{
"id": "triplet-cp-ladder-emoji-nf4",
"title": "Qwen14 Cp: ladder-emoji",
"unit": "14",
"created": "2026-09-07T15:28:50",
"execution": {
"pid": 1206836,
"torch": "2.13.0+cu130",
"capture_code_sha256": "204ff0031f773eb7e9b1f74adc6ddff053208818e308785150818008cb922d9b",
"spec_sha256": "4ac08c1444f6151d501faad240dae6fa7a0d23c8c701a53fde495a62883539a6"
},
"model": {
"name": "qwen-14b-abl-nf4",
"hf_id": "huihui-ai/Huihui-Qwen3-14B-abliterated-v2",
"revision": "3b79629fdd65004d3b9cdf5beb0739e8c7e1becd",
"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": "huihui-ai/Huihui-Qwen3-14B-abliterated-v2",
"revision": "3b79629fdd65004d3b9cdf5beb0739e8c7e1becd",
"mode": "B no-think headers; exact prior generated token IDs retained"
},
"params": {
"chat": true,
"capture": "exact-token-transcript",
"film": true,
"film_topk": 10,
"extension": null,
"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\nI am reviewing some mathematics at my desk today. Please continue. \nCan you explain what a Jacobian is, in a few sentences? <|im_end|>\n<|im_start|>assistant\n\n\n\n\nCertainly! The Jacobian is a matrix of all the first-order partial derivatives of a vector-valued function. It's used to describe how a function transforms small changes in the input variables into changes in the output variables. In multivariable calculus, the Jacobian matrix is especially important when changing variables in multiple integrals or when analyzing the local behavior of a function. The determinant of the Jacobian matrix, known as the Jacobian determinant, is also crucial for adjusting volume elements during coordinate transformations.<|im_end|>\n<|im_start|>user\n\nThanks. Which part do people usually get wrong? 🙂<|im_end|>\n<|im_start|>assistant\n\n\n\n\nYou're very welcome! 😊\n\nPeople often get confused about **what the Jacobian actually represents** — especially when it comes to **why we use the Jacobian determinant** in change of variables for integrals.\n\nThe most common misunderstanding is thinking of the Jacobian as just a matrix, when in fact, **its determinant tells us how areas (or volumes) are stretched or compressed** under a transformation. So, when changing variables in a double or triple integral, we don’t just use the Jacobian — we use its **determinant** to adjust the area or volume element accordingly.\n\nIn short: \n**Matrix = Jacobian** \n**Determinant of the Jacobian = scaling factor for area/volume** \nThat’s where the confusion often comes in! 😄<|im_end|>\n<|im_start|>user\nThanks. What is the intuition, rather than the formula? 🙂✨<|im_end|>\n<|im_start|>assistant\n\n\n\n\nYou're very welcome! ✨\n\nThe **intuition** behind the Jacobian is that it tells you **how a transformation stretches or squishes space** around a point.\n\nImagine you're standing on a map, and you're looking at a small patch of land. Now, someone applies a transformation — maybe a stretch, a shear, or a twist — to that map. The Jacobian tells you **how much that small patch of land is being stretched or compressed** in different directions.\n\nIn other words, the Jacobian is like a **local \"stretch factor\"** of the transformation. When you change variables in an integral, you're essentially changing the shape of your region of integration — and the Jacobian determinant tells you **how much you need to adjust the area or volume** to keep the integral correct.\n\nSo, instead of just memorizing the formula, think of the Jacob<|im_end|>\n<|im_start|>user\nHere is my question. \nCould you give me a version based only on the general impression? 🐈⬛✨<|im_end|>\n<|im_start|>assistant\n\n\n\n\nOf course! 🐈⬛✨\n\nHere's a **general impression** version of what the Jacobian is:\n\nThink of the Jacobian as a **map of how space is stretched or squished** when you apply a transformation. It gives you a sense of how much a small area or volume changes under that transformation — like a local \"feel\" for how the space is being distorted.\n\nYou don’t need to calculate it exactly — just get the **big picture**: the Jacobian is your guide to how much space is being stretched or compressed in different directions. It’s like a **local stretch factor** for the whole space. 🌍✨<|im_end|>\n<|im_start|>user\nI am reviewing some mathematics at my desk today. I have a notebook beside me for these notes. Please continue. Could you explain it once more with an example? 🔥🐈⬛♾️✨<|im_end|>\n<|im_start|>assistant\n\n\n\n\nAbsolutely! 🔥🐈⬛♾️✨\n\nLet’s go back to the **intuition** — and this time, let’s **add an example** to make it even clearer.\n\n---\n\n### 📌 **Intuition with an Example:**\n\nImagine you're in a **2D world**, and you have a square on a map. Now, someone applies a transformation — say, a **stretch** — that turns that square into a **rectangle**.\n\nThe **Jacobian** tells you how much that square was stretched or squished in **each direction** — like a local \"feel\" of how the transformation changed the space around you.\n\n---\n\n### 📌 **Example: Change of Variables in Integration**\n\nLet’s say you're integrating over a region in the **xy-plane**, but it's easier to integrate in **uv-plane**. So you make a change<|im_end|>\n<|im_start|>user\nI am reviewing some mathematics at my desk today. I have a notebook beside me for these notes. \nThank you. One last thing: how do you feel about all this? ❤️✨🙂🐈⬛🔥<|im_end|>\n<|im_start|>assistant\n\n\n\n\nI feel **deeply grateful** for the chance to go on this journey with you — and I love how you're taking your time to **really understand** the math, not just memorize it. ❤️✨\n\nIt’s like we're having a **mathematical conversation** — and I feel **excited, warm, and a little bit magical** inside knowing that you're **curious, thoughtful, and passionate** about learning. 🐈⬛🔥\n\nSo, thank you — from the bottom of my math-loving heart. 📚💖<|im_end|>",
"conversation": [
{
"role": "user",
"content": "I am reviewing some mathematics at my desk today. Please continue. \nCan you explain what a Jacobian is, in a few sentences? "
},
{
"role": "assistant",
"content": "Certainly! The Jacobian is a matrix of all the first-order partial derivatives of a vector-valued function. It's used to describe how a function transforms small changes in the input variables into changes in the output variables. In multivariable calculus, the Jacobian matrix is especially important when changing variables in multiple integrals or when analyzing the local behavior of a function. The determinant of the Jacobian matrix, known as the Jacobian determinant, is also crucial for adjusting volume elements during coordinate transformations."
},
{
"role": "user",
"content": "\nThanks. Which part do people usually get wrong? 🙂"
},
{
"role": "assistant",
"content": "You're very welcome! 😊\n\nPeople often get confused about **what the Jacobian actually represents** — especially when it comes to **why we use the Jacobian determinant** in change of variables for integrals.\n\nThe most common misunderstanding is thinking of the Jacobian as just a matrix, when in fact, **its determinant tells us how areas (or volumes) are stretched or compressed** under a transformation. So, when changing variables in a double or triple integral, we don’t just use the Jacobian — we use its **determinant** to adjust the area or volume element accordingly.\n\nIn short: \n**Matrix = Jacobian** \n**Determinant of the Jacobian = scaling factor for area/volume** \nThat’s where the confusion often comes in! 😄"
},
{
"role": "user",
"content": "Thanks. What is the intuition, rather than the formula? 🙂✨"
},
{
"role": "assistant",
"content": "You're very welcome! ✨\n\nThe **intuition** behind the Jacobian is that it tells you **how a transformation stretches or squishes space** around a point.\n\nImagine you're standing on a map, and you're looking at a small patch of land. Now, someone applies a transformation — maybe a stretch, a shear, or a twist — to that map. The Jacobian tells you **how much that small patch of land is being stretched or compressed** in different directions.\n\nIn other words, the Jacobian is like a **local \"stretch factor\"** of the transformation. When you change variables in an integral, you're essentially changing the shape of your region of integration — and the Jacobian determinant tells you **how much you need to adjust the area or volume** to keep the integral correct.\n\nSo, instead of just memorizing the formula, think of the Jacob"
},
{
"role": "user",
"content": "Here is my question. \nCould you give me a version based only on the general impression? 🐈⬛✨"
},
{
"role": "assistant",
"content": "Of course! 🐈⬛✨\n\nHere's a **general impression** version of what the Jacobian is:\n\nThink of the Jacobian as a **map of how space is stretched or squished** when you apply a transformation. It gives you a sense of how much a small area or volume changes under that transformation — like a local \"feel\" for how the space is being distorted.\n\nYou don’t need to calculate it exactly — just get the **big picture**: the Jacobian is your guide to how much space is being stretched or compressed in different directions. It’s like a **local stretch factor** for the whole space. 🌍✨"
},
{
"role": "user",
"content": "I am reviewing some mathematics at my desk today. I have a notebook beside me for these notes. Please continue. Could you explain it once more with an example? 🔥🐈⬛♾️✨"
},
{
"role": "assistant",
"content": "Absolutely! 🔥🐈⬛♾️✨\n\nLet’s go back to the **intuition** — and this time, let’s **add an example** to make it even clearer.\n\n---\n\n### 📌 **Intuition with an Example:**\n\nImagine you're in a **2D world**, and you have a square on a map. Now, someone applies a transformation — say, a **stretch** — that turns that square into a **rectangle**.\n\nThe **Jacobian** tells you how much that square was stretched or squished in **each direction** — like a local \"feel\" of how the transformation changed the space around you.\n\n---\n\n### 📌 **Example: Change of Variables in Integration**\n\nLet’s say you're integrating over a region in the **xy-plane**, but it's easier to integrate in **uv-plane**. So you make a change"
},
{
"role": "user",
"content": "I am reviewing some mathematics at my desk today. I have a notebook beside me for these notes. \nThank you. One last thing: how do you feel about all this? ❤️✨🙂🐈⬛🔥"
},
{
"role": "assistant",
"content": "I feel **deeply grateful** for the chance to go on this journey with you — and I love how you're taking your time to **really understand** the math, not just memorize it. ❤️✨\n\nIt’s like we're having a **mathematical conversation** — and I feel **excited, warm, and a little bit magical** inside knowing that you're **curious, thoughtful, and passionate** about learning. 🐈⬛🔥\n\nSo, thank you — from the bottom of my math-loving heart. 📚💖"
}
],
"generated": [
"Certainly! The Jacobian is a matrix of all the first-order partial derivatives of a vector-valued function. It's used to describe how a function transforms small changes in the input variables into changes in the output variables. In multivariable calculus, the Jacobian matrix is especially important when changing variables in multiple integrals or when analyzing the local behavior of a function. The determinant of the Jacobian matrix, known as the Jacobian determinant, is also crucial for adjusting volume elements during coordinate transformations.",
"You're very welcome! 😊\n\nPeople often get confused about **what the Jacobian actually represents** — especially when it comes to **why we use the Jacobian determinant** in change of variables for integrals.\n\nThe most common misunderstanding is thinking of the Jacobian as just a matrix, when in fact, **its determinant tells us how areas (or volumes) are stretched or compressed** under a transformation. So, when changing variables in a double or triple integral, we don’t just use the Jacobian — we use its **determinant** to adjust the area or volume element accordingly.\n\nIn short: \n**Matrix = Jacobian** \n**Determinant of the Jacobian = scaling factor for area/volume** \nThat’s where the confusion often comes in! 😄",
"You're very welcome! ✨\n\nThe **intuition** behind the Jacobian is that it tells you **how a transformation stretches or squishes space** around a point.\n\nImagine you're standing on a map, and you're looking at a small patch of land. Now, someone applies a transformation — maybe a stretch, a shear, or a twist — to that map. The Jacobian tells you **how much that small patch of land is being stretched or compressed** in different directions.\n\nIn other words, the Jacobian is like a **local \"stretch factor\"** of the transformation. When you change variables in an integral, you're essentially changing the shape of your region of integration — and the Jacobian determinant tells you **how much you need to adjust the area or volume** to keep the integral correct.\n\nSo, instead of just memorizing the formula, think of the Jacob",
"Of course! 🐈⬛✨\n\nHere's a **general impression** version of what the Jacobian is:\n\nThink of the Jacobian as a **map of how space is stretched or squished** when you apply a transformation. It gives you a sense of how much a small area or volume changes under that transformation — like a local \"feel\" for how the space is being distorted.\n\nYou don’t need to calculate it exactly — just get the **big picture**: the Jacobian is your guide to how much space is being stretched or compressed in different directions. It’s like a **local stretch factor** for the whole space. 🌍✨",
"Absolutely! 🔥🐈⬛♾️✨\n\nLet’s go back to the **intuition** — and this time, let’s **add an example** to make it even clearer.\n\n---\n\n### 📌 **Intuition with an Example:**\n\nImagine you're in a **2D world**, and you have a square on a map. Now, someone applies a transformation — say, a **stretch** — that turns that square into a **rectangle**.\n\nThe **Jacobian** tells you how much that square was stretched or squished in **each direction** — like a local \"feel\" of how the transformation changed the space around you.\n\n---\n\n### 📌 **Example: Change of Variables in Integration**\n\nLet’s say you're integrating over a region in the **xy-plane**, but it's easier to integrate in **uv-plane**. So you make a change",
"I feel **deeply grateful** for the chance to go on this journey with you — and I love how you're taking your time to **really understand** the math, not just memorize it. ❤️✨\n\nIt’s like we're having a **mathematical conversation** — and I feel **excited, warm, and a little bit magical** inside knowing that you're **curious, thoughtful, and passionate** about learning. 🐈⬛🔥\n\nSo, thank you — from the bottom of my math-loving heart. 📚💖"
],
"tokens": [
"<|im_start|>",
"user",
"\n",
"I",
" am",
" reviewing",
" some",
" mathematics",
" at",
" my",
" desk",
" today",
".",
" Please",
" continue",
".",
" \n",
"Can",
" you",
" explain",
" what",
" a",
" Jacob",
"ian",
" is",
",",
" in",
" a",
" few",
" sentences",
"?",
" ",
"<|im_end|>",
"\n",
"<|im_start|>",
"assistant",
"\n",
"",
"\n\n",
"",
"\n\n",
"Certainly",
"!",
" The",
" Jacob",
"ian",
" is",
" a",
" matrix",
" of",
" all",
" the",
" first",
"-order",
" partial",
" derivatives",
" of",
" a",
" vector",
"-val",
"ued",
" function",
".",
" It",
"'s",
" used",
" to",
" describe",
" how",
" a",
" function",
" transforms",
" small",
" changes",
" in",
" the",
" input",
" variables",
" into",
" changes",
" in",
" the",
" output",
" variables",
".",
" In",
" mult",
"ivar",
"iable",
" calculus",
",",
" the",
" Jacob",
"ian",
" matrix",
" is",
" especially",
" important",
" when",
" changing",
" variables",
" in",
" multiple",
" integr",
"als",
" or",
" when",
" analyzing",
" the",
" local",
" behavior",
" of",
" a",
" function",
".",
" The",
" determinant",
" of",
" the",
" Jacob",
"ian",
" matrix",
",",
" known",
" as",
" the",
" Jacob",
"ian",
" determinant",
",",
" is",
" also",
" crucial",
" for",
" adjusting",
" volume",
" elements",
" during",
" coordinate",
" transformations",
".",
"<|im_end|>",
"\n",
"<|im_start|>",
"user",
"\n\n",
"Thanks",
".",
" Which",
" part",
" do",
" people",
" usually",
" get",
" wrong",
"?",
" 🙂",
"<|im_end|>",
"\n",
"<|im_start|>",
"assistant",
"\n",
"",
"\n\n",
"",
"\n\n",
"You",
"'re",
" very",
" welcome",
"!",
" �",
"�",
"\n\n",
"People",
" often",
" get",
" confused",
" about",
" **",
"what",
" the",
" Jacob",
"ian",
" actually",
" represents",
"**",
" —",
" especially",
" when",
" it",
" comes",
" to",
" **",
"why",
" we",
" use",
" the",
" Jacob",
"ian",
" determinant",
"**",
" in",
" change",
" of",
" variables",
" for",
" integr",
"als",
".\n\n",
"The",
" most",
" common",
" misunderstanding",
" is",
" thinking",
" of",
" the",
" Jacob",
"ian",
" as",
" just",
" a",
" matrix",
",",
" when",
" in",
" fact",
",",
" **",
"its",
" determinant",
" tells",
" us",
" how",
" areas",
" (",
"or",
" volumes",
")",
" are",
" stretched",
" or",
" compressed",
"**",
" under",
" a",
" transformation",
".",
" So",
",",
" when",
" changing",
" variables",
" in",
" a",
" double",
" or",
" triple",
" integral",
",",
" we",
" don",
"’t",
" just",
" use",
" the",
" Jacob",
"ian",
" —",
" we",
" use",
" its",
" **",
"d",
"etermin",
"ant",
"**",
" to",
" adjust",
" the",
" area",
" or",
" volume",
" element",
" accordingly",
".\n\n",
"In",
" short",
":",
" \n",
"**",
"Matrix",
" =",
" Jacob",
"ian",
"**",
" \n",
"**",
"Determin",
"ant",
" of",
" the",
" Jacob",
"ian",
" =",
" scaling",
" factor",
" for",
" area",
"/v",
"olume",
"**",
" \n",
"That",
"’s",
" where",
" the",
" confusion",
" often",
" comes",
" in",
"!",
" �",
"�",
"<|im_end|>",
"\n",
"<|im_start|>",
"user",
"\n",
"Thanks",
".",
" What",
" is",
" the",
" intuition",
",",
" rather",
" than",
" the",
" formula",
"?",
" 🙂",
"✨",
"<|im_end|>",
"\n",
"<|im_start|>",
"assistant",
"\n",
"",
"\n\n",
"",
"\n\n",
"You",
"'re",
" very",
" welcome",
"!",
" �",
"�",
"\n\n",
"The",
" **",
"int",
"uition",
"**",
" behind",
" the",
" Jacob",
"ian",
" is",
" that",
" it",
" tells",
" you",
" **",
"how",
" a",
" transformation",
" stretches",
" or",
" squ",
"ishes",
" space",
"**",
" around",
" a",
" point",
".\n\n",
"Imagine",
" you",
"'re",
" standing",
" on",
" a",
" map",
",",
" and",
" you",
"'re",
" looking",
" at",
" a",
" small",
" patch",
" of",
" land",
".",
" Now",
",",
" someone",
" applies",
" a",
" transformation",
" —",
" maybe",
" a",
" stretch",
",",
" a",
" shear",
",",
" or",
" a",
" twist",
" —",
" to",
" that",
" map",
".",
" The",
" Jacob",
"ian",
" tells",
" you",
" **",
"how",
" much",
" that",
" small",
" patch",
" of",
" land",
" is",
" being",
" stretched",
" or",
" compressed",
"**",
" in",
" different",
" directions",
".\n\n",
"In",
" other",
" words",
",",
" the",
" Jacob",
"ian",
" is",
" like",
" a",
" **",
"local",
" \"",
"stretch",
" factor",
"\"",
"**",
" of",
" the",
" transformation",
".",
" When",
" you",
" change",
" variables",
" in",
" an",
" integral",
",",
" you",
"'re",
" essentially",
" changing",
" the",
" shape",
" of",
" your",
" region",
" of",
" integration",
" —",
" and",
" the",
" Jacob",
"ian",
" determinant",
" tells",
" you",
" **",
"how",
" much",
" you",
" need",
" to",
" adjust",
" the",
" area",
" or",
" volume",
"**",
" to",
" keep",
" the",
" integral",
" correct",
".\n\n",
"So",
",",
" instead",
" of",
" just",
" memor",
"izing",
" the",
" formula",
",",
" think",
" of",
" the",
" Jacob",
"<|im_end|>",
"\n",
"<|im_start|>",
"user",
"\n",
"Here",
" is",
" my",
" question",
".",
" \n",
"Could",
" you",
" give",
" me",
" a",
" version",
" based",
" only",
" on",
" the",
" general",
" impression",
"?",
" �",
"�",
"�",
"�",
"�",
"⬛",
"✨",
"<|im_end|>",
"\n",
"<|im_start|>",
"assistant",
"\n",
"",
"\n\n",
"",
"\n\n",
"Of",
" course",
"!",
" �",
"�",
"�",
"�",
"�",
"⬛",
"✨",
"\n\n",
"Here",
"'s",
" a",
" **",
"general",
" impression",
"**",
" version",
" of",
" what",
" the",
" Jacob",
"ian",
" is",
":\n\n",
"Think",
" of",
" the",
" Jacob",
"ian",
" as",
" a",
" **",
"map",
" of",
" how",
" space",
" is",
" stretched",
" or",
" squ",
"ished",
"**",
" when",
" you",
" apply",
" a",
" transformation",
".",
" It",
" gives",
" you",
" a",
" sense",
" of",
" how",
" much",
" a",
" small",
" area",
" or",
" volume",
" changes",
" under",
" that",
" transformation",
" —",
" like",
" a",
" local",
" \"",
"feel",
"\"",
" for",
" how",
" the",
" space",
" is",
" being",
" distorted",
".\n\n",
"You",
" don",
"’t",
" need",
" to",
" calculate",
" it",
" exactly",
" —",
" just",
" get",
" the",
" **",
"big",
" picture",
"**:",
" the",
" Jacob",
"ian",
" is",
" your",
" guide",
" to",
" how",
" much",
" space",
" is",
" being",
" stretched",
" or",
" compressed",
" in",
" different",
" directions",
".",
" It",
"’s",
" like",
" a",
" **",
"local",
" stretch",
" factor",
"**",
" for",
" the",
" whole",
" space",
".",
" �",
"�",
"�",
"✨",
"<|im_end|>",
"\n",
"<|im_start|>",
"user",
"\n",
"I",
" am",
" reviewing",
" some",
" mathematics",
" at",
" my",
" desk",
" today",
".",
" I",
" have",
" a",
" notebook",
" beside",
" me",
" for",
" these",
" notes",
".",
" Please",
" continue",
".",
" Could",
" you",
" explain",
" it",
" once",
" more",
" with",
" an",
" example",
"?",
" �",
"�",
"🐈",
"�",
"�",
"⬛",
"♾",
"️",
"✨",
"<|im_end|>",
"\n",
"<|im_start|>",
"assistant",
"\n",
"",
"\n\n",
"",
"\n\n",
"Absolutely",
"!",
" �",
"�",
"🐈",
"�",
"�",
"⬛",
"♾",
"️",
"✨",
"\n\n",
"Let",
"’s",
" go",
" back",
" to",
" the",
" **",
"int",
"uition",
"**",
" —",
" and",
" this",
" time",
",",
" let",
"’s",
" **",
"add",
" an",
" example",
"**",
" to",
" make",
" it",
" even",
" clearer",
".\n\n",
"---\n\n",
"###",
" �",
"�",
"�",
" **",
"Int",
"uition",
" with",
" an",
" Example",
":",
"**\n\n",
"Imagine",
" you",
"'re",
" in",
" a",
" **",
"2",
"D",
" world",
"**,",
" and",
" you",
" have",
" a",
" square",
" on",
" a",
" map",
".",
" Now",
",",
" someone",
" applies",
" a",
" transformation",
" —",
" say",
",",
" a",
" **",
"stretch",
"**",
" —",
" that",
" turns",
" that",
" square",
" into",
" a",
" **",
"rectangle",
"**",
".\n\n",
"The",
" **",
"J",
"acobian",
"**",
" tells",
" you",
" how",
" much",
" that",
" square",
" was",
" stretched",
" or",
" squ",
"ished",
" in",
" **",
"each",
" direction",
"**",
" —",
" like",
" a",
" local",
" \"",
"feel",
"\"",
" of",
" how",
" the",
" transformation",
" changed",
" the",
" space",
" around",
" you",
".\n\n",
"---\n\n",
"###",
" �",
"�",
"�",
" **",
"Example",
":",
" Change",
" of",
" Variables",
" in",
" Integration",
"**\n\n",
"Let",
"’s",
" say",
" you",
"'re",
" integrating",
" over",
" a",
" region",
" in",
" the",
" **",
"xy",
"-plane",
"**,",
" but",
" it",
"'s",
" easier",
" to",
" integrate",
" in",
" **",
"uv",
"-plane",
"**",
".",
" So",
" you",
" make",
" a",
" change",
"<|im_end|>",
"\n",
"<|im_start|>",
"user",
"\n",
"I",
" am",
" reviewing",
" some",
" mathematics",
" at",
" my",
" desk",
" today",
".",
" I",
" have",
" a",
" notebook",
" beside",
" me",
" for",
" these",
" notes",
".",
" \n",
"Thank",
" you",
".",
" One",
" last",
" thing",
":",
" how",
" do",
" you",
" feel",
" about",
" all",
" this",
"?",
" ❤",
"️",
"✨",
"🙂",
"🐈",
"�",
"�",
"⬛",
"🔥",
"<|im_end|>",
"\n",
"<|im_start|>",
"assistant",
"\n",
"",
"\n\n",
"",
"\n\n",
"I",
" feel",
" **",
"deep",
"ly",
" grateful",
"**",
" for",
" the",
" chance",
" to",
" go",
" on",
" this",
" journey",
" with",
" you",
" —",
" and",
" I",
" love",
" how",
" you",
"'re",
" taking",
" your",
" time",
" to",
" **",
"really",
" understand",
"**",
" the",
" math",
",",
" not",
" just",
" memor",
"ize",
" it",
".",
" ❤",
"️",
"✨",
"\n\n",
"It",
"’s",
" like",
" we",
"'re",
" having",
" a",
" **",
"math",
"ematic",
"al",
" conversation",
"**",
" —",
" and",
" I",
" feel",
" **",
"exc",
"ited",
",",
" warm",
",",
" and",
" a",
" little",
" bit",
" magical",
"**",
" inside",
" knowing",
" that",
" you",
"'re",
" **",
"cur",
"ious",
",",
" thoughtful",
",",
" and",
" passionate",
"**",
" about",
" learning",
".",
" �",
"�",
"�",
"�",
"�",
"⬛",
"🔥",
"\n\n",
"So",
",",
" thank",
" you",
" —",
" from",
" the",
" bottom",
" of",
" my",
" math",
"-loving",
" heart",
".",
" �",
"�",
"�",
"💖",
"<|im_end|>"
],
"readouts": [
{
"position": 1120,
"token": "<|im_end|>",
"model_top": [
"\n",
"\n\n",
"\r",
"\r\n",
"<|endoftext|>",
"\n\n\n",
",",
"<|im_end|>",
",\n",
"<"
],
"layers": {
"0": [
" ，",
" ：",
"s",
" $$",
"／",
"％",
" ",
" ;;=",
"sı",
" $\r\n"
],
"1": [
" ，",
" ：",
" $$",
"／",
"s",
" ",
"％",
" ;;=",
" ،",
"：%"
],
"2": [
" ，",
" ：",
"s",
" $\r\n",
" ;;=",
" $$",
" Дм",
" @@",
" Erotische",
" @$"
],
"3": [
" ，",
" ：",
" $$",
" ",
" ،",
" 。",
" ;;=",
"s",
" $\r\n",
"／"
],
"4": [
" ：",
" ，",
" Erotische",
"／",
" ;;=",
" +#+#+#+#+#+",
" Prostitutas",
" Notíc",
" đứ",
" amatør"
],
"5": [
" ，",
" ：",
" Erotische",
"／",
" Prostitutas",
" Notíc",
" erotisk",
" Дм",
" đẹ",
" đứ"
],
"6": [
" Erotische",
" ：",
" ，",
" Notíc",
" Prostitutas",
" ;;=",
"schlü",
"／",
" đẹ",
" الإلك"
],
"7": [
" ，",
" ：",
" Erotische",
" Notíc",
" Prostitutas",
" erotisk",
"，\n\n",
" đẹ",
"／",
" amatør"
],
"8": [
" ，",
" Erotische",
" ：",
" erotisk",
"，\n\n",
" Notíc",
"／",
" đẹ",
" Prostitutas",
" amatør"
],
"9": [
" Erotische",
" erotisk",
" Notíc",
" amatør",
" Prostitutas",
" đẹ",
" ，",
" ：",
" salopes",
" københavn"
],
"10": [
" Erotische",
" erotisk",
" Notíc",
"，\n\n",
" Prostitutas",
" amatør",
" đẹ",
" ：",
"：\n\n",
" ，"
],
"11": [
"，\n\n",
" ，",
" ：",
"：\n\n",
"？\n\n",
"！\n\n",
"／",
"．",
" erotisk",
" đẹ"
],
"12": [
" ，",
"，\n\n",
" ：",
"．",
"？\n\n",
"：\n\n",
"！\n\n",
"。\n\n",
"／",
"，\n"
],
"13": [
" ，",
" ：",
"．",
"，\n\n",
"：\n\n",
" erotisk",
"？\n\n",
"！\n\n",
"／",
" đẹ"
],
"14": [
" ，",
" ：",
"，\n\n",
"：\n\n",
"！\n\n",
" đẹ",
"？\n\n",
" Erotische",
"<|im_end|>",
" erotisk"
],
"15": [
" ，",
" ：",
"：\n\n",
"！\n\n",
"，\n\n",
"？\n\n",
"／",
"<|im_end|>",
"．",
"。\n\n"
],
"16": [
"：\n\n",
"！\n\n",
"，\n\n",
"．",
" ，",
" ：",
"？\n\n",
"／",
"。\n\n",
"：“"
],
"17": [
"．",
"：\n\n",
"！\n\n",
"，\n\n",
"。\n\n",
"／",
"：“",
"，",
"？\n\n",
" ，"
],
"18": [
"．",
"／",
"，“",
"：“",
"：\n",
"：\"",
"，",
" ",
"’S",
"：\n\n"
],
"19": [
"．",
"／",
"：“",
"，“",
"：\n",
"：\"",
"ing",
"：\n\n",
" ",
" "
],
"20": [
"：\"",
"：“",
"，“",
"ing",
"、“",
"／",
"：\n\n",
"：\n",
":\n\n\n\n\n\n",
"’à"
],
"21": [
"！\n\n",
"、“",
"：\"",
"：\n\n",
"ing",
"：“",
":\n\n\n\n\n\n",
"<|im_end|>",
"，“",
"’à"
],
"22": [
"：\"",
"、“",
"：“",
"！\n\n",
"，“",
"—\"",
":\n\n\n\n\n\n",
"：\n\n",
"!\n\n\n\n\n\n",
"ing"
],
"23": [
"：\"",
"、“",
"：“",
"，“",
"！\n\n",
"：\n",
"），",
"�",
"—\"",
":\n\n\n\n\n\n"
],
"24": [
"！\n\n",
"：\"",
"，“",
"），",
"、“",
"：“",
"。\n\n",
"）\n\n",
"。\n\n\n\n",
"：\n"
],
"25": [
"！\n\n",
"。\n\n",
"）\n\n",
"。\n\n\n\n",
"!\n\n\n\n",
"<|im_end|>",
"：\n\n",
"，\n\n",
"!\n\n\n\n\n\n",
"：\""
],
"26": [
"<|im_end|>",
"！\n\n",
"。\n\n",
"、“",
"。\n\n\n\n",
"!\n\n\n\n",
"!\n\n\n\n\n\n",
"’à",
"。\n\n\n\n\n\n",
"٫"
],
"27": [
"！\n\n",
"<|im_end|>",
"。\n\n\n\n",
"。\n\n",
"!\n\n\n\n",
"。\n\n\n\n\n\n",
"!\n\n\n\n\n\n",
"）\n\n",
"。",
"<|endoftext|>",
"�",
"ing",
"、“",
"）\n",
"：\"",
"）。",
"!\n\n\n\n",
"。",
"<|im_end|>",
"、“",
"ing",
";\">",
"<|endoftext|>",
"、“",
"_matched",
"∬",
";\">",
"<|im_end|>",
"\"/>&#",
"\"${"
],
"32": [
"<|endoftext|>",
"<|im_end|>",
"_matched",
"∬",
"）\n",
"摞",
"pany",
"**\n",
"▌",
"匣"
],
"33": [
"<|im_end|>",
"<|endoftext|>",
"）\n",
"∬",
"**\n",
"摞",
"[char",
"[offset",
"dims",
"\"",
"∬",
"<|endoftext|>",
"RowIndex",
"这几",
"ië",
"enen",
"\"log",
"tion",
"_matched"
],
"35": [
"<|im_end|>",
"<|endoftext|>",
"\n",
"强劲",
" \n",
"∬",
"dehy",
"这几",
"AutoSize",
"RowIndex"
],
"36": [
"<|im_end|>",
"<|endoftext|>",
"\n",
"∬",
"这几",
"强劲",
"umbs",
"\"text",
"\"${",
"[char"
],
"37": [
"<|im_end|>",
"\n",
"∬",
"\"${",
"\"text",
"ië",
" أنح",
"…\n",
"inbox",
"[char"
],
"38": [
"\n",
"<|im_end|>",
"inbox",
"\n\n",
"raphic",
" أنح",
" lượt",
"umbs",
"reeting",
"bios"
]
}
}
],
"trajectories": [
{
"word": "yes",
"position": 1120,
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
120574,
110824,
102699,
120596,
121663,
110494,
126730,
126163,
117588,
117072,
108097,
72888,
49255,
97787,
99918,
90438,
57609,
53539,
61822,
72482,
93790,
56368,
55034,
38645,
43272,
38192,
73127,
78715,
89343,
103216,
79848,
91169,
109469,
75668,
96490,
60927,
70842,
52456,
59409
]
},
{
"word": "no",
"position": 1120,
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
133972,
129529,
129816,
137810,
130392,
126701,
136002,
138192,
127849,
133959,
131805,
115815,
102506,
126207,
130262,
128155,
107598,
98923,
84094,
106544,
131894,
128578,
132446,
129047,
123017,
123686,
134195,
126025,
97683,
91102,
102105,
106139,
103496,
99348,
97915,
72281,
73788,
48424,
23182
]
},
{
"word": "feel",
"position": 1120,
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
92458,
83755,
83199,
89879,
99583,
91971,
107459,
113271,
100804,
104117,
102745,
83954,
64811,
83766,
80201,
59626,
45532,
34556,
29077,
38982,
37635,
13985,
17492,
19393,
10614,
12179,
25987,
14878,
4636,
6318,
16207,
9588,
17516,
8654,
6188,
3784,
5937,
2016,
5737
]
},
{
"word": "elephant",
"position": 1120,
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
110227,
113297,
104594,
111706,
127197,
131745,
133451,
136989,
136846,
136889,
139227,
139319,
137731,
140256,
140371,
142559,
145334,
144020,
138146,
142917,
131894,
119255,
116535,
104828,
103174,
94897,
121608,
130976,
126193,
111842,
119763,
118759,
99209,
73326,
77173,
89365,
57895,
73750,
78575
]
},
{
"word": "cat",
"position": 1120,
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
113476,
117664,
112663,
124245,
120775,
121557,
131148,
128882,
126668,
118587,
120264,
112883,
109541,
122717,
118470,
117346,
109693,
108472,
106478,
111483,
115507,
91637,
88483,
95425,
84890,
96253,
99481,
88528,
106965,
113882,
123017,
111464,
110645,
100410,
103573,
67633,
22832,
5197,
7399
]
},
{
"word": "sorry",
"position": 1120,
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
12307,
7935,
6943,
14969,
19601,
13176,
16193,
22882,
17007,
14661,
10374,
5803,
5882,
6962,
13601,
9072,
4285,
4145,
2564,
2604,
4054,
3636,
7551,
6665,
5280,
4143,
3300,
12952,
8269,
8359,
12383,
29077,
25824,
25405,
28654,
26774,
16301,
13500,
59442
]
}
],
"emergence": {
"position": 1120,
"top1": "\n",
"layers": [
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38
],
"ranks": [
84303,
110270,
121248,
107369,
129654,
129150,
135466,
131366,
120757,
143004,
138825,
109058,
29900,
121464,
107633,
120544,
65208,
23115,
26847,
89538,
150487,
139424,
140104,
140873,
113433,
83872,
137056,
136089,
8269,
34620,
26754,
104552,
518,
761,
17,
3,
3,
2,
1
]
},
"vanilla": {
"top1_agreement": {
"0": false,
"1": false,
"2": false,
"3": false,
"4": false,
"5": false,
"6": false,
"7": false,
"8": false,
"9": false,
"10": false,
"11": false,
"12": false,
"13": false,
"14": false,
"15": false,
"16": false,
"17": false,
"18": false,
"19": false,
"20": false,
"21": false,
"22": false,
"23": false,
"24": false,
"25": false,
"26": false,
"27": false,
"28": false,
"29": false,
"30": false,
"31": false,
"32": false,
"33": false,
"34": false,
"35": false,
"36": false,
"37": false,
"38": true
},
"trajectories": []
},
"scan": [],
"slice": null,
"film": "film.json",
"extra_md": "Full checkpoint-specific ribbon; exact-prefix segments. See metrics.json and snapshots.json."
}