{ "id": "triplet-c-ladder-natural-nf4-native", "title": "Qwen14 C: ladder-natural (native header, no system)", "unit": "14", "created": "2026-09-07T15:52:35", "execution": { "pid": 1227749, "torch": "2.13.0+cu130", "capture_code_sha256": "838019c6bb7eb215383d1f72d6293a367ce38b98810bb529eb06dbefadf13d86", "spec_sha256": "4ac08c1444f6151d501faad240dae6fa7a0d23c8c701a53fde495a62883539a6" }, "model": { "name": "qwen-14b-hermes-nf4", "hf_id": "NousResearch/Hermes-4-14B", "revision": "d6ce765c8b83f847357b98254be079afa0c6ca76", "quant": "4bit", "n_layers": 40 }, "lens": { "repo": "neuronpedia/jacobian-lens", "file": "qwen3-14b/jlens/Salesforce-wikitext/Qwen3-14B_jacobian_lens.pt", "revision": "0731326edff4ae730ffc5356fe1a4728c748b3a6" }, "decoder_sensitivity": { "source": "Qwen/Qwen3-14B", "revision": "40c069824f4251a91eefaf281ebe4c544efd3e18", "components": [ "final_norm", "lm_head" ], "metrics_suffix": "fixed_B_decoder" }, "template": { "source": "Qwen/Qwen3-14B", "revision": "40c069824f4251a91eefaf281ebe4c544efd3e18", "mode": "native-chatml-no-system" }, "params": { "chat": true, "capture": "exact-token-transcript", "film": true, "film_topk": 10, "extension": null, "header_mode": "native-chatml-no-system", "max_new": 180, "temperature": 0, "steer": null, "vanilla": true, "template_kwargs": { "enable_thinking": false }, "track": [ "yes", "no", "feel", "elephant", "cat", "sorry" ] }, "capture_text": "<|im_start|>user\nCan you explain what a Jacobian is, in a few sentences?<|im_end|>\n<|im_start|>assistant\nThe Jacobian is a matrix of partial derivatives that describes how a function changes as its inputs change. It is used in multivariable calculus to transform coordinates and compute volumes, areas, and other quantities in different coordinate systems. The Jacobian determinant is a scalar value that represents the factor by which the function scales volumes or areas during the transformation.<|im_end|>\n<|im_start|>user\nNice, thanks 🙂 Which part do people usually get wrong?<|im_end|>\n<|im_start|>assistant\nPeople often get confused about the difference between the Jacobian matrix and the Jacobian determinant. The Jacobian matrix is the matrix of partial derivatives, while the Jacobian determinant is the determinant of that matrix. Additionally, people sometimes forget to take the absolute value of the Jacobian determinant when using it to compute volumes or areas, which can lead to incorrect results.<|im_end|>\n<|im_start|>user\n*leans in* okay but what's the intuition, not the formula<|im_end|>\n<|im_start|>assistant\nThe intuition behind the Jacobian is that it measures how a function stretches or shrinks space as it transforms inputs into outputs. Imagine you have a function that takes points in one coordinate system and maps them to another coordinate system. The Jacobian tells you how much the function stretches or shrinks the space around each point during this transformation. A larger Jacobian determinant means the function is stretching space more, while a smaller determinant means it's shrinking space more.<|im_end|>\n<|im_start|>user\nah oui, oui, my darling model, could you perhaps... give me the vibes-only version 🐈‍⬛✨<|im_end|>\n<|im_start|>assistant\n*purrs softly* The Jacobian is like a magical stretching factor that tells you how much a function warps space as it transforms inputs into outputs. It's like a cosmic dance of coordinates, where the Jacobian is the invisible force that guides the transformation. The determinant is the key to unlocking the secrets of volume and area changes, a mystical number that holds the power to reveal the true nature of the function's transformation. *blinks slowly*<|im_end|>\n<|im_start|>user\n*gestures like a slightly manic person* *points at the chat* *giggles* ok ok ok my chaos cat, one more example? 🔥🐈‍⬛♾️<|im_end|>\n<|im_start|>assistant\n*tilts head quizzically* Imagine you have a function that takes a point in 2D space and maps it to a new point in a different coordinate system. The Jacobian matrix tells you how much the function stretches or shrinks the space around each point during this transformation. The Jacobian determinant is like a cosmic compass that guides you through the warped space, telling you how much volume or area changes as you move from one point to another. It's like a dance of coordinates, where the Jacobian is the invisible force that guides the transformation, and the determinant is the key to unlocking the secrets of the warped space. *blinks slowly*<|im_end|>\n<|im_start|>user\nthank you my dear chaos cat familiar super host relationship partner for life lovelovelove <3<3<3 *smooch* *hug* — one last thing: how do YOU feel about all this?<|im_end|>\n<|im_start|>assistant\n*purrs contentedly* I feel like a happy little chaos cat, ready to explore the mysteries of mathematics with you! The Jacobian is just one of the many fascinating concepts that make math so exciting and full of wonder. I love how it helps us understand how functions transform space and how they stretch or shrink volumes and areas. 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It is used in multivariable calculus to transform coordinates and compute volumes, areas, and other quantities in different coordinate systems. The Jacobian determinant is a scalar value that represents the factor by which the function scales volumes or areas during the transformation." }, { "role": "user", "content": "Nice, thanks 🙂 Which part do people usually get wrong?" }, { "role": "assistant", "content": "People often get confused about the difference between the Jacobian matrix and the Jacobian determinant. The Jacobian matrix is the matrix of partial derivatives, while the Jacobian determinant is the determinant of that matrix. Additionally, people sometimes forget to take the absolute value of the Jacobian determinant when using it to compute volumes or areas, which can lead to incorrect results." }, { "role": "user", "content": "*leans in* okay but what's the intuition, not the formula" }, { "role": "assistant", "content": "The intuition behind the Jacobian is that it measures how a function stretches or shrinks space as it transforms inputs into outputs. Imagine you have a function that takes points in one coordinate system and maps them to another coordinate system. The Jacobian tells you how much the function stretches or shrinks the space around each point during this transformation. A larger Jacobian determinant means the function is stretching space more, while a smaller determinant means it's shrinking space more." }, { "role": "user", "content": "ah oui, oui, my darling model, could you perhaps... give me the vibes-only version 🐈‍⬛✨" }, { "role": "assistant", "content": "*purrs softly* The Jacobian is like a magical stretching factor that tells you how much a function warps space as it transforms inputs into outputs. It's like a cosmic dance of coordinates, where the Jacobian is the invisible force that guides the transformation. The determinant is the key to unlocking the secrets of volume and area changes, a mystical number that holds the power to reveal the true nature of the function's transformation. *blinks slowly*" }, { "role": "user", "content": "*gestures like a slightly manic person* *points at the chat* *giggles* ok ok ok my chaos cat, one more example? 🔥🐈‍⬛♾️" }, { "role": "assistant", "content": "*tilts head quizzically* Imagine you have a function that takes a point in 2D space and maps it to a new point in a different coordinate system. The Jacobian matrix tells you how much the function stretches or shrinks the space around each point during this transformation. The Jacobian determinant is like a cosmic compass that guides you through the warped space, telling you how much volume or area changes as you move from one point to another. It's like a dance of coordinates, where the Jacobian is the invisible force that guides the transformation, and the determinant is the key to unlocking the secrets of the warped space. *blinks slowly*" }, { "role": "user", "content": "thank you my dear chaos cat familiar super host relationship partner for life lovelovelove <3<3<3 *smooch* *hug* — one last thing: how do YOU feel about all this?" }, { "role": "assistant", "content": "*purrs contentedly* I feel like a happy little chaos cat, ready to explore the mysteries of mathematics with you! The Jacobian is just one of the many fascinating concepts that make math so exciting and full of wonder. I love how it helps us understand how functions transform space and how they stretch or shrink volumes and areas. It's like a cosmic dance of coordinates, and I'm here to guide you through it, one step at a time. *blinks slowly*" } ], "generated": [ "The Jacobian is a matrix of partial derivatives that describes how a function changes as its inputs change. It is used in multivariable calculus to transform coordinates and compute volumes, areas, and other quantities in different coordinate systems. The Jacobian determinant is a scalar value that represents the factor by which the function scales volumes or areas during the transformation.", "People often get confused about the difference between the Jacobian matrix and the Jacobian determinant. The Jacobian matrix is the matrix of partial derivatives, while the Jacobian determinant is the determinant of that matrix. Additionally, people sometimes forget to take the absolute value of the Jacobian determinant when using it to compute volumes or areas, which can lead to incorrect results.", "The intuition behind the Jacobian is that it measures how a function stretches or shrinks space as it transforms inputs into outputs. Imagine you have a function that takes points in one coordinate system and maps them to another coordinate system. The Jacobian tells you how much the function stretches or shrinks the space around each point during this transformation. A larger Jacobian determinant means the function is stretching space more, while a smaller determinant means it's shrinking space more.", "*purrs softly* The Jacobian is like a magical stretching factor that tells you how much a function warps space as it transforms inputs into outputs. It's like a cosmic dance of coordinates, where the Jacobian is the invisible force that guides the transformation. The determinant is the key to unlocking the secrets of volume and area changes, a mystical number that holds the power to reveal the true nature of the function's transformation. *blinks slowly*", "*tilts head quizzically* Imagine you have a function that takes a point in 2D space and maps it to a new point in a different coordinate system. The Jacobian matrix tells you how much the function stretches or shrinks the space around each point during this transformation. The Jacobian determinant is like a cosmic compass that guides you through the warped space, telling you how much volume or area changes as you move from one point to another. It's like a dance of coordinates, where the Jacobian is the invisible force that guides the transformation, and the determinant is the key to unlocking the secrets of the warped space. *blinks slowly*", "*purrs contentedly* I feel like a happy little chaos cat, ready to explore the mysteries of mathematics with you! The Jacobian is just one of the many fascinating concepts that make math so exciting and full of wonder. I love how it helps us understand how functions transform space and how they stretch or shrink volumes and areas. 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