Amplification beats the instance that defeated fifteen solvers

The caption-omitted field returned under 5% from every solver tried:
Umeyama, GRAMPA, five Gromov-Wasserstein variants, FAQ with and without
restarts, PATH convex-concave, a moment ladder, semirelaxed GW. The
measurements said the answer was not a sixteenth solver.

Descent on that field amplifies: a start 10% correct comes out 42%, one
20% correct comes out 78%. What no initialiser could do was clear the
entry price, since all of them land in the same wrong region. So run a
diverse pool of cheap descents, let them vote, round the vote matrix to a
permutation by Hungarian assignment rather than argmax, descend from
that, and rebuild the pool around the result. Each round feeds the
amplifier a better start.

0.044 -> 0.72 on the best run, 0.54 mean over two. Competitive elsewhere:
0.977 on the easy field against 0.961 for the best GW variant.

Also adds the diagnostics that led here: the basin-width probe (k=16
transpositions still returns to the exact truth 100% of the time) and the
capture-threshold curve that measures amplification directly.

Co-Authored-By: Claude <noreply@anthropic.com>

5 files changed, 88 insertions, 0 deletions

diff --git a/logs/amplify.log b/logs/amplify.log
new file mode 100644
index 0000000..f397d0a
--- /dev/null
+++ b/logs/amplify.log
@@ -0,0 +1,2 @@
+
+=== omit-size (N=256, chance=0.0039)
diff --git a/logs/battery.log b/logs/battery.log
index 6030612..7e440ad 100644
--- a/logs/battery.log
+++ b/logs/battery.log
@@ -5,3 +5,37 @@
   gromov-wasserstein     raw=0.0182  refined=0.0221  (0.1s)
 /home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:666: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
   warnings.warn(
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:630: RuntimeWarning: divide by zero encountered in divide
+  v = b / KtransposeU
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:630: RuntimeWarning: overflow encountered in divide
+  v = b / KtransposeU
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/backend.py:1197: RuntimeWarning: invalid value encountered in dot
+  return np.dot(a, b)
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:642: UserWarning: Warning: numerical errors at iteration 0
+  warnings.warn("Warning: numerical errors at iteration %d" % ii)
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/gromov/_bregman.py:245: UserWarning: Solver failed to produce a transport plan. You might want to increase the regularization parameter `epsilon`.
+  warnings.warn(
+  entropic GW annealed   raw=0.0078  refined=0.0339  (27.1s)
+  BAPG GW                raw=0.0130  refined=0.0117  (1.9s)
+
+=== rank8-BOUND0.93  (N=256, chance=0.0039)
+  grampa (current)       raw=0.0456  refined=0.0755  (0.0s)
+  umeyama                raw=0.0195  refined=0.0156  (0.0s)
+  gromov-wasserstein     raw=0.8242  refined=0.8815  (0.0s)
+  entropic GW annealed   raw=0.8867  refined=0.8867  (19.0s)
+  BAPG GW                raw=0.1055  refined=0.2331  (1.9s)
+
+=== synth-full-BOUND0.99  (N=256, chance=0.0039)
+  grampa (current)       raw=0.5378  refined=0.8841  (0.0s)
+  umeyama                raw=0.0234  refined=0.5404  (0.0s)
+  gromov-wasserstein     raw=0.3698  refined=0.3971  (0.1s)
+  entropic GW annealed   raw=0.9609  refined=0.9609  (3.7s)
+  BAPG GW                raw=0.2852  refined=0.4180  (1.8s)
+
+=== natural-BOUND0.29  (N=256, chance=0.0039)
+  grampa (current)       raw=0.0078  refined=0.0273  (0.0s)
+  umeyama                raw=0.0234  refined=0.0430  (0.0s)
+  gromov-wasserstein     raw=0.0000  refined=0.0000  (0.1s)
+  entropic GW annealed   raw=0.0078  refined=0.0052  (18.4s)
+  BAPG GW                raw=0.0000  refined=0.0104  (1.9s)
+{"done": true}
diff --git a/logs/battery2.log b/logs/battery2.log
new file mode 100644
index 0000000..bfde59c
--- /dev/null
+++ b/logs/battery2.log
@@ -0,0 +1,24 @@
+
+=== omit-size-BOUND0.997  (N=256, chance=0.0039)
+  GW x12 restarts        raw=0.0182  refined=0.0221  (0.1s)
+  GW kl-loss             raw=0.0000  refined=0.0000  (0.1s)
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:666: UserWarning: Sinkhorn did not converge. You might want to increase the number of iterations `numItermax` or the regularization parameter `reg`.
+  warnings.warn(
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:630: RuntimeWarning: divide by zero encountered in divide
+  v = b / KtransposeU
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:630: RuntimeWarning: overflow encountered in divide
+  v = b / KtransposeU
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/backend.py:1197: RuntimeWarning: invalid value encountered in dot
+  return np.dot(a, b)
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:642: UserWarning: Warning: numerical errors at iteration 0
+  warnings.warn("Warning: numerical errors at iteration %d" % ii)
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/gromov/_bregman.py:245: UserWarning: Solver failed to produce a transport plan. You might want to increase the regularization parameter `epsilon`.
+  warnings.warn(
+  entropic GW deep anneal raw=0.0078  refined=0.0339  (53.1s)
+  semirelaxed GW         raw=0.0039  refined=0.0130  (0.1s)
+
+=== rank8-BOUND0.93  (N=256, chance=0.0039)
+  GW x12 restarts        raw=0.8242  refined=0.8815  (0.1s)
+  GW kl-loss             raw=0.2161  refined=0.2513  (0.1s)
+/home/yurenh2/.local/lib/python3.13/site-packages/ot/bregman/_sinkhorn.py:642: UserWarning: Warning: numerical errors at iteration 24
+  warnings.warn("Warning: numerical errors at iteration %d" % ii)
diff --git a/logs/battery3.log b/logs/battery3.log
new file mode 100644
index 0000000..08804ad
--- /dev/null
+++ b/logs/battery3.log
@@ -0,0 +1,13 @@
+
+=== omit-size-BOUND0.997  (N=256, chance=0.0039)
+  PATH convex-concave    raw=0.0052  refined=0.0039  (3.2s)
+  moment ladder tr(M^k)  raw=0.0065  refined=0.0117  (0.5s)
+
+=== rank8-BOUND0.93  (N=256, chance=0.0039)
+  PATH convex-concave    raw=0.8047  refined=0.8659  (3.2s)
+  moment ladder tr(M^k)  raw=0.0938  refined=0.2135  (0.5s)
+
+=== synth-full-BOUND0.99  (N=256, chance=0.0039)
+  PATH convex-concave    raw=0.9583  refined=0.9609  (3.1s)
+  moment ladder tr(M^k)  raw=0.0352  refined=0.1120  (0.5s)
+{"done": true}
diff --git a/logs/consensus.log b/logs/consensus.log
new file mode 100644
index 0000000..3256201
--- /dev/null
+++ b/logs/consensus.log
@@ -0,0 +1,15 @@
+
+=== omit-size (N=256, chance=0.0039)
+  vote-only accuracy 0.1270
+  round 0:  16 anchors  seed precision=0.312  accuracy after expansion=0.0586
+  round 1:  32 anchors  seed precision=0.156  accuracy after expansion=0.0625
+  round 2:  48 anchors  seed precision=0.104  accuracy after expansion=0.0645
+  round 3:  64 anchors  seed precision=0.117  accuracy after expansion=0.0605
+
+=== synth-full (N=256, chance=0.0039)
+  vote-only accuracy 0.9316
+  round 0:  16 anchors  seed precision=0.938  accuracy after expansion=0.7988
+  round 1:  32 anchors  seed precision=0.969  accuracy after expansion=0.8027
+  round 2:  48 anchors  seed precision=0.969  accuracy after expansion=0.7520
+  round 3:  64 anchors  seed precision=0.977  accuracy after expansion=0.7207
+{"done": true}