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comparison.py
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comparison.py
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# Example of usage: RAPID vs. other training methods. Part of
# Efficient training of energy-based models via spin-glass control
# arXiv:1910.01592
#
# Authors: Alejandro Pozas-Kerstjens and Gorka Muñoz-Gil
#
# Requires: ebm-torch for ML models (https://www.github.com/apozas/ebm-torch)
# itertools for Cartesian product
# gc for garbage collection
# numpy for numerics
# pytorch as ML framework
# matplotlib for plots
# tqdm for progress bar
# Last modified: Jul, 2020
import gc
import matplotlib.pyplot as plt
import numpy as np
import torch
from tqdm import tqdm
from itertools import product
from rapid import ContrastiveDivergence_pm as CD, \
PersistentContrastiveDivergence_pm as PCD
from rapid import Adam_pm, SGD_xi
from rapid import RBM_pm, RA_RBM
from torch.optim import Adam
from utils import batch_nll, GradientRBM, create_bars_4x4, gs_energy
#------------------------------------------------------------------------------
# Auxiliary functions
#------------------------------------------------------------------------------
def gs_accessibility(machine, gs, steps=5, n_chains=10):
'''Calculates how hard is for Gibbs iterations to get low energy states, by
comparing the average energy of the last of 'steps' Gibbs iterations to the
ground state energy
Arguments:
:param machine: The model one wishes to sample from
:type machine: torch.nn.Module
:param gs: The energy of the ground state of 'machine'
:type gs: float
:param steps: Number of Gibbs steps before retrieval
:type steps: int
:param n_chains: Number of samples run in parallel
:type n_chains: int
:returns float: energy relative to ground state energy
'''
vis = torch.randint(0, 2, (n_chains, machine.weights.shape[1]))
vis = (2 * vis - 1).float().to(machine.device)
for _ in range(steps):
hid = sampler.get_h_from_v(vis, machine.weights, hbias)
vis = sampler.get_v_from_h(hid, machine.weights, vbias)
energy = torch.min(-torch.einsum('bi,ji,bj->b',
(vis, machine.weights, hid))).item()
return energy / gs
#------------------------------------------------------------------------------
# Parameter choices
#------------------------------------------------------------------------------
hidd = 1000 # Number of nodes in the hidden layer
rapid_lr = 0.02 # Learning rate for RAPID
other_lr = 0.001 # Learning rate for other methods
epochs = 300 # Training epochs
K = 8 # Number of patterns for RA model
k = 10 # Gibbs steps for CD-PCD
bs_rapid = 3 # Batch size for RAPID
bs_other = 1 # Batch size for other methods
gpu = True # Use of GPU
#------------------------------------------------------------------------------
# Data preparation
#------------------------------------------------------------------------------
device = torch.device('cuda' if gpu and torch.cuda.is_available() else 'cpu')
all_datasets = create_bars_4x4()
for _ in all_datasets:
dataset = all_datasets.pop(0)
dataset = dataset.to(device)
all_datasets.append(dataset)
train_set, recon_train, test_set, recon_test = all_datasets
vis = len(train_set[0])
all_confs = torch.Tensor(list(product([-1, 1], repeat=vis))).to(device)
# Extra parameters needed for the samplers
hbias = torch.zeros(hidd).to(device)
vbias = torch.zeros(vis).to(device)
# -----------------------------------------------------------------------------
# Construct Models
# -----------------------------------------------------------------------------
sampler = CD(k=k) # Generic sampler
cd = CD(k=k)
pcd = PCD(k=k, n_chains=2048)
opt_ra = SGD_xi(rapid_lr)
opt_cd = Adam_pm(other_lr)
opt_pc = Adam_pm(other_lr)
rbm_ra = RA_RBM(n_visible=vis,
n_hidden=hidd,
K=K,
optimizer=opt_ra,
device=device
).to(device)
rbm_cd = RBM_pm(n_visible=vis,
n_hidden=hidd,
sampler=cd,
optimizer=opt_cd,
device=device
).to(device)
rbm_pc = RBM_pm(n_visible=vis,
n_hidden=hidd,
sampler=pcd,
optimizer=opt_pc,
device=device
).to(device)
rbm_ex = GradientRBM(n_visible=vis,
n_hidden=hidd,
device=device
).to(device)
opt_ex = Adam(rbm_ex.parameters(), lr=other_lr)
# -----------------------------------------------------------------------------
# Training
# -----------------------------------------------------------------------------
access_pc = []
access_cd = []
access_ex = []
access_ra = []
hd_train_cd = []
hd_train_pc = []
hd_train_ex = []
hd_train_ra = []
hd_test_cd = []
hd_test_pc = []
hd_test_ex = []
hd_test_ra = []
min_pc_energy = []
min_cd_energy = []
min_ra_energy = []
machines = [rbm_ra, rbm_ex, rbm_cd, rbm_pc]
for epoch in range(epochs):
train_loader_rapid = torch.utils.data.DataLoader(train_set,
batch_size=bs_rapid,
shuffle=True)
train_loader_other = torch.utils.data.DataLoader(train_set,
batch_size=bs_other,
shuffle=True)
# Training
rbm_cd.train(train_loader_other)
rbm_pc.train(train_loader_other)
rbm_ra.train(train_loader_rapid)
if rbm_ra.optimizer.learning_rate > 1e-5:
rbm_ra.optimizer.learning_rate *= 0.96
for batch in tqdm(train_loader_other, desc=('Epoch ' + str(epoch + 1))):
cost, _ = batch_nll(rbm_ex, batch, all_confs)
opt_ex.zero_grad()
cost.backward()
opt_ex.step()
# Ground state energy
ground_pc = gs_energy(rbm_pc, all_confs)
ground_cd = gs_energy(rbm_cd, all_confs)
ground_ex = gs_energy(rbm_ex, all_confs)
ground_ra = gs_energy(rbm_ra, all_confs)
# Accessibility of GS
pc_gs_acc = gs_accessibility(rbm_pc, ground_pc, steps=k)
cd_gs_acc = gs_accessibility(rbm_cd, ground_cd, steps=k)
ex_gs_acc = gs_accessibility(rbm_ex, ground_ex, steps=k)
ra_gs_acc = gs_accessibility(rbm_ra, ground_ra, steps=k)
access_pc.append(pc_gs_acc)
access_cd.append(cd_gs_acc)
access_ex.append(ex_gs_acc)
access_ra.append(ra_gs_acc)
# Quality of sampling
# PCD: Take energy of the lowest-energy chain of the PCD training
chains_hidd = sampler.get_h_from_v(rbm_pc.sampler.markov_chains,
rbm_pc.weights, hbias)
min_chain_energy = torch.min(-torch.einsum('bi,ji,bj->b',
(rbm_pc.sampler.markov_chains, rbm_pc.weights, chains_hidd)
)).item()
min_pc_energy.append(min_chain_energy / ground_pc)
# CD: Take all training set, do k Gibbs steps, and take the lowest-energy.
# We repeat 10 times to avoid fluctuations
smallest_cd_energies = []
for idx in range(10):
for gibbs_step in range(k):
if gibbs_step == 0:
sample_vis = train_set.clone()
sample_hidd = sampler.get_h_from_v(sample_vis,
rbm_cd.weights,
hbias)
sample_vis = sampler.get_v_from_h(sample_hidd,
rbm_cd.weights,
vbias)
sample_hidd = sampler.get_h_from_v(sample_vis, rbm_cd.weights, hbias)
smallest_cd_energies.append(torch.min(-torch.einsum('bi,ji,bj->b',
(sample_vis, rbm_cd.weights, sample_hidd))
).item())
min_cd_energy.append(np.min(smallest_cd_energies) / ground_cd)
# RAPID: Take the lowest-energy pattern
patt_vis, patt_hidd = rbm_ra.xi[:, :vis], rbm_ra.xi[:, vis:]
smallest_pid_energy = torch.min(-torch.einsum('bi,ji,bj->b',
(patt_vis, rbm_ra.weights, patt_hidd))
).item()
min_ra_energy.append(smallest_pid_energy / ground_ra)
# Hamming distances. Compute averages over 100 reconstruction instances
hamming_train = [[], [], [], []]
for complete, partial in zip(train_set, recon_train):
to_reconstruct = partial.unsqueeze(0).repeat(100, 1).to(device)
for machine_idx, machine in enumerate(machines):
gibbs_vis = to_reconstruct.clone()
gibbs_hidd = sampler.get_h_from_v(gibbs_vis,
machine.weights,
hbias)
gibbs_vis = sampler.get_v_from_h(gibbs_hidd,
machine.weights,
vbias)
hamming_train[machine_idx].append(
(
gibbs_vis - complete.unsqueeze(0).repeat(100, 1).to(device)
).abs().mean().item() / 2)
hd_train_ra.append(np.array(hamming_train[0]).mean())
hd_train_ex.append(np.array(hamming_train[1]).mean())
hd_train_cd.append(np.array(hamming_train[2]).mean())
hd_train_pc.append(np.array(hamming_train[3]).mean())
hamming_test = [[], [], [], []]
for complete, partial in zip(test_set, recon_test):
to_reconstruct = partial.unsqueeze(0).repeat(100, 1).to(device)
for machine_idx, machine in enumerate(machines):
gibbs_vis = to_reconstruct.clone()
gibbs_hidd = sampler.get_h_from_v(gibbs_vis,
machine.weights,
hbias)
gibbs_vis = sampler.get_v_from_h(gibbs_hidd,
machine.weights,
vbias)
hamming_test[machine_idx].append(
(
gibbs_vis - complete.unsqueeze(0).repeat(100, 1).to(device)
).abs().mean().item() / 2)
hd_test_ra.append(np.array(hamming_test[0]).mean())
hd_test_ex.append(np.array(hamming_test[1]).mean())
hd_test_cd.append(np.array(hamming_test[2]).mean())
hd_test_pc.append(np.array(hamming_test[3]).mean())
print('train', hd_train_ra[-1], 'test', hd_test_ra[-1])
#-----------------------------------------------------------------------------
#Save all information
#-----------------------------------------------------------------------------
gc.collect()
np.savetxt('gibbs_access_pc.txt', access_pc)
np.savetxt('gibbs_access_cd.txt', access_cd)
np.savetxt('gibbs_access_ex.txt', access_ex)
np.savetxt('gibbs_access_ra.txt', access_ra)
np.savetxt('pattern_access_pc.txt', min_pc_energy)
np.savetxt('pattern_access_cd.txt', min_cd_energy)
np.savetxt('pattern_access_ra.txt', min_ra_energy)
np.savetxt('hd_train_pc.txt', hd_train_pc)
np.savetxt('hd_train_cd.txt', hd_train_cd)
np.savetxt('hd_train_ex.txt', hd_train_ex)
np.savetxt('hd_train_ra.txt', hd_train_ra)
np.savetxt('hd_test_pc.txt', hd_test_pc)
np.savetxt('hd_test_cd.txt', hd_test_cd)
np.savetxt('hd_test_ex.txt', hd_test_ex)
np.savetxt('hd_test_ra.txt', hd_test_ra)
# -----------------------------------------------------------------------------
# Plot Figures 1 and 2
# -----------------------------------------------------------------------------
x = list(range(1, epochs+1))
# Figure 1
plt.semilogx(x, min_ra_energy, label='RAPID', color='tab:blue')
plt.semilogx(x, min_pc_energy, label='PCD-10', color='tab:green')
plt.semilogx(x, min_cd_energy, label='CD-10', color='tab:orange')
plt.legend(loc=4, fontsize=14)
plt.xlabel('Epoch')
plt.ylabel('Method GS accessibility')
ax = plt.gca()
ax.get_legend().get_title().set_fontsize('14')
plt.savefig('pattern_access.pdf', bbox_inches='tight')
plt.clf()
plt.semilogx(x, access_ra, label='RAPID', color='tab:blue')
plt.semilogx(x, access_pc, label='PCD-10', color='tab:green')
plt.semilogx(x, access_cd, label='CD-10', color='tab:orange')
plt.semilogx(x, access_ex, label='Exact', color='tab:red')
plt.legend(title='Training method', loc=(0.02,0.29), fontsize=14)
plt.xlabel('Epoch')
plt.ylabel('Gibbs GS accessibility')
ax = plt.gca()
ax.get_legend().get_title().set_fontsize('14')
plt.savefig('gibbs_access.pdf', bbox_inches='tight')
plt.clf()
# Figure 2
plt.semilogx(x, hd_train_ra, label='RAPID', color='tab:blue')
plt.semilogx(x, hd_train_pc, label='PCD-10', color='tab:green')
plt.semilogx(x, hd_train_cd, label='CD-10', color='tab:orange')
plt.semilogx(x, hd_train_ex, label='Exact', color='tab:red')
plt.legend(title='Training method', loc=1, fontsize=14)
plt.xlabel('Epoch')
plt.ylabel('Hamming distance')
plt.title('Training set')
ax = plt.gca()
ax.get_legend().get_title().set_fontsize('14')
plt.savefig('hd_train.pdf', bbox_inches='tight')
plt.clf()
plt.semilogx(x, hd_test_ra, label='RAPID', color='tab:blue')
plt.semilogx(x, hd_test_pc, label='PCD-10', color='tab:green')
plt.semilogx(x, hd_test_cd, label='CD-10', color='tab:orange')
plt.semilogx(x, hd_test_ex, label='Exact', color='tab:red')
plt.legend(title='Training method', loc=(0.31,0.21), fontsize=14)
plt.xlabel('Epoch')
plt.ylabel('Hamming distance')
plt.title('Test set')
ax = plt.gca()
ax.get_legend().get_title().set_fontsize('14')
plt.savefig('hd_test.pdf', bbox_inches='tight')
plt.clf()