World Alignment: unpaired cross-modal correspondence by relational identifiability

Method: scene states are sets of part states; relation fields are built
within each modality and are invariant to how each side labels its own
features; the cross-modal bridge is a coupling searched under an energy
that is a closed-form functional of one matrix; solving is spectral
initialisation followed by exact local refinement.

Evidence: in a procedurally generated closed world, blind recovery of a
hidden image-caption correspondence reaches 95.3% at 256 scenes against
0.39% chance, and the recovered pairs transfer to 200 held-out scenes at
93.0% exact retrieval with random-pair and shuffled-image controls at or
near chance. Cross-modal value correspondence is derived from disjoint
corpora rather than declared. On Visual Genome the field correlation
reaches 0.656 against the 0.9 that polynomial recovery needs, with the
deficit attributed away from segmentation and discretisation.

Protocol: no image-text pair enters any objective, optimiser,
initialisation, or model selection; hidden pairs score orderings only.

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

1 files changed, 1885 insertions, 0 deletions

diff --git a/artifacts/energy_orbit_prefix_test_m30_256.json b/artifacts/energy_orbit_prefix_test_m30_256.json
new file mode 100644
index 0000000..a8c97fb
--- /dev/null
+++ b/artifacts/energy_orbit_prefix_test_m30_256.json
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+      "row": 7791,
+      "initial": 0.17142857142857143,
+      "final": 0.22222222222222224,
+      "oracle": 0.3846153846153846
+    },
+    {
+      "row": 7874,
+      "initial": 0.4571428571428572,
+      "final": 0.3448275862068966,
+      "oracle": 0.5714285714285714
+    },
+    {
+      "row": 7881,
+      "initial": 0.380952380952381,
+      "final": 0.3529411764705882,
+      "oracle": 0.7272727272727273
+    },
+    {
+      "row": 7909,
+      "initial": 0.3225806451612903,
+      "final": 0.25,
+      "oracle": 0.5714285714285713
+    },
+    {
+      "row": 7912,
+      "initial": 0.2105263157894737,
+      "final": 0.2702702702702703,
+      "oracle": 0.37500000000000006
+    },
+    {
+      "row": 7921,
+      "initial": 0.22222222222222224,
+      "final": 0.39999999999999997,
+      "oracle": 0.48000000000000004
+    },
+    {
+      "row": 7962,
+      "initial": 0.16,
+      "final": 0.1935483870967742,
+      "oracle": 0.5
+    },
+    {
+      "row": 7973,
+      "initial": 0.14814814814814817,
+      "final": 0.058823529411764705,
+      "oracle": 0.6363636363636364
+    },
+    {
+      "row": 7986,
+      "initial": 0.058823529411764705,
+      "final": 0.1142857142857143,
+      "oracle": 0.5
+    },
+    {
+      "row": 7996,
+      "initial": 0.125,
+      "final": 0.10526315789473684,
+      "oracle": 0.5333333333333333
+    },
+    {
+      "row": 8015,
+      "initial": 0.3,
+      "final": 0.2,
+      "oracle": 0.5365853658536586
+    },
+    {
+      "row": 8023,
+      "initial": 0.12903225806451613,
+      "final": 0.23076923076923078,
+      "oracle": 0.358974358974359
+    },
+    {
+      "row": 8054,
+      "initial": 0.27027027027027023,
+      "final": 0.2978723404255319,
+      "oracle": 0.5833333333333334
+    },
+    {
+      "row": 8070,
+      "initial": 0.23255813953488377,
+      "final": 0.19047619047619047,
+      "oracle": 0.5263157894736842
+    },
+    {
+      "row": 8079,
+      "initial": 0.17142857142857143,
+      "final": 0.18181818181818182,
+      "oracle": 0.35000000000000003
+    },
+    {
+      "row": 8084,
+      "initial": 0.16216216216216217,
+      "final": 0.11764705882352941,
+      "oracle": 0.5714285714285714
+    },
+    {
+      "row": 8175,
+      "initial": 0.20512820512820515,
+      "final": 0.33333333333333337,
+      "oracle": 0.4799999999999999
+    },
+    {
+      "row": 8185,
+      "initial": 0.08888888888888889,
+      "final": 0.18749999999999997,
+      "oracle": 0.6666666666666667
+    },
+    {
+      "row": 8199,
+      "initial": 0.17647058823529413,
+      "final": 0.19047619047619047,
+      "oracle": 0.28571428571428575
+    },
+    {
+      "row": 8225,
+      "initial": 0.23529411764705882,
+      "final": 0.27586206896551724,
+      "oracle": 0.5714285714285714
+    },
+    {
+      "row": 8267,
+      "initial": 0.10526315789473685,
+      "final": 0.33333333333333337,
+      "oracle": 0.45714285714285713
+    },
+    {
+      "row": 8274,
+      "initial": 0.21621621621621623,
+      "final": 0.29787234042553196,
+      "oracle": 0.5263157894736842
+    }
+  ],
+  "examples": [
+    {
+      "row": 25,
+      "references": [
+        "The man with pierced ears is wearing glasses and an orange hat.",
+        "A man with glasses is wearing a beer can crocheted hat.",
+        "A man with gauges and glasses is wearing a Blitz hat.",
+        "A man in an orange hat starring at something.",
+        "A man wears an orange hat and glasses."
+      ],
+      "initial": "Two women make and use small breads.  They are making a necklace.  They are both young. \n A: yes B: no\nYou are",
+      "final": "A man is sitting on a street corner with a red and white striped flag on his back.",
+      "oracle": "A man wearing glasses and hat is holding an electronic watch."
+    },
+    {
+      "row": 34,
+      "references": [
+        "A black and white dog is running in a grassy garden surrounded by a white fence.",
+        "A Boston Terrier is running on lush green grass in front of a white fence.",
+        "A black and white dog is running through the grass.",
+        "A dog runs on the green grass near a wooden fence.",
+        "A Boston terrier is running in the grass."
+      ],
+      "initial": "A young boy is playing with a green and yellow pipe in a suburban area.",
+      "final": "A small child is playing with a toy in a swing while holding a green ball.",
+      "oracle": "A black dog is running through a grassy field in the woods. \nExplanation: A black dog is running through a grassy field in the woods."
+    },
+    {
+      "row": 51,
+      "references": [
+        "A young female student performing a downward kick to break a board held by her Karate instructor.",
+        "Girl about to kick a piece of wood in half while karate instructor holds it",
+        "A girl kicking a stick that a man is holding in tae kwon do class.",
+        "A girl in karate uniform breaking a stick with a front kick.",
+        "A girl breaking boards by using karate."
+      ],
+      "initial": "Two people in a conference room microphone speak to a large audience.  Source: YouTube. 00:00.00.00.0",
+      "final": "A man in a field of snow holding a camera to his face.",
+      "oracle": "A girl in karate striking a stick with her knee before a group of kids."
+    },
+    {
+      "row": 89,
+      "references": [
+        "Five snowmobile riders all wearing helmets and goggles line up in a snowy clearing in a forest in front of their snowmobiles; they are all wearing black snow pants and from left to right they are wearing a black coat, white coat, red coat, blue coat, and black coat.",
+        "Five people wearing winter jackets and helmets stand in the snow, with snowmobiles in the background.",
+        "Five people wearing winter clothing, helmets, and ski goggles stand outside in the snow.",
+        "A group of snowmobile riders gather in the snow.",
+        "Group gathered to go snowmobiling."
+      ],
+      "initial": "A group of men are sitting around a campfire eating food. They all appear to be wearing blue jackets.",
+      "final": "A man is sitting on a tan carpet in a field holding a hat. \nOptions:\n (A). Yes\n (B). No\nAnswer:\n(A).",
+      "oracle": "Three snowmobileers, wearing helmets and winter gear, sit in snowmobiles and snow tires. They are parked in the snow."
+    },
+    {
+      "row": 97,
+      "references": [
+        "Two men sitting on the roof of a house while another one stands on a ladder.",
+        "Two men on a rooftop while another man stands atop a ladder watching them",
+        "Three men, one on a ladder, work on a roof.",
+        "People are fixing the roof of a house.",
+        "Three men are working on a roof."
+      ],
+      "initial": "Two people looking over the crowd of people holding a glass of beer.",
+      "final": "Three individuals are shown together in a crowded market where they are preparing food.  Their surroundings are also crowded with people.  They are all dressed in",
+      "oracle": "Three men are working on a roof on a building while one person is standing on the roof."
+    },
+    {
+      "row": 124,
+      "references": [
+        "A bride in a light pink dress poses for a picture with male relatives and is being photographed by a man in a cream shirt with white pants.",
+        "A man in light colored clothing photographs a group of men wearing dark suits and hats standing around a woman dressed in a strapless gown.",
+        "A photographer takes a picture of a group of one girl in a pink dress and 10 boys in suits and hats.",
+        "A man photographs a woman in a pink dress and a throng of men in suits.",
+        "Man taking a photograph of a well dressed group of teens."
+      ],
+      "initial": "A brown dog runs in the forest with his leash. Laborious in the background. License: CC 3.0.0.0.0. License",
+      "final": "A couple of young women are sitting cross-legged on a wooden bench in a room with other people holding hands. The two women are leaning against each other and one",
+      "oracle": "A woman in a black dress takes a picture with a group of men posing for a photograph, while a man in a white shirt and black hat is in the"
+    },
+    {
+      "row": 133,
+      "references": [
+        "A group of 11 people in winter wear such as beanies, skiing jackets, gloves and backpacks are standing in snow paddles outside a house made of ice blocks while a person in front of the door seems to be leading them.",
+        "A group of people wearing snowshoes, and dressed for winter hiking, is standing in front of a building that looks like it's made of blocks of ice.",
+        "The people are quietly listening while the story of the ice cabin was explained to them.",
+        "A group of people standing in front of an igloo.",
+        "Several students waiting outside an igloo."
+      ],
+      "initial": "Two women wearing red blankets and sandals are sitting on a wooden structure. They are playing with a fire. \nClassification: Natural. \nClassification: Natural. \n",
+      "final": "ten people are sitting in a white table setting, one person is writing on a white board, and another is standing in front of a white table. There is",
+      "oracle": "A group of people standing outside and wearing winter coats and gloves are waiting to see the snow."
+    },
+    {
+      "row": 134,
+      "references": [
+        "A baseball player in red leaps into the air to avoid a player in blue, who is shortly behind him as he catches the ball, while other blue team members look on in the background.",
+        "A boy in a red uniform is attempting to avoid getting out at home plate, while the catcher in the blue uniform is attempting to catch him.",
+        "A baseball player coming into home plate with knee held high and the catcher right in front of him waiting for the ball.",
+        "A baseball player attempting to score a run before the catcher tags the player out.",
+        "A baseball catcher trying to tag a base runner in a baseball game."
+      ],
+      "initial": "A bike rider doing a trick on a bicycle in the background. Motivated to be cool. \n\n\nOutput:\n![bike rider doing trick](https://i.stack",
+      "final": "A boy with a black shirt and a blue ball step into a net with a black and white bat. Footage of a competition is seen. 旁观",
+      "oracle": "A baseball player in red trying to catch a ball as a teammate in white and blue watches him from behind. The player is wearing a blue and white uniform."
+    },
+    {
+      "row": 137,
+      "references": [
+        "A man wearing a hat and a white shirt is cleaning windows.",
+        "A man in a white shirt stands high up on scaffolding",
+        "A man stands on boards on top of a huge ladder.",
+        "Man works on top of scaffolding.",
+        "A guy works on a building."
+      ],
+      "initial": "A brown and white man with a camera and a gray shirt is walking around. He is holding a cellphone. \nAnswer: Step 1: Identify the main",
+      "final": "Two individuals are walking in a garden path with multiple objects being thrown. Together with other people. Summary: Two people are walking in a garden path with multiple objects",
+      "oracle": "A man in a hat climbs on a building."
+    },
+    {
+      "row": 199,
+      "references": [
+        "A man wearing a reflective vest sits on the sidewalk and holds up pamphlets with bicycles on the cover.",
+        "Man in bright yellow vest displays bicycle safety information on street.",
+        "A man and woman talking are interrupted and a man covers his face.",
+        "A man in a vest is sitting in a chair and holding magazines.",
+        "A construction worker holds a sign about bicycling."
+      ],
+      "initial": "A couple in a pink car, with a white and black umbrella on the side.  Neighbors watching.  Pedestrian.  Pink car. ",
+      "final": "A man in a black shirt stands on a wooden bench in a green field surrounded by a large, old, blue car. The man is leaning against the car",
+      "oracle": "A man in a vest holds a sign and talks to police while sitting on a street sign."
+    },
+    {
+      "row": 219,
+      "references": [
+        "A mother decides to take her child on a piggyback ride outside their apartment complex.",
+        "A baby boy in a blue and white striped shirt is sitting on his mother's shoulders.",
+        "A mother and her young song enjoying a beautiful day outside.",
+        "A young woman is giving a baby a ride on her shoulders.",
+        "A woman gives a small child a piggyback ride."
+      ],
+      "initial": "A man sits on a large blanket near a statue of a man with a large hand. \n##### Related Questions:\n\n1. ### Math\n\nA man is standing",
+      "final": "A man wearing a blue jacket and wearing a hat is sitting on a bench with his eyes closed and wearing a blue hat while wearing a blue jacket and wearing a",
+      "oracle": "A mother baby is giving a young girl a hug while she is outside."
+    },
+    {
+      "row": 222,
+      "references": [
+        "A male volleyball player in red trunks tries to block the shot of the opposing player during a professional volleyball game.",
+        "Men playing volleyball, with one player missing the ball but hands still in the air.",
+        "A group of spectators watch a men's sand volleyball game.",
+        "Volleyball players compete on a sunny day at the beach.",
+        "Men playing volleyball in the sand."
+      ],
+      "initial": "A couple with a weird-looking car, a man with a big, orange hat, and a woman with a weird-looking face, all in a window. They",
+      "final": "A group of black and brown clad youth in skirts and shirts standing in front of a stage with other people dressed in black and red. They are holding hands and",
+      "oracle": "A group of athletes in tennis shoes play a game at a beach volleyball tournament.  Image is taken during the game.  Men and women are seen playing."
+    },
+    {
+      "row": 228,
+      "references": [
+        "A woman wearing a pink shirt and red apron stands in her restaurant holding food and surrounded by bagged breads, a microwave and the chalkboard menu up on the wall.",
+        "Woman wearing a yellow hat, pink shirt, and red apron is holding food in a kitchen.",
+        "Employee in pink shirt smiles for camera inside a restaurant kitchen.",
+        "A woman holding a bowl of food in a kitchen.",
+        "Women in store happily holding some food."
+      ],
+      "initial": "A blond boy in a blue shirt is in a white box while being introduced to a large white box.",
+      "final": "A boy in a blue shirt and a girl in a white shirt climb a tree in a forest.",
+      "oracle": "Woman in blue shirt holding food in her hands in a restaurant kitchen. She is smiling. Behind her is a table filled with food."
+    },
+    {
+      "row": 246,
+      "references": [
+        "An Asian man in spectacles and a t-shirt preparing some food.",
+        "A man working diligently while sitting at a table.",
+        "Man sitting using tool at a table in his home.",
+        "Indian man whittles in his own home.",
+        "A man is sharpening a knife."
+      ],
+      "initial": "A man lays blue and gray on the sand to build a pile of sand. He uses a shovel.  A blue and gray man lays on the sand",
+      "final": "A man wearing a black and white striped shirt and a yellow safety vest walks down the street.",
+      "oracle": "A man in a workshop sharpening his tools. \n  \n  A man is sharpening his tools in a workshop.  \n  \n  A man is working on"
+    },
+    {
+      "row": 259,
+      "references": [
+        "Spelunkers pose inside a rock cavern while bathed in sunlight from the surface.",
+        "Shaft of light in a cave shows three spelunkers",
+        "Three rock climbers are posing on big rocks.",
+        "People stand inside a rock dome.",
+        "Three people sit in a cave."
+      ],
+      "initial": "A player in a red jacket playing with a pipe while other people watch. \nSentence: A man in a red jacket is playing with a pipe while other people",
+      "final": "A man in a white shirt and cap is performing on a stage, with a man on a stage to his left and a woman on a stage to his right",
+      "oracle": "Three people are standing in a rock formation while drilling."
+    },
+    {
+      "row": 279,
+      "references": [
+        "A girl in a polka dotted blue jean dress walks barefoot on a balance beam.",
+        "A girl in a jean dress is walking along a raised balance beam.",
+        "The little girl is walking a beam in gymnastics class.",
+        "A little girl balances on a gymnastics beam.",
+        "A little girl is walking on a balance beam."
+      ],
+      "initial": "Two young men in t-shirts ride on ice in front of a crowd of people. Title: Ice Skating in the Snow\n\nCaption: Two young men in",
+      "final": "A man with brown hair and a phone is standing in a room with a mirror and wearing a hat. He is also holding a piece of wood. \n#####",
+      "oracle": "A little girl in a blue skirt is walking on a beam. \nA istrador is walking on a beam. \n\nCristian is a istr"
+    },
+    {
+      "row": 304,
+      "references": [
+        "A couple is sitting on the sand with their feet in the water, and they are shaking hands.",
+        "A man and woman wearing sunglasses sit halfway in the water.",
+        "A boy and a girl holding hands while sitting on a shore.",
+        "A couple with sunglasses are laying on the beach.",
+        "A blond holding hands with a guy in the sand."
+      ],
+      "initial": "The man with a white beard and military-style dress has a white headband and a military-style vest. He is wearing a light jacket and a light hat.",
+      "final": "Two men with black shirts and black hats are walking around with a group of people wearing black shirts and black hats, one of them is playing a guitar and the",
+      "oracle": "A couple of people are sitting on the beach and holding hands. The man is holding a camera.  A girl is holding a towel.  doi"
+    },
+    {
+      "row": 318,
+      "references": [
+        "A woman standing with 3 other people in a store with two tables, some shelves with coffee and tea for sale, and a refrigerated drink case.",
+        "A woman in a gray sweater and black baseball cap is standing in line at a shop.",
+        "A woman in a hat waits to be served at a store.",
+        "Young people are standing in the store.",
+        "A woman in a cap at a coffee shop."
+      ],
+      "initial": "A large dog is lying in a field next to a small brown dog. Large dog is next to a small brown dog. \nQuestion: What is the relationship",
+      "final": "A man in a red jacket is standing on a hill with his son in the background.",
+      "oracle": "A woman in a black shirt stands at a coffee stand in a grocery store."
+    },
+    {
+      "row": 340,
+      "references": [
+        "The person has a striped shirt on and is holding on to a rope on a mountain.",
+        "A kid rock climbing against the backdrop of a green valley",
+        "The person in the striped shirt is mountain climbing.",
+        "A woman in a striped shirt climbs up a mountain.",
+        "A young man climbs a rocky hill."
+      ],
+      "initial": "A black dog is cowed by a brown and white dog.",
+      "final": "A man in a uniform is standing guard while someone else poses for the camera.",
+      "oracle": "A climber in a red shirt climbs a cliff with a mountain in the background."
+    },
+    {
+      "row": 395,
+      "references": [
+        "Two young attractive women in front of a store drop coins for street performers.",
+        "Two women enjoy the entertainment of street performers.",
+        "Two men pretend to be statutes while women look on.",
+        "Two young women stop and watch street performers.",
+        "Pedestrians interact with street artists."
+      ],
+      "initial": "A baseball player swings to make contact with the catcher as he is out of bounds. (USA Baseball) Category: Basketball, Baseball, Baseball Player. Description:",
+      "final": "A boy is standing in a forested area with a large rock in the background while a girl in a green dress takes a picture.",
+      "oracle": "Two young women watch street performers while advertising for food.  They appear to be in the city.  Street performers are seen.  Female audience members. "
+    },
+    {
+      "row": 434,
+      "references": [
+        "A group of people standing on the lawn in front of a building.",
+        "Many people in blue jeans stand in front of a white church.",
+        "A large group of people stand outside of a church.",
+        "Family members standing outside a home.",
+        "People standing outside of a building."
+      ],
+      "initial": "A little boy in a brown shirt is playing with a chain saw. He is jumping.",
+      "final": "A man stands before a building with his eyes closed and a woman sitting on the floor next to him.  She appears to be looking at something in her hand",
+      "oracle": "A group of people standing outside of a building. They are wearing casual clothing."
+    },
+    {
+      "row": 472,
+      "references": [
+        "A young girl wearing a blue shirt marching in a band playing a trumpet",
+        "Girl wearing blue shirt and black shorts plays trumped outside.",
+        "A teenager plays her trumpet on the field at a game.",
+        "A girl playing trumpet in a marching band.",
+        "Girl playing the trumpet in a marching band"
+      ],
+      "initial": "A couple is cleaning on the lower tubs, with a blue shirt. Friendly. \"",
+      "final": "Green shirt with number 100 and yellow ball in hand. Men in green shirt. green ball in hand. 2016. 2",
+      "oracle": "A girl playing the saxophone in a marching band playing her tune. Young girl playing the saxophone.  Avidly playing the saxophone.  License"
+    },
+    {
+      "row": 487,
+      "references": [
+        "Person in a brown sweatshirt does a flip in midair over a trampoline with a river and electrical lines in the background.",
+        "A young adult is doing a back flip on a trampoline near a lake.",
+        "A woman is doing flips on a trampoline in front of a lake.",
+        "A woman does a somersault on a trampoline on the beach.",
+        "Trampolines are a fun way to exercise."
+      ],
+      "initial": "A girl with a pink shirt is sitting in a shopping cart on a table in a store.",
+      "final": "A man with a gun is holding his hand to the chest of another man who is wearing a mask and hat. The man is looking at the camera and the",
+      "oracle": "A woman is doing a flip on a trampoline in front of a park. \nChoices: (A). positive (B). negative\nWhat is the sentiment"
+    },
+    {
+      "row": 520,
+      "references": [
+        "A man standing in a bar with a neon beer sign hanging on the wall",
+        "A man stands next to three video game machines and a beer sign.",
+        "A man stands next to a bank of computer gambling machines.",
+        "A man is standing by a group of video games in a bar.",
+        "A man stands next to three video machines."
+      ],
+      "initial": "Three people are wearing sandals and are setting up a lawn chair. The setting is in the middle of the grass. The weather is sunny. The photographer is behind",
+      "final": "Two little boys wearing blue shirts and yellow pants are sitting on the ground near the base of a toy train.",
+      "oracle": "A man stands next to a display of video games behind a bar. \n##### Top 7 Cleaning Services Near Me\n\n##### Top 7 Cleaning Services Near Me"
+    },
+    {
+      "row": 539,
+      "references": [
+        "A woman in a green tank top looking at a drill while a crowd looks on.",
+        "A woman using a power drill in front of a group of people.",
+        "A woman uses a drill while another man takes her picture.",
+        "A woman, in a teal tank top, holding a power drill.",
+        "Spectators about to watch a woman use a drill."
+      ],
+      "initial": "A man, in a green jacket, works on a large, square area of black and white tiles. The man is about 6 feet tall.  Description",
+      "final": "A person in a red and white outfit is riding a motorcycle on a green and yellow track.",
+      "oracle": "A woman in a helmet and shirt using a drill to blow out a cigarette."
+    }
+  ]
+}
\ No newline at end of file