def test_stochastic_hessian(model,
criterion,
real_hessian,
x,
y,
bs=10,
ntrials=10):
samples = [(x_i, y_i) for x_i, y_i in zip(x, y)]
# full dataset
dataloader = DataLoader(samples, batch_size=bs)
eigenvals = []
eigenvecs = []
nparams = len(real_hessian)
for _ in range(ntrials):
est_eigenvals, est_eigenvecs = compute_hessian_eigenthings(
model,
dataloader,
criterion,
num_eigenthings=nparams,
power_iter_steps=10,
power_iter_err_threshold=1e-5,
momentum=0,
use_gpu=False,
)
est_eigenvals = np.array(est_eigenvals)
est_eigenvecs = np.array([t.numpy() for t in est_eigenvecs])
est_inds = np.argsort(est_eigenvals)
est_eigenvals = np.array(est_eigenvals)[est_inds][::-1]
est_eigenvecs = np.array(est_eigenvecs)[est_inds][::-1]
eigenvals.append(est_eigenvals)
eigenvecs.append(est_eigenvecs)
eigenvals = np.array(eigenvals)
eigenvecs = np.array(eigenvecs)
real_eigenvals, real_eigenvecs = np.linalg.eig(real_hessian)
real_inds = np.argsort(real_eigenvals)
real_eigenvals = np.array(real_eigenvals)[real_inds][::-1]
real_eigenvecs = np.array(real_eigenvecs)[real_inds][::-1]
# Plot eigenvalue error
plt.suptitle("Stochastic Hessian eigendecomposition errors: %d trials" %
ntrials)
plt.subplot(1, 2, 1)
plt.title("Eigenvalues")
plt.plot(list(range(nparams)), real_eigenvals, label="True Eigenvals")
plot_eigenval_estimates(eigenvals, label="Estimates")
plt.legend()
# Plot eigenvector L2 norm error
plt.subplot(1, 2, 2)
plt.title("Eigenvector cosine simliarity")
plot_eigenvec_errors(real_eigenvecs, eigenvecs, label="Estimates")
plt.legend()
plt.savefig("stochastic.png")
plt.clf()
def test_matrix(mat, ntrials, mode):
"""
Tests the accuracy of deflated power iteration on the given matrix.
It computes the average percent eigenval error and eigenvec simliartiy err
"""
tensor = torch.from_numpy(mat).float()
# for non-gpu tests, addmv not implemented for fp16 on CPU. have to do float.
op = LambdaOperator(lambda x: torch.matmul(tensor, x.float()),
tensor.size()[:1])
real_eigenvals, true_eigenvecs = np.linalg.eig(mat)
real_eigenvecs = [true_eigenvecs[:, i] for i in range(len(real_eigenvals))]
eigenvals = []
eigenvecs = []
for _ in range(ntrials):
if mode == 'lanczos':
method = lanczos
else:
method = deflated_power_iteration
est_eigenvals, est_eigenvecs = method(
op,
num_eigenthings=args.num_eigenthings,
use_gpu=False,
fp16=args.fp16)
est_inds = np.argsort(est_eigenvals)
est_eigenvals = np.array(est_eigenvals)[est_inds][::-1]
est_eigenvecs = np.array(est_eigenvecs)[est_inds][::-1]
eigenvals.append(est_eigenvals)
eigenvecs.append(est_eigenvecs)
eigenvals = np.array(eigenvals)
eigenvecs = np.array(eigenvecs)
# truncate estimates
real_inds = np.argsort(real_eigenvals)
real_eigenvals = np.array(
real_eigenvals)[real_inds][-args.num_eigenthings:][::-1]
real_eigenvecs = np.array(
real_eigenvecs)[real_inds][-args.num_eigenthings:][::-1]
# Plot eigenvalue error
plt.suptitle('Random Matrix Eigendecomposition Errors: %d trials' %
ntrials)
plt.subplot(1, 2, 1)
plt.title('Eigenvalues')
plt.plot(list(range(len(real_eigenvals))),
real_eigenvals,
label='True Eigenvals')
plot_eigenval_estimates(eigenvals, label='Estimates')
plt.legend()
# Plot eigenvector L2 norm error
plt.subplot(1, 2, 2)
plt.title('Eigenvector cosine simliarity')
plot_eigenvec_errors(real_eigenvecs, eigenvecs, label='Estimates')
plt.legend()
plt.show()
def test_full_hessian(model, criterion, x, y, ntrials=10):
loss = criterion(model(x), y)
loss_grad = torch.autograd.grad(loss,
model.parameters(),
create_graph=True)
real_hessian = get_full_hessian(loss_grad, model)
samples = [(x_i, y_i) for x_i, y_i in zip(x, y)]
# full dataset
dataloader = DataLoader(samples, batch_size=len(x))
eigenvals = []
eigenvecs = []
nparams = len(real_hessian)
for _ in range(ntrials):
est_eigenvals, est_eigenvecs = compute_hessian_eigenthings(
model,
dataloader,
criterion,
num_eigenthings=nparams,
power_iter_steps=10,
power_iter_err_threshold=1e-5,
momentum=0,
use_gpu=False,
)
est_inds = np.argsort(est_eigenvals)
est_eigenvals = np.array(est_eigenvals)[est_inds][::-1]
est_eigenvecs = np.array(est_eigenvecs)[est_inds][::-1]
eigenvals.append(est_eigenvals)
eigenvecs.append(est_eigenvecs)
eigenvals = np.array(eigenvals)
eigenvecs = np.array(eigenvecs)
real_eigenvals, real_eigenvecs = np.linalg.eig(real_hessian)
real_inds = np.argsort(real_eigenvals)
real_eigenvals = np.array(real_eigenvals)[real_inds][::-1]
real_eigenvecs = np.array(real_eigenvecs)[real_inds][::-1]
# Plot eigenvalue error
plt.suptitle("Hessian eigendecomposition errors: %d trials" % ntrials)
plt.subplot(1, 2, 1)
plt.title("Eigenvalues")
plt.plot(list(range(nparams)), real_eigenvals, label="True Eigenvals")
plot_eigenval_estimates(eigenvals, label="Estimates")
plt.legend()
# Plot eigenvector L2 norm error
plt.subplot(1, 2, 2)
plt.title("Eigenvector cosine simliarity")
plot_eigenvec_errors(real_eigenvecs, eigenvecs, label="Estimates")
plt.legend()
plt.savefig("full.png")
plt.clf()
return real_hessian
def test_fixed_mini(model, criterion, real_hessian, x, y, bs=10, ntrials=10):
x = x[:bs]
y = y[:bs]
samples = [(x_i, y_i) for x_i, y_i in zip(x, y)]
# full dataset
dataloader = DataLoader(samples, batch_size=len(x))
eigenvals = []
eigenvecs = []
nparams = len(real_hessian)
for _ in range(ntrials):
est_eigenvals, est_eigenvecs = compute_hessian_eigenthings(
model,
dataloader,
criterion,
num_eigenthings=nparams,
mode='lanczos',
power_iter_steps=10,
power_iter_err_threshold=1e-5,
momentum=0,
use_gpu=False)
est_eigenvals = np.array(est_eigenvals)
est_eigenvecs = np.array([t.numpy() for t in est_eigenvecs])
est_inds = np.argsort(est_eigenvals)
est_eigenvals = np.array(est_eigenvals)[est_inds][::-1]
est_eigenvecs = np.array(est_eigenvecs)[est_inds][::-1]
eigenvals.append(est_eigenvals)
eigenvecs.append(est_eigenvecs)
eigenvals = np.array(eigenvals)
eigenvecs = np.array(eigenvecs)
real_eigenvals, real_eigenvecs = np.linalg.eig(real_hessian)
real_inds = np.argsort(real_eigenvals)
real_eigenvals = np.array(real_eigenvals)[real_inds][::-1]
real_eigenvecs = np.array(real_eigenvecs)[real_inds][::-1]
# Plot eigenvalue error
plt.suptitle(
'Fixed mini-batch Hessian eigendecomposition errors: %d trials' %
ntrials)
plt.subplot(1, 2, 1)
plt.title('Eigenvalues')
plt.plot(list(range(nparams)), real_eigenvals, label='True Eigenvals')
plot_eigenval_estimates(eigenvals, label='Estimates')
plt.legend()
# Plot eigenvector L2 norm error
plt.subplot(1, 2, 2)
plt.title('Eigenvector cosine simliarity')
plot_eigenvec_errors(real_eigenvecs, eigenvecs, label='Estimates')
plt.legend()
plt.savefig('fixed.png')