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--- |
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tags: |
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- sentence-transformers |
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- sentence-similarity |
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- feature-extraction |
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- dense |
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- generated_from_trainer |
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- dataset_size:2680 |
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- loss:MultipleNegativesRankingLoss |
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base_model: google/embeddinggemma-300m |
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widget: |
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- source_sentence: Let $A, M,$ and $C$ be nonnegative integers such that $A + M + |
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C = 12$. What is the maximum value of $A \cdot M \cdot C + A \cdot M + M \cdot |
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C + A \cdot C$? |
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sentences: |
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- Given that $2^{2004}$ is a $604$-digit number whose first digit is $1$, how many |
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elements of the set $S = \{2^0,2^1,2^2,\ldots ,2^{2003}\}$ have a first digit |
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of $4$? |
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- To complete the grid below, each of the digits 1 through 4 must occur once in |
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each row and once in each column. What number will occupy the lower right-hand |
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square? \[\begin{tabular}{|c|c|c|c|}\hline 1 & & 2 &\\ \hline 2 & 3 & &\\ \hline |
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& &&4\\ \hline & &&\\ \hline\end{tabular}\] |
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- Two non-zero real numbers, $a$ and $b,$ satisfy $ab = a - b$. Which of the following |
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is a possible value of $\frac {a}{b} + \frac {b}{a} - ab$? |
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- source_sentence: What is the sum of the prime factors of $2010$? |
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sentences: |
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- The lengths of the sides of a triangle in inches are three consecutive integers. |
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The length of the shortest side is $30\%$ of the perimeter. What is the length |
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of the longest side? |
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- On a map, a $12$-centimeter length represents $72$ kilometers. How many kilometers |
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does a $17$-centimeter length represent? |
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- The five pieces shown below can be arranged to form four of the five figures shown |
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in the choices. Which figure cannot be formed? [asy] defaultpen(linewidth(0.6)); |
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size(80); real r=0.5, s=1.5; path p=origin--(1,0)--(1,1)--(0,1)--cycle; draw(p); |
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draw(shift(s,r)*p); draw(shift(s,-r)*p); draw(shift(2s,2r)*p); draw(shift(2s,0)*p); |
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draw(shift(2s,-2r)*p); draw(shift(3s,3r)*p); draw(shift(3s,-3r)*p); draw(shift(3s,r)*p); |
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draw(shift(3s,-r)*p); draw(shift(4s,-4r)*p); draw(shift(4s,-2r)*p); draw(shift(4s,0)*p); |
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draw(shift(4s,2r)*p); draw(shift(4s,4r)*p); [/asy] [asy] size(350); defaultpen(linewidth(0.6)); |
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path p=origin--(1,0)--(1,1)--(0,1)--cycle; pair[] a={(0,0), (0,1), (0,2), (0,3), |
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(0,4), (1,0), (1,1), (1,2), (2,0), (2,1), (3,0), (3,1), (3,2), (3,3), (3,4)}; |
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pair[] b={(5,3), (5,4), (6,2), (6,3), (6,4), (7,1), (7,2), (7,3), (7,4), (8,0), |
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(8,1), (8,2), (9,0), (9,1), (9,2)}; pair[] c={(11,0), (11,1), (11,2), (11,3), |
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(11,4), (12,1), (12,2), (12,3), (12,4), (13,2), (13,3), (13,4), (14,3), (14,4), |
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(15,4)}; pair[] d={(17,0), (17,1), (17,2), (17,3), (17,4), (18,0), (18,1), (18,2), |
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(18,3), (18,4), (19,0), (19,1), (19,2), (19,3), (19,4)}; pair[] e={(21,4), (22,1), |
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(22,2), (22,3), (22,4), (23,0), (23,1), (23,2), (23,3), (23,4), (24,1), (24,2), |
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(24,3), (24,4), (25,4)}; int i; for(int i=0; i<15; i=i+1) { draw(shift(a[i])*p); |
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draw(shift(b[i])*p); draw(shift(c[i])*p); draw(shift(d[i])*p); draw(shift(e[i])*p); |
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} [/asy] \[ |
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- source_sentence: A circle and two distinct lines are drawn on a sheet of paper. |
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What is the largest possible number of points of intersection of these figures? |
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sentences: |
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- Three fair six-sided dice are rolled. What is the probability that the values |
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shown on two of the dice sum to the value shown on the remaining die? |
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- In the small country of Mathland, all automobile license plates have four symbols. |
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The first must be a vowel (A, E, I, O, or U), the second and third must be two |
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different letters among the 21 non-vowels, and the fourth must be a digit (0 through |
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9). If the symbols are chosen at random subject to these conditions, what is the |
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probability that the plate will read "AMC8"? |
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- How many different combinations of \$5 bills and \$2 bills can be used to make |
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a total of \$17? Order does not matter in this problem. |
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- source_sentence: Points $K, L, M,$ and $N$ lie in the plane of the square $ABCD$ |
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such that $AKB$, $BLC$, $CMD$, and $DNA$ are equilateral triangles. If $ABCD$ |
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has an area of 16, find the area of $KLMN$. [asy] unitsize(2cm); defaultpen(fontsize(8)+linewidth(0.8)); |
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pair A=(-0.5,0.5), B=(0.5,0.5), C=(0.5,-0.5), D=(-0.5,-0.5); pair K=(0,1.366), |
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L=(1.366,0), M=(0,-1.366), N=(-1.366,0); draw(A--N--K--A--B--K--L--B--C--L--M--C--D--M--N--D--A); |
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label("$A$",A,SE); label("$B$",B,SW); label("$C$",C,NW); label("$D$",D,NE); label("$K$",K,NNW); |
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label("$L$",L,E); label("$M$",M,S); label("$N$",N,W); [/asy] |
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sentences: |
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- A semicircle of diameter $1$ sits at the top of a semicircle of diameter $2$, |
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as shown. The shaded area inside the smaller semicircle and outside the larger |
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semicircle is called a lune. Determine the area of this lune. [asy] import graph; |
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size(150); defaultpen(fontsize(8)); pair A=(-2,0), B=(2,0); filldraw(Arc((0,sqrt(3)),1,0,180)--cycle,mediumgray); |
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filldraw(Arc((0,0),2,0,180)--cycle,white); draw(2*expi(2*pi/6)--2*expi(4*pi/6)); |
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label("1",(0,sqrt(3)),(0,-1)); label("2",(0,0),(0,-1)); [/asy] |
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- The average age of $5$ people in a room is $30$ years. An $18$-year-old person |
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leaves the room. What is the average age of the four remaining people? |
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- Which of the following numbers is a perfect square? |
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- source_sentence: The harmonic mean of a set of non-zero numbers is the reciprocal |
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of the average of the reciprocals of the numbers. What is the harmonic mean of |
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1, 2, and 4? |
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sentences: |
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- Spinners $A$ and $B$ are spun. On each spinner, the arrow is equally likely to |
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land on each number. What is the probability that the product of the two spinners' |
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numbers is even? |
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- Abby, Bridget, and four of their classmates will be seated in two rows of three |
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for a group picture, as shown. \begin{eqnarray*} \text{X}&\quad\text{X}\quad&\text{X} |
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\\ \text{X}&\quad\text{X}\quad&\text{X} \end{eqnarray*} If the seating positions |
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are assigned randomly, what is the probability that Abby and Bridget are adjacent |
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to each other in the same row or the same column? |
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- Semicircle $\Gamma$ has diameter $\overline{AB}$ of length $14$. Circle $\Omega$ |
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lies tangent to $\overline{AB}$ at a point $P$ and intersects $\Gamma$ at points |
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$Q$ and $R$. If $QR=3\sqrt3$ and $\angle QPR=60^\circ$, then the area of $\triangle |
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PQR$ equals $\tfrac{a\sqrt{b}}{c}$, where $a$ and $c$ are relatively prime positive |
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integers, and $b$ is a positive integer not divisible by the square of any prime. |
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What is $a+b+c$? |
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pipeline_tag: sentence-similarity |
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library_name: sentence-transformers |
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--- |
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# SentenceTransformer based on google/embeddinggemma-300m |
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This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [google/embeddinggemma-300m](https://huggingface.co/google/embeddinggemma-300m). It maps sentences & paragraphs to a 768-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more. |
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## Model Details |
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### Model Description |
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- **Model Type:** Sentence Transformer |
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- **Base model:** [google/embeddinggemma-300m](https://huggingface.co/google/embeddinggemma-300m) <!-- at revision 57c266a740f537b4dc058e1b0cda161fd15afa75 --> |
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- **Maximum Sequence Length:** 2048 tokens |
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- **Output Dimensionality:** 768 dimensions |
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- **Similarity Function:** Cosine Similarity |
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<!-- - **Training Dataset:** Unknown --> |
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<!-- - **Language:** Unknown --> |
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<!-- - **License:** Unknown --> |
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### Model Sources |
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- **Documentation:** [Sentence Transformers Documentation](https://sbert.net) |
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- **Repository:** [Sentence Transformers on GitHub](https://github.com/huggingface/sentence-transformers) |
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- **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers) |
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### Full Model Architecture |
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``` |
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SentenceTransformer( |
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(0): Transformer({'max_seq_length': 2048, 'do_lower_case': False, 'architecture': 'Gemma3TextModel'}) |
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(1): Pooling({'word_embedding_dimension': 768, 'pooling_mode_cls_token': False, 'pooling_mode_mean_tokens': True, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True}) |
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(2): Dense({'in_features': 768, 'out_features': 3072, 'bias': False, 'activation_function': 'torch.nn.modules.linear.Identity'}) |
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(3): Dense({'in_features': 3072, 'out_features': 768, 'bias': False, 'activation_function': 'torch.nn.modules.linear.Identity'}) |
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(4): Normalize() |
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) |
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``` |
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## Usage |
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### Direct Usage (Sentence Transformers) |
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First install the Sentence Transformers library: |
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```bash |
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pip install -U sentence-transformers |
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``` |
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Then you can load this model and run inference. |
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```python |
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from sentence_transformers import SentenceTransformer |
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# Download from the 🤗 Hub |
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model = SentenceTransformer("blachang28/my-embedding-gemma") |
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# Run inference |
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queries = [ |
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"The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?", |
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] |
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documents = [ |
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'Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown. \\begin{eqnarray*} \\text{X}&\\quad\\text{X}\\quad&\\text{X} \\\\ \\text{X}&\\quad\\text{X}\\quad&\\text{X} \\end{eqnarray*} If the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjacent to each other in the same row or the same column?', |
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'Semicircle $\\Gamma$ has diameter $\\overline{AB}$ of length $14$. Circle $\\Omega$ lies tangent to $\\overline{AB}$ at a point $P$ and intersects $\\Gamma$ at points $Q$ and $R$. If $QR=3\\sqrt3$ and $\\angle QPR=60^\\circ$, then the area of $\\triangle PQR$ equals $\\tfrac{a\\sqrt{b}}{c}$, where $a$ and $c$ are relatively prime positive integers, and $b$ is a positive integer not divisible by the square of any prime. What is $a+b+c$?', |
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"Spinners $A$ and $B$ are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?", |
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] |
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query_embeddings = model.encode_query(queries) |
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document_embeddings = model.encode_document(documents) |
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print(query_embeddings.shape, document_embeddings.shape) |
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# [1, 768] [3, 768] |
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# Get the similarity scores for the embeddings |
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similarities = model.similarity(query_embeddings, document_embeddings) |
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print(similarities) |
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# tensor([[ 0.9314, -0.3410, 0.9672]]) |
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``` |
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<!-- |
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### Direct Usage (Transformers) |
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<details><summary>Click to see the direct usage in Transformers</summary> |
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</details> |
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--> |
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<!-- |
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### Downstream Usage (Sentence Transformers) |
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You can finetune this model on your own dataset. |
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<details><summary>Click to expand</summary> |
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</details> |
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--> |
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<!-- |
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### Out-of-Scope Use |
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*List how the model may foreseeably be misused and address what users ought not to do with the model.* |
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--> |
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<!-- |
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## Bias, Risks and Limitations |
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*What are the known or foreseeable issues stemming from this model? You could also flag here known failure cases or weaknesses of the model.* |
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--> |
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<!-- |
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### Recommendations |
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*What are recommendations with respect to the foreseeable issues? For example, filtering explicit content.* |
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--> |
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## Training Details |
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### Training Dataset |
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#### Unnamed Dataset |
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* Size: 2,680 training samples |
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* Columns: <code>anchor</code>, <code>positive</code>, and <code>negative</code> |
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* Approximate statistics based on the first 1000 samples: |
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| | anchor | positive | negative | |
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|:--------|:-------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------|:-------------------------------------------------------------------------------------| |
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| type | string | string | string | |
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| details | <ul><li>min: 10 tokens</li><li>mean: 82.06 tokens</li><li>max: 1260 tokens</li></ul> | <ul><li>min: 11 tokens</li><li>mean: 80.7 tokens</li><li>max: 1260 tokens</li></ul> | <ul><li>min: 12 tokens</li><li>mean: 92.86 tokens</li><li>max: 2048 tokens</li></ul> | |
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* Samples: |
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| anchor | positive | negative | |
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|:-------------------------------------------------------------------------------------------------------------------------------------|:-----------------------------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| |
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| <code>$(6?3) + 4 - (2 - 1) = 5.$ To make this statement true, the question mark between the 6 and the 3 should be replaced by</code> | <code>What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?</code> | <code>An insect lives on the surface of a regular tetrahedron with edges of length 1. It wishes to travel on the surface of the tetrahedron from the midpoint of one edge to the midpoint of the opposite edge. What is the length of the shortest such trip? (Note: Two edges of a tetrahedron are opposite if they have no common endpoint.)</code> | |
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| <code>What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?</code> | <code>Which triplet of numbers has a sum NOT equal to 1?</code> | <code>Corners are sliced off a unit cube so that the six faces each become regular octagons. What is the total volume of the removed tetrahedra?</code> | |
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| <code>Which triplet of numbers has a sum NOT equal to 1?</code> | <code>What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?</code> | <code>How many pairs of positive integers $(a,b)$ are there such that $\text{gcd}(a,b)=1$ and $\frac{a}{b} + \frac{14b}{9a}$ is an integer? $\mathrm {(A)}\ 4\quad\mathrm {(B)}\ 6\quad\mathrm {(C)}\ 9\quad\mathrm {(D)}\ 12\quad\mathrm {(E)}\ \text{infinitely many}$</code> | |
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* Loss: [<code>MultipleNegativesRankingLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#multiplenegativesrankingloss) with these parameters: |
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```json |
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{ |
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"scale": 20.0, |
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"similarity_fct": "cos_sim", |
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"gather_across_devices": false |
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} |
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``` |
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### Training Hyperparameters |
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#### Non-Default Hyperparameters |
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- `per_device_train_batch_size`: 1 |
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- `learning_rate`: 2e-05 |
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- `num_train_epochs`: 5 |
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- `warmup_ratio`: 0.1 |
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- `prompts`: task: classification | query: |
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#### All Hyperparameters |
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<details><summary>Click to expand</summary> |
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- `overwrite_output_dir`: False |
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- `do_predict`: False |
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- `eval_strategy`: no |
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- `prediction_loss_only`: True |
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- `per_device_train_batch_size`: 1 |
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- `per_device_eval_batch_size`: 8 |
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- `per_gpu_train_batch_size`: None |
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- `per_gpu_eval_batch_size`: None |
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- `gradient_accumulation_steps`: 1 |
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- `eval_accumulation_steps`: None |
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- `torch_empty_cache_steps`: None |
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- `learning_rate`: 2e-05 |
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- `weight_decay`: 0.0 |
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- `adam_beta1`: 0.9 |
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- `adam_beta2`: 0.999 |
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- `adam_epsilon`: 1e-08 |
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- `max_grad_norm`: 1.0 |
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- `num_train_epochs`: 5 |
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- `max_steps`: -1 |
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- `lr_scheduler_type`: linear |
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- `lr_scheduler_kwargs`: {} |
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- `warmup_ratio`: 0.1 |
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- `warmup_steps`: 0 |
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- `log_level`: passive |
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- `log_level_replica`: warning |
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- `log_on_each_node`: True |
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- `logging_nan_inf_filter`: True |
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- `save_safetensors`: True |
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- `save_on_each_node`: False |
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- `save_only_model`: False |
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- `restore_callback_states_from_checkpoint`: False |
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- `no_cuda`: False |
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- `use_cpu`: False |
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- `use_mps_device`: False |
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- `seed`: 42 |
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- `data_seed`: None |
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- `jit_mode_eval`: False |
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- `bf16`: False |
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- `fp16`: False |
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- `fp16_opt_level`: O1 |
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- `half_precision_backend`: auto |
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- `bf16_full_eval`: False |
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- `fp16_full_eval`: False |
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- `tf32`: None |
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- `local_rank`: 0 |
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- `ddp_backend`: None |
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- `tpu_num_cores`: None |
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- `tpu_metrics_debug`: False |
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- `debug`: [] |
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- `dataloader_drop_last`: False |
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- `dataloader_num_workers`: 0 |
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- `dataloader_prefetch_factor`: None |
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- `past_index`: -1 |
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- `disable_tqdm`: False |
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- `remove_unused_columns`: True |
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- `label_names`: None |
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- `load_best_model_at_end`: False |
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- `ignore_data_skip`: False |
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- `fsdp`: [] |
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- `fsdp_min_num_params`: 0 |
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- `fsdp_config`: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False} |
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- `fsdp_transformer_layer_cls_to_wrap`: None |
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- `accelerator_config`: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None} |
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- `parallelism_config`: None |
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- `deepspeed`: None |
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- `label_smoothing_factor`: 0.0 |
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- `optim`: adamw_torch_fused |
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- `optim_args`: None |
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- `adafactor`: False |
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- `group_by_length`: False |
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- `length_column_name`: length |
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- `project`: huggingface |
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- `trackio_space_id`: trackio |
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- `ddp_find_unused_parameters`: None |
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- `ddp_bucket_cap_mb`: None |
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- `ddp_broadcast_buffers`: False |
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- `dataloader_pin_memory`: True |
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- `dataloader_persistent_workers`: False |
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- `skip_memory_metrics`: True |
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- `use_legacy_prediction_loop`: False |
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- `push_to_hub`: False |
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- `resume_from_checkpoint`: None |
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- `hub_model_id`: None |
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- `hub_strategy`: every_save |
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|
- `hub_private_repo`: None |
|
|
- `hub_always_push`: False |
|
|
- `hub_revision`: None |
|
|
- `gradient_checkpointing`: False |
|
|
- `gradient_checkpointing_kwargs`: None |
|
|
- `include_inputs_for_metrics`: False |
|
|
- `include_for_metrics`: [] |
|
|
- `eval_do_concat_batches`: True |
|
|
- `fp16_backend`: auto |
|
|
- `push_to_hub_model_id`: None |
|
|
- `push_to_hub_organization`: None |
|
|
- `mp_parameters`: |
|
|
- `auto_find_batch_size`: False |
|
|
- `full_determinism`: False |
|
|
- `torchdynamo`: None |
|
|
- `ray_scope`: last |
|
|
- `ddp_timeout`: 1800 |
|
|
- `torch_compile`: False |
|
|
- `torch_compile_backend`: None |
|
|
- `torch_compile_mode`: None |
|
|
- `include_tokens_per_second`: False |
|
|
- `include_num_input_tokens_seen`: no |
|
|
- `neftune_noise_alpha`: None |
|
|
- `optim_target_modules`: None |
|
|
- `batch_eval_metrics`: False |
|
|
- `eval_on_start`: False |
|
|
- `use_liger_kernel`: False |
|
|
- `liger_kernel_config`: None |
|
|
- `eval_use_gather_object`: False |
|
|
- `average_tokens_across_devices`: True |
|
|
- `prompts`: task: classification | query: |
|
|
- `batch_sampler`: batch_sampler |
|
|
- `multi_dataset_batch_sampler`: proportional |
|
|
- `router_mapping`: {} |
|
|
- `learning_rate_mapping`: {} |
|
|
|
|
|
</details> |
|
|
|
|
|
### Training Logs |
|
|
| Epoch | Step | Training Loss | |
|
|
|:-----:|:-----:|:-------------:| |
|
|
| 1.0 | 2680 | 1.5631 | |
|
|
| 2.0 | 5360 | 1.2027 | |
|
|
| 3.0 | 8040 | 0.8526 | |
|
|
| 4.0 | 10720 | 0.6227 | |
|
|
| 5.0 | 13400 | 0.3352 | |
|
|
|
|
|
|
|
|
### Framework Versions |
|
|
- Python: 3.12.12 |
|
|
- Sentence Transformers: 5.1.2 |
|
|
- Transformers: 4.57.2 |
|
|
- PyTorch: 2.9.0+cu126 |
|
|
- Accelerate: 1.12.0 |
|
|
- Datasets: 4.0.0 |
|
|
- Tokenizers: 0.22.1 |
|
|
|
|
|
## 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", |
|
|
} |
|
|
``` |
|
|
|
|
|
#### MultipleNegativesRankingLoss |
|
|
```bibtex |
|
|
@misc{henderson2017efficient, |
|
|
title={Efficient Natural Language Response Suggestion for Smart Reply}, |
|
|
author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil}, |
|
|
year={2017}, |
|
|
eprint={1705.00652}, |
|
|
archivePrefix={arXiv}, |
|
|
primaryClass={cs.CL} |
|
|
} |
|
|
``` |
|
|
|
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