def test_minres_with_jacobi():
vv = theano.shared(v, name='v')
gg = theano.shared(g, name='g')
hh = theano.shared(h, name='h')
dw = T.dot(v.T,g) / M
dv = T.dot(g.T,h) / M
da = T.mean(v, axis=0)
db = T.mean(g, axis=0)
dc = T.mean(h, axis=0)
Ldiag_terms = natural.generic_compute_L_diag([vv,gg,hh])
Ms = [Ldiag_term + 0.1 for Ldiag_term in Ldiag_terms]
newgrads = minres.minres(
lambda xw, xv, xa, xb, xc: natural.compute_Lx(vv,gg,hh,xw,xv,xa,xb,xc),
[dw, dv, da, db, dc],
rtol=1e-5,
damp = 0.,
maxiter = 10000,
Ms = Ms,
profile=0)[0]
f = theano.function([], newgrads)
[new_dw, new_dv, new_da, new_db, new_dc] = f()
numpy.testing.assert_almost_equal(Linv_x_w, new_dw, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_v, new_dv, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_a, new_da, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_b, new_db, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_c, new_dc, decimal=1)
def test_minres_with_jacobi():
vv = theano.shared(v, name='v')
gg = theano.shared(g, name='g')
hh = theano.shared(h, name='h')
dw = T.dot(v.T, g) / M
dv = T.dot(g.T, h) / M
da = T.mean(v, axis=0)
db = T.mean(g, axis=0)
dc = T.mean(h, axis=0)
Ldiag_terms = natural.generic_compute_L_diag([vv, gg, hh])
Ms = [Ldiag_term + 0.1 for Ldiag_term in Ldiag_terms]
newgrads = minres.minres(lambda xw, xv, xa, xb, xc: natural.compute_Lx(
vv, gg, hh, xw, xv, xa, xb, xc), [dw, dv, da, db, dc],
rtol=1e-5,
damp=0.,
maxiter=10000,
Ms=Ms,
profile=0)[0]
f = theano.function([], newgrads)
[new_dw, new_dv, new_da, new_db, new_dc] = f()
numpy.testing.assert_almost_equal(Linv_x_w, new_dw, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_v, new_dv, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_a, new_da, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_b, new_db, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_c, new_dc, decimal=1)
def test_minres_with_xinit():
rng = numpy.random.RandomState(123412)
vv = theano.shared(v, name='v')
gg = theano.shared(g, name='g')
hh = theano.shared(h, name='h')
dw = T.dot(v.T,g) / M
dv = T.dot(g.T,h) / M
da = T.mean(v, axis=0)
db = T.mean(g, axis=0)
dc = T.mean(h, axis=0)
xinit = [ rng.rand(N0,N1),
rng.rand(N1,N2),
rng.rand(N0),
rng.rand(N1),
rng.rand(N2)]
xinit = [xi.astype(floatX) for xi in xinit]
newgrads = minres.minres(
lambda xw, xv, xa, xb, xc: natural.compute_Lx(vv,gg,hh,xw,xv,xa,xb,xc),
[dw, dv, da, db, dc],
rtol=1e-5,
damp = 0.,
maxiter = 10000,
xinit = xinit,
profile=0)[0]
f = theano.function([], newgrads)
[new_dw, new_dv, new_da, new_db, new_dc] = f()
numpy.testing.assert_almost_equal(Linv_x_w, new_dw, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_v, new_dv, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_a, new_da, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_b, new_db, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_c, new_dc, decimal=1)
def test_minres():
vv = theano.shared(v, name='v')
gg = theano.shared(g, name='g')
hh = theano.shared(h, name='h')
dw = T.dot(v.T,g) / M
dv = T.dot(g.T,h) / M
da = T.mean(v, axis=0)
db = T.mean(g, axis=0)
dc = T.mean(h, axis=0)
newgrads = minres.minres(
lambda xw, xv, xa, xb, xc: natural.compute_Lx(vv,gg,hh,xw,xv,xa,xb,xc),
[dw, dv, da, db, dc],
rtol=1e-5,
damp = 0.,
maxit = 30,
profile=0)[0]
f = theano.function([], newgrads)
[new_dw, new_dv, new_da, new_db, new_dc] = f()
numpy.testing.assert_almost_equal(Linv_x_w, new_dw, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_v, new_dv, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_a, new_da, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_b, new_db, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_c, new_dc, decimal=1)
def test_minres():
rval = minres.minres(lambda x: [T.dot(symb['L'], x)], [symb['g']],
rtol=1e-14,
damp=0.,
maxiter=10000,
profile=0)
f = theano.function([symb['L'], symb['g']], [rval[0][0], rval[1], rval[2]])
t1 = time.time()
[Linv_g, flag, iter] = f(vals['L'], vals['g'])
print 'test_minres runtime (s):', time.time() - t1
numpy.testing.assert_almost_equal(Linv_g, vals['Linv_g'], decimal=3)
def test_minres():
rval = minres.minres(
lambda x: [T.dot(symb['L'], x)],
[symb['g']],
rtol=1e-14,
damp = 0.,
maxiter = 10000,
profile=0)
f = theano.function([symb['L'], symb['g']], [rval[0][0], rval[1], rval[2]])
t1 = time.time()
[Linv_g, flag, iter] = f(vals['L'], vals['g'])
print 'test_minres runtime (s):', time.time() - t1
numpy.testing.assert_almost_equal(Linv_g, vals['Linv_g'], decimal=3)
def test_minres_xinit():
symb['xinit'] = T.vector('xinit')
vals['xinit'] = rng.rand(nparams).astype(floatX)
symb_Linv_g = minres.minres(lambda x: [T.dot(symb['L'], x)], [symb['g']],
rtol=1e-14,
damp=0.,
maxiter=10000,
xinit=[symb['xinit']],
profile=0)[0]
f = theano.function([symb['L'], symb['g'], symb['xinit']], symb_Linv_g)
t1 = time.time()
Linv_g = f(vals['L'], vals['g'], vals['xinit'])[0]
print 'test_minres_xinit runtime (s):', time.time() - t1
numpy.testing.assert_almost_equal(Linv_g, vals['Linv_g'], decimal=3)
def test_minres_xinit():
symb['xinit'] = T.vector('xinit')
vals['xinit'] = rng.rand(nparams).astype(floatX)
symb_Linv_g = minres.minres(
lambda x: [T.dot(symb['L'], x)],
[symb['g']],
rtol=1e-14,
damp = 0.,
maxiter = 10000,
xinit = [symb['xinit']],
profile=0)[0]
f = theano.function([symb['L'], symb['g'], symb['xinit']], symb_Linv_g)
t1 = time.time()
Linv_g = f(vals['L'], vals['g'], vals['xinit'])[0]
print 'test_minres_xinit runtime (s):', time.time() - t1
numpy.testing.assert_almost_equal(Linv_g, vals['Linv_g'], decimal=3)
def test_minres_with_xinit():
rng = numpy.random.RandomState(123412)
vv = theano.shared(v, name='v')
gg = theano.shared(g, name='g')
hh = theano.shared(h, name='h')
dw = T.dot(v.T, g) / M
dv = T.dot(g.T, h) / M
da = T.mean(v, axis=0)
db = T.mean(g, axis=0)
dc = T.mean(h, axis=0)
xinit = [
rng.rand(N0, N1),
rng.rand(N1, N2),
rng.rand(N0),
rng.rand(N1),
rng.rand(N2)
]
xinit = [xi.astype(floatX) for xi in xinit]
newgrads = minres.minres(lambda xw, xv, xa, xb, xc: natural.compute_Lx(
vv, gg, hh, xw, xv, xa, xb, xc), [dw, dv, da, db, dc],
rtol=1e-5,
damp=0.,
maxiter=10000,
xinit=xinit,
profile=0)[0]
f = theano.function([], newgrads)
[new_dw, new_dv, new_da, new_db, new_dc] = f()
numpy.testing.assert_almost_equal(Linv_x_w, new_dw, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_v, new_dv, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_a, new_da, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_b, new_db, decimal=1)
numpy.testing.assert_almost_equal(Linv_x_c, new_dc, decimal=1)
def get_natural_direction(self,
ml_cost,
nsamples,
xinit=None,
precondition=None):
"""
Returns: list
See lincg documentation for the meaning of each return value.
rvals[0]: niter
rvals[1]: rerr
"""
assert precondition in [None, 'jacobi']
self.cg_params.setdefault('batch_size', self.batch_size)
nsamples = nsamples[:self.cg_params['batch_size']]
neg_energies = self.energy(nsamples)
if self.computational_bs > 0:
raise NotImplementedError()
else:
def Lx_func(*args):
Lneg_x = fisher.compute_Lx(neg_energies, self.params, args)
if self.flags['minresQLP']:
return Lneg_x, {}
else:
return Lneg_x
M = None
if precondition == 'jacobi':
cnsamples = self.center_samples(nsamples)
raw_M = fisher.compute_L_diag(cnsamples)
M = [(Mi + self.cg_params['damp']) for Mi in raw_M]
if self.flags['minres']:
rvals = minres.minres(
Lx_func, [ml_cost.grads[param] for param in self.params],
rtol=self.cg_params['rtol'],
maxiter=self.cg_params['maxiter'],
damp=self.cg_params['damp'],
xinit=xinit,
Ms=M)
[newgrads, flag, niter, rerr] = rvals[:4]
elif self.flags['minresQLP']:
param_shapes = []
for p in self.params:
param_shapes += [p.get_value().shape]
rvals = minresQLP.minresQLP(
Lx_func, [ml_cost.grads[param] for param in self.params],
param_shapes,
rtol=self.cg_params['rtol'],
maxit=self.cg_params['maxiter'],
damp=self.cg_params['damp'],
Ms=M,
profile=0)
[newgrads, flag, niter, rerr] = rvals[:4]
else:
rvals = lincg.linear_cg(
Lx_func, [ml_cost.grads[param] for param in self.params],
rtol=self.cg_params['rtol'],
damp=self.cg_params['damp'],
maxiter=self.cg_params['maxiter'],
xinit=xinit,
M=M)
[newgrads, niter, rerr] = rvals
# Now replace grad with natural gradient.
cos_dist = 0.
norm2_old = 0.
norm2_new = 0.
for i, param in enumerate(self.params):
norm2_old += T.sum(ml_cost.grads[param]**2)
norm2_new += T.sum(newgrads[i]**2)
cos_dist += T.dot(ml_cost.grads[param].flatten(),
newgrads[i].flatten())
ml_cost.grads[param] = newgrads[i]
cos_dist /= (norm2_old * norm2_new)
return [niter, rerr, cos_dist], self.get_dparam_updates(*newgrads)
def get_natural_direction(self, ml_cost, nsamples, xinit=None,
precondition=None):
"""
Returns: list
See lincg documentation for the meaning of each return value.
rvals[0]: niter
rvals[1]: rerr
"""
assert precondition in [None, 'jacobi']
self.cg_params.setdefault('batch_size', self.batch_size)
nsamples = nsamples[:self.cg_params['batch_size']]
neg_energies = self.energy(nsamples)
if self.computational_bs > 0:
raise NotImplementedError()
else:
def Lx_func(*args):
Lneg_x = fisher.compute_Lx(
neg_energies,
self.params,
args)
if self.flags['minresQLP']:
return Lneg_x, {}
else:
return Lneg_x
M = None
if precondition == 'jacobi':
cnsamples = self.center_samples(nsamples)
raw_M = fisher.compute_L_diag(cnsamples)
M = [(Mi + self.cg_params['damp']) for Mi in raw_M]
if self.flags['minres']:
rvals = minres.minres(
Lx_func,
[ml_cost.grads[param] for param in self.params],
rtol = self.cg_params['rtol'],
maxiter = self.cg_params['maxiter'],
damp = self.cg_params['damp'],
xinit = xinit,
Ms = M)
[newgrads, flag, niter, rerr] = rvals[:4]
elif self.flags['minresQLP']:
param_shapes = []
for p in self.params:
param_shapes += [p.get_value().shape]
rvals = minresQLP.minresQLP(
Lx_func,
[ml_cost.grads[param] for param in self.params],
param_shapes,
rtol = self.cg_params['rtol'],
maxit = self.cg_params['maxiter'],
damp = self.cg_params['damp'],
Ms = M,
profile = 0)
[newgrads, flag, niter, rerr] = rvals[:4]
else:
rvals = lincg.linear_cg(
Lx_func,
[ml_cost.grads[param] for param in self.params],
rtol = self.cg_params['rtol'],
damp = self.cg_params['damp'],
maxiter = self.cg_params['maxiter'],
xinit = xinit,
M = M)
[newgrads, niter, rerr] = rvals
# Now replace grad with natural gradient.
cos_dist = 0.
norm2_old = 0.
norm2_new = 0.
for i, param in enumerate(self.params):
norm2_old += T.sum(ml_cost.grads[param]**2)
norm2_new += T.sum(newgrads[i]**2)
cos_dist += T.dot(ml_cost.grads[param].flatten(),
newgrads[i].flatten())
ml_cost.grads[param] = newgrads[i]
cos_dist /= (norm2_old * norm2_new)
return [niter, rerr, cos_dist], self.get_dparam_updates(*newgrads)