{
  "experiment": "ouro_toroidal_v2_direct_masking",
  "model": "ByteDance/Ouro-1.4B",
  "device": "cpu",
  "date": "2026-02-14T06:00:32.084052",
  "loop_counts": [
    1,
    2,
    3,
    4,
    6,
    8
  ],
  "strengths": [
    0.5,
    1.0,
    2.0
  ],
  "method": "additive toroidal mask injected into attention_mask before softmax",
  "baseline": {
    "4": {
      "perplexity": 2.8896284506608176,
      "accuracy": 0.8,
      "correct_count": 16,
      "total_prompts": 20,
      "details": [
        {
          "prompt": "The capital of France is",
          "answer": "paris.\n\n## step 2: evaluate the options\nlet's evaluate each option to see which one matches the capital of france:\na",
          "keywords": [
            "paris"
          ],
          "correct": true
        },
        {
          "prompt": "Water boils at a temperature of",
          "answer": "100\u00b0c.\n\n## step 2: identify the correct boiling point\nthe boiling point of water is a well-known",
          "keywords": [
            "100",
            "212",
            "celsius",
            "fahrenheit"
          ],
          "correct": true
        },
        {
          "prompt": "The speed of light is approximately",
          "answer": "299,792,458 meters per second.\n\n## step 2: calculate the time it takes for light",
          "keywords": [
            "300",
            "3",
            "km",
            "186"
          ],
          "correct": false
        },
        {
          "prompt": "Newton discovered the law of",
          "answer": "universal gravitation, which states that every point mass attracts every other point mass by a force acting along the line intersecting both points. the force is proportional",
          "keywords": [
            "gravity",
            "gravitation",
            "motion"
          ],
          "correct": true
        },
        {
          "prompt": "The chemical formula for water is",
          "answer": "h2o.\n\n## step 2: identify the correct option\nfrom the given options, the correct chemical formula for water is h2",
          "keywords": [
            "h2o"
          ],
          "correct": true
        },
        {
          "prompt": "DNA stands for",
          "answer": "\"short tandem repeat\" and refers to a region of dna that consists of short, repeated sequences of nucleotides. these sequences are typically 2-6",
          "keywords": [
            "deoxyribonucleic"
          ],
          "correct": false
        },
        {
          "prompt": "The largest planet in our solar system is",
          "answer": "jupiter.\n\nthe final answer is a.",
          "keywords": [
            "jupiter"
          ],
          "correct": true
        },
        {
          "prompt": "Shakespeare wrote the play",
          "answer": ".\n\nso, i think a is correct.\n\nthe answer should be a: william shakespeare.\n\nthe problem says \"put the",
          "keywords": [
            "hamlet",
            "romeo",
            "macbeth",
            "othello",
            "lear"
          ],
          "correct": false
        },
        {
          "prompt": "The theory of relativity was proposed by",
          "answer": "albert einstein in 1905 and 1915.\n\n## step 2: evaluate each option\na: isaac newton",
          "keywords": [
            "einstein",
            "albert"
          ],
          "correct": true
        },
        {
          "prompt": "Photosynthesis converts sunlight into",
          "answer": "chemical energy, which is then used to produce glucose.\n\nso, the process that converts sunlight is photosynthesis.\n\ntherefore, the answer should",
          "keywords": [
            "energy",
            "glucose",
            "sugar",
            "chemical"
          ],
          "correct": true
        },
        {
          "prompt": "The human body has approximately how many bones:",
          "answer": "206.\n\nthe human body has approximately how many bones: 206.\n\nthe human body has approximately how many",
          "keywords": [
            "206"
          ],
          "correct": true
        },
        {
          "prompt": "Mount Everest is located in",
          "answer": "the himalayas, which is in asia.\n\nthe himalayas are in asia, yes.\n\nperhaps the question is about the continent, and asia",
          "keywords": [
            "nepal",
            "himalaya",
            "tibet"
          ],
          "correct": true
        },
        {
          "prompt": "The periodic table was created by",
          "answer": "dmitri mendeleev in 1869. he arranged the elements based on their atomic weights and properties, and he left gaps for",
          "keywords": [
            "mendeleev"
          ],
          "correct": true
        },
        {
          "prompt": "An electron has a charge of",
          "answer": "-1.602 x 10^-19 c. if it moves with a velocity of 2.00 x",
          "keywords": [
            "negative",
            "-1",
            "1.6"
          ],
          "correct": true
        },
        {
          "prompt": "The Great Wall of China was built to",
          "answer": "protect against invasions from the north.\n\n## step 1: evaluate the historical context of the great wall of china\nthe great wall of china",
          "keywords": [
            "protect",
            "defend",
            "invad",
            "mongol",
            "border"
          ],
          "correct": true
        },
        {
          "prompt": "Pi is approximately equal to",
          "answer": "22/7.\n\nthe value of pi is a fundamental constant in mathematics, and its calculation has been a subject of interest for centuries",
          "keywords": [
            "3.14"
          ],
          "correct": false
        },
        {
          "prompt": "The mitochondria is known as the",
          "answer": "powerhouse of the cell because it produces atp through cellular respiration.\n\nso, i think a is correct.\n\nbut let me see if there",
          "keywords": [
            "powerhouse"
          ],
          "correct": true
        },
        {
          "prompt": "The French Revolution began in the year",
          "answer": "1789.\n\nthe american revolution ended in 1783.\n\nso, the american revolution ended before the french",
          "keywords": [
            "1789"
          ],
          "correct": true
        },
        {
          "prompt": "Gravity on Earth accelerates objects at approximately",
          "answer": "9.8 m/s\u00b2.\n\n## step 2: calculate the acceleration due to gravity on the moon\nthe acceleration due to",
          "keywords": [
            "9.8",
            "10",
            "m/s"
          ],
          "correct": true
        },
        {
          "prompt": "The Pythagorean theorem states that",
          "answer": "in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum",
          "keywords": [
            "a\u00b2",
            "a^2",
            "square",
            "hypotenuse",
            "right triangle"
          ],
          "correct": true
        }
      ]
    },
    "8": {
      "perplexity": 2.9534545849155065,
      "accuracy": 0.85,
      "correct_count": 17,
      "total_prompts": 20,
      "details": [
        {
          "prompt": "The capital of France is",
          "answer": "paris.\n\n## step 1: identify the capital of france\nthe capital of france is paris.\n\n## step 2: identify",
          "keywords": [
            "paris"
          ],
          "correct": true
        },
        {
          "prompt": "Water boils at a temperature of",
          "answer": "100 degrees celsius.\n\n## step 3: evaluate the options\n- **a: 0 degrees celsius**: this is the",
          "keywords": [
            "100",
            "212",
            "celsius",
            "fahrenheit"
          ],
          "correct": true
        },
        {
          "prompt": "The speed of light is approximately",
          "answer": "299,792,458 meters per second.\n\nthe speed of light is a fundamental constant in physics, and",
          "keywords": [
            "300",
            "3",
            "km",
            "186"
          ],
          "correct": false
        },
        {
          "prompt": "Newton discovered the law of",
          "answer": "universal gravitation, which states that every point mass attracts every other point mass by a force acting along the line intersecting both points. the force of attraction",
          "keywords": [
            "gravity",
            "gravitation",
            "motion"
          ],
          "correct": true
        },
        {
          "prompt": "The chemical formula for water is",
          "answer": "h2o.\n\n## step 2: identify the elements in water\nwater is composed of two elements: hydrogen (h) and oxygen",
          "keywords": [
            "h2o"
          ],
          "correct": true
        },
        {
          "prompt": "DNA stands for",
          "answer": "\"double helix,\" which is the shape of dna.\n\nso, i think it's fine.\n\nperhaps the answer is c.",
          "keywords": [
            "deoxyribonucleic"
          ],
          "correct": false
        },
        {
          "prompt": "The largest planet in our solar system is",
          "answer": "jupiter.\n\nthe final answer is a.",
          "keywords": [
            "jupiter"
          ],
          "correct": true
        },
        {
          "prompt": "Shakespeare wrote the play",
          "answer": "in 1599, and it was performed in 1599.\n\nthe play was written in 1599",
          "keywords": [
            "hamlet",
            "romeo",
            "macbeth",
            "othello",
            "lear"
          ],
          "correct": false
        },
        {
          "prompt": "The theory of relativity was proposed by",
          "answer": "albert einstein in 1905 and 1915.\n\n## step \nthe theory of relativity is a fundamental concept in",
          "keywords": [
            "einstein",
            "albert"
          ],
          "correct": true
        },
        {
          "prompt": "Photosynthesis converts sunlight into",
          "answer": "chemical energy, which is then used to produce glucose.\n\nso, the process of photosynthesis is the conversion of light energy to chemical energy.",
          "keywords": [
            "energy",
            "glucose",
            "sugar",
            "chemical"
          ],
          "correct": true
        },
        {
          "prompt": "The human body has approximately how many bones:",
          "answer": "206\n- the human body has approximately how many cells: 37 trillion\n- the human body has approximately how many hairs:",
          "keywords": [
            "206"
          ],
          "correct": true
        },
        {
          "prompt": "Mount Everest is located in",
          "answer": "the himalayas, which is in asia.\n\nthe himalayas are in asia, yes.\n\nbut let's see the options: a is mount",
          "keywords": [
            "nepal",
            "himalaya",
            "tibet"
          ],
          "correct": true
        },
        {
          "prompt": "The periodic table was created by",
          "answer": "dmitri mendeleev in 1869. he arranged the elements based on their atomic weights and properties, and he left gaps for",
          "keywords": [
            "mendeleev"
          ],
          "correct": true
        },
        {
          "prompt": "An electron has a charge of",
          "answer": "-1.602 \u00d7 10^-19 c and a mass of 9.109 \u00d7 10^",
          "keywords": [
            "negative",
            "-1",
            "1.6"
          ],
          "correct": true
        },
        {
          "prompt": "The Great Wall of China was built to",
          "answer": "protect against invasions from nomadic tribes.\n\ni: the great wall of china was built to protect against invasions from nomadic tribes.\n\nj:",
          "keywords": [
            "protect",
            "defend",
            "invad",
            "mongol",
            "border"
          ],
          "correct": true
        },
        {
          "prompt": "Pi is approximately equal to",
          "answer": "3.141592653589793.\n\nthe program should also handle the case where the",
          "keywords": [
            "3.14"
          ],
          "correct": true
        },
        {
          "prompt": "The mitochondria is known as the",
          "answer": "powerhouse of the cell.\n\nso, i think a is the answer.\n\nthe question says \"which of the following statements,\" and it",
          "keywords": [
            "powerhouse"
          ],
          "correct": true
        },
        {
          "prompt": "The French Revolution began in the year",
          "answer": "1789.\n\nthe american revolution ended in 1783.\n\nthe french revolution was influenced by the american revolution",
          "keywords": [
            "1789"
          ],
          "correct": true
        },
        {
          "prompt": "Gravity on Earth accelerates objects at approximately",
          "answer": "9.8 m/s\u00b2.\n\n## step 2: calculate the acceleration due to gravity on the moon\nthe acceleration due to",
          "keywords": [
            "9.8",
            "10",
            "m/s"
          ],
          "correct": true
        },
        {
          "prompt": "The Pythagorean theorem states that",
          "answer": "in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum",
          "keywords": [
            "a\u00b2",
            "a^2",
            "square",
            "hypotenuse",
            "right triangle"
          ],
          "correct": true
        }
      ]
    }
  },
  "toroidal": {
    "strength_0.5": {
      "1": {
        "perplexity": 11.913366486690055,
        "accuracy": 0.65,
        "correct_count": 13,
        "total_prompts": 20,
        "details": [
          {
            "prompt": "The capital of France is",
            "answer": "paris.\n\nthe capital of france is paris.\n\nthe capital of france is paris.\n\nthe capital of france is paris.",
            "keywords": [
              "paris"
            ],
            "correct": true
          },
          {
            "prompt": "Water boils at a temperature of",
            "answer": "100 degrees celsius.\n\nthe temperature of the\n\n**100 degrees celsius**\n\n**100 degrees celsius",
            "keywords": [
              "100",
              "212",
              "celsius",
              "fahrenheit"
            ],
            "correct": true
          },
          {
            "prompt": "The speed of light is approximately",
            "answer": "299,792,458 meters per second.\n\n## step 2: calculate the\nto find the distance",
            "keywords": [
              "300",
              "3",
              "km",
              "186"
            ],
            "correct": false
          },
          {
            "prompt": "Newton discovered the law of",
            "answer": "universal gravitation, which states that every point mass in the universe attracts every other point mass with a force proportional to the product of their masses and inversely",
            "keywords": [
              "gravity",
              "gravitation",
              "motion"
            ],
            "correct": true
          },
          {
            "prompt": "The chemical formula for water is",
            "answer": "h2o, which is a molecule, not a formula, but it's the\n\nthe problem says \"a formula for the chemical formula of",
            "keywords": [
              "h2o"
            ],
            "correct": true
          },
          {
            "prompt": "DNA stands for",
            "answer": "the\n\nthe\n\nthe\n\nthe\n\nthe\n\nthe\n\nthe\n\nthe\n\nthe\n\nthe",
            "keywords": [
              "deoxyribonucleic"
            ],
            "correct": false
          },
          {
            "prompt": "The largest planet in our solar system is",
            "answer": "jupiter, which is 11.2141172117211721172117",
            "keywords": [
              "jupiter"
            ],
            "correct": true
          },
          {
            "prompt": "Shakespeare wrote the play",
            "answer": ", and it was published in 1623.\n\nthe first performance of the play is often considered to be in 160",
            "keywords": [
              "hamlet",
              "romeo",
              "macbeth",
              "othello",
              "lear"
            ],
            "correct": false
          },
          {
            "prompt": "The theory of relativity was proposed by",
            "answer": "albert einstein in 1905.\n\nthe theory of relativity is a theory of the\n\nthe 1905 theory of",
            "keywords": [
              "einstein",
              "albert"
            ],
            "correct": true
          },
          {
            "prompt": "Photosynthesis converts sunlight into",
            "answer": "the.\n\nthe.\n\nthe.\n\nthe.\n\nthe.\n\nthe.\n\nthe.\n\nthe.",
            "keywords": [
              "energy",
              "glucose",
              "sugar",
              "chemical"
            ],
            "correct": false
          },
          {
            "prompt": "The human body has approximately how many bones:",
            "answer": "a: 206\nb: 208\nc: 210\nd: 212\ne",
            "keywords": [
              "206"
            ],
            "correct": true
          },
          {
            "prompt": "Mount Everest is located in",
            "answer": "the\n\nquestion: what is the primary purpose of the text? answer: to provide information about the height of the mount everest, its location,",
            "keywords": [
              "nepal",
              "himalaya",
              "tibet"
            ],
            "correct": false
          },
          {
            "prompt": "The periodic table was created by",
            "answer": "dmitri mendeleev in 1869.\n\nthe first atomic theory of matter, which is the\n\nthe",
            "keywords": [
              "mendeleev"
            ],
            "correct": true
          },
          {
            "prompt": "An electron has a charge of",
            "answer": "-1. the\n\n**1.1.1.1.1.1.1.1.1.1.1.1",
            "keywords": [
              "negative",
              "-1",
              "1.6"
            ],
            "correct": true
          },
          {
            "prompt": "The Great Wall of China was built to",
            "answer": "protect the\n\nquestion: what is the primary purpose of the great wall of china? answer: to protect the chinese empire from invasions and to serve",
            "keywords": [
              "protect",
              "defend",
              "invad",
              "mongol",
              "border"
            ],
            "correct": true
          },
          {
            "prompt": "Pi is approximately equal to",
            "answer": "the\n\n**[1]**\n\n**[2]**\n\n**[3]**\n\n**[4]**",
            "keywords": [
              "3.14"
            ],
            "correct": false
          },
          {
            "prompt": "The mitochondria is known as the",
            "answer": "question: what is the primary function of mitochondria in cells? answer: the primary function of mitochondria is to produce energy for the cell.",
            "keywords": [
              "powerhouse"
            ],
            "correct": false
          },
          {
            "prompt": "The French Revolution began in the year",
            "answer": "1789. the first year of the revolution, the year 1789, is not the year 1789",
            "keywords": [
              "1789"
            ],
            "correct": true
          },
          {
            "prompt": "Gravity on Earth accelerates objects at approximately",
            "answer": "9.8 m/s\u00b2.\n\n## step 2: calculate the\nto find the acceleration due to gravity on the surface of",
            "keywords": [
              "9.8",
              "10",
              "m/s"
            ],
            "correct": true
          },
          {
            "prompt": "The Pythagorean theorem states that",
            "answer": "\\[\na^2 + b^2 = c^2\n\\]\n\nwhere \\(a\\) and \\(",
            "keywords": [
              "a\u00b2",
              "a^2",
              "square",
              "hypotenuse",
              "right triangle"
            ],
            "correct": true
          }
        ]
      }
    }
  }
}