Neuroplastic Transfer Learning: LNN / Transformer Hybrids
This is an original experiment I've done and wanted to share the architecture - it's not the latest work, but it shows the direction I'm heading with teaching and informing a Liquid Time Constant neuron to take the place of the perceptron, attention heads and final hidden layers and eventually learn to "be" a transformer, except with a twist: It continuously learns.
This experiment doesn't have deep layers so the learning is surface level - and much of the subsequent work I've done shows that learning slowly or allowing internal reflection on what's learned is important with LTC neurons.
Some of the work here was prophetic - the human brain uses localized synchronization of time and works in groups. My concept was to take recent inferences from the transformer side and cache the tokens in a container and hold it there until the liquid neurons could replicate what was learned. Since the embeddings are laid out in predictable blocks, I thought of a shared memory manager and threads that have hashed identities with pointers to the "cube" of embeddings.
The cubes of data would in theory do transfer learning over time from the transformer and predict the outputs based on past activations. In this hybrid architecture, the LNN gradually influences the outputs of the transformer based, leveraging its strengths with attention and having neuroplastic properties, can adapt over time and make new predictions. My experiments later on on Hebian layers and high precision floating point required for deep learning came later.
Future plans
The original design was to have the cube of inference to have the liquid neurons take over inference for that block and switch off the gate and become a fully mentored LNN matrix.
Cubes would also solve the limitations of the LNNs requiring the whole block of neurons being computed together. By breaking up the inference into chunks and having parallel processing of the chunks, you essentially have a distributed LNN which may be able to take advantage of multiprocessing and threading. This was refined later on, but this does make for an interesting demonstration of how this may happen.
This Python implementation is more or less a proof leading to the Kotlin port which will use Kotlin's actor and channel system to allow LangChain-like interface design with "virtual dendrites" and virtual cortical connections for blocks.
The blocks would then have hybridized LNN/Transformer feed forwards to other blocks and so on, similar to the layering built up in the human brain and leveraging a sort of phonological loop of reflection which strengthens the learning. This part of the design is still pure theory.
Introduction
This paper explores the integration of Transformer and Liquid Neural Network (LNN) architectures, building upon foundational work by Hasani et al. (2020). The key innovation lies in combining the parallel processing capabilities of Transformers with the adaptive dynamics of LNNs.
Mathematical Framework
1. Core LNN Dynamics
Building on recent advances in closed-form continuous-time neural networks (Hasani et al., 2022), we start with the fundamental LNN equation (apologies for the lack of mathematical equation support on LinkedIn):
dx(t)dt=?[1τ+f(x(t),I(t),t,θ)]x(t)+f(x(t),I(t),t,θ)A
Which has the approximate closed-form solution:
x(t)≈(x0?A)e?(wτ+f(I(t),θ))tf(?I(t))+A
This formulation provides several key advantages:
Where:
2. Bounded Dynamics Proof
Key theorem from Hasani et al. (2020):
This guarantees stable system dynamics even with unbounded inputs.
Proposed Architecture Enhancement
Integration with Transformer Blocks
My approach involves implementing this through:
Where:
Cube-to-Cube Communication:
C?? = f(W?C? + W?C?)
Dynamic Time Constants
Building on Hasani's work, we introduce variable time constants:
τ??? = τ? + τf(x(t), I(t), t, θ)
This allows for adaptive computation based on input complexity.
Experimental Validation
Our implementation builds on proven performance metrics from Hasani et al.:
fused_solver_step(x, I, Δt, θ) = x + Δt f(x, I, t, θ)A / (1 + Δt(1/τ + f(x, I, t, θ)))
Theoretical Foundations
Building on established theory from Hasani et al., we prove:
Theorem 1: The combined Transformer-LNN system maintains bounded stability under the conditions:
Proof sketch:
Given the Lyapunov function V(x) = ∥x∥2, we show: dV/dt ≤ 0 under the above conditions.
Appendix: Implementation Guidelines
Stability Constraints
For system stability, maintain:
Implementation
I am primarily using a Transformer architecture combined with a novel liquid neural network approach. Specifically, we are using several key transformer components:
领英推荐
self.attention = nn.MultiheadAttention(hidden_size, num_heads, dropout=dropout)
The innovative aspect is that I'm combining these Transformer components with Liquid Neural Networks (from Hasani et al.'s work), which isn't on the list but represents a novel architecture that uses continuous-time neural dynamics.
Key components from our implementation:
class TransformerLNN(nn.Module):
def __init__(self, input_size, hidden_size, num_heads=4):
# Transformer components
self.attention = nn.MultiheadAttention(...)
# LNN components
self.ltc = LiquidTimeConstant(...)
This is a hybrid architecture that combines:
So while "Transformer" is the base architecture, I'm extending it significantly with the liquid neural network approach for handling temporal dynamics.
I'll break down each section of my experiment and explain what it's doing and how:
Data Generation & Processing
Generate synthetic data with multiple patterns
def generate_synthetic_data(num_samples=1000, seq_length=50, input_dim=10):
# Create time steps
t = torch.linspace(0, 10, seq_length)
# Generate diverse patterns (sine waves with different frequencies)
patterns = []
for i in range(input_dim):
freq1, freq2 = (i + 1) * 0.5, (i + 1) * 0.25
pattern = torch.sin(2 * np.pi * freq1 * t) + \
0.5 * torch.sin(2 * np.pi * freq2 * t)
patterns.append(pattern)
What: Creates synthetic sequential data with multiple overlapping patterns How: Combines sine waves of different frequencies to create complex temporal patterns Why: Provides controlled data to test the model's ability to learn temporal dependencies
Model Architecture
class TransformerLNN(nn.Module): def init(self, input_size, hidden_size, num_heads):
# Transformer component for parallel processing
self.attention = nn.MultiheadAttention(...)
# LNN component for temporal dynamics
self.ltc = LiquidTimeConstant(...)
What: Hybrid architecture combining Transformer attention with liquid neural networks How:
Training Loop
for epoch in range(NUM_EPOCHS):
for batch_idx, (x, y) in enumerate(train_loader):
# Forward pass
y_pred = model(x)
loss = criterion(y_pred, y)
# Backward pass
optimizer.zero_grad()
loss.backward()
optimizer.step()
# Visualization updates
if batch_idx % visualizer.save_intervals == 0:
update_visualizations()
What: Trains the model while tracking multiple metrics How:
The key innovation here is how it combines:
LiquidTimeConstant (LTC) Class?
Core components
Forward pass:
import torch
import torch.nn as nn
import numpy as np
from typing import Optional, Tuple
class LiquidTimeConstant(nn.Module):
"""
Implements time-aware processing with dynamic memory
Like a smart system that knows how to balance past and present information
"""
def __init__(self, input_size: int, hidden_size: int):
super().__init__()
self.input_size = input_size
self.hidden_size = hidden_size
# BACKBONE NETWORK
# Core feature extraction - like a smart filter
self.backbone = nn.Sequential(
nn.Linear(input_size + hidden_size, hidden_size),
nn.Tanh(), # Smooth activation for stability
nn.Linear(hidden_size, hidden_size)
)
# TEMPORAL PROCESSING NETWORKS
# Time-aware processing mechanisms
# Controls how time influences processing
self.time_net = nn.Linear(hidden_size, hidden_size)
# Transform state for short-term memory
self.state_net_g = nn.Linear(hidden_size, hidden_size)
# Transform state for long-term memory
self.state_net_h = nn.Linear(hidden_size, hidden_size)
# LEARNABLE PARAMETERS
# Time constants - control information flow speed
self.tau = nn.Parameter(torch.ones(hidden_size))
# Bias terms - help network learn better
self.A = nn.Parameter(torch.randn(hidden_size))
def forward(self,
x: torch.Tensor, # Current input
h: torch.Tensor, # Memory state
t: torch.Tensor # Time information
) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Updates memory state based on new information and time
Like dynamically updating notes as you get new information
"""
# Combine current input with memory
combined = torch.cat([x, h], dim=-1)
# Extract features
features = self.backbone(combined)
# TEMPORAL GATING
# Compute how much time should influence the update
f_t = torch.sigmoid(self.time_net(features))
# STATE TRANSFORMATIONS
# Process for different timescales
g_x = self.state_net_g(features) # Short-term
h_x = self.state_net_h(features) # Long-term
# TIME-DEPENDENT GATING
# Decide how to blend different timescales
gate = torch.sigmoid(-f_t * t.view(-1, 1))
# MEMORY UPDATE
# Blend short and long-term information
h_new = gate * g_x + (1 - gate) * h_x
return h_new, h_new
TransformerLNN Class?
Core components
Forward pass:
import torch
import torch.nn as nn
import torch.optim as optim
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import clear_output
import seaborn as sns
from typing import List, Dict, Optional
from datetime import datetime
class TrainingVisualizer:
def __init__(self, save_intervals: int = 10, plot_intervals: int = 5):
self.save_intervals = save_intervals
self.plot_intervals = plot_intervals
# History tracking
self.losses: List[float] = []
self.accuracies: List[float] = []
self.ltc_states: List[torch.Tensor] = []
self.attn_weights: List[torch.Tensor] = []
self.timestamps: List[str] = []
def update_metrics(self, loss: float, accuracy: float,
ltc_state: torch.Tensor, attn_weights: torch.Tensor):
"""Update training metrics"""
self.losses.append(loss)
self.accuracies.append(accuracy)
self.ltc_states.append(ltc_state.detach().cpu())
self.attn_weights.append(attn_weights.detach().cpu())
self.timestamps.append(datetime.now().strftime("%H:%M:%S"))
def plot_training_progress(self, epoch: int, batch_idx: int, x: torch.Tensor, y: torch.Tensor, y_pred: torch.Tensor):
"""Plot comprehensive training visualizations"""
# Convert tensors to 2D by taking first channel/feature
x_plot = x[:, :, 0].cpu().detach().numpy() # Take first feature dimension
y_plot = y[:, :, 0].cpu().detach().numpy()
y_pred_plot = y_pred[:, :, 0].cpu().detach().numpy()
clear_output(wait=True)
plt.figure(figsize=(20, 12))
# Plot actual visualizations using 2D data
plt.subplot(231)
plt.plot(self.losses[-100:], label='Training Loss', color='blue')
plt.title(f'Loss Curve (Current: {self.losses[-1]:.4f})')
plt.xlabel('Last 100 Steps')
plt.ylabel('Loss')
plt.grid(True)
# Use the 2D versions for prediction plots
plt.subplot(235)
idx = 0 # Plot first sequence in batch
plt.plot(y_plot[idx], label='Ground Truth', color='blue', alpha=0.7)
plt.plot(y_pred_plot[idx], label='Prediction', color='red', alpha=0.7)
plt.title('Prediction vs Ground Truth')
plt.xlabel('Sequence Step')
plt.ylabel('Value')
plt.legend()
plt.grid(True)
def generate_synthetic_data(num_samples: int = 1000,
seq_length: int = 50,
input_dim: int = 10,
device: str = 'cuda' if torch.cuda.is_available() else 'cpu'
) -> tuple[torch.Tensor, torch.Tensor]:
"""Generate synthetic sequence data with multiple patterns"""
# Time steps
t = torch.linspace(0, 10, seq_length, device=device)
t = t.view(1, -1, 1).repeat(num_samples, 1, input_dim)
# Generate diverse patterns
patterns = []
for i in range(input_dim):
# Combine sine waves with different frequencies
freq1 = (i + 1) * 0.5
freq2 = (i + 1) * 0.25
pattern = torch.sin(2 * np.pi * freq1 * t[..., i]) + \
0.5 * torch.sin(2 * np.pi * freq2 * t[..., i])
patterns.append(pattern)
# Combine patterns
x = torch.stack(patterns, dim=-1)
# Create target with transformations
y = torch.roll(x, shifts=-1, dims=1) * 1.5 + 0.5
return x, y
def train_epoch(model: nn.Module,
train_loader: torch.utils.data.DataLoader,
criterion: nn.Module,
optimizer: torch.optim.Optimizer,
device: str,
visualizer,
epoch: int) -> float:
"""Train for one epoch"""
model.train()
total_loss = 0
for batch_idx, (x, y) in enumerate(train_loader):
x, y = x.to(device), y.to(device)
optimizer.zero_grad()
# Forward pass
y_pred = model(x)
loss = criterion(y_pred, y)
# Backward pass
loss.backward()
optimizer.step()
total_loss += loss.item()
# Update visualizations
if batch_idx % visualizer.save_intervals == 0:
with torch.no_grad():
# Get model states
ltc_state, _ = model.ltc(
model.input_proj(x[0:1]),
torch.zeros(1, model.hidden_size, device=device),
torch.zeros(1, device=device)
)
attn_weights = model.get_attention_weights(x[0:1])
# Compute accuracy
mse = ((y_pred - y) ** 2).mean().item()
accuracy = 100 * (1 - min(mse, 1))
# Update visualizer
visualizer.update_metrics(loss.item(), accuracy, ltc_state, attn_weights)
# Plot progress
if batch_idx % visualizer.plot_intervals == 0:
visualizer.plot_training_progress(epoch, batch_idx, x, y, y_pred)
return total_loss / len(train_loader)
Setup Training Parameters
import torch
import torch.nn as nn
import torch.optim as optim
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
# Model parameters
INPUT_SIZE = 10
HIDDEN_SIZE = 64
NUM_HEADS = 4
# Training parameters
BATCH_SIZE = 32
LEARNING_RATE = 1e-3
NUM_EPOCHS = 50
# Data parameters
NUM_SAMPLES = 1000
SEQ_LENGTH = 50
# Device configuration
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
print(f"Using device: {device}")
Generate Training Data
# Generate training data
x_train, y_train = TrainingVisualizer.generate_synthetic_data(
num_samples=NUM_SAMPLES,
seq_length=SEQ_LENGTH,
input_dim=INPUT_SIZE,
device=device
)
# Create dataloader
train_dataset = torch.utils.data.TensorDataset(x_train, y_train)
train_loader = torch.utils.data.DataLoader(
train_dataset,
batch_size=BATCH_SIZE,
shuffle=True
)
# Plot sample sequence
plt.figure(figsize=(12, 4))
plt.plot(x_train[0, :, 0].cpu().numpy(), label='Input')
plt.plot(y_train[0, :, 0].cpu().numpy(), label='Target')
plt.title('Sample Sequence')
plt.legend()
plt.grid(True)
plt.show()
Create and Initialize Model
# Initialize model
model = TransformerLNN(
input_size=INPUT_SIZE,
hidden_size=HIDDEN_SIZE,
num_heads=NUM_HEADS
).to(device)
# Loss and optimizer
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=LEARNING_RATE)
# Initialize visualizer
visualizer = TrainingVisualizer()
Training Loop with Visualization
for epoch in range(NUM_EPOCHS):
model.train()
epoch_loss = 0
for batch_idx, (x, y) in enumerate(train_loader):
# Forward pass
y_pred = model(x)
loss = criterion(y_pred, y)
# Backward pass
optimizer.zero_grad()
loss.backward()
optimizer.step()
epoch_loss += loss.item()
# Update visualization
if batch_idx % visualizer.save_intervals == 0:
with torch.no_grad():
# Get model states
batch_input = x[0:1] # Shape: [1, seq_len, input_dim]
projected = model.input_proj(batch_input) # Shape: [1, seq_len, hidden_size]
# Take first timestep for LTC state
ltc_input = projected[:, 0, :] # Shape: [1, hidden_size]
ltc_state, _ = model.ltc(
ltc_input,
torch.zeros(1, HIDDEN_SIZE, device=device),
torch.zeros(1, device=device)
)
attn_weights = model.get_attention_weights(batch_input)
# Compute accuracy
mse = ((y_pred - y) ** 2).mean().item()
accuracy = 100 * (1 - min(mse, 1))
# Update visualizer
visualizer.update_metrics(loss.item(), accuracy, ltc_state, attn_weights)
# Plot progress
if batch_idx % visualizer.plot_intervals == 0:
visualizer.plot_training_progress(epoch, batch_idx, x, y, y_pred)
# End of epoch summary
avg_loss = epoch_loss / len(train_loader)
print(f"Epoch {epoch+1}/{NUM_EPOCHS}, Average Loss: {avg_loss:.4f}")
Final Evaluation
# Generate test data
x_test, y_test = TrainingVisualizer.generate_synthetic_data(
num_samples=10,
seq_length=SEQ_LENGTH,
input_dim=INPUT_SIZE,
device=device
)
# Model evaluation
model.eval()
with torch.no_grad():
y_pred = model(x_test)
test_loss = criterion(y_pred, y_test)
# Plot predictions
plt.figure(figsize=(15, 5))
for i in range(3): # Plot first 3 sequences
plt.subplot(1, 3, i+1)
plt.plot(y_test[i, :, 0].cpu().numpy(), label='Ground Truth', alpha=0.7)
plt.plot(y_pred[i, :, 0].cpu().numpy(), label='Prediction', alpha=0.7)
plt.title(f'Sequence {i+1}')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()
print(f"Final Test Loss: {test_loss:.4f}")
Analyze Learning Progression
# Plot training history
plt.figure(figsize=(15, 5))
# Loss progression
plt.subplot(131)
plt.plot(visualizer.losses, label='Training Loss')
plt.title('Loss Progression')
plt.xlabel('Step')
plt.ylabel('Loss')
plt.grid(True)
# Accuracy progression
plt.subplot(132)
plt.plot(visualizer.accuracies, label='Accuracy')
plt.title('Accuracy Progression')
plt.xlabel('Step')
plt.ylabel('Accuracy (%)')
plt.grid(True)
# Final attention pattern
plt.subplot(133)
# Extract a 2D slice from the 3D tensor
attn_weights_2d = visualizer.attn_weights[-1][0].cpu().numpy()
# Plot the 2D attention weights
sns.heatmap(attn_weights_2d, cmap='viridis')
plt.title('Final Attention Pattern')
plt.tight_layout()
plt.show()
View the whole project on Kaggle - this is open source, so feel free to use, modify, sell or whatever (MIT license). There are no warranties here. This is just lab work.