def plot_fmc_by_perf(pdata, perf_attr='logit_perf', use_dlyap=False, npts=15, weight=False, vmax=None):
num_plots = 25
indx_off = [0, len(pdata)-num_plots]
weights = [[], []]
inputs = [[], []]
fmcs = [[], []]
fmc_max = -np.Inf
for k,offset in enumerate(indx_off):
pend = offset + num_plots
for m,p in enumerate(pdata[offset:pend]):
weights[k].append(p.net.W)
inputs[k].append(p.net.Win)
J = fisher_memory_matrix(p.net.W, p.net.Win, use_dlyap=use_dlyap, npts=npts)
fmc = np.diag(J)
fmc[fmc < 0.0] = 0.0
fmcs[k].append(fmc)
fmc_max = max(fmc_max, fmc.max())
perrow = int(np.sqrt(num_plots))
percol = perrow
for j,offset in enumerate(indx_off):
fig = plt.figure()
fig.subplots_adjust(wspace=0.1, hspace=0.1)
for k in range(num_plots):
W = weights[j][k]
v = inputs[j][k]
fmc = fmcs[j][k]
if vmax is None:
vmax = fmc_max
if weight:
indx = np.arange(npts) + 2.0
w = np.log2(indx)
jsum = (w * np.abs(fmc)).sum()
else:
jsum = fmc.sum()
ax = fig.add_subplot(perrow, percol, k)
ax.plot(fmc, 'k-')
ax.set_ylim([0, vmax])
ax.set_title('%0.3f' % jsum)
plt.xticks([], [])
plt.yticks([], [])
p = pdata[offset + k]
if offset == 0:
plt.suptitle('Fisher Memory Curves of Top %d Networks' % num_plots)
else:
plt.suptitle('Fisher Memory Curves of Bottom %d Networks' % num_plots)
plt.show()
def plot_fmm_by_perf(pdata, perf_attr='logit_perf', use_dlyap=False, npts=15, num_plots=25, vbounds=None):
num_plots = num_plots
indx_off = [0, len(pdata)-num_plots]
weights = [[], []]
inputs = [[], []]
perfs = [[], []]
fmms = [[], []]
max_fmm = -np.Inf
min_fmm = np.Inf
for k,offset in enumerate(indx_off):
pend = offset + num_plots
for m,p in enumerate(pdata[offset:pend]):
weights[k].append(p.W)
inputs[k].append(p.Win)
perfs[k].append(p.logit_perf)
J = fisher_memory_matrix(p.net.W, p.net.Win, npts=npts, use_dlyap=use_dlyap)
fmms[k].append(J)
max_fmm = max(max_fmm, J.max())
min_fmm = min(min_fmm, J.min())
perrow = int(np.sqrt(num_plots))
percol = perrow
for j,offset in enumerate(indx_off):
fig = plt.figure()
fig.subplots_adjust(wspace=0.1, hspace=0.1)
for k in range(num_plots):
J = fmms[j][k]
if vbounds is None:
vbounds = [min_fmm, max_fmm]
ax = fig.add_subplot(perrow, percol, k)
res = ax.imshow(J, interpolation='nearest', cmap=cm.jet, vmin=vbounds[0], vmax=vbounds[1])
#fig.colorbar(res)
#ax.set_title('%0.2f' % perfs[j][k])
plt.xticks([], [])
plt.yticks([], [])
p = pdata[offset + k]
if offset == 0:
plt.suptitle('Fisher Memory Matricies of Top %d Networks' % num_plots)
else:
plt.suptitle('Fisher Memory Matricies of Bottom %d Networks' % num_plots)
plt.show()
def plot_fmm_single(perf_data, npts=50):
J = fisher_memory_matrix(perf_data.net.W, perf_data.net.Win, npts=npts, use_dlyap=False)
plt.figure()
fig = plt.gcf()
ax = fig.add_subplot(1, 1, 1)
res = ax.imshow(J, interpolation='nearest', cmap=cm.jet)
fig.colorbar(res)
ax.set_xlabel('Timestep')
ax.set_ylabel('Timestep')
#plt.xticks([], [])
#plt.yticks([], [])
fmc = np.diag(J)
fmc[fmc < 0.0] = 0.0
t = np.arange(len(fmc))
plt.figure()
plt.plot(t, fmc, 'k-', linewidth=3.0)
ax.set_xlabel('Timestep')
ax.set_ylabel('Memory')
plt.axis('tight')
def plot_perf_by_jsum(pdata, perf_attr='logit_perf', use_dlyap=False, use_abs=True, npts=25):
perfs = []
jtots = []
for m,p in enumerate(pdata):
W = p.net.W
Win = p.net.Win
v = Win.squeeze()
J = fisher_memory_matrix(W, v, use_dlyap=use_dlyap, npts=npts)
jt_vals = J[np.triu_indices(len(J))]
if use_abs:
jt_vals = np.abs(jt_vals)
jusum = jt_vals.sum()
perfs.append(getattr(p, perf_attr))
jtots.append(jusum)
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(jtots, perfs, 'ko')
ax.set_title('Upper Triangular Sum of J vs Performance')
plt.xlabel('UT Sum')
plt.ylabel('Performance')
plt.show()
def plot_perf_by_jtot(pdata, perf_attr='logit_perf', use_dlyap=False, npts=15, weight=False):
perfs = []
jtots = []
for m,p in enumerate(pdata):
J = fisher_memory_matrix(p.W, p.Win, use_dlyap=use_dlyap, npts=npts)
fmc = np.diag(J)
fmc[fmc < 0.0] = 0.0
perfs.append(getattr(p, perf_attr))
if weight:
indx = np.arange(npts) + 1.0
w = np.log2(indx)
jsum = (w * fmc).sum()
else:
jsum = fmc.sum()
jtots.append(jsum)
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(jtots, perfs, 'ko')
ax.set_title('Jtot vs Performance')
plt.xlabel('Jtot')
plt.ylabel('Performance')
plt.show()
def compute_net_metrics(pdata, output_file):
npts = 40
data = []
for p in pdata:
J = fisher_memory_matrix(p.net.W, p.net.Win, use_dlyap=False, npts=npts)
feature_names = []
features = []
#compute weighted jtot
fmc = np.diag(J)
fmc[fmc < 0.0] = 0.0
indx = np.arange(len(fmc)) + 1.0
w = np.log2(indx)
wjtot = (w * fmc).sum()
feature_names.append('wjtot')
features.append(wjtot)
#compute upper-triangular abs sum
jt_vals = np.abs(J[np.triu_indices(len(J))])
fmm_sum = jt_vals.sum()
feature_names.append('fmm_sum')
features.append(fmm_sum)
#compute arc length of convex hull around pseudospectra
bounds=[-3, 3, -3, 3]
for eps in [0.5, 0.1]:
(X, Y, Z, smin) = compute_pseudospectra(p.net.W, bounds=bounds, npts=75, invert=False)
arclen = np.NAN
if np.sum(smin < eps) > 0:
arclen = 0.0
xvals = X[smin < eps].ravel()
yvals = Y[smin < eps].ravel()
pnts = zip(xvals, yvals)
ch = np.array(convex_hull(pnts))
for m in range(ch.shape[0]):
if m == 0:
p1 = ch[-1, :]
else:
p1 = ch[m-1, :]
p2 = ch[m, :]
arclen += np.linalg.norm(p2 - p1)
feature_names.append('arclen_%0.2f' % eps)
features.append(arclen)
#compute eigenvalues/schur decomposition
(T, U, sdim) = scipy.linalg.schur(p.net.W, 'complex', sort='rhp')
evals = np.diag(T)
for k,ev in enumerate(evals):
feature_names.append('ev%d_real' % k)
features.append(ev.real)
feature_names.append('ev%d_imag' % k)
features.append(ev.imag)
for i in range(p.net.W.shape[0]):
for j in range(i):
if i != j:
od = T[j, i]
feature_names.append('od%d%d_real' % (j, i))
features.append(od.real)
feature_names.append('od%d%d_imag' % (j, i))
features.append(od.imag)
feature_names.append('perf')
features.append(p.logit_perf)
data.append(features)
f = open(output_file, 'w')
f.write('%s\n' % ','.join(feature_names))
for row in data:
fstr = ['%0.12f' % x for x in row]
f.write('%s\n' % ','.join(fstr))
f.close()