README.md

metadata

tags:
  - sentence-transformers
  - sentence-similarity
  - feature-extraction
  - generated_from_trainer
  - dataset_size:17405
  - loss:CachedMultipleNegativesRankingLoss
widget:
  - source_sentence: |-
      Subject: Range and Interquartile Range from a List of Data
      Construct: Calculate the range from a list of data
      Question: What is the range of the following numbers?
      \[
      1,5,5,17,-6
      \]
      Incorrect Answer: \( 5 \)
    sentences:
      - >-
        To find the range adds the biggest and smallest number rather than
        subtract

        The passage is clarifying a common misunderstanding about how to
        calculate the range of a set of numbers. The misconception here is that
        someone might think the range is found by adding the largest number to
        the smallest number in the dataset. However, this is incorrect. The
        correct method to find the range is to subtract the smallest number from
        the largest number in the dataset. This subtraction gives the
        difference, which represents how spread out the numbers are.
      - >-
        Finds the mode rather than the range

        The passage is indicating a common mistake made in solving math
        problems, particularly those involving statistics. The misconception
        lies in a confusion between two statistical concepts: the mode and the
        range.


        - **Mode**: This is the value that appears most frequently in a set of
        data. It helps to identify the most typical or common value.

        - **Range**: This is the difference between the highest and lowest
        values in a set of data. It gives an idea about the spread or dispersion
        of the values.


        The misconception described here suggests that a student might calculate
        the mode when asked to find the range, or simply mix up these two
        concepts. The important distinction is that while the mode tells you
        about the frequency of the most common value, the range informs you
        about the span of the data.
      - >-
        Believes a cubic expression should have three terms

        The misconception described here is that someone might think a cubic
        expression, which is a polynomial of degree three, should consist of
        exactly three terms. This is a misunderstanding because a cubic
        expression can have any number of terms, but the highest power of the
        variable must be three. 


        For example, both \( x^3 + 2x + 1 \) and \( 4x^3 - 3x^2 + x - 7 \) are
        cubic expressions, even though they have different numbers of terms. The
        defining characteristic is that the highest power of the variable (x in
        these examples) is three. So, a cubic expression can have fewer or more
        than three terms, as long as the degree (the highest power) of the
        expression is three.
  - source_sentence: >-
      Subject: Reflection

      Construct: Reflect an object or a point in a diagonal line with the line
      of reflection drawn, where the line of reflection lies on the edge or
      outside the object

      Question: The triangle is reflected in the dashed line

      What are the new coordinates of point \( \mathrm{P} \) ? ![Four quadrant,
      coordinate grid with the reflection line y=-x drawn and a triangle. The
      triangle has coordinates: (-2,3) (-2,6) and (0,5). The point P is the
      coordinate (0,5)]()

      Incorrect Answer: \( (-4,5) \)
    sentences:
      - >-
        Reflects horizontally or vertically instead of across a diagonal line of
        symmetry

        The passage is discussing a common mistake made in geometry,
        particularly when dealing with reflections of shapes. The misconception
        is that students might incorrectly think that the reflection is
        happening horizontally or vertically (i.e., across a line that is either
        parallel to the x-axis or y-axis). In reality, the reflection might be
        across a diagonal line of symmetry, which means the line that serves as
        the mirror could be at an angle, such as a 45-degree line from one
        corner of a square or rectangle to the opposite corner.


        To correct this misconception, it's important to emphasize the actual
        direction and axis of reflection, understanding that a line of symmetry
        can be oriented in any direction, not just horizontal or vertical.
        Visual aids and examples that include diagonal lines of symmetry can
        help in grasping this concept better.
      - >-
        Fails to reflect across mirror line

        The passage is discussing a common misconception in geometry,
        specifically in relation to reflecting shapes or points across a line,
        often referred to as a "mirror line." This reflection involves creating
        a mirror image of a given figure on the other side of the mirror line,
        maintaining the same distance from the line as the original figure.


        The misconception "Fails to reflect across mirror line" means that
        someone might not correctly understand or apply the rules of reflection
        in their work. They might draw the reflected image incorrectly, perhaps
        by not maintaining the same distance from the mirror line, or by not
        placing it directly opposite the original shape with respect to the
        line.


        In essence, the misconception stems from a misunderstanding of how
        reflection works in geometry, leading to errors in the placement or
        orientation of the reflected figure. Correcting this involves ensuring
        that each point of the original shape is equidistant from the mirror
        line to its corresponding point on the reflected side.
      - >-
        Believes that dividing by 100 gives 10%

        The misconception described here is that someone might think dividing a
        number by 100 results in getting 10% of that number. This is incorrect.
        Dividing a number by 100 gives 1% of that number, not 10%. To get 10% of
        a number, you should divide the number by 10. For example, if you have
        the number 200, dividing it by 100 gives 2, which is 1% of 200. To get
        10%, you would divide 200 by 10, giving 20.
  - source_sentence: >-
      Subject: Time

      Construct: Solve problems involving subtracting a period of time from a
      given end time

      Question: What time is \( 30 \) minutes before midnight?

      Incorrect Answer: 11:30 am
    sentences:
      - >-
        Thinks that times just before midnight are "am" times

        The passage is discussing a common misconception about the timing just
        before midnight. The misconception is that someone might incorrectly
        believe these times are denoted as "am" (ante meridiem), when in fact,
        times just before midnight are part of the "pm" (post meridiem) period.
        Midnight marks the transition from "pm" to "am" — the period from
        midnight to noon is designated as "am", and from noon to midnight, it is
        "pm". Therefore, the correct understanding is that the times just before
        midnight are "pm" times, not "am".
      - >-
        Answers as if there are 100 minutes in an hour

        The passage is indicating a common mistake where individuals incorrectly
        assume there are 100 minutes in an hour, rather than the correct 60
        minutes. This misconception could arise in problems that require
        calculations involving time, leading to inaccurate results. It's
        important to remember there are 60 minutes in an hour to perform
        calculations correctly.
      - >-
        Thinks measures of area must end in squared

        The misconception described here is that some people believe the units
        of measurement for area must always end in "squared," such as square
        meters, square feet, etc. While it is true that area measurements are
        often expressed using squared units (like square meters, m²), this is a
        specific case when the measurements are taken in units like meters,
        feet, etc.


        However, depending on the context and the system of measurement, area
        can be expressed in units that do not explicitly end in "squared." For
        example, when measuring land, units like acres or hectares are used,
        which are not expressed as squared units but represent a specific area.
        An acre, for instance, is a unit of area commonly used in
        English-speaking countries, and it equals 43,560 square feet.


        In summary, while squared units are a common way to express area, it is
        incorrect to assume that all units measuring area must end in "squared."
  - source_sentence: >-
      Subject: Quadratic Equations

      Construct: Solve quadratic equations using factorisation in the form x(x +
      b)

      Question: Solve this equation, giving all solutions:

      \[

      k^{2}=4 k

      \]

      Incorrect Answer: \( k=4 \)
    sentences:
      - >-
        Believes they can divide by a variable without checking whether it could
        equal zero

        The misconception described here pertains to the process of solving
        algebraic equations, particularly when dividing both sides of an
        equation by a variable. The misconception is that one can divide by a
        variable without considering whether that variable could potentially be
        zero.


        In algebra, dividing both sides of an equation by a variable (let's say
        \(x\)) is generally valid only if \(x \neq 0\). If \(x\) could be zero,
        then dividing by \(x\) is not allowed because division by zero is
        undefined in mathematics. This oversight can lead to losing a solution
        (specifically, \(x = 0\)) or deriving incorrect conclusions.


        For example, consider the equation \(x^2 = 3x\). If one incorrectly
        divides both sides by \(x\) without checking whether \(x\) can be zero,
        they might reduce it to \(x = 3\), thereby missing the solution \(x =
        0\).


        The correct approach would be to rearrange the equation to \(x^2 - 3x =
        0\), factor it to \(x(x - 3) = 0\), and then conclude that \(x = 0\) or
        \(x = 3\), thus ensuring no solutions are lost.
      - >-
        Thinks tables of values are symmetrical about (0,0)

        The misconception described here pertains to the assumption that all
        tables of values representing a mathematical function or a set of data
        points are symmetrical about the origin, which is the point (0,0) on the
        coordinate plane. This means someone might incorrectly believe that for
        every value of \(x\), the corresponding \(y\) value would be mirrored on
        the opposite side of the origin, like in the case of the function \(y =
        x^3\), which is symmetrical about the origin.


        However, not all tables of values are symmetrical about (0,0). Symmetry
        about the origin is a specific property that only applies to certain
        types of functions, particularly odd functions, where \(f(-x) = -f(x)\)
        for all \(x\) in the domain of \(f\). Many other functions and sets of
        data points do not exhibit this symmetry. For example, a parabola \(y =
        x^2\) is symmetrical, but not about the origin; it is symmetrical along
        the y-axis. A linear function \(y = mx + b\), unless it passes through
        (0,0) with \(b=0\), would not be symmetrical about the origin either.


        Thus, one should not assume symmetry about (0,0) for any given set of
        data or function without proper analysis or evidence that confirms this
        symmetry.
      - >-
        When solving an equation, multiplies instead of dividing

        The passage is highlighting a common mistake made when solving
        mathematical equations, where a student might mistakenly multiply when
        they should be dividing. This can happen in various contexts, such as
        solving for a variable in an equation or converting units. For example,
        if a problem requires you to divide both sides of an equation by a
        number to isolate the variable, mistakenly multiplying instead would
        lead to an incorrect solution. 


        The key here is to carefully read the problem, understand the operations
        needed, and apply the correct mathematical operations to solve the
        equation accurately.
  - source_sentence: >-
      Subject: Construct Triangle

      Construct: Construct a triangle using Side-Side-Side

      Question: Tom and Katie are arguing about constructing triangles.


      Tom says you can construct a triangle with lengths \( 11 \mathrm{~cm}, 10
      \mathrm{~cm} \) and \( 2 \mathrm{~cm} \).


      Katie says you can construct a triangle with lengths \( 8 \mathrm{~cm}, 5
      \mathrm{~cm} \) and \( 3 \mathrm{~cm} \).


      Who is correct?

      Incorrect Answer: Neither is correct
    sentences:
      - >-
        Does not realise that the sum of the two shorter sides must be greater
        than the third side for it to be a possible triangle

        The passage is discussing a common misconception about the properties
        required to form a triangle. The misconception is that one might think
        any three given side lengths can form a triangle. However, for three
        lengths to actually form a triangle, they must satisfy the triangle
        inequality theorem. This theorem states that the sum of the lengths of
        any two sides of a triangle must be greater than the length of the
        remaining side. This rule must hold true for all three combinations of
        added side lengths. 


        To apply this to the misconception: one does not realize that the sum of
        the lengths of the two shorter sides must be greater than the length of
        the longest side to form a possible triangle. This ensures that the
        sides can actually meet to form a closed figure with three angles.
      - >-
        Does not know that a single letter labels a vertex

        The passage is indicating a common misconception in geometry or graph
        theory, where students or individuals may not understand that a single
        letter can be used to label or identify a vertex (a corner or a point
        where lines or edges meet) in a geometric shape or a graph.


        Explanation: In mathematics, particularly in geometry and graph theory,
        vertices (plural of vertex) are often labeled with single letters (like
        A, B, C, etc.) to easily identify and discuss them. This labeling helps
        in referring to specific points when describing shapes, calculating
        angles, distances, or when analyzing the structure of graphs. The
        misconception arises when someone does not recognize or utilize this
        convention, potentially leading to difficulties in understanding
        problems or communicating solutions effectively.
      - >-
        Draws both angles at the same end of the line when constructing a
        triangle

        The misconception described refers to a common error in geometry when
        students are constructing a triangle based on given angles and a line
        segment. The mistake is to draw both given angles at the same end of the
        given line segment. This is incorrect because in a triangle, each angle
        is located at a different vertex, and each vertex connects two sides. To
        correctly construct the triangle, each given angle should be drawn at
        different ends of the line segment (if constructing based on one line
        segment and two angles) or at vertices defined by the construction steps
        (if additional sides are given). This ensures that the three angles are
        positioned to form the corners of the triangle, with each angle at a
        distinct vertex, thereby creating a proper triangle.
pipeline_tag: sentence-similarity
library_name: sentence-transformers

SentenceTransformer

This is a sentence-transformers model trained. It maps sentences & paragraphs to a 384-dimensional dense vector space and can be used for semantic textual similarity, semantic search, paraphrase mining, text classification, clustering, and more.

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)

First install the Sentence Transformers library:

pip install -U sentence-transformers

Then you can load this model and run inference.

from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("minsuas/Misconceptions_1")
# Run inference
sentences = [
    'Subject: Construct Triangle\nConstruct: Construct a triangle using Side-Side-Side\nQuestion: Tom and Katie are arguing about constructing triangles.\n\nTom says you can construct a triangle with lengths $11mathrmcm,10mathrmcm11\; \backslash \backslash mathrm\{~cm\},\; 10\; \backslash \backslash mathrm\{~cm\}$ and $2mathrmcm2\; \backslash \backslash mathrm\{~cm\}$.\n\nKatie says you can construct a triangle with lengths $8mathrmcm,5mathrmcm8\; \backslash \backslash mathrm\{~cm\},\; 5\; \backslash \backslash mathrm\{~cm\}$ and $3mathrmcm3\; \backslash \backslash mathrm\{~cm\}$.\n\nWho is correct?\nIncorrect Answer: Neither is correct',
    'Does not realise that the sum of the two shorter sides must be greater than the third side for it to be a possible triangle\nThe passage is discussing a common misconception about the properties required to form a triangle. The misconception is that one might think any three given side lengths can form a triangle. However, for three lengths to actually form a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. This rule must hold true for all three combinations of added side lengths. \n\nTo apply this to the misconception: one does not realize that the sum of the lengths of the two shorter sides must be greater than the length of the longest side to form a possible triangle. This ensures that the sides can actually meet to form a closed figure with three angles.',
    'Draws both angles at the same end of the line when constructing a triangle\nThe misconception described refers to a common error in geometry when students are constructing a triangle based on given angles and a line segment. The mistake is to draw both given angles at the same end of the given line segment. This is incorrect because in a triangle, each angle is located at a different vertex, and each vertex connects two sides. To correctly construct the triangle, each given angle should be drawn at different ends of the line segment (if constructing based on one line segment and two angles) or at vertices defined by the construction steps (if additional sides are given). This ensures that the three angles are positioned to form the corners of the triangle, with each angle at a distinct vertex, thereby creating a proper triangle.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 384]

# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]

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 Construct: Given a positive x value, find the corresponding y value for reciprocal graphs 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 Construct: Identify a transversal Question: What is the name given to the red line that intersects the two dashed lines? Incorrect Answer: Parallel	Does not know the meaning of the word parallel 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 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 Construct: Divide a quantity into two parts for a given a ratio, where each part is an integer Question: Share ( £360 ) in the ratio ( 2: 7 ) Incorrect Answer: ( £ 180: £ 51 )	Divides total amount by each side of the ratio instead of dividing by the sum of the parts 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. 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 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:

  {
      "scale": 20.0,
      "similarity_fct": "cos_sim"
  }
  

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

Click to expand

• overwrite_output_dir: False
• do_predict: False
• eval_strategy: no
• prediction_loss_only: True
• per_device_train_batch_size: 512
• per_device_eval_batch_size: 8
• per_gpu_train_batch_size: None
• per_gpu_eval_batch_size: None
• gradient_accumulation_steps: 1
• eval_accumulation_steps: None
• torch_empty_cache_steps: None
• learning_rate: 5e-05
• weight_decay: 0.0
• adam_beta1: 0.9
• adam_beta2: 0.999
• adam_epsilon: 1e-08
• max_grad_norm: 1.0
• num_train_epochs: 1
• max_steps: -1
• lr_scheduler_type: cosine
• lr_scheduler_kwargs: {}
• warmup_ratio: 0.1
• warmup_steps: 0
• log_level: passive
• log_level_replica: warning
• log_on_each_node: True
• logging_nan_inf_filter: True
• save_safetensors: True
• save_on_each_node: False
• save_only_model: False
• restore_callback_states_from_checkpoint: False
• no_cuda: False
• use_cpu: False
• use_mps_device: False
• seed: 42
• data_seed: None
• jit_mode_eval: False
• use_ipex: False
• bf16: False
• fp16: True
• fp16_opt_level: O1
• half_precision_backend: auto
• bf16_full_eval: False
• fp16_full_eval: False
• tf32: None
• local_rank: 0
• ddp_backend: None
• tpu_num_cores: None
• tpu_metrics_debug: False
• debug: []
• dataloader_drop_last: False
• dataloader_num_workers: 0
• dataloader_prefetch_factor: None
• past_index: -1
• disable_tqdm: False
• remove_unused_columns: True
• label_names: None
• load_best_model_at_end: False
• ignore_data_skip: False
• fsdp: []
• fsdp_min_num_params: 0
• fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}
• fsdp_transformer_layer_cls_to_wrap: None
• accelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}
• deepspeed: None
• label_smoothing_factor: 0.0
• optim: adamw_torch
• optim_args: None
• adafactor: False
• group_by_length: False
• length_column_name: length
• ddp_find_unused_parameters: None
• ddp_bucket_cap_mb: None
• ddp_broadcast_buffers: False
• dataloader_pin_memory: True
• dataloader_persistent_workers: False
• skip_memory_metrics: True
• use_legacy_prediction_loop: False
• push_to_hub: False
• resume_from_checkpoint: None
• hub_model_id: None
• hub_strategy: every_save
• hub_private_repo: None
• hub_always_push: False
• 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
• dispatch_batches: None
• split_batches: None
• include_tokens_per_second: False
• include_num_input_tokens_seen: False
• neftune_noise_alpha: None
• optim_target_modules: None
• batch_eval_metrics: False
• eval_on_start: False
• use_liger_kernel: False
• eval_use_gather_object: False
• average_tokens_across_devices: False
• prompts: None
• batch_sampler: batch_sampler
• multi_dataset_batch_sampler: proportional

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

@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",
}

CachedMultipleNegativesRankingLoss

@misc{gao2021scaling,
    title={Scaling Deep Contrastive Learning Batch Size under Memory Limited Setup},
    author={Luyu Gao and Yunyi Zhang and Jiawei Han and Jamie Callan},
    year={2021},
    eprint={2101.06983},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}