SentenceTransformer based on mixedbread-ai/mxbai-embed-large-v1

Model Details

Model Description

• Model Type: Sentence Transformer
• Base model: mixedbread-ai/mxbai-embed-large-v1
• Maximum Sequence Length: 512 tokens
• Output Dimensionality: 1024 tokens
• Similarity Function: Cosine Similarity
• Training Datasets:
  • mathstackexchange
  • socratic
  • stackexchange

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': 512, 'do_lower_case': False}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 1024, 'pooling_mode_cls_token': True, 'pooling_mode_mean_tokens': False, 'pooling_mode_max_tokens': False, 'pooling_mode_mean_sqrt_len_tokens': False, 'pooling_mode_weightedmean_tokens': False, 'pooling_mode_lasttoken': False, 'include_prompt': True})
)

Usage

Direct Usage (Sentence Transformers)

Evaluation

Metrics

Semantic Similarity

• Dataset: sts-dev
• Evaluated with EmbeddingSimilarityEvaluator

Training Details

Training Datasets

mathstackexchange

• Dataset: mathstackexchange
• Size: 1,484,629 training samples
• Columns: anchor and positive
• Approximate statistics based on the first 1000 samples:

  	anchor	positive
  type	string	string
  details	min: 10 tokens mean: 90.61 tokens max: 512 tokens	min: 9 tokens mean: 307.68 tokens max: 512 tokens

• Samples:

  anchor	positive
  Suppose $A$ is a normal subgroup of a group $B$, and the quotient group $B/A$ is cyclic with infinite order. How can we demonstrate, using the correspondence theorem, that for every positive integer $k$, $B$ has a normal subgroup of index $k$?	The correspondence theorem relates subgroups of the quotient group $B/A$ to subgroups of $B$ containing $A$. Since $B/A$ is isomorphic to the infinite cyclic group $\mathbb{Z}$, it has subgroups of every finite index. [object Object][object Object]To find a normal subgroup of $B$ with index $k$, we can follow these steps:[object Object]1. Identify a subgroup $M/A$ of $B/A$ with index $k$. This is possible since $\mathbb{Z}$ has subgroups of index $k$ for any positive integer $k$ (for instance, the subgroup generated by $k$ times the generator of $\mathbb{Z}$).[object Object]2. By the correspondence theorem, there exists an intermediate subgroup $M$ such that $A \leq M \leq B$ with $M/A \cong M/A$.[object Object]3. Now, consider the index of $M$ in $B$: $[B:M] = [B/A : M/A] = k$, as desired.[object Object][object Object]Thus, using the correspondence theorem and exploiting the properties of $\mathbb{Z}$, we can construct a normal subgroup of $B$ with index $k$ for any positive integer $k$.
  If $z$ is a complex number and $a$ is a real number, can we say $	az
  What is the remainder when $x^{2007}$ is divided by $x^2-x+1$?	To find the remainder when $x^{2007}$ is divided by $x^2-x+1$, we can use polynomial long division or synthetic division. Alternatively, we can utilize the properties of the polynomial $x^2-x+1$.[object Object][object Object]Since $x^2-x+1$ is a factor of $x^3+1$, we have $x^3 \equiv -1 \pmod{x^2-x+1}$. Therefore, we can express $x^{2007}$ as $x^{3\cdot669}$, and thus:[object Object][object Object]$$x^{2007} = (x^3)^{669} \equiv (-1)^{669} \pmod{x^2-x+1}$$[object Object][object Object]Now, since $669$ is odd, $(-1)^{669} = -1$. Hence, the remainder is $-1$.[object Object][object Object]Alternatively, we can perform polynomial long division to obtain:[object Object][object Object]$$\frac{x^{2007}}{x^2-x+1} = a(x) - \frac{x+1}{x^2-x+1}$$[object Object][object Object]where $a(x)$ is the quotient polynomial. Since we only care about the remainder, we have:[object Object][object Object]$$x^{2007} \equiv -1 \pmod{x^2-x+1}$$

• Loss: MultipleNegativesRankingLoss with these parameters:
  json

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

socratic

• Dataset: socratic
• Size: 533,383 training samples
• Columns: anchor and positive
• Approximate statistics based on the first 1000 samples:

  	anchor	positive
  type	string	string
  details	min: 8 tokens mean: 30.75 tokens max: 167 tokens	min: 3 tokens mean: 207.41 tokens max: 512 tokens

• Samples:

  anchor	positive
  What is an activated complex?	[object Object]The activated complex is formed when the reactants collide with each other and begin to rearrange their atoms and bonds to form the products. This process requires energy, which is why the activated complex has a higher energy than the reactants. The energy required to reach the activated complex is called the activation energy.[object Object][object Object]Once the activated complex is formed, it can either decompose back into the reactants or proceed to form the products. The probability of the activated complex decomposing back into the reactants is determined by the activation energy. If the activation energy is high, then the activated complex is more likely to decompose back into the reactants. If the activation energy is low, then the activated complex is more likely to proceed to form the products.[object Object][object Object]The activated complex is a key concept in understanding chemical reactions. It helps to explain why some reactions occur quickly and others occur slowly. It also helps to explain why some reactions require a catalyst to occur.[object Object]####[object Object]An activated complex is a high-energy, unstable intermediate state that forms during a chemical reaction. It is the transition state between the reactants and the products. The activated complex has a higher energy than both the reactants and the products, and it represents the maximum energy that must be overcome for the reaction to occur.
  Why does gravity cause planets to be round?	[object Object]The gravitational force of a planet pulls matter towards its center. This force is strongest at the center of the planet and weakest at the surface. As a result, matter is pulled towards the center of the planet, causing it to take on a spherical shape.[object Object][object Object]A sphere is the shape with the lowest surface area for a given volume. This means that a planet with a spherical shape has the least amount of potential energy. Potential energy is the energy that an object has due to its position or condition. In the case of a planet, its potential energy is due to its gravitational force.[object Object][object Object]The lower the potential energy of a planet, the more stable it is. This is because a planet with a lower potential energy is less likely to change its shape. As a result, planets tend to be spherical in shape.[object Object]####[object Object]Gravity causes planets to be round because a sphere is the shape with the lowest surface area for a given volume. This means that a planet with a spherical shape has the least amount of potential energy, which is the energy that an object has due to its position or condition. Gravity pulls matter towards the center of a planet, and this force is strongest at the center. As a result, matter is pulled towards the center of the planet, causing it to take on a spherical shape.
  How many carbon atoms are present in a 5.85-gram sample of carbon tetrabromide (CBr4)?	There are approximately (1 \times 10^{22}) carbon atoms in the given sample.[object Object][object Object]Explanation:[object Object]To determine the number of carbon atoms, we first need to calculate the molar amount of CBr4. The molar mass of CBr4 is 331.63 g/mol. So, we have:[object Object][object Object][[object Object]\frac{5.85\ g}{331.63\ g/mol} = 0.0176\ mol[object Object]][object Object][object Object]Since one molecule of CBr4 contains one carbon atom and four bromine atoms, there are:[object Object][object Object][[object Object]1 \times 0.0176\ mol = 0.0176\ mol\ of\ carbon\ atoms[object Object]][object Object][object Object]Now, multiplying the molar quantity by Avogadro's number (6.022 × 10^23 mol^(-1)) gives us the number of individual carbon atoms:[object Object][object Object][[object Object]0.0176\ mol \times 6.022 \times 10^{23}\ mol^{-1} = 1.06 \times 10^{22}\ carbon\ atoms[object Object]][object Object][object Object]Therefore, there are approximately (1 \times 10^{22}) carbon atoms in a 5.85-gram sample of CBr4.

• Loss: MultipleNegativesRankingLoss with these parameters:
  json

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

stackexchange

• Dataset: stackexchange
• Size: 317,208 training samples
• Columns: anchor and positive
• Approximate statistics based on the first 1000 samples:

  	anchor	positive
  type	string	string
  details	min: 12 tokens mean: 64.07 tokens max: 512 tokens	min: 50 tokens mean: 264.62 tokens max: 512 tokens

• Samples:

  anchor	positive
  Should I use a tip activator to recoat the worn protective coating on my iron tip, or is it better to replace the tip entirely? My 48W ZD99 Solder Station's tip is showing signs of peeling due to moisture exposure and inadequate care. Can the tip activator effectively restore the tip, or should I opt for a new one?	To address the issue, first clean the iron tip with a wire brush to remove any debris. Then, apply flux and tin the tip to protect it and maintain its performance. Tip activators are available as a means to recoat tips, but their effectiveness may vary. While they can be a viable solution, it's essential to ensure proper tip care to prevent future wear. If the tip's condition significantly deteriorates despite these efforts, consider replacing it with a new one.
  What are the fundamental limits, if any, for the speed of sound in different materials, and how do these limits relate to the speed of light?	The speed of sound is limited by the properties of the material it travels through and the fundamental principles of physics. In a theoretical sense, the maximum speed of sound is constrained by the speed of light (approximately 299,792 km/s in vacuum), which is the maximum speed at which information can propagate. This limit is reached when the material has an incompressible equation of state, such as in the core of a neutron star, where the strong nuclear force creates immense pressure resistance.[object Object][object Object]For an ideal gas, where particles do not interact, the equation of state is the softest possible with $P = \rho c^2/3$, where $P$ is pressure, $\rho$ is density, and $c$ is the speed of light. In this case, the maximum speed of sound would be $c/\sqrt{3}$.[object Object][object Object]It's important to note that in practice, materials with extremely high sound speeds are unlikely to exist due to the conditions required for an incompressible equation of state. In reality, materials like solids and liquids generally have faster sound speeds than gases, but they are still far below the speed of light.[object Object][object Object]When dealing with exotic materials, such as short-lived isotopes or neutron stars, the speed of sound may be even more challenging to determine due to the unique properties and states involved. However, the underlying principles remain the same: the speed of sound is determined by the material's properties, and it cannot exceed the speed of light in a vacuum.
  What could be causing a 1996 Honda Civic to stop running suddenly, and how can it be started?	A potential issue is a faulty ignition switch. When you attempt to start the car, the switch might be malfunctioning in such a way that it disrupts power to the engine ignition system, causing the dash lights to go out and preventing the car from starting. However, when you perform a push start (crash start), the car starts because the ignition switch remains in position 2, providing power to the engine.[object Object][object Object]Another possibility is a problem with the battery or its connections. If the battery terminals have a poor connection, it might lead to high resistance, making it difficult for the car to start. Alternatively, if the battery is weak, it might not supply enough power to crank the engine effectively. In this case, the starter motor would sound sluggish as it tries to turn the engine. To resolve the issue, inspect the ignition switch, battery connections, and consider testing or replacing the battery if necessary.

• Loss: MultipleNegativesRankingLoss with these parameters:
  json

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

Training Hyperparameters

Non-Default Hyperparameters

• eval_strategy: steps
• per_device_train_batch_size: 32
• per_device_eval_batch_size: 32
• num_train_epochs: 1
• warmup_ratio: 0.1
• bf16: True
• batch_sampler: no_duplicates
• multi_dataset_batch_sampler: round_robin

All Hyperparameters

Training Logs

Framework Versions

• Python: 3.10.12
• Sentence Transformers: 3.0.1
• Transformers: 4.44.2
• PyTorch: 2.4.0+cu121
• Accelerate: 0.34.0
• Datasets: 2.21.0
• Tokenizers: 0.19.1

Citation

BibTeX

Sentence Transformers

MultipleNegativesRankingLoss