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mxbai-embed-large-v1-ft-webinstruct

Sentence Similarity
sentence-transformers
Safetensors
bert
feature-extraction
Generated from Trainer
dataset_size:2335220
loss:MultipleNegativesRankingLoss
Eval Results
text-embeddings-inference
Inference Endpoints
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base_model: mixedbread-ai/mxbai-embed-large-v1
datasets: []
language: []
library_name: sentence-transformers
metrics:
  - pearson_cosine
  - spearman_cosine
  - pearson_manhattan
  - spearman_manhattan
  - pearson_euclidean
  - spearman_euclidean
  - pearson_dot
  - spearman_dot
  - pearson_max
  - spearman_max
pipeline_tag: sentence-similarity
tags:
  - sentence-transformers
  - sentence-similarity
  - feature-extraction
  - generated_from_trainer
  - dataset_size:2335220
  - loss:MultipleNegativesRankingLoss
widget:
  - source_sentence: 'How do you solve the equation #-6 = \frac{y}{5} + 4#?'
    sentences:
      - |-
        To solve the equation, follow these steps:

        1. Subtract 4 from both sides:
           \[-6 - 4 = \frac{y}{5} + 4 - 4\]
           \[-10 = \frac{y}{5}\]

        2. Multiply both sides by 5 to isolate y:
           \[-10 \cdot 5 = \frac{y}{5} \cdot 5\]
           \[-50 = y\]

        So the solution is \(y = -50\).
      - >-
        An organism refers to a living entity, typically composed of cells,
        capable of growth, reproduction, and response to stimuli. The definition
        primarily includes all forms of life, excluding viruses, which are
        considered non-living by some scientists due to their inability to
        replicate independently.


        One of the smallest known organisms is Mycoplasma gallicepticum, a
        parasitic bacterium measuring approximately 200 to 300 nanometers (nm).
        It infects primates, inhabiting the bladder, waste disposal organs,
        genital tracts, and respiratory system.


        For comparison, the smallest virus known to humans is the Porcine
        circovirus type 1 (PCV1), a single-stranded DNA virus. Its genome
        consists of just 1759 nucleotides, and its capsid diameter measures a
        mere 17 nm. This virus causes wasting disease in weaned pigs.


        [Insert images of Mycoplasma gallicepticum and Porcine circovirus type 1
        here, with appropriate captions.]


        Keep in mind that the boundary of what constitutes the "smallest
        organism" can change with advances in scientific research and
        understanding.
      - >-
        Slope is given by #"rise"/"run"#, or the change in the #y# coordinate
        divided by the change in #x#. Mathematically this is written as 

        #(deltay)/(deltax)#

        You calculate it by taking the second coordinate and subtracting the
        first, so

        #(deltay)/(deltax) = (y_2 - y_1)/(x_2 - x_1)#

        # = (8 - (-2))/(10 - 10) = 10/0#

        Since division by zero is undefined, this line has an undefined slope.
        This means that it is a vertical line.
  - source_sentence: >-
      Let $f$ be an analytic function defined on the domain $D = \{z \in
      \mathbb{C} : |z| < 1\}$ with the property that the range of $f$ lies
      within $\mathbb{C} \setminus (-\infty, 0]$. Show that there exists an
      analytic function $g$ on $D$ such that $\text{Re}(g(z)) \geq 0$ and
      $g(z)^2 = f(z)$ for all $z \in D$.
    sentences:
      - >-
        In mathematics, equality is often treated as a primitive notion,
        especially in modern first-order logic. It is understood that two
        objects, such as real numbers, are equal if they are the same object.
        However, for a more formal approach in different settings:


        1. Set Theory: Equality on a set $I$ can be seen as a chosen equivalence
        relation that defines equality. For example, in Zermelo-Frankel set
        theory, equality can be defined as:
           $$x = y \equiv \forall z(z \in x \iff z \in y)$$
           While this works well in set theory, it may not align with the intuitive understanding of equality in other branches of mathematics.

        2. Category Theory: Equality in a fibration $E\to B$ can be viewed
        categorically as a left adjoint to the re-indexing functor induced by
        the diagonal $I\to I\times I$, evaluated at the terminal object in the
        fiber.


        3. Type Theory: Equality can be understood through the concept of
        evaluation. For instance, in arithmetic, the equation $2 + 2 = 3 + 1$
        can be verified by evaluating both sides to the same result, $s(s(2))$.


        The idea of proving two things are equal often involves demonstrating
        that they satisfy the same properties or relations. For example, to show
        $\pi \neq 2\pi$, one would compare their algebraic or geometric
        properties rather than their "membership" in sets.


        For further exploration, consider the work of Ansten Klev on identity
        elimination in Martin-Löf’s Type Theory, and the philosophical
        discussion in Benecereaf's paper "What numbers could not be." Category
        theory and type theory also offer rich perspectives on equality.
      - >-
        Given that $f$ is analytic in the unit disc and has no zeros, we can
        define an analytic logarithm of $f(z)$, denoted by $Log f(z)$. We
        consider the principal branch of the logarithm, which has a branch cut
        along the negative real axis.


        We define $g(z)$ as follows:

        \[ g(z) = \sqrt{f(z)} = e^{\frac{1}{2} Log f(z)} \]


        Now, the real part of $g(z)$ is given by:

        \[ \text{Re}(g(z)) = e^{\frac{1}{2} \log|f(z)|}
        \cos\left(\frac{\arg{f(z)}}{2}\right) \]


        Since $f(z)$ lies outside the negative real axis, we have $|f(z)| > 0$
        and $-\pi < \arg{f(z)} < \pi$. Thus,
        $\cos\left(\frac{\arg{f(z)}}{2}\right)$ is non-negative, which implies
        that $\text{Re}(g(z)) \geq 0$.


        As a result, $g(z)$ is an analytic function on $D$ with a non-negative
        real part, and it satisfies the property $g(z)^2 = f(z)$ for all $z \in
        D$.
      - >-
        Let $\epsilon > 0$ be given. We need to find a natural number
        $N_\varepsilon$ such that

        $$ \left|\frac{1}{1+n+2^n}\right| < \epsilon $$

        for all $n > N_\varepsilon$. Since $1/n \to 0$ as $n \to \infty$, there
        exists an $N_\varepsilon$ such that $1/n < \epsilon$ for all $n >
        N_\varepsilon$. Since $2^n \ge n$ for all $n$, we have

        $$ \frac{1}{1+n+2^n} < \frac{1}{n+2^n} < \frac{1}{n} < \epsilon $$

        for all $n > N_\varepsilon$. Therefore,

        $$ \lim_{n\to\infty} \frac{1}{1+n+2^n} = 0.$$
  - source_sentence: >-
      I know that by definition of basis, the vectors v1 and v2 should span the
      entire subspace. Therefore, if the first constant is not equal to the
      second constant, and if both of the constants give a linear
      transformation, then they must be linearly independent and therefore must
      form a basis. Is that the correct proof, or am I missing something? Also,
      I don't know what the matrix of the linear transformation is.
    sentences:
      - >-
        To prove that v1 and v2 form a basis, we need to show that they are
        linearly independent and that they span the entire subspace.


        To show linear independence, suppose that c1v1 + c2v2 = 0 for some
        scalars c1 and c2. Multiplying both sides by A, we get c1λ1v1 + c2λ2v2 =
        0. Multiplying the first equation by λ1 and subtracting it from the
        second, we get (λ2 - λ1)c2v2 = 0. Since λ2 - λ1 is nonzero (because the
        eigenvalues are distinct), we must have c2 = 0. Substituting this back
        into the first equation, we get c1v1 = 0, so c1 = 0. Therefore, v1 and
        v2 are linearly independent.


        To show that v1 and v2 span the entire subspace, we need to show that
        every vector in the subspace can be written as a linear combination of
        v1 and v2. Let w be an arbitrary vector in the subspace. Then w can be
        written as a linear combination of the eigenvectors of A, so w = c1v1 +
        c2v2 for some scalars c1 and c2. Therefore, v1 and v2 span the entire
        subspace.


        Since v1 and v2 are linearly independent and span the entire subspace,
        they form a basis for the subspace.


        The matrix of the linear transformation T_A is the matrix whose columns
        are the coordinate vectors of the images of the basis vectors of the
        domain under T_A. In this case, the basis vectors of the domain are v1
        and v2, and their images under T_A are λ1v1 and λ2v2, respectively.
        Therefore, the matrix of T_A is


        $$\begin{bmatrix} \lambda_1 & 0\\ 0 & \lambda_2\end{bmatrix}.$$
      - >-
        To find $E[\tilde{\beta_1}]$, we first need to derive the formula for
        $\tilde{\beta_1}$. Under the assumption that the intercept is 0, the
        slope estimator $\tilde{\beta_1}$ is given by:


        $$\tilde{\beta_1} = \frac{\sum_{i=1}^n (x_i - \bar{x})y_i}{\sum_{i=1}^n
        (x_i - \bar{x})^2}$$


        where $\bar{x}$ is the sample mean of the $x_i$.


        Next, we can substitute the true regression model $y_i = \beta_0 +
        \beta_1 x_i + u_i$ into the formula for $\tilde{\beta_1}$:


        $$\tilde{\beta_1} = \frac{\sum_{i=1}^n (x_i - \bar{x})(\beta_0 + \beta_1
        x_i + u_i)}{\sum_{i=1}^n (x_i - \bar{x})^2}$$


        Simplifying this expression, we get:


        $$\tilde{\beta_1} = \beta_1 + \frac{\sum_{i=1}^n (x_i -
        \bar{x})u_i}{\sum_{i=1}^n (x_i - \bar{x})^2}$$


        Now, we can take the expected value of both sides of this equation:


        $$E[\tilde{\beta_1}] = E[\beta_1] + E\left[\frac{\sum_{i=1}^n (x_i -
        \bar{x})u_i}{\sum_{i=1}^n (x_i - \bar{x})^2}\right]$$


        Since $\beta_1$ is a constant, $E[\beta_1] = \beta_1$. For the second
        term, we can use the fact that $E(u_i) = 0$ (by assumption SLR.3) and
        the linearity of expectation to get:


        $$E\left[\frac{\sum_{i=1}^n (x_i - \bar{x})u_i}{\sum_{i=1}^n (x_i -
        \bar{x})^2}\right] = \frac{\sum_{i=1}^n (x_i -
        \bar{x})E(u_i)}{\sum_{i=1}^n (x_i - \bar{x})^2} = 0$$


        Therefore, we have:


        $$E[\tilde{\beta_1}] = \beta_1 + 0 = \beta_1$$


        This shows that $\tilde{\beta_1}$ is an unbiased estimator of $\beta_1$
        when the intercept is assumed to be 0.


        In addition to the case where $\beta_0 = 0$, $\tilde{\beta_1}$ is also
        an unbiased estimator of $\beta_1$ when $\sum_{i=1}^n x_i = 0$. This can
        be seen by noting that in this case, $\bar{x} = 0$ and the formula for
        $\tilde{\beta_1}$ simplifies to:


        $$\tilde{\beta_1} = \frac{\sum_{i=1}^n x_iy_i}{\sum_{i=1}^n x_i^2}$$


        which is the same as the formula for the ordinary least squares (OLS)
        estimator of $\beta_1$ when the intercept is included in the model.
      - >-
        Sure. Here is an example of a continuous map that is not proper:


        $$

        f: \mathbb{R} \to [0, 1]

        $$


        $$

        x \mapsto \frac{1}{1 + |x|}

        $$


        This map is continuous because it is the composition of continuous
        functions. However, it is not proper because the preimage of the compact
        set [0, 1] is not compact. Specifically, the preimage of [0, 1] is the
        set of all real numbers, which is not compact.


        This example shows that the converse of the statement "if a map is
        proper then it is continuous" is not true.
  - source_sentence: >-
      Consider the scenario from the original question, but now suppose that you
      draw two balls from the same random box. If both balls are gold, what is
      the probability that the box contains exactly two gold balls?
    sentences:
      - >-
        The term $\frac{\partial{F}}{\partial{u}}$ appears because $F$ is a
        function of not only $x$, $y$, and $z$, but also of $u$ and $v$. When we
        differentiate $F$ with respect to $x$, we must consider how $F$ changes
        with respect to $u$ as well, since $u$ is a function of $x$.
      - >-
        To prove that U ∪ V is an open set, we must show that for every point x
        in U ∪ V, there exists a ball B(x, r) with radius r > 0, entirely
        contained within U ∪ V.


        Let x be an arbitrary point in U ∪ V. We consider two cases:


        Case 1: If x ∈ U, since U is open, there exists a ball B(x, r_1) with
        r_1 > 0 such that B(x, r_1) ⊆ U.


        Case 2: If x ∈ V, as V is also open, there exists a ball B(x, r_2) with
        r_2 > 0 such that B(x, r_2) ⊆ V.


        Now, consider the ball B(x, r), where r = min(r_1, r_2). In both cases
        (x ∈ U and x ∈ V), this ball has a radius that is less than or equal to
        the radii of the balls in the respective sets. Therefore, B(x, r) will
        be entirely contained within either U or V, and as x is in U ∪ V, B(x,
        r) must be contained within the union of U and V.


        Since the choice of x was arbitrary, this shows that for all points in U
        ∪ V, there exists a corresponding open ball contained within U ∪ V.
        Hence, U ∪ V is an open set in $\mathbb{C}$.
      - >-
        There are a total of 12 balls in the boxes, and 6 of them are gold. If
        we draw two gold balls, we can eliminate box 4. Out of the remaining 3
        boxes, only one box has exactly two gold balls. Therefore, the
        probability that the box contains exactly two gold balls is
        $\frac{1}{3}$.
  - source_sentence: >-
      What should I do if I'm not satisfied with the answers to a question for
      which I've offered a bounty?


      In my case, I've put a bounty on a question, but the two responses I
      received don't address the issue effectively. I requested the original
      poster (OP) to provide an answer so I could reward them for the
      interesting question, but they haven't done so. 


      Are there any acceptable actions in this scenario? For instance, can I
      post my own non-answer, award myself the bounty, and then start a new
      bounty on a different question? Or are there alternative suggestions?
    sentences:
      - >-
        To improve RF signal strength under the given conditions, consider the
        following suggestions:


        1. Bit Rate: Keep the transmitted bit rate low, around 500 bits per
        second (bps).

        2. Balanced Energy Protocol: Implement a biphase or Manchester encoding
        to ensure a 50% duty cycle, which helps reduce DC offset at the
        receiver.

        3. Preamble: Include a long preamble in your protocol for the receiver
        to lock onto the signal and set its Automatic Gain Control (AGC) before
        decoding data.

        4. Receiver Tolerance: Design the decoding protocol to tolerate a wide
        range of pulse widths, as variations due to multi-path, noise, and other
        factors can affect signal integrity.


        While the current setup might be suitable for short distances,
        increasing the transmitter power voltage could potentially improve
        range. However, since you cannot change the 3.7V for the receiver, focus
        on optimizing the mentioned parameters.


        For more detailed information and implementation examples, refer to a
        previous post or access the resources at:
        http://www.carousel-design.com/ManchesterDesignDocs.zip
      - >-
        The issue you're experiencing with your 40kHz crystal oscillator might
        be due to insufficient drive strength and an incorrect load capacitance.
        Here are two potential causes and solutions:


        1. High Series Resistance: The 150 kΩ series resistance in your circuit
        might be too high, which results in a low drive strength for the
        crystal. This can lead to a reduced overall loop gain and prevents the
        oscillator from properly starting. To resolve this, try using a lower
        resistance value as recommended in the crystal's datasheet.


        2. Incorrect Load Capacitance: Ensure that the 33 pF load capacitors
        you're using are compatible with your crystal. Some low-power "watch"
        crystals require only 5-10 pF load capacitors. Always refer to the
        crystal's datasheet to verify the appropriate load capacitance value.


        In summary, carefully review the crystal's datasheet to determine the
        correct series resistance and load capacitance values, and make the
        necessary adjustments to your circuit. By doing so, you should be able
        to resolve the issue and get your oscillator functioning properly.
      - >-
        If all the provided answers do not adequately address your question,
        it's advisable to let the bounty expire. The system will handle the
        distribution of the bounty in such situations according to predefined
        rules.


        Bounties carry a risk, as there is no guarantee that you will receive a
        satisfactory answer, even with the incentive. It's important to
        understand that you cannot reclaim your bounty once it's been offered. 


        Instead of posting a non-answer, you might consider editing and
        clarifying your original question to attract better responses, or
        seeking assistance from the community through comments or chat. If
        needed, you can also start a new bounty on a different question, but
        ensure that it's clear and well-defined to increase the likelihood of
        receiving quality answers.
model-index:
  - name: SentenceTransformer based on mixedbread-ai/mxbai-embed-large-v1
    results:
      - task:
          type: semantic-similarity
          name: Semantic Similarity
        dataset:
          name: sts dev
          type: sts-dev
        metrics:
          - type: pearson_cosine
            value: 0.7434948318262279
            name: Pearson Cosine
          - type: spearman_cosine
            value: 0.7806376828669657
            name: Spearman Cosine
          - type: pearson_manhattan
            value: 0.7436816396985431
            name: Pearson Manhattan
          - type: spearman_manhattan
            value: 0.749038875811761
            name: Spearman Manhattan
          - type: pearson_euclidean
            value: 0.744095244507457
            name: Pearson Euclidean
          - type: spearman_euclidean
            value: 0.7494747710401942
            name: Spearman Euclidean
          - type: pearson_dot
            value: 0.6964434748177516
            name: Pearson Dot
          - type: spearman_dot
            value: 0.707847590788814
            name: Spearman Dot
          - type: pearson_max
            value: 0.744095244507457
            name: Pearson Max
          - type: spearman_max
            value: 0.7806376828669657
            name: Spearman Max

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

This is a sentence-transformers model finetuned from mixedbread-ai/mxbai-embed-large-v1 on the mathstackexchange, socratic and stackexchange datasets. It maps sentences & paragraphs to a 1024-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
  • 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

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)

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("mrm8488/mxbai-embed-large-v1-ft-webinstruct")
# Run inference
sentences = [
    "What should I do if I'm not satisfied with the answers to a question for which I've offered a bounty?\n\nIn my case, I've put a bounty on a question, but the two responses I received don't address the issue effectively. I requested the original poster (OP) to provide an answer so I could reward them for the interesting question, but they haven't done so. \n\nAre there any acceptable actions in this scenario? For instance, can I post my own non-answer, award myself the bounty, and then start a new bounty on a different question? Or are there alternative suggestions?",
    "If all the provided answers do not adequately address your question, it's advisable to let the bounty expire. The system will handle the distribution of the bounty in such situations according to predefined rules.\n\nBounties carry a risk, as there is no guarantee that you will receive a satisfactory answer, even with the incentive. It's important to understand that you cannot reclaim your bounty once it's been offered. \n\nInstead of posting a non-answer, you might consider editing and clarifying your original question to attract better responses, or seeking assistance from the community through comments or chat. If needed, you can also start a new bounty on a different question, but ensure that it's clear and well-defined to increase the likelihood of receiving quality answers.",
    'The issue you\'re experiencing with your 40kHz crystal oscillator might be due to insufficient drive strength and an incorrect load capacitance. Here are two potential causes and solutions:\n\n1. High Series Resistance: The 150 kΩ series resistance in your circuit might be too high, which results in a low drive strength for the crystal. This can lead to a reduced overall loop gain and prevents the oscillator from properly starting. To resolve this, try using a lower resistance value as recommended in the crystal\'s datasheet.\n\n2. Incorrect Load Capacitance: Ensure that the 33 pF load capacitors you\'re using are compatible with your crystal. Some low-power "watch" crystals require only 5-10 pF load capacitors. Always refer to the crystal\'s datasheet to verify the appropriate load capacitance value.\n\nIn summary, carefully review the crystal\'s datasheet to determine the correct series resistance and load capacitance values, and make the necessary adjustments to your circuit. By doing so, you should be able to resolve the issue and get your oscillator functioning properly.',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 1024]

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

Evaluation

Metrics

Semantic Similarity

Metric Value
pearson_cosine 0.7435
spearman_cosine 0.7806
pearson_manhattan 0.7437
spearman_manhattan 0.749
pearson_euclidean 0.7441
spearman_euclidean 0.7495
pearson_dot 0.6964
spearman_dot 0.7078
pearson_max 0.7441
spearman_max 0.7806

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.

    To find a normal subgroup of $B$ with index $k$, we can follow these steps:
    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 $\mathbb{Z}$).
    2. By the correspondence theorem, there exists an intermediate subgroup $M$ such that $A \leq M \leq B$ with $M/A \cong M/A$.
    3. Now, consider the index of $M$ in $B$: $[B:M] = [B/A : M/A] = k$, as desired.

    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 $x^2-x+1$.

    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:

    $$x^{2007} = (x^3)^{669} \equiv (-1)^{669} \pmod{x^2-x+1}$$

    Now, since $669$ is odd, $(-1)^{669} = -1$. Hence, the remainder is $-1$.

    Alternatively, we can perform polynomial long division to obtain:

    $$\frac{x^{2007}}{x^2-x+1} = a(x) - \frac{x+1}{x^2-x+1}$$

    where $a(x)$ is the quotient polynomial. Since we only care about the remainder, we have:

    $$x^{2007} \equiv -1 \pmod{x^2-x+1}$$
  • Loss: MultipleNegativesRankingLoss with these parameters:
    {
    "scale": 20.0,
    "similarity_fct": "cos_sim"
}

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?
    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.

    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.

    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.
    ####
    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?
    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.

    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.

    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.
    ####
    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.

    Explanation:
    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:

    [
    \frac{5.85\ g}{331.63\ g/mol} = 0.0176\ mol
    ]

    Since one molecule of CBr4 contains one carbon atom and four bromine atoms, there are:

    [
    1 \times 0.0176\ mol = 0.0176\ mol\ of\ carbon\ atoms
    ]

    Now, multiplying the molar quantity by Avogadro's number (6.022 × 10^23 mol^(-1)) gives us the number of individual carbon atoms:

    [
    0.0176\ mol \times 6.022 \times 10^{23}\ mol^{-1} = 1.06 \times 10^{22}\ carbon\ atoms
    ]

    Therefore, there are approximately (1 \times 10^{22}) carbon atoms in a 5.85-gram sample of CBr4.
  • Loss: MultipleNegativesRankingLoss with these parameters:
    {
    "scale": 20.0,
    "similarity_fct": "cos_sim"
}

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.

    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 $c/\sqrt{3}$.

    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.

    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.

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

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

Click to expand
  • overwrite_output_dir: False
  • do_predict: False
  • eval_strategy: steps
  • prediction_loss_only: True
  • per_device_train_batch_size: 32
  • per_device_eval_batch_size: 32
  • 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: linear
  • 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: True
  • fp16: False
  • 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: False
  • hub_always_push: False
  • gradient_checkpointing: False
  • gradient_checkpointing_kwargs: None
  • include_inputs_for_metrics: False
  • 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
  • eval_use_gather_object: False
  • batch_sampler: no_duplicates
  • multi_dataset_batch_sampler: round_robin

Training Logs

Click to expand
Epoch Step Training Loss sts-dev_spearman_cosine
0.0034 100 0.1339 -
0.0067 200 0.0535 -
0.0101 300 0.0372 -
0.0135 400 0.0329 -
0.0168 500 0.0277 -
0.0202 600 0.0287 -
0.0235 700 0.0217 -
0.0269 800 0.0257 -
0.0303 900 0.0262 -
0.0336 1000 0.02 0.8994
0.0370 1100 0.0196 -
0.0404 1200 0.0231 -
0.0437 1300 0.0228 -
0.0471 1400 0.0187 -
0.0504 1500 0.0197 -
0.0538 1600 0.0245 -
0.0572 1700 0.028 -
0.0605 1800 0.0242 -
0.0639 1900 0.0255 -
0.0673 2000 0.0324 0.8936
0.0706 2100 0.0231 -
0.0740 2200 0.0335 -
0.0773 2300 0.0221 -
0.0807 2400 0.0285 -
0.0841 2500 0.0394 -
0.0874 2600 0.0306 -
0.0908 2700 0.0305 -
0.0942 2800 0.0349 -
0.0975 2900 0.0327 -
0.1009 3000 0.0241 0.8788
0.1042 3100 0.0344 -
0.1076 3200 0.0315 -
0.1110 3300 0.035 -
0.1143 3400 0.0365 -
0.1177 3500 0.0363 -
0.1211 3600 0.0402 -
0.1244 3700 0.0332 -
0.1278 3800 0.0317 -
0.1311 3900 0.0292 -
0.1345 4000 0.0357 0.8686
0.1379 4100 0.0365 -
0.1412 4200 0.0349 -
0.1446 4300 0.0344 -
0.1480 4400 0.0295 -
0.1513 4500 0.0356 -
0.1547 4600 0.036 -
0.1580 4700 0.0301 -
0.1614 4800 0.039 -
0.1648 4900 0.0279 -
0.1681 5000 0.0388 0.8635
0.1715 5100 0.0261 -
0.1749 5200 0.0308 -
0.1782 5300 0.0404 -
0.1816 5400 0.0315 -
0.1849 5500 0.0397 -
0.1883 5600 0.0361 -
0.1917 5700 0.031 -
0.1950 5800 0.0271 -
0.1984 5900 0.0287 -
0.2018 6000 0.0356 0.8571
0.2051 6100 0.0243 -
0.2085 6200 0.0193 -
0.2118 6300 0.0232 -
0.2152 6400 0.032 -
0.2186 6500 0.0282 -
0.2219 6600 0.0275 -
0.2253 6700 0.026 -
0.2287 6800 0.0333 -
0.2320 6900 0.0298 -
0.2354 7000 0.033 0.8218
0.2387 7100 0.0265 -
0.2421 7200 0.0247 -
0.2455 7300 0.0233 -
0.2488 7400 0.0303 -
0.2522 7500 0.0272 -
0.2556 7600 0.028 -
0.2589 7700 0.0259 -
0.2623 7800 0.0305 -
0.2656 7900 0.0237 -
0.2690 8000 0.0227 0.8368
0.2724 8100 0.0216 -
0.2757 8200 0.0277 -
0.2791 8300 0.0197 -
0.2825 8400 0.0231 -
0.2858 8500 0.0232 -
0.2892 8600 0.0315 -
0.2925 8700 0.0198 -
0.2959 8800 0.0236 -
0.2993 8900 0.0243 -
0.3026 9000 0.0213 0.8118
0.3060 9100 0.0264 -
0.3094 9200 0.0218 -
0.3127 9300 0.0232 -
0.3161 9400 0.0192 -
0.3194 9500 0.018 -
0.3228 9600 0.0225 -
0.3262 9700 0.0225 -
0.3295 9800 0.0207 -
0.3329 9900 0.0264 -
0.3363 10000 0.0314 0.8286
0.3396 10100 0.0246 -
0.3430 10200 0.0224 -
0.3463 10300 0.0246 -
0.3497 10400 0.0212 -
0.3531 10500 0.0166 -
0.3564 10600 0.0253 -
0.3598 10700 0.0221 -
0.3632 10800 0.0175 -
0.3665 10900 0.0254 -
0.3699 11000 0.0181 0.7995
0.3732 11100 0.0176 -
0.3766 11200 0.0196 -
0.3800 11300 0.02 -
0.3833 11400 0.0219 -
0.3867 11500 0.0265 -
0.3901 11600 0.0217 -
0.3934 11700 0.0161 -
0.3968 11800 0.0145 -
0.4001 11900 0.0184 -
0.4035 12000 0.0166 0.8185
0.4069 12100 0.0177 -
0.4102 12200 0.0231 -
0.4136 12300 0.0215 -
0.4170 12400 0.0226 -
0.4203 12500 0.0144 -
0.4237 12600 0.0174 -
0.4270 12700 0.0176 -
0.4304 12800 0.0214 -
0.4338 12900 0.0206 -
0.4371 13000 0.0197 0.7957
0.4405 13100 0.0216 -
0.4439 13200 0.0211 -
0.4472 13300 0.0198 -
0.4506 13400 0.0161 -
0.4539 13500 0.0123 -
0.4573 13600 0.0168 -
0.4607 13700 0.0188 -
0.4640 13800 0.0145 -
0.4674 13900 0.0221 -
0.4708 14000 0.0207 0.8036
0.4741 14100 0.0186 -
0.4775 14200 0.0199 -
0.4809 14300 0.0219 -
0.4842 14400 0.0131 -
0.4876 14500 0.0152 -
0.4909 14600 0.0159 -
0.4943 14700 0.0165 -
0.4977 14800 0.0145 -
0.5010 14900 0.0143 -
0.5044 15000 0.0135 0.7920
0.5078 15100 0.0159 -
0.5111 15200 0.0111 -
0.5145 15300 0.0198 -
0.5178 15400 0.0142 -
0.5212 15500 0.0167 -
0.5246 15600 0.0118 -
0.5279 15700 0.0151 -
0.5313 15800 0.0172 -
0.5347 15900 0.0135 -
0.5380 16000 0.0159 0.8073
0.5414 16100 0.0146 -
0.5447 16200 0.0127 -
0.5481 16300 0.0158 -
0.5515 16400 0.0138 -
0.5548 16500 0.0102 -
0.5582 16600 0.0127 -
0.5616 16700 0.0166 -
0.5649 16800 0.0137 -
0.5683 16900 0.0127 -
0.5716 17000 0.014 0.7942
0.5750 17100 0.0151 -
0.5784 17200 0.0134 -
0.5817 17300 0.0119 -
0.5851 17400 0.0096 -
0.5885 17500 0.0129 -
0.5918 17600 0.0133 -
0.5952 17700 0.0084 -
0.5985 17800 0.0114 -
0.6019 17900 0.0123 -
0.6053 18000 0.0115 0.7615
0.6086 18100 0.0109 -
0.6120 18200 0.0098 -
0.6154 18300 0.0167 -
0.6187 18400 0.0117 -
0.6221 18500 0.0133 -
0.6254 18600 0.0089 -
0.6288 18700 0.0125 -
0.6322 18800 0.0101 -
0.6355 18900 0.0143 -
0.6389 19000 0.0108 0.8011
0.6423 19100 0.0164 -
0.6456 19200 0.0099 -
0.6490 19300 0.0112 -
0.6523 19400 0.0184 -
0.6557 19500 0.0178 -
0.6591 19600 0.0111 -
0.6624 19700 0.0101 -
0.6658 19800 0.0146 -
0.6692 19900 0.0149 -
0.6725 20000 0.0139 0.8151
0.6759 20100 0.0146 -
0.6792 20200 0.0086 -
0.6826 20300 0.0168 -
0.6860 20400 0.0101 -
0.6893 20500 0.0101 -
0.6927 20600 0.0086 -
0.6961 20700 0.0108 -
0.6994 20800 0.0092 -
0.7028 20900 0.0119 -
0.7061 21000 0.0136 0.8046
0.7095 21100 0.0106 -
0.7129 21200 0.0123 -
0.7162 21300 0.0108 -
0.7196 21400 0.0112 -
0.7230 21500 0.0096 -
0.7263 21600 0.0074 -
0.7297 21700 0.0104 -
0.7330 21800 0.0079 -
0.7364 21900 0.0061 -
0.7398 22000 0.0064 0.7948
0.7431 22100 0.0091 -
0.7465 22200 0.0091 -
0.7499 22300 0.006 -
0.7532 22400 0.0081 -
0.7566 22500 0.0084 -
0.7599 22600 0.0109 -
0.7633 22700 0.0124 -
0.7667 22800 0.0108 -
0.7700 22900 0.009 -
0.7734 23000 0.0118 0.7956
0.7768 23100 0.011 -
0.7801 23200 0.0093 -
0.7835 23300 0.0097 -
0.7868 23400 0.0069 -
0.7902 23500 0.0081 -
0.7936 23600 0.0092 -
0.7969 23700 0.01 -
0.8003 23800 0.0112 -
0.8037 23900 0.0076 -
0.8070 24000 0.0098 0.8005
0.8104 24100 0.0083 -
0.8137 24200 0.0089 -
0.8171 24300 0.0125 -
0.8205 24400 0.0051 -
0.8238 24500 0.009 -
0.8272 24600 0.0086 -
0.8306 24700 0.0075 -
0.8339 24800 0.0069 -
0.8373 24900 0.0065 -
0.8406 25000 0.0092 0.7830
0.8440 25100 0.0077 -
0.8474 25200 0.0049 -
0.8507 25300 0.0061 -
0.8541 25400 0.0115 -
0.8575 25500 0.0086 -
0.8608 25600 0.006 -
0.8642 25700 0.0083 -
0.8675 25800 0.0067 -
0.8709 25900 0.0069 -
0.8743 26000 0.0083 0.7734
0.8776 26100 0.007 -
0.8810 26200 0.0086 -
0.8844 26300 0.0077 -
0.8877 26400 0.0138 -
0.8911 26500 0.0054 -
0.8944 26600 0.008 -
0.8978 26700 0.0076 -
0.9012 26800 0.0094 -
0.9045 26900 0.0069 -
0.9079 27000 0.0066 0.7821
0.9113 27100 0.0068 -
0.9146 27200 0.0056 -
0.9180 27300 0.0067 -
0.9213 27400 0.0061 -
0.9247 27500 0.0072 -
0.9281 27600 0.0086 -
0.9314 27700 0.006 -
0.9348 27800 0.0063 -
0.9382 27900 0.0095 -
0.9415 28000 0.007 0.7833
0.9449 28100 0.0128 -
0.9482 28200 0.0081 -
0.9516 28300 0.0059 -
0.9550 28400 0.0067 -
0.9583 28500 0.0059 -
0.9617 28600 0.0057 -
0.9651 28700 0.0055 -
0.9684 28800 0.0065 -
0.9718 28900 0.0065 -
0.9752 29000 0.0072 0.7806
0.9785 29100 0.0107 -
0.9819 29200 0.0083 -
0.9852 29300 0.01 -
0.9886 29400 0.0044 -
0.9920 29500 0.0056 -
0.9953 29600 0.0053 -
0.9987 29700 0.0081 -

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 

@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 

@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}
}