metadata
base_model: BAAI/bge-base-en-v1.5
language:
- en
library_name: sentence-transformers
license: apache-2.0
metrics:
- cosine_accuracy@1
- cosine_accuracy@3
- cosine_accuracy@5
- cosine_accuracy@10
- cosine_precision@1
- cosine_precision@3
- cosine_precision@5
- cosine_precision@10
- cosine_recall@1
- cosine_recall@3
- cosine_recall@5
- cosine_recall@10
- cosine_ndcg@10
- cosine_mrr@10
- cosine_map@100
pipeline_tag: sentence-similarity
tags:
- sentence-transformers
- sentence-similarity
- feature-extraction
- generated_from_trainer
- dataset_size:3078
- loss:MatryoshkaLoss
- loss:MultipleNegativesRankingLoss
widget:
- source_sentence: >-
[ q_{\text{ut}} = \frac{1}{2} \rho g B N_{\gamma} + c N_{c} + (p_{q} +
\rho g D_{f}) N_{q} \quad \text{[SI]} \quad (36.1a) ] [ q_{\text{ut}} =
\frac{1}{2} \gamma B N_{\gamma} + c N_{c} + (p_{q} + \gamma D_{f}) N_{q}
\quad \text{[U.S.]} \quad (36.1b) ]
Various researchers have made improvements on the theory supporting this
equation, leading to somewhat different terms and sophistication in
evaluating (N_0), (N_c), and (N_g). The approaches differ in the
assumptions made of the shape of the failure zone beneath the footing.
However, the general form of the equation is the same in most cases.
Figure 36.2 and Table 36.2 can be used to evaluate the capacity factors
(N_0), (N_c), and (N_g) in Equation 36.1. Alternatively, Table 36.3 can be
used. The bearing capacity factors in Table 36.2 are based on Terzaghi's
1943 studies. The values in Table 36.3 are based on Meyerhof's 1955
studies and others, and have been widely used. Other values are also in
use.
Equation 36.1 is appropriate for a foundation in a continuous wall
footing. Corrections, called shape factors, for various footing geometries
are presented in Table 36.4 and Table 36.5 using the parameters identified
in Figure 36.3. The bearing capacity factors (N_c) and (N_0) are
multiplied by the appropriate shape factors when they are used in Equation
36.1.
Several researchers have recommended corrections to (N_0) to account for
footing depth. (Corrections to (N_0) for footing depth have also been
suggested. No corrections to (N_c) for footing depth have been suggested.)
There is considerable variation in the method of calculating this
correction if it is used at all. A multiplicative correction factor,
(d_c), which is used most often, has the form:
[ d_{c} = 1 + \frac{K D_{f}}{B} ]
(K) is a constant for which values of 0.2 and 0.4 have been proposed. The
depth factor correction is applied to (N_0) along with the shape factor
correction in Equation 36.1. Once the ultimate bearing capacity is
determined, it is corrected by the overburden, giving the net bearing
capacity. This is the net pressure the soil can support beyond the
pressure applied by the existing overburden.
[ q_{\text{net}} = q_{\text{ult}} - \rho g D_{f} \quad \text{[SI]} \quad
(36.3a) ] [ q_{\text{net}} = q_{\text{ut}} - \gamma D_{f} \quad
\text{[U.S.]} \quad (36.3b) ]
[ \begin{array}{r l}{{\mathrm{[U.S.]}}}&{{}36.3(b)}\end{array} ]
[ q_{\text{net}} = q_{\text{ult}} - \gamma D_{f} ]
Figure 36.2: Terzaghi Bearing Capacity Factors
sentences:
- What does the net bearing capacity represent in foundation engineering?
- >-
Can anyone explain the difference between ductility and percent
elongation?
- How do you compute the inverse of a 3x3 matrix?
- source_sentence: >-
Backwashing with filtered water pumped back through the filter from the
bottom to the top expands the sand layer by 30-50%, which dislodges
trapped material. Backwashing for 3-5 minutes at a rate of 8-15 gpm/ft²
(5.4-10 L/s-m²) is a typical specification. The head loss is reduced to
approximately 1 ft (0.3 m) after washing. Experience has shown that
supplementary agitation of the filter media is necessary to prevent
"caking" and "mudballs" in almost all installations. Prior to backwashing,
the filter material may be expanded by an air prewash volume of 1-8 (2-5
typical) times the sand filter volume per minute for 2-10 minutes (3-5
minutes typical). Alternatively, turbulence in the filter material may be
encouraged during backwashing with an air wash or with rotating hydraulic
surface jets.
During backwashing, the water in the filter housing will rise at a rate of
1-3 ft/min (0.5-1.5 cm/s). This rise should not exceed the settling
velocity of the smallest particle that is to be retained in the filter.
The wash water, which is collected in troughs for disposal, constitutes
approximately 1-5% of the total processed water. The total water used is
approximately 75-100 gal/ft² (3-4 kL/m²). The actual amount of backwash
water is given by the equation:
$$ V = A_{\text{filter}} \cdot (\text{rate of rise}) \cdot
t_{\text{backwash}} $$
The temperature of the water used in backwashing is important since
viscosity changes with temperature (the effect of temperature on water
density is negligible). Water at 40°F (4°C) is more viscous than water at
70°F (21°C). Therefore, media particles may be expanded to the same extent
using lower upflow rates at lower backwash temperatures. ```markdown
26. Other Filtration Methods
Pressure (sand) filters for water supply treatment operate similarly to
rapid sand filters except that incoming water is typically pressurized to
25-75 psig (170-520 kPa gage). Single media filter rates are typically 4-5
gpm/ft² (1.4-14 L/s-m²), with 2-10 gpm/ft² (2.7-3.4 L/s-m² typical), while
dual media filters run at 1.5 to 2.0 times these rates. Pressure filters
are not used in large installations.
Ultrafilters are membranes that act as sieves to retain turbidity,
microorganisms, and large organic molecules that are THM precursors, while
allowing water, salts, and small molecules to pass through.
Ultrafiltration is effective in removing particles ranging in size of
0.001 to 10 µm. A pressure of 15-75 psig (100-500 kPa) is required to
drive the water through the membrane.
Biofilm filtration (biofilm process) uses microorganisms to remove
selected contaminants (e.g., aromatics and other hydrocarbons). The
operation of biofilters is similar to trickling filters used in wastewater
processing. Sand filter facilities are relatively easy to modify—sand is
replaced with gravel in the 4-14 mm size range, application rates are
decreased, and exposure to chlorine from incoming and backwash water is
eliminated. While the maximum may never be used, a maximum backwash rate
of 20 gpm/ft² (14 L/s-m²) should be provided for. A µm is the same as a
micron.
sentences:
- How do I calculate the total water used for backwashing?
- >-
How do I calculate flow rate if the water depth is 5 ft and channel
width is 8 ft?
- >-
What is the formula for estimating the percent time spent following on
highways?
- source_sentence: >-
Here is the LaTeX representation of the angles and the radius of the
circle:
\begin{align} \alpha &= \angle PQR \ \beta &= \angle QNR \ \gamma &=
\angle RPN \ \end{align}
\begin{align} a &= \text{radius of the circle} \ I &= \text{line segment}
\ \end{align}
The figure also includes a dashed line representing a chord and a tangent
line from point P to the circle, with a point of tangency labeled 'T'. The
tangent line is perpendicular to the radius of the circle at point T.
Figure 79.5 Tangent and Chord Offset Geometry
The short chord distance is
[ \mathrm{NQ} = C = 2R \sin \alpha ] [ \mathrm{NP} = (2R \sin \alpha) \cos
\alpha = C \cos \alpha ] [ \mathrm{PQ} = (2R \sin \alpha) \sin \alpha = 2R
\sin^2 \alpha ]
\tag{79.23} \tag{79.24} \tag{79.25} ```
7. Curve Layout By Chord Offset
The chord offset method is a third method for laying out horizontal
curves. This method is also suitable for short curves. The method is named
for the way in which the measurements are made, which is by measuring
distances along the main chord from the instrument location at PC.
[ \mathrm{NR} = \mathrm{chord~distance} =
\mathrm{NQ}\cos\left({\frac{I}{2}} - \alpha\right) ]
[ \sqrt{2} = (2R\sin\alpha)\cos\left(\frac{I}{2} - \alpha\right) =
C\cos\left(\frac{I}{2} - \alpha\right) = (I - \alpha)^{2} ]
[ \mathrm{RQ} = \mathrm{chord~offset} =
\mathrm{NQ}~\sin\left({\frac{I}{2}} - \alpha\right) ]
[ = (2R\sin\alpha)\sin\left({\frac{I}{2}} - \alpha\right) =
C\sin\left({\frac{I}{2}} - \alpha\right) ]
[ 79.27 ]
8. Horizontal Curves Through Points
Occasionally, it is necessary to design a horizontal curve to pass through
a specific point. The following procedure can be used. (Refer to Fig.
79.6.)
Step 1: Calculate ( \alpha ) and ( m ) from ( x ) and ( y ). (If ( x ) and
( m ) are known, skip this step.) [ \alpha =
\arctan\left(\frac{y}{x}\right) ] [ m = \sqrt{x^{2} + y^{2}} ]
Step 2: Calculate ( y ). Since ( 90^\circ + \frac{I}{2} + \alpha =
180^\circ ), [ \gamma = 90^\circ - \frac{I}{2} - \alpha ]
Step 3: Calculate ( \phi ). [ \phi = 180^\circ -
\arcsin\left(\frac{\sin\gamma}{\cos\left(\frac{I}{2}\right)}\right) ] [ =
180^\circ - \gamma - \phi ]
Step 4: Calculate ( O ). (Refer to Eq. 79.32)
sentences:
- >-
What's the difference between horizontal and vertical parabolas in their
equations?
- What does the distance of 50 ft represent in the wave illustration?
- >-
What is the relationship between tangent lines and radius in circular
geometry?
- source_sentence: >-
Description: The image provided is not clear enough to discern any
specific details, text, or formulas. It appears to be a blurred image with
no distinguishable content. Therefore, I cannot extract any formulas or
provide a description of the image content.
Unfortunately, it is extremely difficult to prove compensatory fraud
(i.e., fraud for which damages are available). Proving fraud requires
showing beyond a reasonable doubt (a) a reckless or intentional
misstatement of a material fact, (b) an intention to deceive, (c) it
resulted in misleading the innocent party to contract, and (d) it was to
the innocent party's detriment. For example, if an engineer claims to have
experience in designing steel buildings but actually has none, the court
might consider the misrepresentation a fraudulent action. If, however, the
engineer has some experience, but an insufficient amount to do an adequate
job, the engineer probably will not be considered to have acted
fraudulently.
Torts
A tort is a civil wrong committed by one person causing lamage to another
person or person's property, emoional well-being, or reputation.11 It is a
breach of the ights of an individual to be secure in person or propxty. In
order to correct the wrong, a civil lawsuit (tort iction or civil
complaint) is brought by the alleged njured party (the plaintiff) against
the defendant. To be a valid tort action (i.e., lawsuit), there must have
been injury (i.e., damage). Generally, there will be no contract between
the two parties, so the tort action annot claim a breach of contract. 12
Cort law is concerned with compensation for the injury, not punishment.
Therefore, tort awards usually consist
f general, compensatory, and special damages and arely include punitive
and exemplary damages. (See Damages" for definitions of these damages.)
Strict Liability In Tort
itrict liability in tort means that the injured party wins f the injury
can be proven. It is not necessary to prove egligence, breach of explicit
or implicit warranty, or he existence of a contract (privity of contract).
Strict ability in tort is most commonly encountered in prodct liability
cases. A defect in a product, regardless of ow the defect got there, is
sufficient to create strict ability in tort.
lase law surrounding defective products has developed nd refined the
following requirements for winning a trict liability in tort case. The
following points must e proved.
The difference between a civil tort (lausuit) and a criminal lausuit is ie
alleged injured party. A crime is a wrong against society. A iminal
lawsuit is brought by the state against a defendant.
It is possible for an injury to be both a breach of contract and a tort.
ippose an owner has an agreement with a contractor to construct a ilding,
and the contract requires the contractor to comply with all ate and
federal safety regulations. If the owner is subsequently jured on a
stairway because there was no guardrail, the injury could · recoverable
both as a tort and as a breach of contract. If a third irty unrelated to
the contract was injured, however, that party could cover only through a
tort action. · The product was defective in manufacture, design, labeling,
and so on.
The product was defective when used.
The defect rendered the product unreasonably dangerous.
The defect caused the injury. .
The specific use of the product that caused the damage was reasonably
foreseeable.
Manufacturing And Design Liability
sentences:
- >-
What factors influence the instantaneous center of rotation in welded
structures?
- How do you establish if fraud has occurred in a contract?
- How do you calculate the probability of multiple events happening?
- source_sentence: >-
9. Area
Equation 9.35 calculates the area, ( A ), bounded by ( x = a ), ( x = b ),
( f_1(x) ) above, and ( f_2(x) ) below. (Note: ( f_2(x) = 0 ) if the area
is bounded by the x-axis.) This is illustrated in Fig. 9.1. [ A =
\int_{a}^{b} \left( f_{1}(x) - f_{2}(x) \right) \, dx \qquad \qquad (9.35)
] Figure 9.1 Area Between Two Curves
Description: The image shows a graph with two curves labeled f1(x) and
f2(x). The graph is plotted on a Cartesian coordinate system with an
x-axis and a y-axis. There are two vertical dashed lines intersecting the
x-axis at points labeled 'a' and 'b'. The curve f1(x) is above the line y
= 0 and the curve f2(x) is below the line y = 0. The area between the two
curves from x = a to x = b is shaded, indicating a region of interest or
calculation.
The LaTeX representation of the curves is not provided in the image, so I
cannot write them in LaTeX form. However, if the curves were described by
functions, they could be represented as follows:
f1(x) could be represented as ( f_1(x) = ax^2 + bx + c ) for some
constants a, b, and c.
f2(x) could be represented as ( f_2(x) = -ax^2 - bx - c ) for some
constants a, b, and c.
The area between the curves from x = a to x = b could be calculated using
the integral of the difference between the two functions over the interval
[a, b].
Description: The image provided is not clear enough to describe in detail
or to extract any formulas. The text is not legible, and no other
discernible features can be identified.
Find the area between the x-axis and the parabola ( y = x^2 ) in the
interval ([0, 4]).
Description: The image shows a graph with a curve that represents a
function y = x^2. There is a vertical dashed line at x = 4, indicating a
point of interest or a specific value on the x-axis. The graph is plotted
on a Cartesian coordinate system with the x-axis labeled 'x' and the
y-axis labeled 'y'. The curve is a parabola that opens upwards, showing
that as x increases, y increases at an increasing rate. The point where x
= 4 is marked on the x-axis, and the corresponding y-value on the curve is
not explicitly shown but can be inferred from the equation y = x^2.
Solution: Referring to Eq. 9.35, [ f_{1}(x) = x^{2} \quad \text{and} \quad
f_{2}(x) = 0 ] Thus, [ A = \int_{a}^{b} \left( f_1(x) - f_2(x) \right) dx
= \int_{0}^{4} x^2 \, dx = \left[ \frac{x^3}{3} \right]_{0}^{4} =
\frac{64}{3} ] ...
10. Arc Length
sentences:
- >-
Can you show me how to find the area using the integral of the
difference of two functions?
- >-
Can you explain how to calculate the force BC using trigonometric
components?
- >-
What is the minimum requirement for steel area in slab reinforcement
according to ACI guidelines?
model-index:
- name: deep learning project
results:
- task:
type: information-retrieval
name: Information Retrieval
dataset:
name: dim 768
type: dim_768
metrics:
- type: cosine_accuracy@1
value: 0.2543859649122807
name: Cosine Accuracy@1
- type: cosine_accuracy@3
value: 0.5789473684210527
name: Cosine Accuracy@3
- type: cosine_accuracy@5
value: 0.7017543859649122
name: Cosine Accuracy@5
- type: cosine_accuracy@10
value: 0.7982456140350878
name: Cosine Accuracy@10
- type: cosine_precision@1
value: 0.2543859649122807
name: Cosine Precision@1
- type: cosine_precision@3
value: 0.19298245614035087
name: Cosine Precision@3
- type: cosine_precision@5
value: 0.14035087719298245
name: Cosine Precision@5
- type: cosine_precision@10
value: 0.07982456140350876
name: Cosine Precision@10
- type: cosine_recall@1
value: 0.2543859649122807
name: Cosine Recall@1
- type: cosine_recall@3
value: 0.5789473684210527
name: Cosine Recall@3
- type: cosine_recall@5
value: 0.7017543859649122
name: Cosine Recall@5
- type: cosine_recall@10
value: 0.7982456140350878
name: Cosine Recall@10
- type: cosine_ndcg@10
value: 0.5289463979794752
name: Cosine Ndcg@10
- type: cosine_mrr@10
value: 0.4422630650700826
name: Cosine Mrr@10
- type: cosine_map@100
value: 0.45071327302764325
name: Cosine Map@100
- task:
type: information-retrieval
name: Information Retrieval
dataset:
name: dim 512
type: dim_512
metrics:
- type: cosine_accuracy@1
value: 0.2631578947368421
name: Cosine Accuracy@1
- type: cosine_accuracy@3
value: 0.5760233918128655
name: Cosine Accuracy@3
- type: cosine_accuracy@5
value: 0.695906432748538
name: Cosine Accuracy@5
- type: cosine_accuracy@10
value: 0.783625730994152
name: Cosine Accuracy@10
- type: cosine_precision@1
value: 0.2631578947368421
name: Cosine Precision@1
- type: cosine_precision@3
value: 0.19200779727095513
name: Cosine Precision@3
- type: cosine_precision@5
value: 0.13918128654970757
name: Cosine Precision@5
- type: cosine_precision@10
value: 0.0783625730994152
name: Cosine Precision@10
- type: cosine_recall@1
value: 0.2631578947368421
name: Cosine Recall@1
- type: cosine_recall@3
value: 0.5760233918128655
name: Cosine Recall@3
- type: cosine_recall@5
value: 0.695906432748538
name: Cosine Recall@5
- type: cosine_recall@10
value: 0.783625730994152
name: Cosine Recall@10
- type: cosine_ndcg@10
value: 0.525405284677311
name: Cosine Ndcg@10
- type: cosine_mrr@10
value: 0.4422096908939014
name: Cosine Mrr@10
- type: cosine_map@100
value: 0.45077185641932777
name: Cosine Map@100
- task:
type: information-retrieval
name: Information Retrieval
dataset:
name: dim 256
type: dim_256
metrics:
- type: cosine_accuracy@1
value: 0.260233918128655
name: Cosine Accuracy@1
- type: cosine_accuracy@3
value: 0.5526315789473685
name: Cosine Accuracy@3
- type: cosine_accuracy@5
value: 0.6754385964912281
name: Cosine Accuracy@5
- type: cosine_accuracy@10
value: 0.7573099415204678
name: Cosine Accuracy@10
- type: cosine_precision@1
value: 0.260233918128655
name: Cosine Precision@1
- type: cosine_precision@3
value: 0.18421052631578946
name: Cosine Precision@3
- type: cosine_precision@5
value: 0.1350877192982456
name: Cosine Precision@5
- type: cosine_precision@10
value: 0.07573099415204677
name: Cosine Precision@10
- type: cosine_recall@1
value: 0.260233918128655
name: Cosine Recall@1
- type: cosine_recall@3
value: 0.5526315789473685
name: Cosine Recall@3
- type: cosine_recall@5
value: 0.6754385964912281
name: Cosine Recall@5
- type: cosine_recall@10
value: 0.7573099415204678
name: Cosine Recall@10
- type: cosine_ndcg@10
value: 0.5082788808907895
name: Cosine Ndcg@10
- type: cosine_mrr@10
value: 0.4281189083820665
name: Cosine Mrr@10
- type: cosine_map@100
value: 0.4372871346521922
name: Cosine Map@100
- task:
type: information-retrieval
name: Information Retrieval
dataset:
name: dim 128
type: dim_128
metrics:
- type: cosine_accuracy@1
value: 0.2134502923976608
name: Cosine Accuracy@1
- type: cosine_accuracy@3
value: 0.5116959064327485
name: Cosine Accuracy@3
- type: cosine_accuracy@5
value: 0.6403508771929824
name: Cosine Accuracy@5
- type: cosine_accuracy@10
value: 0.7368421052631579
name: Cosine Accuracy@10
- type: cosine_precision@1
value: 0.2134502923976608
name: Cosine Precision@1
- type: cosine_precision@3
value: 0.1705653021442495
name: Cosine Precision@3
- type: cosine_precision@5
value: 0.12807017543859647
name: Cosine Precision@5
- type: cosine_precision@10
value: 0.07368421052631578
name: Cosine Precision@10
- type: cosine_recall@1
value: 0.2134502923976608
name: Cosine Recall@1
- type: cosine_recall@3
value: 0.5116959064327485
name: Cosine Recall@3
- type: cosine_recall@5
value: 0.6403508771929824
name: Cosine Recall@5
- type: cosine_recall@10
value: 0.7368421052631579
name: Cosine Recall@10
- type: cosine_ndcg@10
value: 0.4726924534205871
name: Cosine Ndcg@10
- type: cosine_mrr@10
value: 0.3880070546737214
name: Cosine Mrr@10
- type: cosine_map@100
value: 0.39701781193586744
name: Cosine Map@100
- task:
type: information-retrieval
name: Information Retrieval
dataset:
name: dim 64
type: dim_64
metrics:
- type: cosine_accuracy@1
value: 0.1871345029239766
name: Cosine Accuracy@1
- type: cosine_accuracy@3
value: 0.47076023391812866
name: Cosine Accuracy@3
- type: cosine_accuracy@5
value: 0.5789473684210527
name: Cosine Accuracy@5
- type: cosine_accuracy@10
value: 0.6695906432748538
name: Cosine Accuracy@10
- type: cosine_precision@1
value: 0.1871345029239766
name: Cosine Precision@1
- type: cosine_precision@3
value: 0.15692007797270952
name: Cosine Precision@3
- type: cosine_precision@5
value: 0.11578947368421051
name: Cosine Precision@5
- type: cosine_precision@10
value: 0.06695906432748537
name: Cosine Precision@10
- type: cosine_recall@1
value: 0.1871345029239766
name: Cosine Recall@1
- type: cosine_recall@3
value: 0.47076023391812866
name: Cosine Recall@3
- type: cosine_recall@5
value: 0.5789473684210527
name: Cosine Recall@5
- type: cosine_recall@10
value: 0.6695906432748538
name: Cosine Recall@10
- type: cosine_ndcg@10
value: 0.42447214920635656
name: Cosine Ndcg@10
- type: cosine_mrr@10
value: 0.3461802654785111
name: Cosine Mrr@10
- type: cosine_map@100
value: 0.3562882551304709
name: Cosine Map@100
deep learning project
This is a sentence-transformers model finetuned from BAAI/bge-base-en-v1.5 on the json dataset. It maps sentences & paragraphs to a 768-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-base-en-v1.5
- Maximum Sequence Length: 512 tokens
- Output Dimensionality: 768 dimensions
- Similarity Function: Cosine Similarity
- Training Dataset:
- json
- Language: en
- License: apache-2.0
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': True}) with Transformer model: BertModel
(1): Pooling({'word_embedding_dimension': 768, '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:
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("bbmb/deep-learning-for-embedding-model-ssilwal-qpham6")
# Run inference
sentences = [
"9. Area\n\nEquation 9.35 calculates the area, ( A ), bounded by ( x = a ), ( x = b ), ( f_1(x) ) above, and ( f_2(x) ) below. (Note: ( f_2(x) = 0 ) if the area is bounded by the x-axis.) This is illustrated in Fig. 9.1. [ A = \\int_{a}^{b} \\left( f_{1}(x) - f_{2}(x) \\right) \\, dx \\qquad \\qquad (9.35) ] Figure 9.1 Area Between Two Curves\n\nDescription: The image shows a graph with two curves labeled f1(x) and f2(x). The graph is plotted on a Cartesian coordinate system with an x-axis and a y-axis. There are two vertical dashed lines intersecting the x-axis at points labeled 'a' and 'b'. The curve f1(x) is above the line y = 0 and the curve f2(x) is below the line y = 0. The area between the two curves from x = a to x = b is shaded, indicating a region of interest or calculation.\n\nThe LaTeX representation of the curves is not provided in the image, so I cannot write them in LaTeX form. However, if the curves were described by functions, they could be represented as follows:\n\nf1(x) could be represented as ( f_1(x) = ax^2 + bx + c ) for some constants a, b, and c.\n\nf2(x) could be represented as ( f_2(x) = -ax^2 - bx - c ) for some constants a, b, and c.\n\nThe area between the curves from x = a to x = b could be calculated using the integral of the difference between the two functions over the interval [a, b].\n\nDescription: The image provided is not clear enough to describe in detail or to extract any formulas. The text is not legible, and no other discernible features can be identified.\n\nFind the area between the x-axis and the parabola ( y = x^2 ) in the interval ([0, 4]).\n\nDescription: The image shows a graph with a curve that represents a function y = x^2. There is a vertical dashed line at x = 4, indicating a point of interest or a specific value on the x-axis. The graph is plotted on a Cartesian coordinate system with the x-axis labeled 'x' and the y-axis labeled 'y'. The curve is a parabola that opens upwards, showing that as x increases, y increases at an increasing rate. The point where x = 4 is marked on the x-axis, and the corresponding y-value on the curve is not explicitly shown but can be inferred from the equation y = x^2.\n\nSolution: Referring to Eq. 9.35, [ f_{1}(x) = x^{2} \\quad \\text{and} \\quad f_{2}(x) = 0 ] Thus, [ A = \\int_{a}^{b} \\left( f_1(x) - f_2(x) \\right) dx = \\int_{0}^{4} x^2 \\, dx = \\left[ \\frac{x^3}{3} \\right]_{0}^{4} = \\frac{64}{3} ] ...\n\n10. Arc Length",
'Can you show me how to find the area using the integral of the difference of two functions?',
'What is the minimum requirement for steel area in slab reinforcement according to ACI guidelines?',
]
embeddings = model.encode(sentences)
print(embeddings.shape)
# [3, 768]
# Get the similarity scores for the embeddings
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [3, 3]
Evaluation
Metrics
Information Retrieval
- Datasets:
dim_768,dim_512,dim_256,dim_128anddim_64 - Evaluated with
InformationRetrievalEvaluator
| Metric | dim_768 | dim_512 | dim_256 | dim_128 | dim_64 |
|---|---|---|---|---|---|
| cosine_accuracy@1 | 0.2544 | 0.2632 | 0.2602 | 0.2135 | 0.1871 |
| cosine_accuracy@3 | 0.5789 | 0.576 | 0.5526 | 0.5117 | 0.4708 |
| cosine_accuracy@5 | 0.7018 | 0.6959 | 0.6754 | 0.6404 | 0.5789 |
| cosine_accuracy@10 | 0.7982 | 0.7836 | 0.7573 | 0.7368 | 0.6696 |
| cosine_precision@1 | 0.2544 | 0.2632 | 0.2602 | 0.2135 | 0.1871 |
| cosine_precision@3 | 0.193 | 0.192 | 0.1842 | 0.1706 | 0.1569 |
| cosine_precision@5 | 0.1404 | 0.1392 | 0.1351 | 0.1281 | 0.1158 |
| cosine_precision@10 | 0.0798 | 0.0784 | 0.0757 | 0.0737 | 0.067 |
| cosine_recall@1 | 0.2544 | 0.2632 | 0.2602 | 0.2135 | 0.1871 |
| cosine_recall@3 | 0.5789 | 0.576 | 0.5526 | 0.5117 | 0.4708 |
| cosine_recall@5 | 0.7018 | 0.6959 | 0.6754 | 0.6404 | 0.5789 |
| cosine_recall@10 | 0.7982 | 0.7836 | 0.7573 | 0.7368 | 0.6696 |
| cosine_ndcg@10 | 0.5289 | 0.5254 | 0.5083 | 0.4727 | 0.4245 |
| cosine_mrr@10 | 0.4423 | 0.4422 | 0.4281 | 0.388 | 0.3462 |
| cosine_map@100 | 0.4507 | 0.4508 | 0.4373 | 0.397 | 0.3563 |
Training Details
Training Dataset
json
- Dataset: json
- Size: 3,078 training samples
- Columns:
positiveandanchor - Approximate statistics based on the first 1000 samples:
positive anchor type string string details - min: 117 tokens
- mean: 508.1 tokens
- max: 512 tokens
- min: 8 tokens
- mean: 15.93 tokens
- max: 28 tokens
- Samples:
positive anchor The PHF is used to convert hourly volumes to flow rates and represents the hourly variation in traffic flow. If the demand volume is measured in 15 min increments, it is unnecessary to use the PHF to convert to flow rates.
Therefore, since two-lane highway analysis is based on demand flow rates for a peak 15 min period within the analysis hour (usually the peak hour), the PHF in Equation 73.22 and Equation 73.23 is given a value of 1.00.
The average travel speed in the analysis direction, ( ATS_d ), is estimated from the FFS, the demand flow rate, the opposing flow rate, and the adjustment factor for the percentage of no-passing zones in the analysis direction, ( f_{np} ), as given in HCM Exh. 15-15. Equation 73.24 only applies to Class I and Class III two-lane highways.
[ \mathrm{ATS}{d} = \mathrm{FFS} - 0.0076(v{d,s} + v_{o,s}) - f_{\mathrm{np},s} \quad (73.24) ]
If the PTSF methodology is used, the formula for the demand flow rate, ( v_{i, \text{ATS}} ), is the same, although di...What is the formula for estimating the percent time spent following on highways?However, if the initial point on the limb is close to the critical point (i.e., the nose of the curve), then a small change in the specific energy (such as might be caused by a small variation in the channel floor) will cause a large change in depth. That is why severe turbulence commonly occurs near points of critical flow. Given that ( 4 , \text{ft/sec} ) (or ( 1.2 , \text{m/s} )) of water flows in a ( 7 , \text{ft} ) (or ( 2.1 , \text{m} )) wide, ( 6 , \text{ft} ) (or ( 1.8 , \text{m} )) deep open channel, the flow encounters a ( 1.0 , \text{ft} ) (or ( 0.3 , \text{m} )) step in the channel bottom. What is the depth of flow above the step? Actually, specific energy curves are typically plotted for flow per unit width, ( q = \frac{Q}{w} ). If that is the case, a jump from one limb to the other could take place if the width were allowed to change as well as the depth. A rise in the channel bottom does not always produce a drop in the water surface. Only if the flow is initiall...What happens to the water depth when it encounters a step in a channel?The shear strength, ( S ) or ( S_{ys} ), of a material is the maximum shear stress that the material can support without yielding in shear. (The ultimate shear strength, ( S_{us} ), is rarely encountered.) For ductile materials, maximum shear stress theory predicts the shear strength as one-half of the tensile yield strength. A more accurate relationship is derived from the distortion energy theory (also known as von Mises theory).
Figure 43.16: Uniform Bar in Torsion
Description: The image shows a diagram of a mechanical system with a cylindrical object, a rod, and a spring. There are two forces acting on the system: one is the weight of the rod, labeled 'L', acting downwards, and the other is the spring force, labeled 'T', acting upwards. The rod is shown to be in equilibrium, with the spring force balancing the weight of the rod. The distance from the pivot point to the center of mass of the rod is labeled 'r'. There is also a variable 'y' indicating the vertical displacement of t...Can you explain what maximum shear stress theory is? - Loss:
MatryoshkaLosswith these parameters:{ "loss": "MultipleNegativesRankingLoss", "matryoshka_dims": [ 768, 512, 256, 128, 64 ], "matryoshka_weights": [ 1, 1, 1, 1, 1 ], "n_dims_per_step": -1 }
Training Hyperparameters
Non-Default Hyperparameters
eval_strategy: epochper_device_train_batch_size: 32per_device_eval_batch_size: 16gradient_accumulation_steps: 16learning_rate: 2e-05num_train_epochs: 4lr_scheduler_type: cosinewarmup_ratio: 0.1bf16: Truetf32: Trueload_best_model_at_end: Trueoptim: adamw_torch_fusedbatch_sampler: no_duplicates
All Hyperparameters
Click to expand
overwrite_output_dir: Falsedo_predict: Falseeval_strategy: epochprediction_loss_only: Trueper_device_train_batch_size: 32per_device_eval_batch_size: 16per_gpu_train_batch_size: Noneper_gpu_eval_batch_size: Nonegradient_accumulation_steps: 16eval_accumulation_steps: Nonelearning_rate: 2e-05weight_decay: 0.0adam_beta1: 0.9adam_beta2: 0.999adam_epsilon: 1e-08max_grad_norm: 1.0num_train_epochs: 4max_steps: -1lr_scheduler_type: cosinelr_scheduler_kwargs: {}warmup_ratio: 0.1warmup_steps: 0log_level: passivelog_level_replica: warninglog_on_each_node: Truelogging_nan_inf_filter: Truesave_safetensors: Truesave_on_each_node: Falsesave_only_model: Falserestore_callback_states_from_checkpoint: Falseno_cuda: Falseuse_cpu: Falseuse_mps_device: Falseseed: 42data_seed: Nonejit_mode_eval: Falseuse_ipex: Falsebf16: Truefp16: Falsefp16_opt_level: O1half_precision_backend: autobf16_full_eval: Falsefp16_full_eval: Falsetf32: Truelocal_rank: 0ddp_backend: Nonetpu_num_cores: Nonetpu_metrics_debug: Falsedebug: []dataloader_drop_last: Falsedataloader_num_workers: 0dataloader_prefetch_factor: Nonepast_index: -1disable_tqdm: Falseremove_unused_columns: Truelabel_names: Noneload_best_model_at_end: Trueignore_data_skip: Falsefsdp: []fsdp_min_num_params: 0fsdp_config: {'min_num_params': 0, 'xla': False, 'xla_fsdp_v2': False, 'xla_fsdp_grad_ckpt': False}fsdp_transformer_layer_cls_to_wrap: Noneaccelerator_config: {'split_batches': False, 'dispatch_batches': None, 'even_batches': True, 'use_seedable_sampler': True, 'non_blocking': False, 'gradient_accumulation_kwargs': None}deepspeed: Nonelabel_smoothing_factor: 0.0optim: adamw_torch_fusedoptim_args: Noneadafactor: Falsegroup_by_length: Falselength_column_name: lengthddp_find_unused_parameters: Noneddp_bucket_cap_mb: Noneddp_broadcast_buffers: Falsedataloader_pin_memory: Truedataloader_persistent_workers: Falseskip_memory_metrics: Trueuse_legacy_prediction_loop: Falsepush_to_hub: Falseresume_from_checkpoint: Nonehub_model_id: Nonehub_strategy: every_savehub_private_repo: Falsehub_always_push: Falsegradient_checkpointing: Falsegradient_checkpointing_kwargs: Noneinclude_inputs_for_metrics: Falseeval_do_concat_batches: Truefp16_backend: autopush_to_hub_model_id: Nonepush_to_hub_organization: Nonemp_parameters:auto_find_batch_size: Falsefull_determinism: Falsetorchdynamo: Noneray_scope: lastddp_timeout: 1800torch_compile: Falsetorch_compile_backend: Nonetorch_compile_mode: Nonedispatch_batches: Nonesplit_batches: Noneinclude_tokens_per_second: Falseinclude_num_input_tokens_seen: Falseneftune_noise_alpha: Noneoptim_target_modules: Nonebatch_eval_metrics: Falseprompts: Nonebatch_sampler: no_duplicatesmulti_dataset_batch_sampler: proportional
Training Logs
| Epoch | Step | Training Loss | dim_768_cosine_ndcg@10 | dim_512_cosine_ndcg@10 | dim_256_cosine_ndcg@10 | dim_128_cosine_ndcg@10 | dim_64_cosine_ndcg@10 |
|---|---|---|---|---|---|---|---|
| 0.9897 | 6 | - | 0.5417 | 0.5428 | 0.5145 | 0.4630 | 0.3945 |
| 1.6495 | 10 | 3.7867 | - | - | - | - | - |
| 1.9794 | 12 | - | 0.5269 | 0.5206 | 0.4992 | 0.4751 | 0.4082 |
| 2.9691 | 18 | - | 0.5298 | 0.5238 | 0.5107 | 0.4761 | 0.4268 |
| 3.2990 | 20 | 1.9199 | - | - | - | - | - |
| 3.9588 | 24 | - | 0.5289 | 0.5254 | 0.5083 | 0.4727 | 0.4245 |
- The bold row denotes the saved checkpoint.
Framework Versions
- Python: 3.10.12
- Sentence Transformers: 3.3.1
- Transformers: 4.41.2
- PyTorch: 2.1.2+cu121
- Accelerate: 0.34.2
- Datasets: 2.19.1
- 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",
}
MatryoshkaLoss
@misc{kusupati2024matryoshka,
title={Matryoshka Representation Learning},
author={Aditya Kusupati and Gantavya Bhatt and Aniket Rege and Matthew Wallingford and Aditya Sinha and Vivek Ramanujan and William Howard-Snyder and Kaifeng Chen and Sham Kakade and Prateek Jain and Ali Farhadi},
year={2024},
eprint={2205.13147},
archivePrefix={arXiv},
primaryClass={cs.LG}
}
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}
}