SentenceTransformer

Model Details

Model Description

• Model Type: Sentence Transformer

• Maximum Sequence Length: 256 tokens
• Output Dimensionality: 384 dimensions
• Similarity Function: Cosine Similarity

Model Sources

• Documentation: Sentence Transformers Documentation
• Repository: Sentence Transformers on GitHub
• Hugging Face: Sentence Transformers on Hugging Face

Full Model Architecture

SentenceTransformer(
  (0): Transformer({'max_seq_length': 256, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 384, '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})
  (2): Normalize()
)

Usage

Direct Usage (Sentence Transformers)

Training Details

Training Dataset

Unnamed Dataset

• Size: 17,405 training samples
• Columns: anchor, positive, and negative
• Approximate statistics based on the first 1000 samples:

  	anchor	positive	negative
  type	string	string	string
  details	min: 32 tokens mean: 87.49 tokens max: 256 tokens	min: 79 tokens mean: 179.08 tokens max: 256 tokens	min: 75 tokens mean: 180.1 tokens max: 256 tokens

• Samples:

  anchor	positive	negative
  Subject: Cubics and Reciprocals[object Object]Construct: Given a positive x value, find the corresponding y value for reciprocal graphs[object Object]Question: This is a part of the table of values for the equation ( y=\frac{3}{x} ) \begin{tabular}{	l	l
  Subject: Angle Facts with Parallel Lines[object Object]Construct: Identify a transversal[object Object]Question: What is the name given to the red line that intersects the two dashed lines? [object Object][object Object]Incorrect Answer: Parallel	Does not know the meaning of the word parallel[object Object]The passage is indicating a misconception related to a math problem, specifically one that involves the concept of "parallel." In mathematics, particularly in geometry, "parallel" refers to lines or planes that are equidistant from each other at every point and never intersect, no matter how far they are extended. A misunderstanding or lack of knowledge about this definition can lead to errors when solving problems that involve parallel lines or planes, such as determining angles or distances. Thus, to correctly interpret and solve problems involving parallel lines or planes, one must understand that they maintain a constant distance from each other and never meet.	Does not know the term transversal[object Object]The passage is indicating a common pitfall in geometry where a student may not be familiar with the term "transversal." A transversal is a line that passes through two or more other lines, often creating several angles with them. When discussing parallel lines and the angles formed when a transversal intersects them, understanding the term and its implications is crucial. The misconception here is likely that without knowing what a transversal is, a student might struggle to identify the relationships between the angles formed (such as alternate interior angles, corresponding angles, etc.), which are fundamental concepts in solving geometry problems involving parallel lines.
  Subject: Sharing in a Ratio[object Object]Construct: Divide a quantity into two parts for a given a ratio, where each part is an integer[object Object]Question: Share ( £360 ) in the ratio ( 2: 7 )[object Object]Incorrect Answer: ( £ 180: £ 51 )	Divides total amount by each side of the ratio instead of dividing by the sum of the parts[object Object]The misconception described refers to a mistake made when dividing a total amount according to a given ratio. For instance, if someone has to divide $100 in the ratio 2:3, a correct approach would be to first add the parts of the ratio (2+3=5) to find the total number of parts. Then, divide the total amount by this sum ($100 ÷ 5 = $20) to determine the value of one part. This $20 can then be multiplied by each number in the ratio (2 and 3) to correctly distribute the $100.[object Object][object Object]The misconception occurs when someone divides the total amount ($100) by each individual number in the ratio (2 and 3) rather than by the sum of the parts (5). This method would incorrectly distribute the $100, as it does not account for the proportional relationship that the ratio is meant to establish.	Estimates shares of a ratio instead of calculating[object Object]The passage is discussing a common mistake made in mathematics, particularly when dealing with ratio problems. The misconception lies in estimating the shares or parts of a ratio rather than calculating them accurately. For example, if a problem involves dividing a quantity in the ratio of 2:3, the misconception would be to guess or estimate what parts of the quantity correspond to 2 and 3, instead of using the correct method to find the exact shares. The correct approach involves first adding the parts of the ratio (in this case, 2 + 3 = 5) and then using this sum to calculate each part's exact share of the total quantity. Thus, it's important to calculate each part of the ratio precisely rather than estimating.

• Loss: CachedMultipleNegativesRankingLoss with these parameters:
  json

  1{ 2 "scale": 20.0, 3 "similarity_fct": "cos_sim" 4}

Training Hyperparameters

Non-Default Hyperparameters

• per_device_train_batch_size: 512
• num_train_epochs: 1
• lr_scheduler_type: cosine
• warmup_ratio: 0.1
• fp16: True

All Hyperparameters

Framework Versions

• Python: 3.10.12
• Sentence Transformers: 3.3.1
• Transformers: 4.47.1
• PyTorch: 2.5.1+cu121
• Accelerate: 1.2.1
• Datasets: 3.2.0
• Tokenizers: 0.21.0

Citation

BibTeX

Sentence Transformers

CachedMultipleNegativesRankingLoss