File size: 9,546 Bytes
d4fff7c | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 | """
Wave Processor — Meaning Resolution via Interference.
Instead of softmax attention, ambiguity is resolved through wave
interference patterns. Constructive interference amplifies the
"correct" interpretation; destructive interference suppresses
alternatives.
This is inspired by how holograms work — information is encoded
in interference patterns, not in individual beams.
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np
from typing import Tuple, Optional
from .particle import ParticleState
from ..utils.math_utils import complex_wave, phase_coherence, resonance_detect
class WaveProcessor(nn.Module):
"""Process information via wave interference.
Key insight: when multiple particles are "in phase" (semantically
aligned), their waves constructively interfere, amplifying their
shared meaning. When "out of phase," they destructively interfere,
suppressing noise.
This replaces the softmax(Q·K^T)·V computation in Transformers.
"""
def __init__(
self,
d_semantic: int = 256,
n_wave_heads: int = 8,
d_wave: int = 32,
):
super().__init__()
self.d_semantic = d_semantic
self.n_heads = n_wave_heads
self.d_wave = d_wave
# Wave generation — particles emit waves based on their state
self.wave_generator = nn.Sequential(
nn.Linear(d_semantic, n_wave_heads * d_wave * 2), # amplitude + phase
nn.GELU(),
)
# Wave reception — particles decode received waves
self.wave_receiver = nn.Sequential(
nn.Linear(n_wave_heads * d_wave, d_semantic),
nn.GELU(),
)
# Resonance detector — finds standing wave patterns
self.resonance_net = nn.Sequential(
nn.Linear(d_wave, 64),
nn.GELU(),
nn.Linear(64, 1),
nn.Sigmoid(),
)
# Interference decoder — extracts meaning from interference
self.interference_decoder = nn.Sequential(
nn.Linear(d_wave * 2, d_wave),
nn.GELU(),
nn.Linear(d_wave, d_wave),
)
def forward(self, particles: ParticleState) -> Tuple[torch.Tensor, dict]:
"""Process particles via wave interference.
Returns:
output: Processed semantic representation [batch, seq, d_semantic]
diagnostics: Wave processing diagnostics
"""
batch, seq_len, _ = particles.semantic.shape
device = particles.semantic.device
# === Step 1: Generate waves from particles ===
wave_params = self.wave_generator(particles.semantic)
wave_params = wave_params.reshape(batch, seq_len, self.n_heads, self.d_wave, 2)
amplitudes = torch.sigmoid(wave_params[..., 0]) # [batch, seq, heads, d_wave]
phases = wave_params[..., 1] * np.pi # [batch, seq, heads, d_wave]
# Modulate amplitude by particle's own amplitude
amplitudes = amplitudes * particles.amplitude.unsqueeze(-1).unsqueeze(-1)
# === Step 2: Create complex waves ===
waves = amplitudes * torch.exp(1j * phases) # [batch, seq, heads, d_wave]
# === Step 3: Compute interference patterns ===
# For each head, compute the total wave field
# This is the sum of all particle waves at each point
# Total field at each position = sum of all other particles' waves
# received at this position (with distance-based phase shift)
# Simplified: interference = sum of waves weighted by phase alignment
# Phase alignment between particles i and j = cos(phase_i - phase_j)
phase_i = phases.unsqueeze(3) # [batch, seq, 1, heads, d_wave]
phase_j = phases.unsqueeze(2) # [batch, 1, seq, heads, d_wave]
phase_diff = phase_i - phase_j # [batch, seq, seq, heads, d_wave]
# Interference factor: constructive (+1) or destructive (-1)
interference = torch.cos(phase_diff) # [batch, seq, seq, heads, d_wave]
# Amplitude-weighted interference
amp_i = amplitudes.unsqueeze(3)
amp_j = amplitudes.unsqueeze(2)
weighted_interference = interference * amp_i * amp_j
# Sum over source particles → received interference at each position
received = weighted_interference.sum(dim=2) # [batch, seq, heads, d_wave]
# === Step 4: Detect resonances ===
# Resonances are standing wave patterns — stable meanings
resonance_scores = self.resonance_net(received) # [batch, seq, heads, d_wave, 1]
resonance_scores = resonance_scores.squeeze(-1)
# Weight received waves by resonance
resonant_waves = received * resonance_scores.unsqueeze(-1)
# === Step 5: Decode interference patterns ===
# Split into real and imaginary parts for processing
received_real = resonant_waves.real
received_imag = resonant_waves.imag
# Decode meaning from interference
decoded = self.interference_decoder(
torch.cat([received_real, received_imag], dim=-1)
) # [batch, seq, heads, d_wave]
# Flatten heads
decoded = decoded.reshape(batch, seq_len, self.n_heads * self.d_wave)
# Final projection
output = self.wave_receiver(decoded)
# === Diagnostics ===
coherence = phase_coherence(particles.phase)
diagnostics = {
'coherence': coherence.mean().item(),
'mean_amplitude': amplitudes.mean().item(),
'resonance_strength': resonance_scores.mean().item(),
}
return output, diagnostics
class WaveAttention(nn.Module):
"""Wave-based alternative to standard attention.
Instead of: softmax(Q·K^T/√d)·V
We compute: interference_pattern(waves)·V
Key differences:
1. No quadratic matrix — waves propagate linearly
2. Phase-based selection — not softmax
3. Constructive/destructive interference — not weighted average
"""
def __init__(self, d_model: int = 256, n_heads: int = 8):
super().__init__()
self.d_model = d_model
self.n_heads = n_heads
self.d_head = d_model // n_heads
# Wave generation (replaces Q, K projections)
self.emit_proj = nn.Linear(d_model, n_heads * self.d_head * 2) # amp + phase
# Value projection (same as Transformer — values are values)
self.v_proj = nn.Linear(d_model, d_model)
# Output projection
self.out_proj = nn.Linear(d_model, d_model)
# Learned wavelength (how far waves travel)
self.wavelength = nn.Parameter(torch.ones(n_heads) * 2.0)
def forward(self, x: torch.Tensor, mask: Optional[torch.Tensor] = None) -> torch.Tensor:
"""Wave-based attention.
Args:
x: [batch, seq, d_model]
mask: [batch, seq, seq] optional attention mask
Returns:
output: [batch, seq, d_model]
"""
batch, seq, _ = x.shape
# Generate waves
wave_params = self.emit_proj(x)
wave_params = wave_params.reshape(batch, seq, self.n_heads, self.d_head, 2)
amplitudes = torch.sigmoid(wave_params[..., 0])
phases = wave_params[..., 1] * np.pi
# Values
V = self.v_proj(x).reshape(batch, seq, self.n_heads, self.d_head)
# Compute interference between all pairs
# Phase difference
p_i = phases.unsqueeze(2) # [batch, seq_i, 1, heads, d_head]
p_j = phases.unsqueeze(1) # [batch, 1, seq_j, heads, d_head]
# Distance-based phase shift (waves travel and phase-shift)
positions = torch.arange(seq, device=x.device, dtype=torch.float32)
dist = (positions.unsqueeze(0) - positions.unsqueeze(1)).abs() # [seq, seq]
# Phase shift = 2π * distance / wavelength
wavelength = self.wavelength.view(1, 1, 1, self.n_heads, 1)
phase_shift = 2 * np.pi * dist.unsqueeze(-1).unsqueeze(-1) / wavelength
# Total phase difference (emitter phase + travel phase - receiver phase)
total_phase_diff = p_j + phase_shift - p_i
# Interference factor
interference = torch.cos(total_phase_diff) # [batch, seq, seq, heads, d_head]
# Amplitude-weighted
amp_i = amplitudes.unsqueeze(2)
amp_j = amplitudes.unsqueeze(1)
weights = (interference * amp_i * amp_j).sum(dim=-1) # [batch, seq, seq, heads]
weights = weights / (self.d_head ** 0.5)
if mask is not None:
weights = weights.masked_fill(mask.unsqueeze(-1) == 0, float('-inf'))
# Normalize (like softmax but based on wave physics)
weights = F.softmax(weights, dim=2)
# Apply to values
V_expanded = V.transpose(1, 2) # [batch, heads, seq, d_head]
weights_t = weights.permute(0, 3, 1, 2) # [batch, heads, seq_i, seq_j]
output = torch.bmm(weights_t, V_expanded) # [batch, heads, seq, d_head]
# Reshape and project
output = output.transpose(1, 2).reshape(batch, seq, self.d_model)
return self.out_proj(output)
|