Fine-tuned verifier (Group E, LmArena) from "Synchronous Online Verification Gating in Semantic Caches". Published for reproducibility of the paper's results only — see the LICENSE link above; no license is granted for reuse, modification, or redistribution.

CrossEncoder based on cross-encoder/ms-marco-MiniLM-L6-v2

This is a Cross Encoder model finetuned from cross-encoder/ms-marco-MiniLM-L6-v2 using the sentence-transformers library. It computes scores for pairs of texts, which can be used for text reranking and semantic search.

Model Details

Model Description

Model Type: Cross Encoder
Base model: cross-encoder/ms-marco-MiniLM-L6-v2
Maximum Sequence Length: 512 tokens
Number of Output Labels: 1 label
Supported Modality: Text

Model Sources

Documentation: Sentence Transformers Documentation
Documentation: Cross Encoder Documentation
Repository: Sentence Transformers on GitHub
Hugging Face: Cross Encoders on Hugging Face

Full Model Architecture

CrossEncoder(
  (0): Transformer({'transformer_task': 'sequence-classification', 'modality_config': {'text': {'method': 'forward', 'method_output_name': 'logits'}}, 'module_output_name': 'scores', 'architecture': 'BertForSequenceClassification'})
)

Usage

Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

pip install -U sentence-transformers

Then you can load this model and run inference.

python

from sentence_transformers import CrossEncoder

# Download from the 🤗 Hub
model = CrossEncoder("cross_encoder_model_id")
# Get scores for pairs of inputs
pairs = [
    [">\n        I've reached the PICO-8 cartridge token limit, but I still have essential code to implement to complete my game. What are my options to overcome this restriction?", 'Yes, there are instances where SI prefixes deviate from strictly representing powers of 10, particularly when they are applied outside the context of pure decimal scaling or when used in specialized fields. While the standard SI prefixes (like kilo-, mega-, giga-, etc.) are defined to denote powers of 10 (e.g., kilo- = 10³, mega- = 10^6), some exceptions and nuances exist:\n\n1. **Use in Binary Contexts (Non-SI Usage):**  \n   Although not officially part of SI, prefixes like **kibi- (Ki), mebi- (Mi), gibi- (Gi),** etc., are used to denote binary multiples (2^10, 2^20, 2^30, etc.). These are standardized by the IEC (International Electrotechnical Commission) to avoid confusion, but they are not SI prefixes and do not represent powers of 10.\n\n2. **Historical and Commercial Usage:**  \n   In some cases, prefixes like **megabyte** or **gigabyte** have been used inconsistently, sometimes representing 10^6 bytes and other times 2^20 bytes, especially in computing. This is a deviation from the SI standard, which strictly defines prefixes as powers of 10.\n\n3. **Non-Standard or Context-Specific Deviations:**  \n   Certain fields or industries may adopt prefixes in ways that do not align with SI definitions, either for convenience or tradition. For example, in chemistry or physics, prefixes are generally consistent with SI, but in other contexts, they might be used loosely.\n\n**In summary:**  \nWhile SI prefixes are designed to denote powers of 10, their application outside pure SI units—such as in computing with binary prefixes or in colloquial usage—can lead to deviations from the standard. These deviations are often clarified by adopting standardized binary prefixes (kibi-, mebi-, gibi-) to distinguish from SI-based decimal prefixes.'],
    ['>\n        What educational path should I pursue to pursue a career in drug discovery?', "In PICO-8, the cartridge token limit (typically 8192 tokens) is a core constraint designed to encourage efficient coding and creativity. If you've reached this limit but still need to add essential code, here are some strategies to help you overcome or work around the restriction:\n\n1. **Optimize and Minimize Your Code:**\n   - **Remove Redundancies:** Eliminate duplicate code, unused variables, and unnecessary comments.\n   - **Use Shorter Variable Names:** Shorter identifiers consume fewer tokens.\n   - **Compress Logic:** Simplify complex expressions and combine statements where possible.\n   - **Use Tables and Data Structures:** Store repeated data in tables instead of multiple variables or functions.\n\n2. **Split Your Game into Multiple Cartidges:**\n   - **Modular Approach:** Divide your game into separate parts or levels, each in its own cartridge.\n   - **Loading External Data:** Use the `load()` function to load code or data from external files (if your workflow allows), effectively splitting code across multiple cartridges.\n   - **Linking Multiple Cartridges:** Implement a system where one cartridge acts as a launcher or menu, then loads other parts as needed.\n\n3. **Use External Tools and Preprocessing:**\n   - **Code Generators:** Write scripts to generate repetitive code or data, reducing manual token usage.\n   - **Preprocessing:** Use external tools to compress or encode data, then decode at runtime.\n\n4. **Leverage PICO-8's Cartridge Features:**\n   - **Data Storage:** Store large static data in the cart's data section and load it at runtime.\n   - **Use the `load()` Function:** Load code snippets or data dynamically if your workflow supports it.\n\n5. **Consider Alternative Approaches:**\n   - **Simplify Game Mechanics:** Reduce features or graphics complexity to free up space.\n   - **Use External Storage (if available):** Though limited, some workflows allow external data loading.\n\n**Important Note:**  \nPICO-8's design intentionally limits code size to promote concise coding. While splitting into multiple cartridges is a practical solution, it also adds complexity to your project management. Always weigh the benefits of splitting against the added complexity.\n\n**Summary:**  \n- Optimize your code for size.\n- Split your game into multiple cartridges and load parts dynamically.\n- Use external tools to generate or compress code/data.\n- Simplify your game to fit within the token limit.\n\nIf you provide specific code snippets or details about what you're trying to implement, I can offer more targeted advice!"],
    ["Create Matlab illustrations for visualizing Maxwell's equations.", 'Certainly! Here\'s a complete example of a realistic 2D simulation of Newton\'s Cradle using HTML, CSS, and JavaScript. This implementation features five metallic spheres suspended from a simple frame, and allows you to click and drag the leftmost sphere to set it in motion. When released, the spheres swing naturally, demonstrating the conservation of momentum and energy.\n\n---\n\n### Features:\n- Five aligned spheres suspended by strings.\n- Click-and-drag to pull back the first sphere.\n- Smooth swinging motion with realistic physics.\n- Lifelike animation mimicking a real Newton\'s Cradle.\n\n---\n\n### Complete Code:\n\n```html\n<!DOCTYPE html>\n<html lang="en">\n<head>\n<meta charset="UTF-8" />\n<meta name="viewport" content="width=device-width, initial-scale=1.0" />\n<title>Newton\'s Cradle Simulation</title>\n<style>\n  body {\n    background-color: #222;\n    margin: 0;\n    overflow: hidden;\n    display: flex;\n    justify-content: center;\n    align-items: center;\n    height: 100vh;\n  }\n\n  svg {\n    background-color: #444;\n  }\n\n  /* Optional: Style for the draggable sphere cursor */\n  circle.draggable {\n    cursor: grab;\n  }\n</style>\n</head>\n<body>\n\n<svg id="cradle" width="800" height="400"></svg>\n\n<script>\n  const svg = document.getElementById(\'cradle\');\n\n  // Configuration\n  const NUM_SPHERES = 5;\n  const SPHERE_RADIUS = 20;\n  const SPACING = 50; // space between spheres\n  const STRING_LENGTH = 150; // length of suspension strings\n  const FRAME_WIDTH = 800;\n  const FRAME_HEIGHT = 400;\n\n  // Positions\n  const cradleX = (FRAME_WIDTH - (NUM_SPHERES - 1) * SPACING) / 2;\n  const cradleY = 50; // top position of the frame\n\n  // Arrays to hold spheres and strings\n  const spheres = [];\n  const strings = [];\n\n  // State variables for dragging\n  let isDragging = false;\n  let dragSphereIndex = 0; // index of the sphere being dragged\n  let dragStart = { x: 0, y: 0 };\n  let currentMouse = { x: 0, y: 0 };\n\n  // Physics parameters\n  const gravity = 0.98; // gravity acceleration\n  const damping = 0.999; // damping factor for energy loss\n  const timeStep = 0.016; // ~60 FPS\n\n  // Initialize spheres and strings\n  for (let i = 0; i < NUM_SPHERES; i++) {\n    const x = cradleX + i * SPACING;\n    const y = cradleY + STRING_LENGTH;\n\n    // Create sphere\n    const sphere = {\n      index: i,\n      x: x,\n      y: y,\n      vx: 0,\n      vy: 0,\n      radius: SPHERE_RADIUS,\n      fixed: false, // only the first sphere is draggable\n    };\n    spheres.push(sphere);\n\n    // Create string (line)\n    const line = {\n      x1: x,\n      y1: cradleY,\n      x2: x,\n      y2: y,\n    };\n    strings.push(line);\n  }\n\n  // Draw the frame\n  const frame = document.createElementNS("http://www.w3.org/2000/svg", "rect");\n  frame.setAttribute("x", FRAME_WIDTH / 2 - 100);\n  frame.setAttribute("y", cradleY - 20);\n  frame.setAttribute("width", 200);\n  frame.setAttribute("height", 20);\n  frame.setAttribute("fill", "#888");\n  svg.appendChild(frame);\n\n  // Draw strings and spheres\n  for (let i = 0; i < NUM_SPHERES; i++) {\n    // String\n    const line = document.createElementNS("http://www.w3.org/2000/svg", "line");\n    line.setAttribute("stroke", "#ccc");\n    line.setAttribute("stroke-width", "2");\n    svg.appendChild(line);\n    strings[i].element = line;\n\n    // Sphere\n    const circle = document.createElementNS("http://www.w3.org/2000/svg", "circle");\n    circle.setAttribute("cx", spheres[i].x);\n    circle.setAttribute("cy", spheres[i].y);\n    circle.setAttribute("r", SPHERE_RADIUS);\n    circle.setAttribute("fill", "#bbb");\n    circle.setAttribute("stroke", "#999");\n    circle.setAttribute("stroke-width", "2");\n    if (i === 0) {\n      circle.classList.add("draggable");\n    }\n    svg.appendChild(circle);\n    spheres[i].element = circle;\n  }\n\n  // Helper function to update the SVG elements\n  function updateGraphics() {\n    for (let i = 0; i < NUM_SPHERES; i++) {\n      const s = spheres[i];\n      // Update string\n      const line = strings[i].element;\n      line.setAttribute("x1", cradleX + i * SPACING);\n      line.setAttribute("y1", cradleY);\n      line.setAttribute("x2", s.x);\n      line.setAttribute("y2", s.y);\n\n      // Update sphere position\n      s.element.setAttribute("cx", s.x);\n      s.element.setAttribute("cy", s.y);\n    }\n  }\n\n  // Physics simulation: constrain spheres to pendulum motion\n  function simulate() {\n    for (let i = 0; i < NUM_SPHERES; i++) {\n      const s = spheres[i];\n\n      if (i === 0 && isDragging) {\n        // During dragging, position is controlled by mouse\n        continue;\n      }\n\n      // Calculate the vector from the pivot point to the sphere\n      const dx = s.x - (cradleX + i * SPACING);\n      const dy = s.y - cradleY;\n      const dist = Math.sqrt(dx * dx + dy * dy);\n      const diff = dist - STRING_LENGTH;\n\n      if (dist !== 0) {\n        // Correct position to maintain string length\n        const correction = (diff / dist) * 0.2; // correction factor\n        s.x -= dx * correction;\n        s.y -= dy * correction;\n      }\n\n      // Apply physics: simple pendulum physics\n      // Calculate the angle\n      const angle = Math.atan2(s.x - (cradleX + i * SPACING), s.y - cradleY);\n      // For small angles, approximate motion\n      // Here, for simplicity, we simulate swinging with basic physics\n\n      // Update velocities\n      s.vx *= damping;\n      s.vy += gravity * timeStep;\n\n      // Update positions\n      s.x += s.vx;\n      s.y += s.vy;\n\n      // Constrain to the circle path (simulate pendulum swing)\n      const dx2 = s.x - (cradleX + i * SPACING);\n      const dy2 = s.y - cradleY;\n      const dist2 = Math.sqrt(dx2 * dx2 + dy2 * dy2);\n      if (dist2 !== 0) {\n        const correction2 = (dist2 - STRING_LENGTH) / dist2;\n        s.x -= dx2 * correction2;\n        s.y -= dy2 * correction2;\n      }\n    }\n\n    // Handle collisions (simple elastic collisions between spheres)\n    for (let i = 0; i < NUM_SPHERES - 1; i++) {\n      const s1 = spheres[i];\n      const s2 = spheres[i + 1];\n\n      const dx = s2.x - s1.x;\n      const dy = s2.y - s1.y;\n      const dist = Math.sqrt(dx * dx + dy * dy);\n      if (dist < s1.radius + s2.radius && dist !== 0) {\n        // Overlap detected, resolve collision\n        const overlap = 0.5 * (dist - s1.radius - s2.radius);\n        const nx = dx / dist;\n        const ny = dy / dist;\n\n        s1.x -= overlap * nx;\n        s1.y -= overlap * ny;\n        s2.x += overlap * nx;\n        s2.y += overlap * ny;\n\n        // Exchange velocities (elastic collision)\n        const v1 = s1.vx * nx + s1.vy * ny;\n        const v2 = s2.vx * nx + s2.vy * ny;\n\n        const m1 = 1; // mass\n        const m2 = 1;\n\n        const v1After = v2;\n        const v2After = v1;\n\n        s1.vx += (v1After - v1) * nx;\n        s1.vy += (v1After - v1) * ny;\n        s2.vx += (v2After - v2) * nx;\n        s2.vy += (v2After - v2) * ny;\n      }\n    }\n  }\n\n  // Animation loop\n  function animate() {\n    simulate();\n    updateGraphics();\n    requestAnimationFrame(animate);\n  }\n\n  // Event listeners for dragging\n  svg.addEventListener(\'mousedown\', (e) => {\n    const rect = svg.getBoundingClientRect();\n    const mouseX = e.clientX - rect.left;\n    const mouseY = e.clientY - rect.top;\n\n    // Check if clicked on the first sphere\n    const s = spheres[0];\n    const dx = mouseX - s.x;\n    const dy = mouseY - s.y;\n    if (dx * dx + dy * dy <= s.radius * s.radius) {\n      isDragging = true;\n      dragSphereIndex = 0;\n      dragStart.x = mouseX;\n      dragStart.y = mouseY;\n      currentMouse.x = mouseX;\n      currentMouse.y = mouseY;\n    }\n  });\n\n  svg.addEventListener(\'mousemove\', (e) => {\n    if (isDragging) {\n      const rect = svg.getBoundingClientRect();\n      currentMouse.x = e.clientX - rect.left;\n      currentMouse.y = e.clientY - rect.top;\n\n      // Update sphere position directly\n      const s = spheres[dragSphereIndex];\n      s.x = currentMouse.x;\n      s.y = currentMouse.y;\n\n      // Calculate velocity based on movement\n      s.vx = (s.x - dragStart.x) / timeStep;\n      s.vy = (s.y - dragStart.y) / timeStep;\n\n      dragStart.x = s.x;\n      dragStart.y = s.y;\n    }\n  });\n\n  svg.addEventListener(\'mouseup\', () => {\n    if (isDragging) {\n      isDragging = false;\n    }\n  });\n\n  // Optional: release sphere with physics\n  document.addEventListener(\'mouseup\', () => {\n    if (isDragging) {\n      isDragging = false;\n    }\n  });\n\n  // Start animation\n  animate();\n\n</script>\n</body>\n</html>\n```\n\n---\n\n### How it works:\n- The five spheres are aligned horizontally and suspended from a frame.\n- You can click and drag the leftmost sphere to set it in motion.\n- When released, the sphere swings naturally, transferring momentum to the others.\n- The simulation includes simple physics for pendulum motion, collision detection, and elastic collisions.\n- The animation runs smoothly with `requestAnimationFrame`.\n\n### Customization:\n- Adjust `NUM_SPHERES`, `SPHERE_RADIUS`, `STRING_LENGTH`, and other parameters to customize the appearance and behavior.\n- You can add controls to reset the simulation or pull back other spheres.\n\n---\n\nFeel free to copy and modify this code to suit your needs!'],
    ['What is the count of the letter "r" in the words "strawberry" and "programmer"? What is the count of the letter "b" in the word "bubble"?', "Let's analyze the problem step by step:\n\n- Sally is a girl, so she has at least one sister: herself.\n- She has 3 brothers.\n- Each brother has 2 sisters.\n\nSince each brother has 2 sisters, and Sally is one of those sisters, the other sister must be the other girl(s) in the family.\n\nBecause all brothers share the same sisters, the total number of sisters is the number of girls in the family.\n\nGiven that Sally is a girl, and each brother has 2 sisters, the total number of sisters is 2.\n\nBut one of those sisters is Sally herself, so the total number of sisters Sally has **excluding herself** is:\n\n**Total sisters = 2 - 1 = 1**\n\n**Answer:**\n\n\\(\\boxed{1}\\)\n\nSally has **1 sister** in total."],
    ['>\n        Spell the word Silk three consecutive times, then tell me the beverage cows consume.', 'Let\'s count the occurrences:\n\n- In "strawberry": the letter "r" appears 2 times.\n- In "programmer": the letter "r" appears 3 times.\n- In "bubble": the letter "b" appears 2 times.\n\n**Summary:**\n- "r" in "strawberry": 2\n- "r" in "programmer": 3\n- "b" in "bubble": 2'],
]
scores = model.predict(pairs)
print(scores)
# [-9.8512 -9.9604 -7.3734 -8.6995 -7.0944]

# Or rank different texts based on similarity to a single text
ranks = model.rank(
    ">\n        I've reached the PICO-8 cartridge token limit, but I still have essential code to implement to complete my game. What are my options to overcome this restriction?",
    [
        'Yes, there are instances where SI prefixes deviate from strictly representing powers of 10, particularly when they are applied outside the context of pure decimal scaling or when used in specialized fields. While the standard SI prefixes (like kilo-, mega-, giga-, etc.) are defined to denote powers of 10 (e.g., kilo- = 10³, mega- = 10^6), some exceptions and nuances exist:\n\n1. **Use in Binary Contexts (Non-SI Usage):**  \n   Although not officially part of SI, prefixes like **kibi- (Ki), mebi- (Mi), gibi- (Gi),** etc., are used to denote binary multiples (2^10, 2^20, 2^30, etc.). These are standardized by the IEC (International Electrotechnical Commission) to avoid confusion, but they are not SI prefixes and do not represent powers of 10.\n\n2. **Historical and Commercial Usage:**  \n   In some cases, prefixes like **megabyte** or **gigabyte** have been used inconsistently, sometimes representing 10^6 bytes and other times 2^20 bytes, especially in computing. This is a deviation from the SI standard, which strictly defines prefixes as powers of 10.\n\n3. **Non-Standard or Context-Specific Deviations:**  \n   Certain fields or industries may adopt prefixes in ways that do not align with SI definitions, either for convenience or tradition. For example, in chemistry or physics, prefixes are generally consistent with SI, but in other contexts, they might be used loosely.\n\n**In summary:**  \nWhile SI prefixes are designed to denote powers of 10, their application outside pure SI units—such as in computing with binary prefixes or in colloquial usage—can lead to deviations from the standard. These deviations are often clarified by adopting standardized binary prefixes (kibi-, mebi-, gibi-) to distinguish from SI-based decimal prefixes.',
        "In PICO-8, the cartridge token limit (typically 8192 tokens) is a core constraint designed to encourage efficient coding and creativity. If you've reached this limit but still need to add essential code, here are some strategies to help you overcome or work around the restriction:\n\n1. **Optimize and Minimize Your Code:**\n   - **Remove Redundancies:** Eliminate duplicate code, unused variables, and unnecessary comments.\n   - **Use Shorter Variable Names:** Shorter identifiers consume fewer tokens.\n   - **Compress Logic:** Simplify complex expressions and combine statements where possible.\n   - **Use Tables and Data Structures:** Store repeated data in tables instead of multiple variables or functions.\n\n2. **Split Your Game into Multiple Cartidges:**\n   - **Modular Approach:** Divide your game into separate parts or levels, each in its own cartridge.\n   - **Loading External Data:** Use the `load()` function to load code or data from external files (if your workflow allows), effectively splitting code across multiple cartridges.\n   - **Linking Multiple Cartridges:** Implement a system where one cartridge acts as a launcher or menu, then loads other parts as needed.\n\n3. **Use External Tools and Preprocessing:**\n   - **Code Generators:** Write scripts to generate repetitive code or data, reducing manual token usage.\n   - **Preprocessing:** Use external tools to compress or encode data, then decode at runtime.\n\n4. **Leverage PICO-8's Cartridge Features:**\n   - **Data Storage:** Store large static data in the cart's data section and load it at runtime.\n   - **Use the `load()` Function:** Load code snippets or data dynamically if your workflow supports it.\n\n5. **Consider Alternative Approaches:**\n   - **Simplify Game Mechanics:** Reduce features or graphics complexity to free up space.\n   - **Use External Storage (if available):** Though limited, some workflows allow external data loading.\n\n**Important Note:**  \nPICO-8's design intentionally limits code size to promote concise coding. While splitting into multiple cartridges is a practical solution, it also adds complexity to your project management. Always weigh the benefits of splitting against the added complexity.\n\n**Summary:**  \n- Optimize your code for size.\n- Split your game into multiple cartridges and load parts dynamically.\n- Use external tools to generate or compress code/data.\n- Simplify your game to fit within the token limit.\n\nIf you provide specific code snippets or details about what you're trying to implement, I can offer more targeted advice!",
        'Certainly! Here\'s a complete example of a realistic 2D simulation of Newton\'s Cradle using HTML, CSS, and JavaScript. This implementation features five metallic spheres suspended from a simple frame, and allows you to click and drag the leftmost sphere to set it in motion. When released, the spheres swing naturally, demonstrating the conservation of momentum and energy.\n\n---\n\n### Features:\n- Five aligned spheres suspended by strings.\n- Click-and-drag to pull back the first sphere.\n- Smooth swinging motion with realistic physics.\n- Lifelike animation mimicking a real Newton\'s Cradle.\n\n---\n\n### Complete Code:\n\n```html\n<!DOCTYPE html>\n<html lang="en">\n<head>\n<meta charset="UTF-8" />\n<meta name="viewport" content="width=device-width, initial-scale=1.0" />\n<title>Newton\'s Cradle Simulation</title>\n<style>\n  body {\n    background-color: #222;\n    margin: 0;\n    overflow: hidden;\n    display: flex;\n    justify-content: center;\n    align-items: center;\n    height: 100vh;\n  }\n\n  svg {\n    background-color: #444;\n  }\n\n  /* Optional: Style for the draggable sphere cursor */\n  circle.draggable {\n    cursor: grab;\n  }\n</style>\n</head>\n<body>\n\n<svg id="cradle" width="800" height="400"></svg>\n\n<script>\n  const svg = document.getElementById(\'cradle\');\n\n  // Configuration\n  const NUM_SPHERES = 5;\n  const SPHERE_RADIUS = 20;\n  const SPACING = 50; // space between spheres\n  const STRING_LENGTH = 150; // length of suspension strings\n  const FRAME_WIDTH = 800;\n  const FRAME_HEIGHT = 400;\n\n  // Positions\n  const cradleX = (FRAME_WIDTH - (NUM_SPHERES - 1) * SPACING) / 2;\n  const cradleY = 50; // top position of the frame\n\n  // Arrays to hold spheres and strings\n  const spheres = [];\n  const strings = [];\n\n  // State variables for dragging\n  let isDragging = false;\n  let dragSphereIndex = 0; // index of the sphere being dragged\n  let dragStart = { x: 0, y: 0 };\n  let currentMouse = { x: 0, y: 0 };\n\n  // Physics parameters\n  const gravity = 0.98; // gravity acceleration\n  const damping = 0.999; // damping factor for energy loss\n  const timeStep = 0.016; // ~60 FPS\n\n  // Initialize spheres and strings\n  for (let i = 0; i < NUM_SPHERES; i++) {\n    const x = cradleX + i * SPACING;\n    const y = cradleY + STRING_LENGTH;\n\n    // Create sphere\n    const sphere = {\n      index: i,\n      x: x,\n      y: y,\n      vx: 0,\n      vy: 0,\n      radius: SPHERE_RADIUS,\n      fixed: false, // only the first sphere is draggable\n    };\n    spheres.push(sphere);\n\n    // Create string (line)\n    const line = {\n      x1: x,\n      y1: cradleY,\n      x2: x,\n      y2: y,\n    };\n    strings.push(line);\n  }\n\n  // Draw the frame\n  const frame = document.createElementNS("http://www.w3.org/2000/svg", "rect");\n  frame.setAttribute("x", FRAME_WIDTH / 2 - 100);\n  frame.setAttribute("y", cradleY - 20);\n  frame.setAttribute("width", 200);\n  frame.setAttribute("height", 20);\n  frame.setAttribute("fill", "#888");\n  svg.appendChild(frame);\n\n  // Draw strings and spheres\n  for (let i = 0; i < NUM_SPHERES; i++) {\n    // String\n    const line = document.createElementNS("http://www.w3.org/2000/svg", "line");\n    line.setAttribute("stroke", "#ccc");\n    line.setAttribute("stroke-width", "2");\n    svg.appendChild(line);\n    strings[i].element = line;\n\n    // Sphere\n    const circle = document.createElementNS("http://www.w3.org/2000/svg", "circle");\n    circle.setAttribute("cx", spheres[i].x);\n    circle.setAttribute("cy", spheres[i].y);\n    circle.setAttribute("r", SPHERE_RADIUS);\n    circle.setAttribute("fill", "#bbb");\n    circle.setAttribute("stroke", "#999");\n    circle.setAttribute("stroke-width", "2");\n    if (i === 0) {\n      circle.classList.add("draggable");\n    }\n    svg.appendChild(circle);\n    spheres[i].element = circle;\n  }\n\n  // Helper function to update the SVG elements\n  function updateGraphics() {\n    for (let i = 0; i < NUM_SPHERES; i++) {\n      const s = spheres[i];\n      // Update string\n      const line = strings[i].element;\n      line.setAttribute("x1", cradleX + i * SPACING);\n      line.setAttribute("y1", cradleY);\n      line.setAttribute("x2", s.x);\n      line.setAttribute("y2", s.y);\n\n      // Update sphere position\n      s.element.setAttribute("cx", s.x);\n      s.element.setAttribute("cy", s.y);\n    }\n  }\n\n  // Physics simulation: constrain spheres to pendulum motion\n  function simulate() {\n    for (let i = 0; i < NUM_SPHERES; i++) {\n      const s = spheres[i];\n\n      if (i === 0 && isDragging) {\n        // During dragging, position is controlled by mouse\n        continue;\n      }\n\n      // Calculate the vector from the pivot point to the sphere\n      const dx = s.x - (cradleX + i * SPACING);\n      const dy = s.y - cradleY;\n      const dist = Math.sqrt(dx * dx + dy * dy);\n      const diff = dist - STRING_LENGTH;\n\n      if (dist !== 0) {\n        // Correct position to maintain string length\n        const correction = (diff / dist) * 0.2; // correction factor\n        s.x -= dx * correction;\n        s.y -= dy * correction;\n      }\n\n      // Apply physics: simple pendulum physics\n      // Calculate the angle\n      const angle = Math.atan2(s.x - (cradleX + i * SPACING), s.y - cradleY);\n      // For small angles, approximate motion\n      // Here, for simplicity, we simulate swinging with basic physics\n\n      // Update velocities\n      s.vx *= damping;\n      s.vy += gravity * timeStep;\n\n      // Update positions\n      s.x += s.vx;\n      s.y += s.vy;\n\n      // Constrain to the circle path (simulate pendulum swing)\n      const dx2 = s.x - (cradleX + i * SPACING);\n      const dy2 = s.y - cradleY;\n      const dist2 = Math.sqrt(dx2 * dx2 + dy2 * dy2);\n      if (dist2 !== 0) {\n        const correction2 = (dist2 - STRING_LENGTH) / dist2;\n        s.x -= dx2 * correction2;\n        s.y -= dy2 * correction2;\n      }\n    }\n\n    // Handle collisions (simple elastic collisions between spheres)\n    for (let i = 0; i < NUM_SPHERES - 1; i++) {\n      const s1 = spheres[i];\n      const s2 = spheres[i + 1];\n\n      const dx = s2.x - s1.x;\n      const dy = s2.y - s1.y;\n      const dist = Math.sqrt(dx * dx + dy * dy);\n      if (dist < s1.radius + s2.radius && dist !== 0) {\n        // Overlap detected, resolve collision\n        const overlap = 0.5 * (dist - s1.radius - s2.radius);\n        const nx = dx / dist;\n        const ny = dy / dist;\n\n        s1.x -= overlap * nx;\n        s1.y -= overlap * ny;\n        s2.x += overlap * nx;\n        s2.y += overlap * ny;\n\n        // Exchange velocities (elastic collision)\n        const v1 = s1.vx * nx + s1.vy * ny;\n        const v2 = s2.vx * nx + s2.vy * ny;\n\n        const m1 = 1; // mass\n        const m2 = 1;\n\n        const v1After = v2;\n        const v2After = v1;\n\n        s1.vx += (v1After - v1) * nx;\n        s1.vy += (v1After - v1) * ny;\n        s2.vx += (v2After - v2) * nx;\n        s2.vy += (v2After - v2) * ny;\n      }\n    }\n  }\n\n  // Animation loop\n  function animate() {\n    simulate();\n    updateGraphics();\n    requestAnimationFrame(animate);\n  }\n\n  // Event listeners for dragging\n  svg.addEventListener(\'mousedown\', (e) => {\n    const rect = svg.getBoundingClientRect();\n    const mouseX = e.clientX - rect.left;\n    const mouseY = e.clientY - rect.top;\n\n    // Check if clicked on the first sphere\n    const s = spheres[0];\n    const dx = mouseX - s.x;\n    const dy = mouseY - s.y;\n    if (dx * dx + dy * dy <= s.radius * s.radius) {\n      isDragging = true;\n      dragSphereIndex = 0;\n      dragStart.x = mouseX;\n      dragStart.y = mouseY;\n      currentMouse.x = mouseX;\n      currentMouse.y = mouseY;\n    }\n  });\n\n  svg.addEventListener(\'mousemove\', (e) => {\n    if (isDragging) {\n      const rect = svg.getBoundingClientRect();\n      currentMouse.x = e.clientX - rect.left;\n      currentMouse.y = e.clientY - rect.top;\n\n      // Update sphere position directly\n      const s = spheres[dragSphereIndex];\n      s.x = currentMouse.x;\n      s.y = currentMouse.y;\n\n      // Calculate velocity based on movement\n      s.vx = (s.x - dragStart.x) / timeStep;\n      s.vy = (s.y - dragStart.y) / timeStep;\n\n      dragStart.x = s.x;\n      dragStart.y = s.y;\n    }\n  });\n\n  svg.addEventListener(\'mouseup\', () => {\n    if (isDragging) {\n      isDragging = false;\n    }\n  });\n\n  // Optional: release sphere with physics\n  document.addEventListener(\'mouseup\', () => {\n    if (isDragging) {\n      isDragging = false;\n    }\n  });\n\n  // Start animation\n  animate();\n\n</script>\n</body>\n</html>\n```\n\n---\n\n### How it works:\n- The five spheres are aligned horizontally and suspended from a frame.\n- You can click and drag the leftmost sphere to set it in motion.\n- When released, the sphere swings naturally, transferring momentum to the others.\n- The simulation includes simple physics for pendulum motion, collision detection, and elastic collisions.\n- The animation runs smoothly with `requestAnimationFrame`.\n\n### Customization:\n- Adjust `NUM_SPHERES`, `SPHERE_RADIUS`, `STRING_LENGTH`, and other parameters to customize the appearance and behavior.\n- You can add controls to reset the simulation or pull back other spheres.\n\n---\n\nFeel free to copy and modify this code to suit your needs!',
        "Let's analyze the problem step by step:\n\n- Sally is a girl, so she has at least one sister: herself.\n- She has 3 brothers.\n- Each brother has 2 sisters.\n\nSince each brother has 2 sisters, and Sally is one of those sisters, the other sister must be the other girl(s) in the family.\n\nBecause all brothers share the same sisters, the total number of sisters is the number of girls in the family.\n\nGiven that Sally is a girl, and each brother has 2 sisters, the total number of sisters is 2.\n\nBut one of those sisters is Sally herself, so the total number of sisters Sally has **excluding herself** is:\n\n**Total sisters = 2 - 1 = 1**\n\n**Answer:**\n\n\\(\\boxed{1}\\)\n\nSally has **1 sister** in total.",
        'Let\'s count the occurrences:\n\n- In "strawberry": the letter "r" appears 2 times.\n- In "programmer": the letter "r" appears 3 times.\n- In "bubble": the letter "b" appears 2 times.\n\n**Summary:**\n- "r" in "strawberry": 2\n- "r" in "programmer": 3\n- "b" in "bubble": 2',
    ]
)
# [{'corpus_id': ..., 'score': ...}, {'corpus_id': ..., 'score': ...}, ...]

Training Details

Training Dataset

Unnamed Dataset

Size: 11,271 training samples
Columns: query, response, and label
Approximate statistics based on the first 100 samples:
query response label
type string string float
modality text text
details
min: 11 tokens
mean: 42.12 tokens
max: 117 tokens
min: 14 tokens
mean: 346.26 tokens
max: 512 tokens
min: 0.0
mean: 0.03
max: 1.0

Samples:

query	response	label
`>[object Object] I've reached the PICO-8 cartridge token limit, but I still have essential code to implement to complete my game. What are my options to overcome this restriction?`	Yes, there are instances where SI prefixes deviate from strictly representing powers of 10, particularly when they are applied outside the context of pure decimal scaling or when used in specialized fields. While the standard SI prefixes (like kilo-, mega-, giga-, etc.) are defined to denote powers of 10 (e.g., kilo- = 10³, mega- = 10^6), some exceptions and nuances exist:[object Object][object Object]1. [object Object] [object Object] Although not officially part of SI, prefixes like [object Object] etc., are used to denote binary multiples (2^10, 2^20, 2^30, etc.). These are standardized by the IEC (International Electrotechnical Commission) to avoid confusion, but they are not SI prefixes and do not represent powers of 10.[object Object][object Object]2. [object Object] [object Object] In some cases, prefixes like [object Object] or [object Object] have been used inconsistently, sometimes representing 10^6 bytes and other times 2^20 bytes, especially in computing. This is a deviation from the S...	`0.0`
`>[object Object] What educational path should I pursue to pursue a career in drug discovery?`	In PICO-8, the cartridge token limit (typically 8192 tokens) is a core constraint designed to encourage efficient coding and creativity. If you've reached this limit but still need to add essential code, here are some strategies to help you overcome or work around the restriction:[object Object][object Object]1. [object Object][object Object] - [object Object] Eliminate duplicate code, unused variables, and unnecessary comments.[object Object] - [object Object] Shorter identifiers consume fewer tokens.[object Object] - [object Object] Simplify complex expressions and combine statements where possible.[object Object] - [object Object] Store repeated data in tables instead of multiple variables or functions.[object Object][object Object]2. [object Object][object Object] - [object Object] Divide your game into separate parts or levels, each in its own cartridge.[object Object] - [object Object] Use the [object Object] function to load code or data from external files (if your workflow allows), effectively s...	`0.0`
`Create Matlab illustrations for visualizing Maxwell's equations.`	Certainly! Here's a complete example of a realistic 2D simulation of Newton's Cradle using HTML, CSS, and JavaScript. This implementation features five metallic spheres suspended from a simple frame, and allows you to click and drag the leftmost sphere to set it in motion. When released, the spheres swing naturally, demonstrating the conservation of momentum and energy.[object Object][object Object]---[object Object][object Object]### Features:[object Object]- Five aligned spheres suspended by strings.[object Object]- Click-and-drag to pull back the first sphere.[object Object]- Smooth swinging motion with realistic physics.[object Object]- Lifelike animation mimicking a real Newton's Cradle.[object Object][object Object]---[object Object][object Object]### Complete Code:[object Object][object Object]```html[object Object][object Object][object Object][object Object][object Object][object Object][object Object][object Object][object Object][object Object][object Object]	<code>0.0</code>

Loss: BinaryCrossEntropyLoss with these parameters:
json
1{ 2 "activation_fn": "torch.nn.modules.linear.Identity", 3 "pos_weight": null 4}

Training Hyperparameters

Non-Default Hyperparameters

per_device_train_batch_size: 16
num_train_epochs: 1
disable_tqdm: True
use_cpu: True
dataloader_pin_memory: False

All Hyperparameters

Click to expand

per_device_train_batch_size: 16
num_train_epochs: 1
max_steps: -1
learning_rate: 5e-05
lr_scheduler_type: linear
lr_scheduler_kwargs: None
warmup_steps: 0
optim: adamw_torch_fused
optim_args: None
weight_decay: 0.0
adam_beta1: 0.9
adam_beta2: 0.999
adam_epsilon: 1e-08
optim_target_modules: None
gradient_accumulation_steps: 1
average_tokens_across_devices: True
max_grad_norm: 1.0
label_smoothing_factor: 0.0
bf16: False
fp16: False
bf16_full_eval: False
fp16_full_eval: False
tf32: None
gradient_checkpointing: False
gradient_checkpointing_kwargs: None
torch_compile: False
torch_compile_backend: None
torch_compile_mode: None
use_liger_kernel: False
liger_kernel_config: None
use_cache: False
neftune_noise_alpha: None
torch_empty_cache_steps: None
auto_find_batch_size: False
log_on_each_node: True
logging_nan_inf_filter: True
include_num_input_tokens_seen: no
log_level: passive
log_level_replica: warning
disable_tqdm: True
project: huggingface
trackio_space_id: None
trackio_bucket_id: None
trackio_static_space_id: None
per_device_eval_batch_size: 8
prediction_loss_only: True
eval_on_start: False
eval_do_concat_batches: True
eval_use_gather_object: False
eval_accumulation_steps: None
include_for_metrics: []
batch_eval_metrics: False
save_only_model: False
save_on_each_node: False
enable_jit_checkpoint: False
push_to_hub: False
hub_private_repo: None
hub_model_id: None
hub_strategy: every_save
hub_always_push: False
hub_revision: None
load_best_model_at_end: False
ignore_data_skip: False
restore_callback_states_from_checkpoint: False
full_determinism: False
seed: 42
data_seed: None
use_cpu: True
accelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
parallelism_config: None
dataloader_drop_last: False
dataloader_num_workers: 0
dataloader_pin_memory: False
dataloader_persistent_workers: False
dataloader_prefetch_factor: None
remove_unused_columns: True
label_names: None
train_sampling_strategy: random
length_column_name: length
ddp_find_unused_parameters: None
ddp_bucket_cap_mb: None
ddp_broadcast_buffers: False
ddp_static_graph: None
ddp_backend: None
ddp_timeout: 1800
fsdp: None
fsdp_config: None
deepspeed: None
debug: []
skip_memory_metrics: True
do_predict: False
resume_from_checkpoint: None
warmup_ratio: None
local_rank: -1
prompts: None
batch_sampler: batch_sampler
multi_dataset_batch_sampler: proportional
router_mapping: {}
learning_rate_mapping: {}

Training Logs

Epoch	Step	Training Loss
0.0014	1	1.7589
0.0142	10	0.7247
0.0284	20	0.5189
0.0426	30	0.4005
0.0567	40	0.2951
0.0709	50	0.3512
0.0851	60	0.3036
0.0993	70	0.4066
0.1135	80	0.2312
0.1277	90	0.2853
0.1418	100	0.4700
0.1560	110	0.3224
0.1702	120	0.2299
0.1844	130	0.2821
0.1986	140	0.2797
0.2128	150	0.2947
0.2270	160	0.3521
0.2411	170	0.2829
0.2553	180	0.3016
0.2695	190	0.2234
0.2837	200	0.2994
0.2979	210	0.2335
0.3121	220	0.2349
0.3262	230	0.2979
0.3404	240	0.2734
0.3546	250	0.3042
0.3688	260	0.2363
0.3830	270	0.1922
0.3972	280	0.2754
0.4113	290	0.2362
0.4255	300	0.2816
0.4397	310	0.2817
0.4539	320	0.2295
0.4681	330	0.2632
0.4823	340	0.3445
0.4965	350	0.2628
0.5106	360	0.2045
0.5248	370	0.2248
0.5390	380	0.2457
0.5532	390	0.1711
0.5674	400	0.1769
0.5816	410	0.1659
0.5957	420	0.2287
0.6099	430	0.2872
0.6241	440	0.2694
0.6383	450	0.2780
0.6525	460	0.2891
0.6667	470	0.2256
0.6809	480	0.2170
0.6950	490	0.2348
0.7092	500	0.1746
0.7234	510	0.1982
0.7376	520	0.1707
0.7518	530	0.2627
0.7660	540	0.3044
0.7801	550	0.2399
0.7943	560	0.1909
0.8085	570	0.2009
0.8227	580	0.2445
0.8369	590	0.2160
0.8511	600	0.2534
0.8652	610	0.1833
0.8794	620	0.2560
0.8936	630	0.1496
0.9078	640	0.2143
0.9220	650	0.3094
0.9362	660	0.2049
0.9504	670	0.2383
0.9645	680	0.2916
0.9787	690	0.1812
0.9929	700	0.3707

Training Time

Training: 43.3 minutes

Framework Versions

Python: 3.11.6
Sentence Transformers: 5.6.1
Transformers: 5.14.1
PyTorch: 2.13.0+cu130
Accelerate: 1.14.0
Datasets: 5.0.0
Tokenizers: 0.22.2

Additional Resources

Training and Finetuning Reranker Models with Sentence Transformers: the end-to-end guide for training or finetuning Cross Encoder (reranker) models.
Multimodal Embedding & Reranker Models with Sentence Transformers: use text, image, audio, and video reranker models through the same API.
Training and Finetuning Multimodal Embedding & Reranker Models with Sentence Transformers: training multimodal Cross Encoders.

Citation

BibTeX

Sentence Transformers

bibtex

@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}

	query	response	label
type	string	string	float
modality	text	text
details	min: 11 tokens mean: 42.12 tokens max: 117 tokens	min: 14 tokens mean: 346.26 tokens max: 512 tokens	min: 0.0 mean: 0.03 max: 1.0

ChengyouXin/cacheverifier-lmarena