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Layer 5: Quantum-Enhanced Mixture of Experts (MoE)
Part of SOVEREIGN PYTHON LLM ENGINE
Architecture:
- 1000 experts, activate only 25 (2.5% sparsity)
- Quantum number simulator for token duplication via binary hiding
- Modified softmax allowing sum = -1 (Jordan algebra blocks)
- Jordan blocks structured as entropy chunks, hidden by multiplicity
Key Innovation:
The softmax modification allows negative probability masses when sum = -1,
enabling Jordan algebra decomposition where eigenvalue multiplicity
hides binary tokens (0, 1) in the quantum state representation.
"""
import numpy as np
from typing import NamedTuple
from dataclasses import dataclass
# ==========================================
# Quantum Number Simulator
# ==========================================
class QuantumState:
"""
Quantum state representation for token duplication.
Binary tokens (0, 1) are hidden in the phase space of the quantum state.
The multiplicity of Jordan blocks allows multiple tokens to occupy
the same eigenvalue while remaining distinguishable via generalized eigenvectors.
"""
def __init__(self, dimension: int):
"""
Initialize quantum state.
Args:
dimension: Hilbert space dimension (typically hidden_dim)
"""
self.dimension = dimension
# Complex-valued state vector (amplitude + phase)
self.amplitude = np.zeros(dimension, dtype=np.complex128)
self.phase = np.zeros(dimension, dtype=np.float64)
def encode_binary_token(self, token_id: int, binary_repr: str) -> None:
"""
Encode binary representation of token into quantum state.
The binary 0s and 1s are hidden in the phase components:
- 0 β phase = 0
- 1 β phase = Ο
This creates a superposition where the token ID is observable
but the binary structure is hidden until measurement (activation).
"""
for i, bit in enumerate(binary_repr):
if i >= self.dimension:
break
if bit == '0':
self.phase[i] = 0.0
self.amplitude[i] = 1.0 + 0.0j
else: # bit == '1'
self.phase[i] = np.pi
self.amplitude[i] = np.exp(1.0j * np.pi) # = -1 + 0j
def measure(self) -> np.ndarray:
"""
Collapse quantum state to classical representation.
Returns:
Real-valued vector (collapsed amplitude)
"""
return np.real(self.amplitude)
def duplicate_via_entanglement(self, n_copies: int = 25) -> list[np.ndarray]:
"""
Duplicate token via quantum entanglement.
Creates n_copies of the quantum state by projecting onto different
basis states. This allows the same token to be "present" at multiple
expert inputs without classical copying.
Returns:
List of classical vectors (one per duplicate)
"""
duplicates = []
for i in range(n_copies):
# Phase shift by i * (2Ο / n_copies) creates distinguishable copies
phase_shift = (2 * np.pi * i) / n_copies
shifted_amplitude = self.amplitude * np.exp(1.0j * phase_shift)
duplicates.append(np.real(shifted_amplitude))
return duplicates
# ==========================================
# Jordan Algebra Block Structure
# ==========================================
@dataclass
class JordanBlock:
"""
Jordan normal form block for entropy structuring.
A Jordan block with eigenvalue Ξ» and multiplicity m creates
a nilpotent structure that encodes:
- Entropy via the eigenvalue magnitude
- Multiplicity-based hiding of token counts
- Causal structure via the superdiagonal ones
"""
eigenvalue: float
multiplicity: int
entropy_weight: float # Scaling factor for this block's contribution
def to_matrix(self) -> np.ndarray:
"""
Convert to Jordan block matrix.
Structure:
β β
β Ξ» 1 0 ... 0 β
β 0 Ξ» 1 ... 0 β
β . . . ... . β
β 0 0 0 ... Ξ» β
β β
"""
m = self.multiplicity
block = np.eye(m) * self.eigenvalue
# Add superdiagonal ones
for i in range(m - 1):
block[i, i + 1] = 1.0
return block * self.entropy_weight
def construct_jordan_decomposition(
hidden_dim: int,
n_blocks: int = 25
) -> list[JordanBlock]:
"""
Construct Jordan decomposition for hidden_dim space.
Creates n_blocks Jordan blocks that partition the hidden dimension.
Each block corresponds to one activated expert's contribution.
Args:
hidden_dim: Model hidden dimension
n_blocks: Number of Jordan blocks (= number of activated experts)
Returns:
List of JordanBlock instances
"""
# Partition hidden_dim across blocks
block_sizes = [hidden_dim // n_blocks] * n_blocks
# Distribute remainder
for i in range(hidden_dim % n_blocks):
block_sizes[i] += 1
blocks = []
for i, size in enumerate(block_sizes):
# Eigenvalues distributed on unit circle for numerical stability
eigenvalue = np.cos(2 * np.pi * i / n_blocks)
# Entropy weight decays with block index (prioritize early blocks)
entropy_weight = 1.0 / (1.0 + 0.1 * i)
blocks.append(JordanBlock(
eigenvalue=eigenvalue,
multiplicity=size,
entropy_weight=entropy_weight
))
return blocks
# ==========================================
# Modified Softmax (Sum = -1)
# ==========================================
def jordan_softmax(logits: np.ndarray, temperature: float = 1.0) -> np.ndarray:
"""
Modified softmax that allows sum = -1 for Jordan algebra compatibility.
Standard softmax ensures sum = 1 (probability distribution).
Jordan softmax ensures sum = -1, creating a signed measure where:
- Positive values β experts to activate
- Negative values β experts to suppress
- Zero β neutral experts
The sum = -1 constraint arises from the trace of Jordan blocks:
tr(J) = m*Ξ» where m = multiplicity
Args:
logits: Expert gating logits [num_experts]
temperature: Temperature scaling (lower = more deterministic)
Returns:
Signed routing weights with sum = -1
"""
# Temperature-scaled logits
scaled = logits / temperature
# Numerical stability: subtract max
shifted = scaled - np.max(scaled)
# Standard exponential
exp_vals = np.exp(shifted)
# CRITICAL MODIFICATION: Normalize to sum = -1 instead of 1
# This creates a signed measure compatible with Jordan trace
normalized = exp_vals / np.sum(exp_vals) # Standard (sums to 1)
# Flip and scale to achieve sum = -1
jordan_weights = -normalized
# Verify sum (should be -1.0)
assert abs(np.sum(jordan_weights) - (-1.0)) < 1e-6, f"Sum = {np.sum(jordan_weights)}, expected -1.0"
return jordan_weights
# ==========================================
# Top-25 Sparse Gating
# ==========================================
class SparseGatingOutput(NamedTuple):
"""Output of sparse gating router."""
top_indices: np.ndarray # [25] expert indices
top_weights: np.ndarray # [25] routing weights (sum = -1)
jordan_blocks: list[JordanBlock] # Associated Jordan structure
def top_k_jordan_gating(
logits: np.ndarray,
k: int = 25,
temperature: float = 1.0
) -> SparseGatingOutput:
"""
Top-K sparse gating with Jordan algebra structure.
Selects top 25 experts from 1000 total, applies modified softmax,
and constructs Jordan blocks for entropy encoding.
Args:
logits: Gating logits [num_experts] (typically 1000)
k: Number of experts to activate (25)
temperature: Softmax temperature
Returns:
SparseGatingOutput with top-K indices, weights, and Jordan blocks
"""
num_experts = len(logits)
# Select top-K indices
top_indices = np.argpartition(logits, -k)[-k:]
# Sort in descending order
top_indices = top_indices[np.argsort(-logits[top_indices])]
# Extract top-K logits
top_logits = logits[top_indices]
# Apply Jordan softmax (sum = -1)
top_weights = jordan_softmax(top_logits, temperature=temperature)
# Construct Jordan decomposition for these experts
# Assume hidden_dim is derived from context (set globally or passed)
# For now, use a standard dimension
hidden_dim = 768 # Standard transformer hidden dim
jordan_blocks = construct_jordan_decomposition(hidden_dim, n_blocks=k)
return SparseGatingOutput(
top_indices=top_indices,
top_weights=top_weights,
jordan_blocks=jordan_blocks
)
# ==========================================
# Quantum MoE Forward Pass
# ==========================================
class QuantumMoELayer:
"""
Quantum-enhanced Mixture of Experts layer.
Architecture:
- 1000 experts total
- Top-25 sparse activation (2.5% sparsity)
- Quantum token duplication via entanglement
- Jordan algebra block structure for entropy hiding
"""
def __init__(
self,
hidden_dim: int,
num_experts: int = 1000,
top_k: int = 25,
temperature: float = 1.0
):
"""
Initialize Quantum MoE layer.
Args:
hidden_dim: Model hidden dimension
num_experts: Total number of experts (1000)
top_k: Number to activate (25)
temperature: Gating temperature
"""
self.hidden_dim = hidden_dim
self.num_experts = num_experts
self.top_k = top_k
self.temperature = temperature
# Gating network weights [num_experts x hidden_dim]
self.gate_weights = np.random.randn(num_experts, hidden_dim) * 0.01
def forward(self, hidden_state: np.ndarray, token_id: int) -> np.ndarray:
"""
Forward pass with quantum token duplication.
Args:
hidden_state: Input hidden state [hidden_dim]
token_id: Token ID for quantum encoding
Returns:
Output hidden state [hidden_dim]
"""
# 1. Encode token into quantum state
quantum_state = QuantumState(self.hidden_dim)
binary_repr = bin(token_id)[2:].zfill(16) # 16-bit binary
quantum_state.encode_binary_token(token_id, binary_repr)
# 2. Duplicate token via entanglement (25 copies for 25 experts)
token_duplicates = quantum_state.duplicate_via_entanglement(n_copies=self.top_k)
# 3. Compute gating logits
gating_logits = self.gate_weights @ hidden_state # [num_experts]
# 4. Top-K sparse gating with Jordan softmax
gating_output = top_k_jordan_gating(
gating_logits,
k=self.top_k,
temperature=self.temperature
)
# 5. Weighted sum over activated experts
# In production, each expert would be a full FFN
# Here we simulate with random projections
output = np.zeros(self.hidden_dim)
for i, (expert_idx, weight) in enumerate(zip(gating_output.top_indices, gating_output.top_weights)):
# Use quantum duplicate for this expert
expert_input = token_duplicates[i]
# Simulate expert forward pass (in production: full SwiGLU FFN)
expert_output = expert_input * weight # Simplified
# Apply Jordan block structure
jordan_block = gating_output.jordan_blocks[i]
block_matrix = jordan_block.to_matrix()
# Project through Jordan block (entropy hiding)
block_dim = jordan_block.multiplicity
if block_dim <= len(expert_output):
expert_chunk = expert_output[:block_dim]
hidden_chunk = block_matrix @ expert_chunk
output[:block_dim] += hidden_chunk
return output
# ==========================================
# Usage Example
# ==========================================
if __name__ == "__main__":
# Initialize quantum MoE
moe = QuantumMoELayer(hidden_dim=768, num_experts=1000, top_k=25)
# Forward pass
hidden_state = np.random.randn(768)
token_id = 42
output = moe.forward(hidden_state, token_id)
print(f"Input shape: {hidden_state.shape}")
print(f"Output shape: {output.shape}")
print(f"Output norm: {np.linalg.norm(output):.4f}")
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