q16.16 Fixed-Point for Scoring
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-- ═══════════════════════════════════════════════════════════════════════════
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structure Q16_16 where
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raw : Int
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deriving Repr, DecidableEq, Inhabited, BEq
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namespace Q16_16
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def zero : Q16_16 := ⟨0⟩
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def one : Q16_16 := ⟨65536⟩
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def ofNat (n : Nat) : Q16_16 := ⟨n * 65536⟩
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def toNat (q : Q16_16) : Nat := q.raw.toNat / 65536
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def ofFrac (num denom : Nat) : Q16_16 :=
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if denom = 0 then zero else ⟨(num * 65536) / denom⟩
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instance : LE Q16_16 := ⟨fun a b => a.raw ≤ b.raw⟩
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instance : LT Q16_16 := ⟨fun a b => a.raw < b.raw⟩
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instance : Add Q16_16 := ⟨fun a b => ⟨a.raw + b.raw⟩⟩
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instance : Sub Q16_16 := ⟨fun a b => ⟨a.raw - b.raw⟩⟩
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instance : Mul Q16_16 := ⟨fun a b => ⟨(a.raw * b.raw) / 65536⟩⟩
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instance : HDiv Q16_16 Q16_16 Q16_16 := ⟨fun a b => ⟨(a.raw * 65536) / b.raw⟩⟩
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end Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Virtual GPU Specification
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-- ═══════════════════════════════════════════════════════════════════════════
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structure VirtualGPUSpec where
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virtualMemoryGb : Q16_16
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compressionRatio : Q16_16
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tensorCores : Nat
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cudaCores : Nat
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manifoldDimensions : Nat
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curvatureNodes : Nat
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bindingCoefficient : Q16_16
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physicalNodes : Nat
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distributedShards : Nat
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effectiveComputeTflops : Q16_16
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effectiveMemoryBandwidthGbps : Q16_16
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deriving Repr, Inhabited
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/-- Initialize virtual GPU based on combined resources. -/
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def initializeVirtualGPU : VirtualGPUSpec :=
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-- From combined_resource_layers.py
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let effectiveMemory := Q16_16.ofFrac 6566 10 -- 656.6 GB with 9.12x expansion
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let compression := Q16_16.ofFrac 16 10 -- 1.6 BIND L3
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-- Compute units
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let physicalCores := 36
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let builderSlots := 144 -- From triumvirate
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let tensorCores := builderSlots
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let cudaCores := physicalCores + (builderSlots / 4)
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-- Topology specs
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let manifoldDims := 4
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let curvaturePts := 10000
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let bindingCoef := Q16_16.ofFrac 95 100 -- 0.95
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-- Distributed across 6 nodes
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let nodes := 6
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-- Estimate effective compute
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let tflopsPerCore := Q16_16.ofFrac 1 10 -- 0.1 TFLOPS per core
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let effectiveTflops := Q16_16.ofNat cudaCores * tflopsPerCore * compression
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-- Memory bandwidth
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let bandwidthPerNode := Q16_16.ofNat 50 -- 50 GB/s
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let effectiveBandwidth := bandwidthPerNode * Q16_16.ofNat nodes * compression
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{
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virtualMemoryGb := effectiveMemory,
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compressionRatio := compression,
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tensorCores := tensorCores,
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cudaCores := cudaCores,
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manifoldDimensions := manifoldDims,
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curvatureNodes := curvaturePts,
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bindingCoefficient := bindingCoef,
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physicalNodes := nodes,
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distributedShards := nodes,
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effectiveComputeTflops := effectiveTflops,
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effectiveMemoryBandwidthGbps := effectiveBandwidth
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Model Shard Structures
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-- ═══════════════════════════════════════════════════════════════════════════
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structure ManifoldCoordinates where
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radial : Q16_16
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angular : Q16_16
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height : Q16_16
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bindingStrength : Q16_16
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deriving Repr, Inhabited
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structure ModelShard where
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shardId : String
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nodeAssignment : String
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tensorCount : Nat
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parameterCount : Nat
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compressionLevel : Q16_16
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manifoldCoordinates : ManifoldCoordinates
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curvatureMatch : Q16_16
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deriving Repr, Inhabited
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structure ModelSpec where
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sizeGb : Q16_16
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params : Nat
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layers : Nat
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deriving Repr, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Model Placement Calculation
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Calculate manifold coordinates for a shard. -/
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def calculateManifoldCoordinates (index : Nat) (totalNodes : Nat) (bindingCoef : Q16_16) : ManifoldCoordinates :=
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let theta := Q16_16.ofFrac (2 * 314159 * index) (100000 * totalNodes) -- Even distribution
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let r := Q16_16.ofFrac 7 10 + (Q16_16.ofFrac 3 10 * bindingCoef) -- Radius based on binding
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{
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radial := r * (Q16_16.one + Q16_16.ofFrac (1 * index) 10),
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angular := theta,
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height := Q16_16.ofFrac 5 10,
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bindingStrength := bindingCoef
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}
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/-- Calculate curvature match for a shard. -/
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def calculateCurvatureMatch (index : Nat) (bindingCoef : Q16_16) : Q16_16 :=
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bindingCoef * (Q16_16.one - Q16_16.ofFrac (5 * index) 100)
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/-- Calculate model placement on manifold topology. -/
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def calculateModelPlacement (spec : VirtualGPUSpec) (modelSizeGb : Q16_16) (modelName : String) : List ModelShard :=
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-- Check if fits in virtual memory
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if modelSizeGb.raw > spec.virtualMemoryGb.raw then []
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else
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let shardSize := modelSizeGb / Q16_16.ofNat spec.distributedShards
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let nodes := ["qfox", "architect", "judge", "ip-172-31-25-81", "netcup-router", "racknerd-510bd9c"]
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let rec buildShards (i : Nat) : List ModelShard :=
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if i ≥ spec.distributedShards then []
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else
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let coords := calculateManifoldCoordinates i spec.distributedShards spec.bindingCoefficient
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let curvatureMatch := calculateCurvatureMatch i spec.bindingCoefficient
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let shard := {
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shardId := s!"{modelName}_shard_{i+1}",
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nodeAssignment := nodes[i % 6]!,
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tensorCount := Q16_16.toNat (shardSize * Q16_16.ofNat 1000),
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parameterCount := Q16_16.toNat (shardSize * Q16_16.ofNat 1000000000 / Q16_16.ofNat 4),
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compressionLevel := spec.compressionRatio,
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manifoldCoordinates := coords,
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curvatureMatch := curvatureMatch
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}
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shard :: buildShards (i + 1)
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buildShards 0
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Kimi Model Loading
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-- ═══════════════════════════════════════════════════════════════════════════
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structure ModelLoadResult where
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model : String
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rawSizeGb : Q16_16
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compressedSizeGb : Q16_16
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compression : Q16_16
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shards : Nat
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shardDistribution : List (String × String)
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placement : String
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curvatureGuided : Bool
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bindingOptimized : Bool
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inferenceLatencyMs : Q16_16
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throughputTokensPerSec : Q16_16
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deriving Repr, Inhabited
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/-- Get model specification by variant. -/
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def getModelSpec (variant : String) : ModelSpec :=
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match variant with
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| "kimi-k1.5-32b" => { sizeGb := Q16_16.ofNat 60, params := 32000000000, layers := 64 }
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| "kimi-k1.5-7b" => { sizeGb := Q16_16.ofNat 14, params := 7000000000, layers := 32 }
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| _ => { sizeGb := Q16_16.ofNat 8, params := 4000000000, layers := 24 }
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/-- Load Kimi model onto virtual GPU topology. -/
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def loadKimiModel (spec : VirtualGPUSpec) (modelVariant : String) : ModelLoadResult :=
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let modelSpec := getModelSpec modelVariant
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let modelSize := modelSpec.sizeGb
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-- Calculate effective size with compression
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let effectiveSize := modelSize / spec.compressionRatio
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-- Place on manifold
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let shards := calculateModelPlacement spec effectiveSize modelVariant
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-- Calculate inference performance
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let shardLatency := Q16_16.ofNat 50 -- ms per token
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let parallelLatency := shardLatency / Q16_16.ofNat spec.distributedShards
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let throughput := Q16_16.ofNat 1000 / parallelLatency
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let shardDist := shards.map (fun s => (s.nodeAssignment, s.shardId))
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{
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model := modelVariant,
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rawSizeGb := modelSize,
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compressedSizeGb := effectiveSize,
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compression := spec.compressionRatio,
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shards := shards.length,
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shardDistribution := shardDist,
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placement := "manifold_topology",
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curvatureGuided := true,
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bindingOptimized := true,
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inferenceLatencyMs := parallelLatency,
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throughputTokensPerSec := throughput
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Example Usage
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval initializeVirtualGPU
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#eval calculateManifoldCoordinates 0 6 (Q16_16.ofFrac 95 100)
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#eval calculateCurvatureMatch 0 (Q16_16.ofFrac 95 100)
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#eval loadKimiModel initializeVirtualGPU "kimi-4b"
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end Semantics.VirtualGPUTopology
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