conversations listlengths 2 2 | shard_id stringclasses 9
values | output stringlengths 1 40.3k | ngram_3_uniqueness float64 0.41 0.41 | entropy float64 12 12 ⌀ | gini_index float64 0 0 ⌀ | self_bleu float64 0.82 0.82 ⌀ | embeddings stringlengths 12.5k 12.5k ⌀ | kmeans_inertia_embeddings float64 2.18M 2.18M ⌀ | kmeans_inertia_embeddings_normalized float64 5.97 5.97 ⌀ | projected_gradients_embeddings float64 191 191 ⌀ | new_conversations stringlengths 91 9.22k ⌀ | projected_gradients stringlengths 71 102 ⌀ | projected_gradients_vendi float64 19 19 ⌀ | projected_gradients_log_det float64 | projected_embeddings_log_det float64 | kmeans_inertia_gradients float64 3.01k 3.01k ⌀ | kmeans_inertia_gradients_normalized float64 0.3 0.3 ⌀ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "human",
"value": "**Problem: Singular Value Decomposition (SVD)**\n\nLet \\( A \\) be the \\( 3 \\times 2 \\) matrix given by\n\n\\[\nA = \\begin{pmatrix}\n4 & 0 \\\\\n3 & -5 \\\\\n1 & 2\n\\end{pmatrix}.\n\\]\n\n1. Compute the singular values of the matrix \\( A \\).\n2. Perform the singular valu... | camel_math_gpt-4o-mini::convert_to_sharegpt | To solve the problem of Singular Value Decomposition (SVD) for the given matrix \( A \), we'll follow the steps outlined in the problem statement.
**Step 1: Compute the singular values of the matrix \( A \)**
First, calculate \( A^T A \):
\[
A^T = \begin{pmatrix}
4 & 3 & 1 \\
0 & -5 & 2
\end{pmatrix}
\]
Now, comput... | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [-5.55779599e-02 -2.62038969e-02 -8.51547439e-03 6.42842799e-02
1.99772164e-01 -3.28491181e-02 -5.53658456e-02 2.84111314e-02
3.04492768e-02 -5.75360954e-02 -2.11708073e-04 1.96627602e-01
1.84093527e-02 2.36262828e-02 -7.60766193e-02 9.00173783e-02
4.10104245e-02 1.32822350e-01 -1.36725157e-01 -6.32472485... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': '**Problem: Singular Value Decomposition (SVD)**\n\nLet \\( A \\) be the \\( 3 \\times 2 \\) matrix given by\n\n\\[\nA = \\begin{pmatrix}\n4 & 0 \\\\\n3 & -5 \\\\\n1 & 2\n\\end{pmatrix}.\n\\]\n\n1. Compute the singular values of the matrix \\( A \\).\n2. Perform the singular value decomposition (SVD) of \\... | [-0.00738267 -0.00740571 0.00526797 ... 0.01509495 0.00056465
0.00023061] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Identify and categorize the grammatical elements in this statement: \"The students eagerly awaited the arrival of the guest speaker.\""
},
{
"from": "gpt",
"value": "In the sentence \"The students eagerly awaited the arrival of the guest speaker,\" we can identify an... | evol_instruct_gpt-4o-mini::to_sharegpt | In the sentence "The students eagerly awaited the arrival of the guest speaker," we can identify and categorize the grammatical elements as follows:
1. **Noun Phrase (Subject)**:
- "The students"
- "The" (definite article)
- "students" (noun, plural)
2. **Adverb**:
- "eagerly" (modifies the verb "a... | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [ 1.52563125e-01 -6.91817049e-03 -8.54339004e-02 1.66520327e-01
-7.72445723e-02 -7.75873587e-02 -1.89352274e-01 -3.19579169e-02
-4.87864017e-02 -8.94879028e-02 3.58010121e-02 -9.91055295e-02
-3.99975628e-02 -1.22223198e-01 -4.64749113e-02 1.13551514e-02
1.44105941e-01 2.51586195e-02 -1.45613745e-01 5.16383834... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'Identify and categorize the grammatical elements in this statement: "The students eagerly awaited the arrival of the guest speaker."', 'role': 'user'}
{'content': 'In the sentence "The students eagerly awaited the arrival of the guest speaker," we can identify and categorize the grammatical elements as f... | [-0.00218513 0.00601561 -0.00324547 ... 0.00038133 -0.01461453
-0.0078644 ] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "The government gives the bottom 20% of people a $2000 stimulus. They have found that X times as much money to the government, in terms of tax revenue, as it cost. The city has 1000 people in it. What was the government profit from this project? If we know the answer to the above... | metamath_gpt-4o-mini::convert_instruction_response_to_sharegpt | To solve this problem, we need to determine how much profit the government made from giving the bottom 20% of the people a $2000 stimulus and how that relates to the unknown variable X.
Let's break down the information given:
- The total population of the city is 1000 people.
- The bottom 20% of people is 20% of 1000,... | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [-5.14843054e-02 1.40476957e-01 -5.92565536e-02 1.40697807e-01
-3.56461518e-02 8.78391340e-02 -7.52238110e-02 -1.39616756e-02
-2.05778271e-01 -4.17868532e-02 9.18873698e-02 3.16319652e-02
6.93458095e-02 2.33510107e-01 -2.06946768e-02 -9.46800187e-02
-6.60899933e-03 5.94767518e-02 -1.70217566e-02 3.66960205... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'The government gives the bottom 20% of people a $2000 stimulus. They have found that X times as much money to the government, in terms of tax revenue, as it cost. The city has 1000 people in it. What was the government profit from this project? If we know the answer to the above question is 1600000, what ... | [-0.00220331 0.00600328 -0.0032329 ... 0.00035708 -0.01461178
-0.00784493] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Generate a possible title for a book about overcoming anxiety."
},
{
"from": "gpt",
"value": "\"Finding Calm: A Journey through Anxiety to Inner Peace.\""
}
] | alpaca_gpt-4o-mini::convert_alpaca_to_sharegpt | "Finding Calm: A Journey through Anxiety to Inner Peace." | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [ 8.42469186e-02 1.00446872e-01 -1.68725140e-02 -2.67781578e-02
1.59583483e-02 6.01588227e-02 -3.63534093e-02 -4.98342998e-02
6.09143004e-02 9.95807350e-02 4.47446331e-02 5.14631066e-03
7.67101394e-03 -2.40212753e-01 -8.25460851e-02 -1.46692812e-01
5.60616329e-02 1.53748065e-01 1.35013357e-01 8.91521052... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'Generate a possible title for a book about overcoming anxiety.', 'role': 'user'}
{'content': '"Finding Calm: A Journey through Anxiety to Inner Peace."', 'role': 'assistant'}] | [-0.00101006 0.00659143 -0.00271213 ... 0.00118232 -0.01460503
-0.00992067] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Please categorize the provided title according to the following topics: 0 for 'Society & Culture', 1 for 'Science & Mathematics', 2 for 'Health', 3 for 'Education & Reference', 4 for 'Computers & Internet', 5 for 'Sports', 6 for 'Business & Finance', 7 for 'Entertainment & Music... | unnatural_instructions_gpt-4o-mini::convert_to_sharegpt | 2 | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [ 1.44317120e-01 9.89982411e-02 5.96167482e-02 -8.80127326e-02
-8.87244344e-02 -1.60565451e-01 -1.52557278e-02 6.18139207e-02
-5.07040620e-02 1.82581376e-02 2.98491359e-01 -1.42718270e-01
-5.06210513e-02 4.88236882e-02 -1.32450582e-02 2.59406622e-02
6.93058372e-02 5.09113073e-03 -5.81662767e-02 7.40180388... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'Categorize the question title according to the following 10 topics: 0 for ‘Society & Culture’, 1 for ‘Science & Mathematics’, 2 for ‘Health’, 3 for ‘Education & Reference’, 4 for ‘Computers & Internet’, 5 for ‘Sports’, 6 for ‘Business & Finance’, 7 for ‘Entertainment & Music’, 8 for ‘Family & Relationship... | [-0.00236019 0.0059175 -0.00279227 ... 0.00068623 -0.01510442
-0.00803687] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Train is to travel as boat is to"
},
{
"from": "gpt",
"value": "Travel by water."
}
] | evol_instruct_gpt-4o-mini::to_sharegpt | Travel by water. | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [-3.66583467e-02 1.97393343e-01 -9.63318348e-02 -1.10757910e-01
-6.48498014e-02 -2.75093392e-02 -6.58674762e-02 -1.25747174e-05
3.60347144e-02 6.81347772e-03 -1.02676880e-02 9.30024683e-02
1.04553021e-01 6.68066517e-02 9.90871787e-02 -2.44390801e-01
1.51452407e-01 -1.64238855e-01 -2.37735510e-01 -5.72325885... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'Train is to travel as boat is to', 'role': 'user'}
{'content': 'Travel by water.', 'role': 'assistant'}] | [-0.00102399 0.00657299 -0.00268189 ... 0.00115456 -0.01461867
-0.0098773 ] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Sure! Here’s a problem based on Fermat's Little Theorem:\n\n**Problem:**\n\nLet \\( p \\) be a prime number and \\( a \\) be an integer such that \\( a \\) is not divisible by \\( p \\).\n\n1. Verify Fermat's Little Theorem for \\( a = 3 \\) and \\( p = 7 \\) by calculating \\( ... | camel_math_gpt-4o-mini::convert_to_sharegpt | Let's go through the problem step by step using Fermat's Little Theorem, which states that if \( p \) is a prime number and \( a \) is an integer not divisible by \( p \), then:
\[
a^{p-1} \equiv 1 \mod p
\]
### Part 1: Verify Fermat's Little Theorem for \( a = 3 \) and \( p = 7 \)
Given \( a = 3 \) and \( p = 7 \),... | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [ 1.70481607e-01 1.46284262e-02 -3.68601754e-02 1.06141135e-01
-4.49117273e-02 -2.02421360e-02 -2.73336489e-02 1.10654101e-01
-8.72691721e-02 2.21081376e-02 -3.68911400e-02 3.13263297e-01
1.87592693e-02 -2.29187503e-01 -4.40726951e-02 -2.66971886e-02
-3.00673582e-02 1.07556880e-01 3.07307169e-02 8.14310741... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': "Sure! Here’s a problem based on Fermat's Little Theorem:\n\n**Problem:**\n\nLet \\( p \\) be a prime number and \\( a \\) be an integer such that \\( a \\) is not divisible by \\( p \\).\n\n1. Verify Fermat's Little Theorem for \\( a = 3 \\) and \\( p = 7 \\) by calculating \\( 3^6 \\mod 7 \\).\n2. Determ... | [ 1.05907554e-02 -8.22879840e-03 4.89812763e-03 ... 4.47951118e-03
-8.49853922e-03 1.70589374e-05] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Based on the context of personal growth and skill acquisition in education, the following insights can be drawn from the provided information: Should I learn a new language?."
},
{
"from": "gpt",
"value": "8"
}
] | unnatural_instructions_gpt-4o-mini::convert_to_sharegpt | 8 | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [-8.05418715e-02 6.02551214e-02 2.53381697e-03 1.42762838e-02
-7.75061920e-02 -5.23859449e-02 9.82740298e-02 9.61089600e-03
1.11530729e-01 5.74504631e-03 1.33648589e-01 -5.53845167e-02
-1.75869703e-01 -9.88204870e-03 -6.04974246e-03 6.92302063e-02
7.61800334e-02 7.25522637e-02 1.11693829e-01 -1.13627255... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'John has 5 apples and he buys 3 more. How many apples does he have now? The solution to the problem is', 'role': 'user'}
{'content': '8', 'role': 'assistant'}] | [-0.00205553 0.00602538 -0.00304261 ... 0.00054097 -0.01477756
-0.00816957] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Sure! Here's a problem related to the topic of differentiating under the integral sign:\n\n**Problem:**\n\nLet \\( f(x) = \\int_0^x e^{-t^2} \\, dt \\).\n\n1. Show that \\( f(x) \\) is differentiable on \\( \\mathbb{R} \\).\n2. Use the Fundamental Theorem of Calculus to find \\(... | camel_math_gpt-4o-mini::convert_to_sharegpt | To solve the problem step-by-step, we'll start with the given function:
\[
f(x) = \int_0^x e^{-t^2} \, dt.
\]
### 1. Show that \( f(x) \) is differentiable on \( \mathbb{R} \).
The function \( e^{-t^2} \) is continuous for all \( t \in \mathbb{R} \), as the exponential function is continuous everywhere. Given that \... | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [ 1.14886791e-01 -9.52475369e-02 -1.31723374e-01 2.39939868e-01
-4.20942083e-02 -4.42520976e-02 1.41238049e-02 5.59401251e-02
-2.47538388e-02 -3.99777666e-02 -2.30370127e-02 7.41813183e-02
-6.15449324e-02 1.09392598e-01 -1.22884363e-01 1.74790323e-02
-6.52920678e-02 2.62258388e-03 -2.15646140e-02 2.51105484... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': "Sure! Here's a problem related to the topic of differentiating under the integral sign:\n\n**Problem:**\n\nLet \\( f(x) = \\int_0^x e^{-t^2} \\, dt \\).\n\n1. Show that \\( f(x) \\) is differentiable on \\( \\mathbb{R} \\).\n2. Use the Fundamental Theorem of Calculus to find \\( f'(x) \\).\n3. Calculate \... | [-0.00226597 0.0056243 -0.00299979 ... 0.00047987 -0.01489123
-0.00789478] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Share a brief story about a memorable travel experience."
},
{
"from": "gpt",
"value": "During my trip to Japan, I wandered through the serene streets of Kyoto's Arashiyama Bamboo Grove. Surrounded by towering bamboo, I felt a deep sense of tranquility. As I reached ... | alpaca_gpt-4o-mini::convert_alpaca_to_sharegpt | During my trip to Japan, I wandered through the serene streets of Kyoto's Arashiyama Bamboo Grove. Surrounded by towering bamboo, I felt a deep sense of tranquility. As I reached the end, I stumbled upon a traditional tea house and enjoyed matcha, feeling connected to the rich culture around me. | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [ 1.06690049e-01 2.00379401e-01 -2.61257663e-02 9.61234644e-02
7.23762810e-02 5.94266653e-02 1.39559414e-02 3.57261412e-02
-1.45409092e-01 8.58357027e-02 -1.44886240e-01 8.83921310e-02
1.18861891e-01 2.72751935e-02 -1.47533743e-02 -2.35534921e-01
7.03780055e-02 9.69782770e-02 -1.77508593e-01 -2.76499093... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'Share a brief story about a memorable travel experience.', 'role': 'user'}
{'content': "During my trip to Japan, I wandered through the serene streets of Kyoto's Arashiyama Bamboo Grove. Surrounded by towering bamboo, I felt a deep sense of tranquility. As I reached the end, I stumbled upon a traditional... | [-0.00245839 0.00603757 -0.0033788 ... 0.00039535 -0.01502516
-0.00846135] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
[
{
"from": "human",
"value": "Develop a Python function that simulates rolling a 12-sided die, returning a random integer between 1 and 12."
},
{
"from": "gpt",
"value": "You can simulate rolling a 12-sided die in Python using the `random` module, which provides various functions to generate rand... | evol_instruct_gpt-4o-mini::to_sharegpt | You can simulate rolling a 12-sided die in Python using the `random` module, which provides various functions to generate random numbers. Below is a simple function that rolls a 12-sided die and returns a random integer between 1 and 12:
```python
import random
def roll_dodecahedron():
return random.randint(1, 12... | 0.409365 | 12.019583 | 0.000001 | 0.822522 | [-6.12463616e-02 -4.27792855e-02 -3.31230164e-02 -9.32965241e-03
-4.16736715e-02 -8.47317744e-03 7.67898560e-02 -1.39308311e-02
5.55330664e-02 -6.24175929e-02 5.72929941e-02 4.80550677e-02
-1.17832990e-02 5.46933636e-02 2.75946017e-02 -1.65286269e-02
-6.59615695e-02 -3.15177217e-02 -1.47542758e-02 -5.89479469... | 2,181,367.534014 | 5.968762 | 191.223893 | [{'content': 'Develop a Python function that simulates rolling a 12-sided die, returning a random integer between 1 and 12.', 'role': 'user'}
{'content': 'You can simulate rolling a 12-sided die in Python using the `random` module, which provides various functions to generate random numbers. Below is a simple function... | [-0.00245242 0.00603056 -0.00337829 ... 0.00039369 -0.01501959
-0.00844714] | 18.975454 | null | null | 3,005.894393 | 0.300589 |
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