README.md

---
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:98112
- loss:MultipleNegativesRankingLoss
base_model: BAAI/bge-small-en-v1.5
widget:
- source_sentence: 'Represent this question for retrieving relevant documents: I''m
    curious about strategies businesses can use to ensure data privacy and security.'
  sentences:
  - 'The Vicsek fractal is a self-replicating fractal, where each square is replaced
    by a pattern of five smaller squares in each iteration. The number of line segments
    in each iteration can be calculated using the formula:


    Number of line segments = 4 * (5^(n-1))


    where n is the iteration number.


    For the fifth iteration (n=5):


    Number of line segments = 4 * (5^(5-1))

    Number of line segments = 4 * (5^4)

    Number of line segments = 4 * (625)

    Number of line segments = 2500


    So, there are 2500 line segments needed to draw the fifth iteration of the Vicsek
    fractal.'
  - '**Advanced Techniques and Strategies for Data Privacy and Security:**


    1. **Data encryption:** Encrypting data both at rest and in transit ensures it
    remains protected even if accessed by unauthorized individuals.


    2. **Regular security audits:** Conducting regular security audits helps businesses
    identify and address vulnerabilities in their systems and processes.


    3. **Data masking:** Data masking techniques such as tokenization and pseudonymization
    protect sensitive data by replacing it with non-identifiable values.


    4. **Access control management:** Implementing robust access control measures,
    such as role-based access control (RBAC) and multi-factor authentication (MFA),
    restricts access to data to authorized personnel only.


    5. **Data minimization:** Businesses should only collect and store data that is
    absolutely necessary for their operations to reduce the risk of data breaches.


    **Practical Examples of Data Privacy and Security:**


    - **Healthcare:** Hospitals and medical facilities use data encryption to protect
    patient health records, ensuring compliance with HIPAA regulations.


    - **Financial Services:** Banks and financial institutions implement MFA and access
    control measures to safeguard customer financial data.


    - **Retail:** E-commerce companies use data masking techniques to protect sensitive
    customer information, such as credit card numbers.


    **Interview Questions on Data Privacy and Security:**


    - Describe the key principles of data privacy and security.


    - Explain the different methods used for data encryption and their strengths and
    weaknesses.


    - How can organizations implement effective access control mechanisms to protect
    data?


    - What are the best practices for conducting security audits to ensure data privacy?


    - Discuss the ethical and legal implications of data privacy and security breaches.'
  - 'First, let''s write the system of linear equations as an augmented matrix:


    [ 1  2 -1 |  5]

    [ 2 -3  4 |  7]

    [-6  7 -5 | -1]


    Now, we''ll perform forward elimination to convert the matrix into an upper triangular
    matrix.


    Step 1: Eliminate x from the second and third rows.


    To eliminate x from the second row, we''ll subtract 2 times the first row from
    the second row:


    [ 1  2 -1 |  5]

    [ 0 -7  6 | -3]

    [-6  7 -5 | -1]


    To eliminate x from the third row, we''ll add 6 times the first row to the third
    row:


    [ 1  2 -1 |  5]

    [ 0 -7  6 | -3]

    [ 0  5 -1 | 29]


    Step 2: Eliminate y from the third row.


    To eliminate y from the third row, we''ll add (5/7) times the second row to the
    third row:


    [ 1  2 -1 |  5]

    [ 0 -7  6 | -3]

    [ 0  0  1 |  4]


    Now, we have an upper triangular matrix, and we can perform back substitution
    to find the values of x, y, and z.


    Step 3: Back substitution


    From the third row, we have z = 4.


    Now, we''ll substitute z into the second row to find y:


    -7y + 6(4) = -3

    -7y + 24 = -3

    -7y = -27

    y = 27/7


    Finally, we''ll substitute y and z into the first row to find x:


    x + 2(27/7) - 4 = 5

    x + 54/7 - 4 = 5

    x = 5 - 54/7 + 4

    x = (35 - 54 + 28)/7

    x = 9/7


    So, the solution to the system of linear equations is:


    x = 9/7

    y = 27/7

    z = 4'
- source_sentence: "Represent this question for retrieving relevant documents: Solve\
    \ the following system of linear equations with complex coefficients: \n\n2x +\
    \ 5y + 3iz = 8i \n\nx - 3y + 2z = 1 \n\n-4x + 2y + 5iz = -5"
  sentences:
  - To determine whether tympanic membrane (TM) electrodes induce behavioral pure-tone
    threshold shifts. Pure-tone thresholds (250 to 8000 Hz) were measured twice in
    test (n = 18) and control (n = 10) groups. TM electrodes were placed between first
    and second threshold measurements in the test group, whereas the control group
    did not receive electrodes. Pure-tone threshold shifts were compared between groups.
    The effect of TM electrode contact location on threshold shifts was evaluated
    in the test group. TM electrodes significantly increased average low-frequency
    thresholds, 7.5 dB at 250 Hz and 4.2 dB at 500 Hz, and shifts were as large as
    25 dB in individual ears. Also, threshold shifts did not appear to vary at any
    frequency with TM electrode contact location.
  - 'To solve the given system of linear equations with complex coefficients, we can
    use the Gaussian elimination method. The given system of equations is:


    (1) 2x + 5y + 3iz = 8i

    (2) x - 3y + 2z = 1

    (3) -4x + 2y + 5iz = -5


    First, we will write the augmented matrix for this system:


    |  2   5   3i |  8i |

    |  1  -3   2  |  1  |

    | -4   2   5i | -5  |


    Next, we will perform row operations to get the matrix in row-echelon form. We
    will start by making the first element of the second row 0. To do this, we can
    subtract half of the first row from the second row:


    |  2   5   3i |  8i |

    |  0  -5.5 -1i | -3i |

    | -4   2   5i | -5  |


    Now, we will make the first element of the third row 0. To do this, we can add
    twice the first row to the third row:


    |  2   5   3i |  8i  |

    |  0  -5.5 -1i | -3i  |

    |  0   12  11i | 11i  |


    Next, we will make the second element of the third row 0. To do this, we can add
    (12/5.5) times the second row to the third row:


    |  2   5    3i  |  8i  |

    |  0  -5.5 -1i  | -3i  |

    |  0   0   10.8i|  6i  |


    Now, we have the matrix in row-echelon form. We can now solve for the variables
    using back-substitution.


    From the third row, we have:


    10.8i * z = 6i


    Dividing both sides by 10.8i, we get:


    z = 6i / 10.8i = 6/10.8 = 1/1.8 = 5/9


    Now, we can substitute z back into the second row to find y:


    -5.5y - 1i(5/9) = -3i


    Multiplying both sides by -1, we get:


    5.5y + (5i/9) = 3i


    Subtracting 5i/9 from both sides, we get:


    5.5y = 3i - 5i/9 = (22i - 5i) / 9 = 17i/9


    Dividing both sides by 5.5, we get:


    y = (17i/9) / 5.5 = 17i / 49.5 = 17i / (99/2) = 34i / 99


    Finally, we can substitute y and z back into the first row to find x:


    2x + 5(34i/99) + 3i(5/9) = 8i


    Multiplying both sides by 99, we get:


    198x + 5(34i) + 3i(55) = 792i


    198x + 170i + 165i = 792i


    198x = 792i - 335i = 457i


    Dividing both sides by 198, we get:


    x = 457i / 198


    So, the solution to the given system of linear equations is:


    x = 457i / 198

    y = 34i / 99

    z = 5/9'
  - Remodelling of the asthmatic airway includes increased deposition of proteoglycan
    (PG) molecules. One of the stimuli driving airway remodelling may be excessive
    mechanical stimulation. We hypothesized that fibroblasts from asthmatic patients
    would respond to excessive mechanical strain with up-regulation of message for
    PGs. We obtained fibroblasts from asthmatic patients (AF) and normal volunteers
    (NF) using endobronchial biopsy. Cells were maintained in culture until the fifth
    passage and then grown on a flexible collagen-coated membrane. Using the Flexercell
    device, cells were then subjected to cyclic stretch at 30% amplitude at 1 Hz for
    24 h. Control cells were unstrained. Total RNA was extracted from the cell layer
    and quantitative RT-PCR performed for decorin, lumican and versican mRNA. In unstrained
    cells, the expression of decorin mRNA was greater in AF than NF. With strain,
    NF showed increased expression of versican mRNA and AF showed increased expression
    of versican and decorin mRNA. The relative increase in versican mRNA expression
    with strain was greater in AF than NF.
- source_sentence: 'Represent this question for retrieving relevant documents: What
    is the total arc length of the Lévy C curve after iterating 8 times if the original
    line segment had a length of 1 unit?'
  sentences:
  - "Pose estimation is indeed a fascinating area in computer vision, but it's not\
    \ entirely a walk in the park. Estimating the pose of a human or object involves\
    \ a combination of complex mathematical techniques and algorithms. Let's delve\
    \ deeper into some key aspects of pose estimation:\n\n1). **3D vs 2D Pose Estimation**:\
    \ \n - 3D Pose Estimation aims to determine the 3-dimensional pose of a subject,\
    \ providing depth information along with the 2D coordinates. This requires specialized\
    \ techniques like stereo cameras or depth sensors to capture the 3D structure\
    \ of the scene.\n - In comparison, 2D Pose Estimation focuses on estimating the\
    \ 2D pose of a subject within a single image or video frame, providing information\
    \ about joint locations in the image plane.\n\n2). **Model-based Pose Estimation**:\
    \ \n - This approach leverages predefined models of human (or object) skeletons\
    \ with known joint connections. The model is then fitted to the input image or\
    \ video data to estimate the pose of the subject.  \n - A prominent example of\
    \ Model-based Pose Estimation is the popular OpenPose library, which utilizes\
    \ a part-based model to estimate human poses.\n\n3). **Model-free Pose Estimation**:\
    \ \n - Contrary to model-based methods, model-free approaches do not rely on predefined\
    \ models. Instead, they directly learn to estimate the pose from raw image or\
    \ video data. \n - One such technique is the Convolutional Pose Machine (CPM)\
    \ which uses convolutional neural networks to predict heatmaps for body joints,\
    \ which are then refined to obtain the final pose estimation.\n\n4). **Case Study:\
    \ Human Pose Estimation in Sports Analysis**: \n - Pose estimation plays a crucial\
    \ role in sports analysis, enabling the quantification of player movements and\
    \ kinematics. \n - For instance, in soccer, pose estimation techniques can be\
    \ employed to track player positions, analyze their running patterns, and evaluate\
    \ their performance during matches.\n\n5). **Comparative Analysis with Similar\
    \ Concepts**: \n - Object Detection: While both pose estimation and object detection\
    \ involve locating and identifying objects in images or videos, pose estimation\
    \ specifically focuses on determining the pose or configuration of the object,\
    \ while object detection primarily aims to identify and localize the object's\
    \ presence.\n - Motion Capture: Pose estimation is closely related to motion capture,\
    \ which involves tracking and recording the movements of human subjects. Motion\
    \ capture systems typically employ specialized sensors or cameras to capture highly\
    \ accurate 3D pose data, whereas pose estimation algorithms typically rely on\
    \ computer vision techniques to infer poses from 2D or 3D image or video data.\n\
    \n6). **Common Misconceptions and Clarifications**: \n - Pose estimation is not\
    \ limited to humans: It can also be used to estimate the pose of objects, animals,\
    \ and even vehicles.\n - Pose estimation is distinct from facial expression recognition:\
    \ While both involve analyzing images or videos of people, pose estimation focuses\
    \ on body posture and joint locations, whereas facial expression recognition aims\
    \ to identify and interpret facial expressions."
  - "The Lévy C curve is a self-replicating fractal that is created by iteratively\
    \ replacing a straight line segment with two segments, each of which is 1/sqrt(2)\
    \ times the length of the original segment, and joined at a right angle. \n\n\
    After each iteration, the total arc length of the curve increases by a factor\
    \ of 2/sqrt(2), which is equal to sqrt(2). \n\nIf the original line segment has\
    \ a length of 1 unit, then after 8 iterations, the total arc length of the Lévy\
    \ C curve will be:\n\nArc length = Original length * (sqrt(2))^n\nArc length =\
    \ 1 * (sqrt(2))^8\nArc length = 1 * 2^4\nArc length = 1 * 16\nArc length = 16\
    \ units\n\nSo, the total arc length of the Lévy C curve after iterating 8 times\
    \ is 16 units."
  - 'If the dictator keeps X points for themselves, the receiver will get the remaining
    points, which can be calculated as:


    Y = 10 - X


    To find the fractional amount of the total points the receiver received, we can
    create a fraction with Y as the numerator and the total points (10) as the denominator:


    Fraction = Y/10 = (10 - X)/10


    So, the receiver gets a fractional amount of (10 - X)/10 of the total points.'
- source_sentence: 'Represent this question for retrieving relevant documents: Detailed
    Elaboration on Dimensionality Reduction and Industry Application'
  sentences:
  - '**Dimensionality Reduction: A Comprehensive Overview**


    Dimensionality reduction is a fundamental concept in machine learning and data
    analysis. It involves transforming high-dimensional data into a lower-dimensional
    representation while preserving the most important information. Dimensionality
    reduction techniques have a wide range of applications in various industries,
    such as:


    * **Feature engineering:** reducing the number of features in a dataset to improve
    the efficiency of machine learning algorithms.

    * **Visualization:** enabling the visualization of high-dimensional data by projecting
    it onto a lower-dimensional subspace.

    * **Data compression:** reducing the storage and transmission costs of large datasets.


    **Specific Industry Applications:**


    * **Computer vision:** Extracting meaningful features from images and videos for
    object recognition, image segmentation, and facial recognition.

    * **Natural language processing:** Reducing the dimensionality of text data for
    text classification, document summarization, and machine translation.

    * **Bioinformatics:** Analyzing gene expression data and identifying biomarkers
    for disease diagnosis and drug discovery.

    * **Financial modeling:** Identifying patterns and trends in financial data for
    risk assessment, portfolio optimization, and fraud detection.

    * **Recommendation systems:** Generating personalized recommendations for products,
    movies, or music based on user preferences.


    To further enhance your understanding, I can provide detailed explanations of
    specific techniques, industry case studies, or address any specific questions
    you may have.'
  - Hepatocellular carcinoma is one of the most common malignancies worldwide. The
    only curative treatment is surgery. As hepatocellular carcinoma is often associated
    with liver cirrhosis, patients are at risk for postoperative liver failure. In
    the recent years, platelets are thought to play an important role in liver regeneration.The
    aim of this study was to discover the relevance of postoperative platelet counts
    after liver resection for hepatocellular carcinoma. Data of 68 patients who underwent
    liver resection for hepatocellular carcinoma between July 2007 and July 2012 in
    a single centre were analysed. Postoperative morbidity and mortality were evaluated
    in regard to postoperative platelet counts. Comparative analysis between patients
    with platelet counts ≤100 2x109/ l and >100 x109/ l at d1 was performed in regard
    to postoperative outcome. Within this cohort, 43 patients (63%) suffered from
    histologically proven liver cirrhosis. Postoperative mortality was statistically
    significant associated with postoperative reduced platelet counts. Comparative
    analysis showed significantly elevated postoperative bilirubin levels and lower
    prothrombin time in patients with platelet counts ≤ 100 1x109/ l at d1.
  - "Let G be a group of order 25. Since 25 = 5^2 and 5 is prime, by the Sylow theorems,\
    \ the number of 5-Sylow subgroups in G, denoted by n_5, satisfies:\n\n1. n_5 divides\
    \ 25/5 = 5, and\n2. n_5 ≡ 1 (mod 5).\n\nFrom these conditions, we have that n_5\
    \ can only be 1 or 5. \n\nCase 1: n_5 = 1\nIn this case, there is only one 5-Sylow\
    \ subgroup, say H, in G. By the Sylow theorems, H is a normal subgroup of G. Since\
    \ the order of H is 5, which is prime, H is cyclic, i.e., H ≅ C_5 (the cyclic\
    \ group of order 5). \n\nNow, let g be an element of G that is not in H. Since\
    \ H is normal in G, the set {gh : h ∈ H} is also a subgroup of G. Let K = {gh\
    \ : h ∈ H}. Note that the order of K is also 5, as there is a one-to-one correspondence\
    \ between the elements of H and K. Thus, K is also a cyclic group of order 5,\
    \ i.e., K ≅ C_5.\n\nSince the orders of H and K are both 5, their intersection\
    \ is trivial, i.e., H ∩ K = {e}, where e is the identity element of G. Moreover,\
    \ since the order of G is 25, any element of G can be written as a product of\
    \ elements from H and K. Therefore, G is the internal direct product of H and\
    \ K, i.e., G ≅ H × K ≅ C_5 × C_5.\n\nCase 2: n_5 = 5\nIn this case, there are\
    \ five 5-Sylow subgroups in G. Let H be one of these subgroups. Since the order\
    \ of H is 5, which is prime, H is cyclic, i.e., H ≅ C_5.\n\nNow, consider the\
    \ action of G on the set of 5-Sylow subgroups by conjugation. This action gives\
    \ rise to a homomorphism φ: G → S_5, where S_5 is the symmetric group on 5 elements.\
    \ The kernel of φ, say N, is a normal subgroup of G. Since the action is nontrivial,\
    \ N is a proper subgroup of G, and thus, the order of N is either 1 or 5. If the\
    \ order of N is 1, then G is isomorphic to a subgroup of S_5, which is a contradiction\
    \ since the order of G is 25 and there is no subgroup of S_5 with order 25. Therefore,\
    \ the order of N must be 5.\n\nSince the order of N is 5, N is a cyclic group\
    \ of order 5, i.e., N ≅ C_5. Moreover, N is a normal subgroup of G. Let g be an\
    \ element of G that is not in N. Then, the set {gn : n ∈ N} is also a subgroup\
    \ of G. Let K = {gn : n ∈ N}. Note that the order of K is also 5, as there is\
    \ a one-to-one correspondence between the elements of N and K. Thus, K is also\
    \ a cyclic group of order 5, i.e., K ≅ C_5.\n\nSince the orders of N and K are\
    \ both 5, their intersection is trivial, i.e., N ∩ K = {e}, where e is the identity\
    \ element of G. Moreover, since the order of G is 25, any element of G can be\
    \ written as a product of elements from N and K. Therefore, G is the internal\
    \ direct product of N and K, i.e., G ≅ N × K ≅ C_5 × C_5.\n\nIn conclusion, a\
    \ group of order 25 is either cyclic or isomorphic to the direct product of two\
    \ cyclic groups of order 5."
- source_sentence: 'Represent this question for retrieving relevant documents: Does
    low 25-Hydroxyvitamin D Level be Associated with Peripheral Arterial Disease in
    Type 2 Diabetes Patients?'
  sentences:
  - 'Patients with type 2 diabetes have an increased risk of atherosclerosis and vascular
    disease. Vitamin D deficiency is associated with vascular disease and is prevalent
    in diabetes patients. We undertook this study to determine the association between
    25-hydroxyvitamin D (25[OH]D) levels and prevalence of peripheral arterial disease
    (PAD) in type 2 diabetes patients. A total of 1028 type 2 diabetes patients were
    recruited at Nanjing Medical University Affiliated Nanjing Hospital from November
    2011 to October 2013. PAD was defined as an ankle-brachial index (ABI) < 0.9.
    Cardiovascular risk factors (blood pressure, HbA1c, lipid profile), comorbidities,
    carotid intima-media thickness (IMT) and 25(OH)D were assessed. Overall prevalence
    of PAD and of decreased 25(OH)D (<30 ng/mL) were 20.1% (207/1028) and 54.6% (561/1028),
    respectively. PAD prevalence was higher in participants with decreased (23.9%)
    than in those with normal (15.6%) 25(OH)D (≥30 ng/mL, p <0.01). Decreased 25(OH)D
    was associated with increased risk of PAD (odds ratio [OR], 1.69, 95% CI: 1.17-2.44,
    p <0.001) and PAD was significantly more likely to occur in participants ≥65 years
    of age (OR, 2.56, 95% CI: 1.51 -4.48, vs. 1.21, 95% CI: 0.80-1.83, p-interaction = 0.027).
    After adjusting for known cardiovascular risk factors and potential confounding
    variables, the association of decreased 25(OH)D and PAD remained significant in
    patients <65 years of age (OR, 1.55; 95% CI: 1.14-2.12, p = 0.006).'
  - No study has been performed to compare the impacts of migraine and major depressive
    episode (MDE) on depression, anxiety and somatic symptoms, and health-related
    quality of life (HRQoL) among psychiatric outpatients. The aim of this study was
    to investigate the above issue. This study enrolled consecutive psychiatric outpatients
    with mood and/or anxiety disorders who undertook a first visit to a medical center.
    Migraine was diagnosed according to the International Classification of Headache
    Disorders, 2nd edition. Three psychometric scales and the Short-Form 36 were administered.
    General linear models were used to estimate the difference in scores contributed
    by either migraine or MDE. Multiple linear regressions were employed to compare
    the variance of these scores explained by migraine or MDE. Among 214 enrolled
    participants, 35.0% had migraine. Bipolar II disorder patients (70.0%) had the
    highest percentage of migraine, followed by major depressive disorder (49.1%)
    and only anxiety disorder (24.5%). Patients with migraine had worse depression,
    anxiety, and somatic symptoms and lower SF-36 scores than those without. The estimated
    differences in the scores of physical functioning, bodily pain, and somatic symptoms
    contributed by migraine were not lower than those contributed by MDE. The regression
    model demonstrated the variance explained by migraine was significantly greater
    than that explained by MDE in physical and pain symptoms.
  - 'Based on the information provided, we only know the number of patients who died
    within the first year after the surgery. To determine the probability of a patient
    surviving at least two years, we would need additional information about the number
    of patients who died in the second year or survived beyond that.


    Without this information, it is not possible to calculate the probability of a
    patient surviving at least two years after the surgery.'
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics:
- cosine_accuracy@1
- cosine_accuracy@3
- cosine_accuracy@5
- cosine_accuracy@10
- cosine_precision@1
- cosine_precision@3
- cosine_precision@5
- cosine_recall@1
- cosine_recall@3
- cosine_recall@5
- cosine_ndcg@10
- cosine_mrr@10
- cosine_map@100
model-index:
- name: SentenceTransformer based on BAAI/bge-small-en-v1.5
  results:
  - task:
      type: logging
      name: Logging
    dataset:
      name: ir eval
      type: ir-eval
    metrics:
    - type: cosine_accuracy@1
      value: 0.9241493167018252
      name: Cosine Accuracy@1
    - type: cosine_accuracy@3
      value: 0.9788131706869669
      name: Cosine Accuracy@3
    - type: cosine_accuracy@5
      value: 0.9906447766669724
      name: Cosine Accuracy@5
    - type: cosine_accuracy@10
      value: 0.9965147207190681
      name: Cosine Accuracy@10
    - type: cosine_precision@1
      value: 0.9241493167018252
      name: Cosine Precision@1
    - type: cosine_precision@3
      value: 0.3262710568956556
      name: Cosine Precision@3
    - type: cosine_precision@5
      value: 0.1981289553333945
      name: Cosine Precision@5
    - type: cosine_recall@1
      value: 0.9241493167018252
      name: Cosine Recall@1
    - type: cosine_recall@3
      value: 0.9788131706869669
      name: Cosine Recall@3
    - type: cosine_recall@5
      value: 0.9906447766669724
      name: Cosine Recall@5
    - type: cosine_ndcg@10
      value: 0.9634519649573985
      name: Cosine Ndcg@10
    - type: cosine_mrr@10
      value: 0.9524509418552345
      name: Cosine Mrr@10
    - type: cosine_map@100
      value: 0.9526115405885596
      name: Cosine Map@100
---

# SentenceTransformer based on BAAI/bge-small-en-v1.5

This is a [sentence-transformers](https://www.SBERT.net) model finetuned from [BAAI/bge-small-en-v1.5](https://huggingface.co/BAAI/bge-small-en-v1.5). 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
- **Base model:** [BAAI/bge-small-en-v1.5](https://huggingface.co/BAAI/bge-small-en-v1.5) <!-- at revision 5c38ec7c405ec4b44b94cc5a9bb96e735b38267a -->
- **Maximum Sequence Length:** 512 tokens
- **Output Dimensionality:** 384 dimensions
- **Similarity Function:** Cosine Similarity
<!-- - **Training Dataset:** Unknown -->
<!-- - **Language:** Unknown -->
<!-- - **License:** Unknown -->

### Model Sources

- **Documentation:** [Sentence Transformers Documentation](https://sbert.net)
- **Repository:** [Sentence Transformers on GitHub](https://github.com/UKPLab/sentence-transformers)
- **Hugging Face:** [Sentence Transformers on Hugging Face](https://huggingface.co/models?library=sentence-transformers)

### Full Model Architecture

```
SentenceTransformer(
  (0): Transformer({'max_seq_length': 512, 'do_lower_case': True}) with Transformer model: BertModel 
  (1): Pooling({'word_embedding_dimension': 384, '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})
  (2): Normalize()
)
```

## Usage

### Direct Usage (Sentence Transformers)

First install the Sentence Transformers library:

```bash
pip install -U sentence-transformers
```

Then you can load this model and run inference.
```python
from sentence_transformers import SentenceTransformer

# Download from the 🤗 Hub
model = SentenceTransformer("sucharush/bge_MNR")
# Run inference
sentences = [
    'Represent this question for retrieving relevant documents: Does low 25-Hydroxyvitamin D Level be Associated with Peripheral Arterial Disease in Type 2 Diabetes Patients?',
    'Patients with type 2 diabetes have an increased risk of atherosclerosis and vascular disease. Vitamin D deficiency is associated with vascular disease and is prevalent in diabetes patients. We undertook this study to determine the association between 25-hydroxyvitamin D (25[OH]D) levels and prevalence of peripheral arterial disease (PAD) in type 2 diabetes patients. A total of 1028 type 2 diabetes patients were recruited at Nanjing Medical University Affiliated Nanjing Hospital from November 2011 to October 2013. PAD was defined as an ankle-brachial index (ABI)\xa0<\xa00.9. Cardiovascular risk factors (blood pressure, HbA1c, lipid profile), comorbidities, carotid intima-media thickness (IMT) and 25(OH)D were assessed. Overall prevalence of PAD and of decreased 25(OH)D (<30\xa0ng/mL) were 20.1% (207/1028) and 54.6% (561/1028), respectively. PAD prevalence was higher in participants with decreased (23.9%) than in those with normal (15.6%) 25(OH)D (≥30\xa0ng/mL, p\xa0<0.01). Decreased 25(OH)D was associated with increased risk of PAD (odds ratio [OR], 1.69, 95% CI: 1.17-2.44, p\xa0<0.001) and PAD was significantly more likely to occur in participants ≥65\xa0years of age (OR, 2.56, 95% CI: 1.51 -4.48, vs. 1.21, 95% CI: 0.80-1.83, p-interaction\xa0=\xa00.027). After adjusting for known cardiovascular risk factors and potential confounding variables, the association of decreased 25(OH)D and PAD remained significant in patients <65\xa0years of age (OR, 1.55; 95% CI: 1.14-2.12, p\xa0=\xa00.006).',
    'Based on the information provided, we only know the number of patients who died within the first year after the surgery. To determine the probability of a patient surviving at least two years, we would need additional information about the number of patients who died in the second year or survived beyond that.\n\nWithout this information, it is not possible to calculate the probability of a patient surviving at least two years after the surgery.',
]
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]
```

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## Evaluation

### Metrics

#### Logging

* Dataset: `ir-eval`
* Evaluated with <code>__main__.LoggingEvaluator</code>

| Metric             | Value      |
|:-------------------|:-----------|
| cosine_accuracy@1  | 0.9241     |
| cosine_accuracy@3  | 0.9788     |
| cosine_accuracy@5  | 0.9906     |
| cosine_accuracy@10 | 0.9965     |
| cosine_precision@1 | 0.9241     |
| cosine_precision@3 | 0.3263     |
| cosine_precision@5 | 0.1981     |
| cosine_recall@1    | 0.9241     |
| cosine_recall@3    | 0.9788     |
| cosine_recall@5    | 0.9906     |
| **cosine_ndcg@10** | **0.9635** |
| cosine_mrr@10      | 0.9525     |
| cosine_map@100     | 0.9526     |

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## Training Details

### Training Dataset

#### Unnamed Dataset

* Size: 98,112 training samples
* Columns: <code>sentence_0</code> and <code>sentence_1</code>
* Approximate statistics based on the first 1000 samples:
  |         | sentence_0                                                                          | sentence_1                                                                          |
  |:--------|:------------------------------------------------------------------------------------|:------------------------------------------------------------------------------------|
  | type    | string                                                                              | string                                                                              |
  | details | <ul><li>min: 18 tokens</li><li>mean: 55.27 tokens</li><li>max: 512 tokens</li></ul> | <ul><li>min: 9 tokens</li><li>mean: 317.52 tokens</li><li>max: 512 tokens</li></ul> |
* Samples:
  | sentence_0                                                                                                                                                                                                                                                                                                                                                   | sentence_1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |
  |:-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  | <code>Represent this question for retrieving relevant documents: Are elevated levels of pro-inflammatory oxylipins in older subjects normalized by flaxseed consumption?</code>                                                                                                                                                                              | <code>Oxylipins, including eicosanoids, are highly bioactive molecules endogenously produced from polyunsaturated fatty acids. Oxylipins play a key role in chronic disease progression. It is possible, but unknown, if oxylipin concentrations change with the consumption of functional foods or differ with subject age. Therefore, in a parallel comparator trial, 20 healthy individuals were recruited into a younger (19-28years) or older (45-64years) age group (n=10/group). Participants ingested one muffin/day containing 30g of milled flaxseed (6g alpha-linolenic acid) for 4weeks. Plasma oxylipins were isolated through solid phase extraction, analyzed with HPLC-MS/MS targeted lipidomics, and quantified with the stable isotope dilution method. At baseline, the older group exhibited 13 oxylipins ≥2-fold the concentration of the younger group. Specifically, pro-inflammatory oxylipins 5-hydroxyeicosatetraenoic acid, 9,10,13-trihydroxyoctadecenoic acid, and 9,12,13-trihydroxyoctadecenoic acid were signi...</code>                                                 |
  | <code>Represent this question for retrieving relevant documents: Find the isometries of the metric $ds^2 = dx^2 + dy^2$ over the rectangle $R=[0,a] \times [0,b]$, subject to the additional condition that any isometry $f$ maps $(0,0)$ to $(x_0, y_0)$. Find $x_0$ and $y_0$ such that the isometry $f$ is given by $f(x,y) = (x_0 + x, y_0 - y)$.</code> | <code>An isometry is a transformation that preserves the distance between points. In this case, we are looking for transformations that preserve the metric $ds^2 = dx^2 + dy^2$. Let's consider the transformation $f(x,y) = (x_0 + x, y_0 - y)$ and find the conditions on $x_0$ and $y_0$ for it to be an isometry.<br><br>First, let's compute the differential of the transformation:<br><br>$$df = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} dx \\ dy \end{pmatrix} = \begin{pmatrix} dx \\ -dy \end{pmatrix}$$<br><br>Now, let's compute the metric under this transformation:<br><br>$$ds'^2 = (dx')^2 + (dy')^2 = dx^2 + (-dy)^2 = dx^2 + dy^2$$<br><br>Since $ds'^2 = ds^2$, the transformation $f(x,y) = (x_0 + x, y_0 - y)$ is an isometry.<br><br>Now, let's find the conditions on $x_0$ and $y_0$ such that the isometry maps $(0,0)$ to $(x_0, y_0)$. Applying the transformation to $(0,0)$, we get:<br><br>$$f(0,0) = (x_0 + 0, y_0 - 0) = (x_0, y_0)$$<br><br>Since the transformation maps $(0,0)$ to $(x_0, y_0)$, there are no additional conditions...</code> |
  | <code>Represent this question for retrieving relevant documents: Do two di-leucine motifs regulate trafficking and function of mouse ASIC2a?</code>                                                                                                                                                                                                          | <code>Acid-sensing ion channels (ASICs) are proton-gated cation channels that mediate acid-induced responses in neurons. ASICs are important for mechanosensation, learning and memory, fear, pain, and neuronal injury. ASIC2a is widely expressed in the nervous system and modulates ASIC channel trafficking and activity in both central and peripheral systems. Here, to better understand mechanisms regulating ASIC2a, we searched for potential protein motifs that regulate ASIC2a trafficking.</code>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |
* Loss: [<code>MultipleNegativesRankingLoss</code>](https://sbert.net/docs/package_reference/sentence_transformer/losses.html#multiplenegativesrankingloss) with these parameters:
  ```json
  {
      "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
- `batch_sampler`: no_duplicates
- `multi_dataset_batch_sampler`: round_robin

#### All Hyperparameters
<details><summary>Click to expand</summary>

- `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
- `num_train_epochs`: 1
- `max_steps`: -1
- `lr_scheduler_type`: linear
- `lr_scheduler_kwargs`: {}
- `warmup_ratio`: 0.0
- `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`: 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}
- `tp_size`: 0
- `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
- `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`: no_duplicates
- `multi_dataset_batch_sampler`: round_robin

</details>

### Training Logs
| Epoch  | Step | Training Loss | ir-eval_cosine_ndcg@10 |
|:------:|:----:|:-------------:|:----------------------:|
| 0.1631 | 500  | 0.021         | 0.9523                 |
| 0.3262 | 1000 | 0.0069        | 0.9600                 |
| 0.4892 | 1500 | 0.0051        | 0.9593                 |
| 0.6523 | 2000 | 0.0055        | 0.9605                 |
| 0.8154 | 2500 | 0.0053        | 0.9638                 |
| 0.9785 | 3000 | 0.0056        | 0.9634                 |
| 1.0    | 3066 | -             | 0.9635                 |


### Framework Versions
- Python: 3.12.8
- Sentence Transformers: 3.4.1
- Transformers: 4.51.3
- PyTorch: 2.5.1+cu124
- Accelerate: 1.3.0
- Datasets: 3.2.0
- Tokenizers: 0.21.0

## Citation

### BibTeX

#### Sentence Transformers
```bibtex
@inproceedings{reimers-2019-sentence-bert,
    title = "Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks",
    author = "Reimers, Nils and Gurevych, Iryna",
    booktitle = "Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing",
    month = "11",
    year = "2019",
    publisher = "Association for Computational Linguistics",
    url = "https://arxiv.org/abs/1908.10084",
}
```

#### MultipleNegativesRankingLoss
```bibtex
@misc{henderson2017efficient,
    title={Efficient Natural Language Response Suggestion for Smart Reply},
    author={Matthew Henderson and Rami Al-Rfou and Brian Strope and Yun-hsuan Sung and Laszlo Lukacs and Ruiqi Guo and Sanjiv Kumar and Balint Miklos and Ray Kurzweil},
    year={2017},
    eprint={1705.00652},
    archivePrefix={arXiv},
    primaryClass={cs.CL}
}
```

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