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Brain-like Predictive Coding Code World Model
=============================================
A hierarchical predictive coding network built with Nengo + Numba.
Architecture (inspired by cortical hierarchy):
- L1 (V1-like): Code token embeddings β LIF-rate neurons
- L2 (IT-like): Hidden associative representations
- L3 (PFC-like): Higher-level context / sequence memory
Key brain-like features:
1. LIF-rate neurons β biologically plausible spiking (rate approximation)
2. Top-down predictions β like cortical feedback connections
3. Prediction error minimization β like free-energy principle
4. PES learning β error-driven weight updates (biologically plausible)
5. Numba JIT β acceleration for core kernels
Acceleration (CPU, free):
- Vectorized NumPy + Numba for hot paths
- Nengo backend uses optimized NumPy/BLAS
References:
- Rao & Ballard (1999) "Predictive Coding in the Visual Cortex"
- Friston (2005) "A free energy principle for the brain"
- Eliasmith & Anderson (2003) "Neural Engineering"
"""
import os
os.environ["TF_CPP_MIN_LOG_LEVEL"] = "2"
import numpy as np
import nengo
from numba import njit, prange
from typing import List, Dict
import time
# ============================================================
# NUMBA KERNELS
# ============================================================
@njit(fastmath=True, parallel=True)
def fast_relu(drive: np.ndarray, tau_rc: float = 0.02) -> np.ndarray:
"""LIF rate approximation: rectified linear"""
out = np.empty_like(drive)
inv_tau = 1.0 / tau_rc
for i in prange(drive.shape[0]):
val = drive[i] * inv_tau
out[i] = val if val > 0.0 else 0.0
return out
# ============================================================
# PREDICTIVE CODING LAYER
# ============================================================
class PredictiveCodingLayer:
"""
A single cortical-like layer with:
- Encoder: input β activities (fixed)
- Predictor: higher activities β predicted activities (learned)
- Decoder: activities β reconstructed input (learned)
"""
def __init__(self, name: str, input_dim: int, n_neurons: int,
lr: float = 5e-5, tau_rc: float = 0.02, max_weight: float = 2.0):
self.name = name
self.input_dim = input_dim
self.n_neurons = n_neurons
self.lr = lr
self.tau_rc = tau_rc
self.max_weight = max_weight
# Encoder: input β activities (fixed, scaled)
scale = 1.0 / np.sqrt(input_dim)
self.W_enc = np.random.randn(input_dim, n_neurons).astype(np.float32) * scale
self.b_enc = np.zeros(n_neurons, dtype=np.float32)
# Predictor: higher β this layer activities (learned)
self.W_pred = None
self.b_pred = None
# Decoder: activities β input reconstruction (learned)
self.W_dec = np.random.randn(n_neurons, input_dim).astype(np.float32) * 0.01
self.b_dec = np.zeros(input_dim, dtype=np.float32)
# State
self.activities = np.zeros(n_neurons, dtype=np.float32)
def _clip_weights(self):
"""Clip weights to prevent explosion."""
if self.W_pred is not None:
np.clip(self.W_pred, -self.max_weight, self.max_weight, out=self.W_pred)
np.clip(self.W_dec, -self.max_weight, self.max_weight, out=self.W_dec)
def forward(self, x: np.ndarray, higher: np.ndarray = None) -> tuple:
"""Forward pass. Returns (activities, prediction_error)."""
# Feedforward drive β ReLU (stable rate approximation)
ff = np.dot(x, self.W_enc) + self.b_enc
self.activities = np.maximum(ff, 0).astype(np.float32)
np.clip(self.activities, 0, 10, out=self.activities)
# Top-down prediction error
if higher is not None and self.W_pred is not None:
pred = np.dot(higher, self.W_pred) + self.b_pred
pred_err = self.activities - pred
else:
pred_err = np.zeros(self.n_neurons, dtype=np.float32)
return self.activities, pred_err
def predict(self, higher: np.ndarray) -> np.ndarray:
"""Top-down prediction from higher layer."""
if self.W_pred is not None:
return np.dot(higher, self.W_pred) + self.b_pred
return np.zeros(self.n_neurons, dtype=np.float32)
def decode(self, acts: np.ndarray) -> np.ndarray:
"""Reconstruct input from activities."""
return np.dot(acts, self.W_dec) + self.b_dec
def learn_pred(self, higher: np.ndarray, actual: np.ndarray, predicted: np.ndarray):
"""PES: update prediction weights to reduce error."""
err = actual - predicted
delta = self.lr * np.outer(higher, err)
delta_norm = np.linalg.norm(delta)
if delta_norm > 1.0:
delta /= delta_norm
self.W_pred += delta
self.b_pred += self.lr * err
self._clip_weights()
def learn_dec(self, acts: np.ndarray, target: np.ndarray):
"""Update decoder weights."""
recon = self.decode(acts)
err = target - recon
delta = self.lr * np.outer(acts, err)
delta_norm = np.linalg.norm(delta)
if delta_norm > 1.0:
delta /= delta_norm
self.W_dec += delta
self.b_dec += self.lr * err
self._clip_weights()
# ============================================================
# HIERARCHICAL PREDICTIVE CODING NETWORK
# ============================================================
class PredictiveCodingNetwork:
"""
3-layer hierarchical predictive coding for code sequences.
L3(context) ββpredictsβββ L2(hidden)
β β
βββββββββpredictsββββββββββ L1(sensory)
β
Input (embeddings)
Learning: PES on prediction errors at each layer.
"""
def __init__(self, embed_dim=32, l1_n=128, l2_n=96, l3_n=64,
l1_lr=5e-5, l2_lr=5e-5, l3_lr=5e-5):
self.embed_dim = embed_dim
self.l1 = PredictiveCodingLayer("L1_sensory", embed_dim, l1_n, l1_lr)
self.l2 = PredictiveCodingLayer("L2_hidden", l1_n, l2_n, l2_lr)
self.l3 = PredictiveCodingLayer("L3_context", l2_n, l3_n, l3_lr)
# Top-down prediction weights (scaled init)
scale1 = 1.0 / np.sqrt(l2_n)
self.l1.W_pred = np.random.randn(l2_n, l1_n).astype(np.float32) * scale1 * 0.1
self.l1.b_pred = np.zeros(l1_n, dtype=np.float32)
scale2 = 1.0 / np.sqrt(l3_n)
self.l2.W_pred = np.random.randn(l3_n, l2_n).astype(np.float32) * scale2 * 0.1
self.l2.b_pred = np.zeros(l2_n, dtype=np.float32)
# Context accumulator
self.context = np.zeros(l2_n, dtype=np.float32)
def process_seq(self, seq: np.ndarray, train: bool = True) -> Dict:
"""Process a sequence, optionally training prediction weights."""
T = seq.shape[0]
l1_errs, l2_errs = [], []
preds = []
for t in range(T):
x = seq[t].astype(np.float32)
# Bottom-up pass
l1_acts, l1_err = self.l1.forward(x)
l2_acts, l2_err = self.l2.forward(l1_acts)
# L3 gets L2 + context
l3_input = l2_acts + self.context * 0.05
l3_acts, _ = self.l3.forward(l3_input)
# Top-down predictions
l2_pred = self.l2.predict(l3_acts)
l2_pe = l2_acts - l2_pred
l1_pred = self.l1.predict(l2_acts)
l1_pe = l1_acts - l1_pred
# Decode next input prediction
next_pred = self.l1.decode(l1_acts)
preds.append(next_pred)
# Update context
self.context = 0.92 * self.context + 0.08 * l2_acts
# Learning
if train:
self.l1.learn_pred(l2_acts, l1_acts, l1_pred)
self.l2.learn_pred(l3_acts, l2_acts, l2_pred)
self.l1.learn_dec(l1_acts, x)
self.l2.learn_dec(l2_acts, l1_acts)
self.l3.learn_dec(l3_acts, l3_input)
l1_errs.append(float(np.mean(np.abs(l1_pe))))
l2_errs.append(float(np.mean(np.abs(l2_pe))))
return {
"l1_errors": l1_errs,
"l2_errors": l2_errs,
"predictions": np.array(preds),
}
def predict_next(self, seq: np.ndarray, n_steps: int = 1) -> np.ndarray:
"""Predict next token embeddings."""
self.context = np.zeros_like(self.context)
self.process_seq(seq, train=False)
preds = []
l1_a = self.l1.activities.copy()
l2_a = self.l2.activities.copy()
l3_a = self.l3.activities.copy()
for _ in range(n_steps):
pred_l2 = self.l2.predict(l3_a)
pred_l1 = self.l1.predict(pred_l2)
pred_emb = self.l1.decode(pred_l1)
preds.append(pred_emb)
# Roll forward (using same ReLU activation as forward)
l1_a = np.maximum(np.dot(pred_emb, self.l1.W_enc), 0)
np.clip(l1_a, 0, 10, out=l1_a)
l2_a = np.maximum(np.dot(l1_a, self.l2.W_enc), 0)
np.clip(l2_a, 0, 10, out=l2_a)
l3_a = np.maximum(np.dot(l2_a, self.l3.W_enc), 0)
np.clip(l3_a, 0, 10, out=l3_a)
return np.array(preds)
# ============================================================
# NENGO SPINKING VERSION
# ============================================================
class NengoSpikingPC:
"""Pure Nengo implementation with actual LIF spiking (2-layer demo)."""
def __init__(self, embed_dim=32, l1_n=80, l2_n=60, lr=1e-5):
self.network = nengo.Network(label="PC_Spiking")
with self.network:
self.inp = nengo.Node(np.zeros(embed_dim), label="input")
# Layer 1: sensory
self.ens1 = nengo.Ensemble(
n_neurons=l1_n, dimensions=embed_dim,
neuron_type=nengo.LIF(tau_rc=0.02, tau_ref=0.002),
label="L1"
)
nengo.Connection(self.inp, self.ens1, synapse=0.005)
# Layer 2: associative (higher-level)
self.ens2 = nengo.Ensemble(
n_neurons=l2_n, dimensions=embed_dim,
neuron_type=nengo.LIF(tau_rc=0.02, tau_ref=0.002),
label="L2"
)
# Feedforward
nengo.Connection(self.ens1, self.ens2, synapse=0.005,
function=lambda x: np.zeros(embed_dim))
# Target signal (what we want L1 to represent)
self.target = nengo.Node(np.zeros(embed_dim))
# Top-down prediction connection (learned)
self.conn_pred = nengo.Connection(
self.ens2, self.ens1, synapse=0.005,
function=lambda x: np.zeros(embed_dim),
learning_rule_type=nengo.PES(learning_rate=lr)
)
# Error = target - predicted (via ens1 as proxy for prediction output)
self.error = nengo.Ensemble(
n_neurons=l1_n, dimensions=embed_dim, label="error"
)
nengo.Connection(self.target, self.error, transform=1, synapse=0.005)
nengo.Connection(self.ens1, self.error, transform=-1, synapse=0.005)
nengo.Connection(self.error, self.conn_pred.learning_rule)
# Probes
self.p_l1 = nengo.Probe(self.ens1, synapse=0.01)
self.p_l2 = nengo.Probe(self.ens2, synapse=0.01)
self.p_err = nengo.Probe(self.error, synapse=0.01)
self.p_target = nengo.Probe(self.target, synapse=0.01)
def run(self, seq: np.ndarray, dur_per_step: float = 0.05, dt: float = 0.001) -> Dict:
"""Run Nengo simulation."""
T = seq.shape[0]
def input_fn(t):
step = int(t / dur_per_step)
if step < T:
return seq[step]
return np.zeros(seq.shape[1])
def target_fn(t):
# Target = next timestep's input (predict next token)
step = int(t / dur_per_step)
next_step = step + 1
if next_step < T:
return seq[next_step]
return np.zeros(seq.shape[1])
with self.network:
self.inp.output = input_fn
self.target.output = target_fn
with nengo.Simulator(self.network, dt=dt) as sim:
sim.run(T * dur_per_step)
return {
"l1": sim.data[self.p_l1],
"l2": sim.data[self.p_l2],
"error": sim.data[self.p_err],
"target": sim.data[self.p_target],
"time": sim.trange()
}
# ============================================================
# TOKENIZER
# ============================================================
class SimpleCodeTokenizer:
"""Simple char-level tokenizer."""
def __init__(self, vocab_size: int = 128):
self.vocab_size = vocab_size
special = ['<PAD>', '<UNK>', '<S>', '</S>']
self.c2i = {c: i for i, c in enumerate(special)}
self.i2c = {i: c for i, c in enumerate(special)}
for i in range(32, 127):
if len(self.c2i) < vocab_size:
ch = chr(i)
self.c2i[ch] = len(self.c2i)
self.i2c[len(self.i2c)] = ch
np.random.seed(42)
self.embed = np.random.randn(vocab_size, 32).astype(np.float32) * 0.05
def encode(self, text: str, max_len: int = 16) -> np.ndarray:
tokens = [self.c2i.get(c, 1) for c in text]
if len(tokens) < max_len:
tokens += [0] * (max_len - len(tokens))
return np.array(tokens[:max_len])
def embed_seq(self, token_ids: np.ndarray) -> np.ndarray:
return self.embed[token_ids].astype(np.float32)
def nearest(self, emb: np.ndarray) -> str:
sims = np.dot(self.embed, emb)
return self.i2c.get(int(np.argmax(sims)), '?')
def generate_code(n: int = 50, max_len: int = 16) -> List[str]:
"""Generate synthetic code."""
templates = [
"def {fn}({args}):\n return {ret}",
"if {cond}:\n {stmt}\nelse:\n {stmt2}",
"for {var} in {iter}:\n {body}",
"while {cond}:\n {body}",
"class {cls}:\n def __init__(self):\n pass",
"{var} = {val}\nif {cond}:\n {var} = {val2}",
]
fillers = {
'fn': ['foo', 'bar', 'compute', 'train'],
'args': ['x', 'x, y', 'data'],
'ret': ['x', 'x + y', 'None'],
'cond': ['x > 0', 'len(data) > 0'],
'stmt': ['pass', 'return x', 'print(x)'],
'stmt2': ['pass', 'return None'],
'var': ['i', 'x', 'val'],
'iter': ['range(10)', 'data'],
'body': ['print(x)', 'x += 1', 'pass'],
'cls': ['Model', 'Agent'],
'val': ['0', '1', 'None'],
'val2': ['1', 'None'],
}
samples = []
for _ in range(n):
tmpl = templates[np.random.randint(len(templates))]
try:
s = tmpl.format(**{k: fillers[k][np.random.randint(len(fillers[k]))]
for k in fillers})
except:
s = "def foo():\n return x"
samples.append(s[:max_len])
return samples
# ============================================================
# MAIN
# ============================================================
def main():
print("=" * 68)
print(" π§ Brain-like Predictive Coding Code World Model")
print("=" * 68)
print()
print("Architecture: L3(context) β L2(hidden) β L1(sensory) β Input")
print("Learning: PES error-driven (biologically plausible)")
print("Neurons: LIF-rate (Leaky Integrate-and-Fire)")
print("Acceleration: NumPy vectorized + Numba JIT + Nengo BLAS")
print()
print("=" * 68)
print()
# Config (small for fast CPU demo)
SEQ_LEN = 16
EMBED = 32
N_SAMPLES = 40
EPOCHS = 15
print("[1/4] Creating tokenizer...")
tok = SimpleCodeTokenizer(vocab_size=128)
print("[2/4] Generating synthetic code...")
code = generate_code(n=N_SAMPLES, max_len=SEQ_LEN)
sequences = np.array([tok.embed_seq(tok.encode(c, SEQ_LEN)) for c in code])
print(f" Data: {sequences.shape}")
print("[3/4] Building network (128β96β64 neurons)...")
net = PredictiveCodingNetwork(
embed_dim=EMBED,
l1_n=128, l2_n=96, l3_n=64,
l1_lr=5e-5, l2_lr=5e-5, l3_lr=5e-5
)
print(" β Network built")
print(f"[4/4] Training {N_SAMPLES} samples Γ {EPOCHS} epochs...")
print()
l1_hist, l2_hist, recon_hist = [], [], []
t0 = time.time()
for epoch in range(EPOCHS):
e_l1, e_l2, e_recon = [], [], []
for i in range(N_SAMPLES):
net.context = np.zeros_like(net.context)
r = net.process_seq(sequences[i], train=True)
e_l1.append(np.mean(r["l1_errors"]))
e_l2.append(np.mean(r["l2_errors"]))
# Reconstruction error
preds = r["predictions"]
if len(preds) > 1:
actual_next = sequences[i][1:]
pred_next = preds[:-1]
recon_err = float(np.mean((actual_next - pred_next) ** 2))
e_recon.append(recon_err)
l1_hist.append(float(np.mean(e_l1)))
l2_hist.append(float(np.mean(e_l2)))
recon_hist.append(float(np.mean(e_recon)) if e_recon else 0.0)
if epoch % 3 == 0 or epoch == EPOCHS - 1:
print(f" Epoch {epoch:2d} | L1_err: {l1_hist[-1]:.4f} | "
f"L2_err: {l2_hist[-1]:.4f} | Recon: {recon_hist[-1]:.4f}")
elapsed = time.time() - t0
print(f"\nTraining time: {elapsed:.1f}s ({elapsed/EPOCHS:.1f}s/epoch)")
print()
print("=" * 68)
print("Training Results:")
print(f" L1 prediction: {l1_hist[0]:.4f} β {l1_hist[-1]:.4f}")
print(f" L2 prediction: {l2_hist[0]:.4f} β {l2_hist[-1]:.4f}")
print(f" Reconstruction: {recon_hist[0]:.4f} β {recon_hist[-1]:.4f}")
print("=" * 68)
print()
# Test predictions
print("Testing next-token prediction:")
test = "def compute(x):\n r"
test_emb = tok.embed_seq(tok.encode(test, SEQ_LEN))
net.context = np.zeros_like(net.context)
preds = net.predict_next(test_emb, n_steps=5)
pred_chars = [tok.nearest(p) for p in preds]
print(f" Input: '{test}'")
print(f" Predicted next chars: {pred_chars}")
print()
# Brain stats
print("=" * 68)
print("Brain-like Statistics:")
print("=" * 68)
stats = {
"L1 mean activity": float(np.mean(net.l1.activities)),
"L1 sparsity": float(np.mean(net.l1.activities > 0)),
"L2 mean activity": float(np.mean(net.l2.activities)),
"L2 sparsity": float(np.mean(net.l2.activities > 0)),
"L3 mean activity": float(np.mean(net.l3.activities)),
"L3 sparsity": float(np.mean(net.l3.activities > 0)),
"Context magnitude": float(np.linalg.norm(net.context)),
}
for k, v in stats.items():
print(f" {k:20s}: {v:.4f}")
print()
# Nengo spiking demo
print("=" * 68)
print("Nengo Spiking Simulation (bonus demo)...")
print("=" * 68)
nengo_net = NengoSpikingPC(embed_dim=EMBED, l1_n=80, l2_n=60, lr=1e-5)
short = test_emb[:5]
t0 = time.time()
sim_data = nengo_net.run(short, dur_per_step=0.05, dt=0.001)
t_nengo = time.time() - t0
print(f" Simulated {len(short)} tokens in {t_nengo:.2f}s")
print(f" L1 rate (mean): {np.mean(sim_data['l1']):.4f}")
print(f" L2 rate (mean): {np.mean(sim_data['l2']):.4f}")
print(f" Prediction error: {np.mean(np.abs(sim_data['error'])):.4f}")
print(f" Sparsity: {np.mean(sim_data['l1'] > 0):.2%}")
print()
# Save
print("Saving artifacts...")
np.savez('pc_model.npz',
w_enc_l1=net.l1.W_enc, w_pred_l1=net.l1.W_pred, w_dec_l1=net.l1.W_dec,
w_enc_l2=net.l2.W_enc, w_pred_l2=net.l2.W_pred, w_dec_l2=net.l2.W_dec,
w_enc_l3=net.l3.W_enc, w_dec_l3=net.l3.W_dec)
np.savez('pc_history.npz',
l1_errors=l1_hist, l2_errors=l2_hist, recon_errors=recon_hist)
np.save('tokenizer_embed.npy', tok.embed)
print(" β pc_model.npz")
print(" β pc_history.npz")
print(" β tokenizer_embed.npy")
print()
print("=" * 68)
print("β
Brain-like Predictive Coding Code World Model Complete!")
print("=" * 68)
print()
print("Features:")
print(" β 3-layer hierarchical predictive coding")
print(" β LIF-rate neurons (biologically plausible)")
print(" β PES error-driven learning (brain-like)")
print(" β Top-down predictions + bottom-up errors")
print(" β Sequence context accumulation")
print(" β Numba JIT + vectorized NumPy (CPU-optimized)")
print(" β Nengo spiking simulation backend")
print(" β Code tokenizer with char-level embeddings")
print()
return net, tok, nengo_net
if __name__ == "__main__":
model, tokenizer, nengo_model = main()
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