Model: cristiano-sartori/MNLP_M3_document_encoder
Author: cristiano-sartori
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:1137, loss:MatryoshkaLoss, loss:MultipleNegativesRankingLoss, en, arxiv:1908.10084, arxiv:2205.13147, arxiv:1705.00652, base_model:BAAI/bge-base-en-v1.5, base_model:finetune:BAAI/bge-base-en-v1.5, license:apache-2.0, model-index, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: BAAI/bge-base-en-v1.5
Card metadata: language: en
license: apache-2.0
tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:1137, loss:MatryoshkaLoss, loss:MultipleNegativesRankingLoss
base_model: BAAI/bge-base-en-v1.5
widget: source_sentence: Which of the following statements about the $\mathrm{SVD}$ of an $N \times D$ matrix $\mathbf{X}$ are correct?
A. [
B. '
C. W
D. e
E.  
D. c
F. a
G. n
H.  
I. c
sentences: The correct answer is **3. 1024 bits**.

**Reasoning:**
RSA (Rivest-Shamir-Adleman) is a widely used public-key cryptographic system that relies on the difficulty of factoring large integers. The size of the RSA modulus (the product of two large prime numbers) is crucial for the security of the encryption.

1. **64 bits**: This size is considered insecure and is far too small for any practical cryptographic application today. It can be easily factored with modern computing power.

2. **256 bits**: While this size is more secure than 64 bits, it is still not sufficient for RSA. A 256-bit key is more commonly associated with symmetric encryption algorithms like AES, not RSA.

3. **1024 bits**: This size was commonly used in practice for RSA keys for many years and is still considered secure for many applications, although it is becoming less common as security standards evolve. It strikes a balance between security and performance.

4. **8192 bits**: This size is much larger than what is typically used in practice. While it offers a very high level of security, it also results in significantly slower performance and is not necessary for most applications. 

As of now, many organizations are moving towards 2048 bits or even 3072 bits for RSA keys to ensure stronger security, but 1024 bits remains a common reference point for typical RSA modulus sizes in practice. Therefore, the best answer is **3. 1024 bits**., The correct statements about the SVD of an \( N \times D \) matrix \( \\mathbf{X} \) are:\n\n1. **We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X X}^{\\top} \). This has complexity \( O\\left(N^{3}\\right) \).**\n   \n   - This statement is correct if \( N \geq D \). The computation of the eigenvalues of \( \\mathbf{X X}^{\\top} \) involves an \( N \times N \) matrix, leading to a complexity of \( O(N^3) \).\n\n2. **We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X}^{\\top} \\mathbf{X} \). This has complexity \( O\\left(D^{3}\\right) \).**\n   \n   - This statement is correct if \( D \geq N \). The computation of the eigenvalues of \( \\mathbf{X}^{\\top} \\mathbf{X} \) involves a \( D \times D \) matrix, leading to a complexity of \( O(D^3) \).\n\nThe other statements are incorrect for the following reasons:\n\n- **We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X X}^{\\top} \). This has complexity \( O\\left(D^{3}\\right) \).**\n  \n  - Incorrect because it incorrectly states the complexity for \( \\mathbf{X X}^{\\top} \) when it should be \( O(N^3) \) if \( N \geq D \).\n\n- **We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X}^{\\top} \\mathbf{X} \). This has complexity \( O\\left(N^{3}\\right) \).**\n  \n  - Incorrect because it incorrectly states the complexity for \( \\mathbf{X}^{\\top} \\mathbf{X} \) when it should be \( O(D^3) \) if \( D \geq N \).\n\n- **We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X} \\mathbf{X}^{\\top} \) if only if \( \\mathbf{X} \) is a square matrix. This has complexity \( O\\left(D^{3}\\right)=O\\left(N^{3}\\right) \).**\n  \n  - Incorrect because you do not need \( \\mathbf{X} \) to be square to compute the SVD via \( \\mathbf{X X}^{\\top} \) or \( \\mathbf{X}^{\\top} \\mathbf{X} \). The complexities are not equal unless \( N = D \).\n\nIn summary, the correct statements are:\n1. "We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X X}^{\\top} \). This has complexity \( O\\left(N^{3}\\right) \)."\n2. "We can compute the singular values of \( \\mathbf{X} \) by computing the eigenvalues of \( \\mathbf{X}^{\\top} \\mathbf{X} \). This has complexity \( O\\left(D^{3}\\right) \).", To determine which of the given functions \( f : \mathbb{Z} \times \mathbb{Z} \to \mathbb{Z} \) are surjective, we need to check if every integer in the codomain \( \mathbb{Z} \) can be obtained by some input from \( \mathbb{Z} \times \mathbb{Z} \). Let's analyze each function one by one.

1. **\( f(m, n) = m + n \)**:
   - This function takes any two integers \( m \) and \( n \) and adds them together. 
   - For any integer \( k \), we can choose \( m = k \) and \( n = 0 \) (or \( m = 0 \) and \( n = k \)), and we will get \( f(m, n) = k + 0 = k \).
   - Therefore, every integer can be expressed as the sum of two integers, so this function is **surjective**.

2. **\( f(m, n) = m^2 + n^2 \)**:
   - This function computes the sum of the squares of \( m \) and \( n \).
   - The result \( m^2 + n^2 \) is always non-negative (i.e., \( \geq 0 \)), since squares of integers are non-negative.
   - Therefore, there is no way to obtain negative integers (like -1, -2, etc.) from this function.
   - Thus, this function is **not surjective**.

3. **\( f(m, n) = m \)**:
   - Here, the function simply returns the first integer \( m \).
   - For any integer \( k \), we can choose \( m = k \) and \( n \) can be any integer (it doesn't affect the output).
   - Since we can obtain every integer \( k \) by choosing \( m = k \), this function is **surjective**.

4. **\( f(m, n) = |n| \)**:
   - This function returns the absolute value of \( n \).
   - The output \( |n| \) is always non-negative (i.e., \( \geq 0 \)), since absolute values cannot be negative.
   - Therefore, similar to the previous case, we cannot achieve negative integers with this function.
   - Thus, this function is **not surjective**.

In summary, the surjective functions from the given options are:
- **\( f(m, n) = m + n \)**
- **\( f(m, n) = m \)**

The functions \( f(m, n) = m^2 + n^2 \) and \( f(m, n) = |n| \) are not surjective., source_sentence: Consider a binary classification problem with classifier $f(\mathbf{x})$ given by $$ f(\mathbf{x})= \begin{cases}1, & g(\mathbf{x}) \geq 0 \\ -1, & g(\mathbf{x})<0\end{cases} $$ and $\mathbf{x} \in \mathbb{R}^{6}$. Consider a specific pair $(\mathbf{x}, y=1)$ and assume that $g(\mathbf{x})=8$. In particular this means that this point is classified correctly by $f$. Assume further that we have computed the gradient of $g$ at $\mathbf{x}$ to be $\nabla_{\mathbf{x}} g(\mathbf{x})=(+1,-2,+3,-4,+5,-6)$. You are allowed to make one step in order to (hopefully) find an adversarial example. In the following four questions, assume $\epsilon=1$. Which offset $\delta$ with $\|\delta\|_{1} \leq 1$ yields the smallest value for $g(\mathbf{x}+\delta)$, assuming that $g$ is (locally) linear?
A. $
B. (
C. 0
D. ,
E. 0
D. ,
F. 0
G. ,
H. 0
I. ,
sentences: To compute the convex hull of a collection of rectangles in a plane in parallel, we need to follow a structured approach and ensure certain properties hold true for the hull algorithm we choose to implement, referred to here as hull2. 

### Plan
1. **Understand the Convex Hull of Rectangles**: Define what it means to find the convex hull for a set of rectangles and how the representation of rectangles can be simplified for this purpose.
2. **Discuss a Parallel Approach**: Outline a parallel strategy for computing the convex hull of these rectangles based on dividing the problem into smaller subproblems.
3. **Identify Necessary Properties for hull2**: Discuss the properties that must hold for the hull2 algorithm to ensure correctness when computing the convex hull in parallel.
4. **Prove the Properties**: Provide a proof or justification for each property identified in the previous step.

### Steps
1. **Understand the Convex Hull of Rectangles**: The convex hull of a set of rectangles can be computed by first identifying the extreme points (corners) of each rectangle. Each rectangle contributes its four corners: 
   - Lower left corner: \((x_1, y_1)\)
   - Upper right corner: \((x_2, y_2)\)
   - Lower right corner: \((x_2, y_1)\)
   - Upper left corner: \((x_1, y_2)\)

   The goal is to find the smallest convex shape that can enclose all these points.

2. **Discuss a Parallel Approach**: 
   - Split the collection of rectangles into smaller subsets, e.g., based on their spatial location (quadrants of the plane).
   - Compute the convex hull for each subset in parallel, using a suitable parallel convex hull algorithm (like Chan's algorithm or others suitable for parallel processing).
   - After obtaining the convex hulls for each subset, combine these hulls to form a single convex hull. The merging step can again be done in parallel, as it involves comparing the extreme points of the smaller hulls.

3. **Identify Necessary Properties for hull2**: For the hull2 algorithm to work correctly in a parallel setting, the following properties must hold:
   - **Associativity**: The merging of smaller convex hulls must be associative. This means that the order in which we combine sub-hulls should not affect the final result.
   - **Commutativity**: The merging function must also be commutative, allowing any two hulls to be merged in any order.
   - **Correctness of Sub-hulls**: Each sub-hull computed must be correct, meaning it must accurately represent the convex hull of the points (corners of rectangles) in its respective subset.

4. **Prove the Properties**: 
   - **Associativity**: 
     - Given three subsets A, B, and C, merging them can be done as \(g(g(A, B), C)\) or \(g(A, g(B, C))\). Both methods must yield the same final hull. This is true because the merging function combines points from each hull without losing any points that contribute to the convex shape.
   - **Commutativity**: 
     - For any two hulls \(H_1\) and \(H_2\), merging \(H_1\) and \(H_2\) should yield the same result as merging \(H_2\) and \(H_1\). This holds since the definition of the convex hull does not depend on the order of inputs when merging; it only depends on the set of points.
   - **Correctness of Sub-hulls**: 
     - Each sub-hull must include all relevant points (corners of rectangles) in its area. If each sub-hull correctly computes the convex shape of its respective set of points, the combined hull of all sub-hulls will also be correct. This can be shown by induction on the number of rectangles: if it holds for \(n\) rectangles, it will hold for \(n + 1\) by adding the new rectangle's corners and reevaluating the hull.

### Conclusion
By applying a parallel approach to compute the convex hull of rectangles and ensuring that the properties of associativity, commutativity, and correctness of sub-hulls hold, we can efficiently and correctly compute a convex hull in parallel. 

Thus, the answer is **the parallel convex hull can be computed by dividing the rectangles into subsets, computing sub-hulls in parallel, and then merging these hulls while ensuring associativity and commutativity hold true**., ### AddressSanitizer and Use-After-Free Bugs: A Step-by-Step Analysis

#### Step 1: Understanding Use-After-Free Bugs

To begin with, let's clarify what a use-after-free (UAF) bug is. Imagine you have a toy box filled with various toys (objects) that you play with. When you're done, you decide to throw away a broken toy (free memory) without realizing that you still have a friend playing with it (a dangling pointer). If your friend tries to play with that broken toy, it can lead to all sorts of problems – just like UAF bugs in programming can lead to unexpected behaviors or crashes.

#### Step 2: What is AddressSanitizer?

AddressSanitizer (ASan) is like a vigilant security system designed to protect your toy box. It monitors memory usage in a program, looking for any unsafe practices, such as trying to use memory that has already been freed. When memory is freed, ASan marks it as invalid or unusable, helping to prevent accidental access.

#### Step 3: Analyzing the Options

Now, let's analyze the options provided to see if ASan can prevent all use-after-free bugs:

1. **"No, because quarantining free’d memory chunks forever prevents legit memory reuse and could potentially lead to out-of-memory situations."**
   - While quarantining can help prevent access to freed memory, it doesn't solve the problem entirely. If memory chunks are kept in quarantine indefinitely, it can lead to memory wastage and, eventually, out-of-memory errors. However, this option highlights a limitation of ASan but does not directly address the capability of detecting UAF bugs.

2. **"No, because UAF detection is not part of ASan's feature set."**
   - This statement is misleading. ASan does have capabilities to catch UAF bugs. However, it may not cover every scenario. Therefore, while ASan is not solely defined by its UAF detection feature, it does include mechanisms for identifying UAF bugs.

3. **"Yes, because free’d memory chunks are poisoned."**
   - While ASan does poison freed memory, marking it as invalid, it does not guarantee that all access attempts will lead to a crash. Some scenarios may still slip through the cracks if the memory is accessed before ASan can react.

4. **"Yes, because free’d memory is unmapped and accesses therefore cause segmentation faults."**
   - ASan does indeed map out freed memory, leading to segmentation faults if accessed afterward. However, there are instances where memory may still be accessible in a way that doesn’t trigger an immediate fault, which means not all UAF bugs are caught.

#### Step 4: Conclusion

Given the analysis of each option, we arrive at a crucial understanding: **AddressSanitizer does not prevent all use-after-free bugs.** While it provides significant protection by marking freed memory as invalid and potentially causing segmentation faults, it does not catch every scenario, especially if the memory is accessed in specific ways before ASan can intervene.

### Why This Matters in Practice

Understanding the limitations of AddressSanitizer is essential for developers. It emphasizes the importance of careful memory management beyond relying solely on tools. While ASan is a valuable resource in the toolkit for identifying and preventing memory-related errors, developers must still adopt best practices in code to ensure robust memory safety. This includes diligent tracking of memory allocations and deallocations, thorough testing, and, when possible, utilizing additional tools or methodologies to complement ASan’s capabilities.

By comprehending these nuances, developers can write safer and more efficient code, thus creating robust applications that minimize the risk of memory-related bugs and enhance overall user experience., To find the offset \(\delta\) that yields the smallest value for \(g(\mathbf{x} + \delta)\), we can utilize the linear approximation of \(g\) around \(\mathbf{x}\):

\[
g(\mathbf{x} + \delta) \approx g(\mathbf{x}) + \nabla_{\mathbf{x}} g(\mathbf{x}) \cdot \delta
\]

Given that \(g(\mathbf{x}) = 8\) and \(\nabla_{\mathbf{x}} g(\mathbf{x}) = (+1, -2, +3, -4, +5, -6)\), we need to minimize:

\[
g(\mathbf{x} + \delta) \approx 8 + (+1, -2, +3, -4, +5, -6) \cdot \delta
\]

This is equivalent to minimizing:

\[
\nabla_{\mathbf{x}} g(\mathbf{x}) \cdot \delta = 1\delta_1 - 2\delta_2 + 3\delta_3 - 4\delta_4 + 5\delta_5 - 6\delta_6
\]

We will evaluate each option while ensuring that the L1 norm constraint (\(\|\delta\|_1 \leq 1\)) is satisfied.

- **Option: (0,0,0,0,0,1)**  
  Contribution: \(0*1 + 0*(-2) + 0*3 + 0*(-4) + 0*5 + 1*(-6) = -6\)

- **Option: (+1,-1,+1,-1,+1,-1)**  
  Contribution: \(+1*1 - 2*(-1) + 3*1 - 4*(-1) + 5*1 - 6*(-1) = 1 + 2 + 3 + 4 + 5 + 6 = 21\)

- **Option: (+1,-2,+3,-4,+5,-6)**  
   This exceeds the L1 norm constraint as it sums to more than \(1\).

- **Option: (+1,+1,+1,+1,+1,+1)**  
   Exceeds L1 norm constraint.

- **Option: (-1,+2,-3,+4,-5,+6)**  
   Exceeds L1 norm constraint.

- **Option: (0,0,0,0,0,1)** (repeated)

- **Option: (-1,+1,-1,+1,-1,+1)**  
   Contribution: \( -(-1) + (-2)(+1) + (-3)(-(-1)) + (-4)(+(-(-2))) - (-5)(+(-(-5))) - (-6)(+(-(-6))) = ... > large value.\)

- **Option: (-1,-1,-1,-1,-1,-1)**  
   Exceeds Lnorm constraint.

The offset that minimizes \(g(\mathbf{x}+\delta)\) is therefore:

**Answer:** $(0,0,0,0,0,1)$, source_sentence: What is the main difficulty in performing a Prime+Probe attack
                    on a system with L1 caches private to each core and a shared LLC,
                    and with attacker and victim running on different cores? How can
                    this difficulty be circumvented?
                    
sentences: The main difficulty in performing a Prime+Probe attack in this scenario is distinguishing between the effects of the shared LLC and the private L1 caches, which can lead to ambiguous results. This challenge can be circumvented by flushing the attacker's L1 cache prior to probing, thereby clarifying the observed timing differences and ensuring they predominantly reflect LLC behavior. Larger page sizes may also assist in this systematic approach., To prove Hall's Theorem, we need to show two directions:

1. **If \( G \) has a perfect matching, then \( |S| \leq |N(S)| \) for all \( S \subseteq A \)**:
   - If \( G \) has a perfect matching \( M \), then each vertex in \( A \) is matched to a unique vertex in \( B \).
   - For any subset \( S \subseteq A \), the vertices in \( N(S) \) (the neighbors of \( S \) in \( B \)) must cover all vertices in \( S \) because each vertex in \( S \) is matched to a vertex in \( N(S) \).
   - Thus, \( |S| \leq |N(S)| \).

2. **If \( |S| \leq |N(S)| \) for all \( S \subseteq A \), then \( G \) has a perfect matching**:
   - Assume \( M \) is a maximum matching that does not cover a vertex \( a_0 \in A \).
   - Let \( A_0 = \{a_0\} \) and \( B_0 = N(a_0) \).
   - Since \( M \) is maximum, all vertices in \( B_0 \) must be matched by \( M \). If \( B_0 = \emptyset \), then \( |N(A_0)| < |A_0| \) holds, which contradicts our assumption.
   - If \( B_0 \) is not empty, let \( A_1 = N_M(B_0) \cup \{a_0\} \). We have \( |A_1| = |B_0| + 1 \geq 1 \).
   - Define \( B_1 = N(A_1) \). Since no vertex in \( B_1 \) is exposed (all are covered by \( M \)), if \( |B_1| < |A_1| \), we find \( |N(A_1)| < |A_1| \), contradicting the assumption that Hall's condition holds.
   - If \( |B_1| \geq |A_1| \), we can continue this process, defining \( A_2 = N_M(B_1) \cup \{ a_0 \} \) and so on.
   - The sequence of sets \( A_i \) strictly increases in size, ensuring that the process cannot continue indefinitely without reaching a contradiction.
   - Eventually, we will find a set \( S \subseteq A \) for which \( |N(S)| < |S| \), contradicting our assumption.

Thus, we conclude that if \( |S| \leq |N(S)| \) for all \( S \subseteq A \), then \( G \) must have a perfect matching. 

This completes the proof of Hall's Theorem., To prove the inequality \( x + |x - 7| \geq 7 \), we will consider two cases based on the definition of the absolute value.

**Case 1: \( x - 7 \geq 0 \) (i.e., \( x \geq 7 \))**

In this case, \( |x - 7| = x - 7 \). Substituting this into the inequality, we get:
\[
x + |x - 7| = x + (x - 7) = 2x - 7
\]
Now, we want to show that:
\[
2x - 7 \geq 7
\]
Adding 7 to both sides:
\[
2x \geq 14
\]
Dividing by 2:
\[
x \geq 7
\]
This holds true since we assumed \( x \geq 7 \).

**Case 2: \( x - 7 < 0 \) (i.e., \( x < 7 \))**

In this case, \( |x - 7| = -(x - 7) = 7 - x \). Substituting this into the inequality, we have:
\[
x + |x - 7| = x + (7 - x) = 7
\]
Thus, the inequality becomes:
\[
7 \geq 7
\]
This is always true.

Since both cases lead to the conclusion that \( x + |x - 7| \geq 7 \), we can conclude that the inequality \( x + |x - 7| \geq 7 \) holds for all \( x \in \mathbb{R} \). 

Thus, the proof is complete., source_sentence: With respect to reorder buffers, Would you expect to find the memory address where a particular
  instruction was fetched (i.e., the value of the PC at the time of fetching) inside the reorder buffer? If so, why would it be there? If not, elaborate on why it would it be unneeded.
sentences: Answer: 

Yes, the memory address where a particular instruction was fetched (the value of the Program Counter, or PC) is typically found inside the reorder buffer (ROB). The ROB is designed to track the state of instructions as they progress through the pipeline, including their dispatch, execution, and eventual retirement. Storing the PC value in the ROB is important for several reasons. First, it allows the processor to maintain the original context of each instruction, which is crucial for debugging and handling exceptions. If a branch is mispredicted or an exception occurs, having the PC stored in the ROB enables the processor to reference the original instruction address, facilitating correct recovery and state maintenance. Additionally, including the PC in the ROB ensures that instructions retire in the correct order, which is essential for maintaining the integrity of the architectural state in out-of-order execution scenarios. Overall, the presence of the PC in the ROB enhances the processor's ability to manage instruction flow and respond to various scenarios effectively., To determine which cryptographic primitive(s) are used in S/Key - OTP, let's analyze the components of S/Key:

1. **S/Key Overview**: S/Key is a one-time password (OTP) system that generates passwords based on a secret key and a hash function.

2. **Hash Function**: The primary cryptographic primitive used in S/Key is a hash function. It takes an initial secret and produces a series of one-time passwords by hashing the previous password or value.

3. **Encryption**: While encryption is a common cryptographic primitive, S/Key does not directly use encryption in the same manner as other systems (e.g., encrypting data). Instead, it relies on the hash function to create the OTPs.

4. **MAC (Message Authentication Code)**: S/Key does not utilize a MAC, as it does not involve message integrity or authentication in the way MACs are typically applied.

Given this breakdown, the answer to which cryptographic primitive(s) are used in S/Key is:

3. Only a hash function, 1. **Interpret the Problem**: The Hedge algorithm aims to allocate investments effectively across $N$ options by adapting to their performance over time. The goal is to ensure that the total return from our investments closely matches that of the best-performing investment, despite the uncertainty of daily changes.

2. **Outline Your Approach**: Each day, we need to define a cost vector $\vec{m}^{(t)}$ that reflects the performance of each investment based on their observed percentage changes. This will allow Hedge to adjust its allocations dynamically, favoring investments that yield higher returns.

3. **Execute the Solution**:
   - For each investment $i$, calculate its daily return based on the observed percentage change: 
     \[
     r_i^{(t)} = 1 + \frac{\text{change}(i)}{100}
     \]
   - The cost vector $\vec{m}^{(t)}$ is then defined as:
     \[
     m_i^{(t)} = -\log(r_i^{(t)})
     \]
   - This transformation ensures that higher returns (positive changes) result in lower costs, while losses yield higher costs.
   - Apply Hedge's updating rule using the cost vector to adjust the weights for each investment.

4. **Verify or Interpret the Result**: By setting the cost vector this way, Hedge minimizes the regret against the best single investment over time. The logarithmic transformation allows us to convert percentage changes into a form that emphasizes performance differences, ensuring that if one investment consistently outperforms others, Hedge will allocate more capital towards it. Thus, the expected performance of our portfolio closely aligns with that of the best individual investment, achieving near-optimal results in an uncertain environment., source_sentence: Which of the following statements about coverage-guided fuzzing is/are correct?
A. [
B. '
C. R
D. e
E. d
D. u
F. n
G. d
H. a
I. n
sentences: To decrypt the ciphertext \( c = 14 \) in RSA, we first need to find the private key \( d \) such that \( e \cdot d \equiv 1 \mod \phi(n) \), where \( n = p \cdot q = 77 \) and \( \phi(n) = (p-1)(q-1) = 6 \cdot 10 = 60 \). 

Given \( e = 13 \), we need to find \( d \) such that:

\[
13d \equiv 1 \mod 60
\]

Using the Extended Euclidean Algorithm, we find \( d \):

1. \( 60 = 4 \cdot 13 + 8 \)
2. \( 13 = 1 \cdot 8 + 5 \)
3. \( 8 = 1 \cdot 5 + 3 \)
4. \( 5 = 1 \cdot 3 + 2 \)
5. \( 3 = 1 \cdot 2 + 1 \)
6. \( 2 = 2 \cdot 1 + 0 \)

Back substituting to find \( 1 = 3 - 1 \cdot 2 \):

\[
1 = 3 - (5 - 1 \cdot 3) = 2 \cdot 3 - 5
\]
\[
1 = 2 \cdot (8 - 1 \cdot 5) - 5 = 2 \cdot 8 - 3 \cdot 5
\]
\[
= 2 \cdot 8 - 3 \cdot (13 - 1 \cdot 8) = 5 \cdot 8 - 3 \cdot 13
\]
\[
= 5 \cdot (60 - 4 \cdot 13) - 3 \cdot 13 = 5 \cdot 60 - 23 \cdot 13
\]

Thus, \( d \equiv -23 \mod 60 \), or \( d \equiv 37 \mod 60 \).

Now we can decrypt the ciphertext \( c = 14 \):

\[
m \equiv c^d \mod n
\]
\[
m \equiv 14^{37} \mod 77
\]

To simplify this computation, we can use the Chinese Remainder Theorem by calculating \( m \mod 7 \) and \( m \mod 11 \):

1. Calculate \( 14^{37} \mod 7 \):
   \[
   14 \equiv 0 \mod 7 \implies 14^{37} \equiv 0 \mod 7
   \]

2. Calculate \( 14^{37} \mod 11 \):
   \[
   14 \equiv 3 \mod 11
   \]
   Using Fermat's Little Theorem, \( 3^{10} \equiv 1 \mod 11 \). Thus:
   \[
   37 \mod 10 = 7 \implies 3^{37} \equiv 3^7 \mod 11
   \]
   We calculate \( 3^7 \):
   \[
   3^2 = 9, \quad 3^4 = 81 \equiv 4 \mod 11
   \]
   \[
   3^6 = 3^4 \cdot 3^2 = 4 \cdot 9 = 36 \equiv 3 \mod 11
   \]
   \[
   3^7 = 3^6 \cdot 3 = 3 \cdot 3 = 9 \mod 11
   \]

Now we have:
- \( m \equiv 0 \mod 7 \)
- \( m \equiv 9 \mod 11 \)

We can solve these congruences using the method of successive substitutions or direct computation. 

Let \( m = 7k \). Then:

\[
7k \equiv 9 \mod 11 \implies 7k = 9 + 11j
\]
Solving for \( k \) modulo 11, we need the modular inverse of 7 mod 11, which is 8 (since \( 7 \cdot 8 \equiv 1 \mod 11 \)). Thus:

\[
k \equiv 8 \cdot 9 \mod 11 \equiv 72 \mod 11 \equiv 6 \mod 11
\]

So \( k = 11m + 6 \). Substituting back, we have:

\[
m = 7(11m + 6) = 77m + 42
\]
Thus, \( m \equiv 42 \mod 77 \).

The message sent was \( m = 42 \).

Therefore, the correct answer is:

**$t = 42$**., In regression tasks, the loss function most affected by outliers is typically the Mean Squared Error (MSE), because it squares the differences between predicted and actual values, which can disproportionately increase the loss for outlier data points.

On the other hand, the **Mean Absolute Error (MAE)** is less sensitive to outliers. This is because MAE calculates the absolute differences between predicted and actual values, treating all errors equally regardless of their magnitude. For example, if a prediction is off by 1 or by 1000, the impact on the total loss is linear in MAE, while it would be quadratic in MSE.

Thus, if you are working with a dataset that contains many outliers and do not wish to preprocess the data, using **Mean Absolute Error (MAE)** as your loss function will be less affected by those outliers compared to Mean Squared Error (MSE)., To determine which statements about coverage-guided fuzzing are correct, let's analyze each option step by step.

1. **Redundant seeds in the corpus will reduce fuzzing efficiency.**
   - **Analysis:** This statement is generally true. In coverage-guided fuzzing, the goal is to explore as many different paths and code branches as possible. If the corpus contains many redundant seeds (i.e., inputs that lead to the same code paths), it can lead to wasted effort and reduced efficiency since the fuzzer may spend more time exploring the same paths rather than discovering new ones.

2. **Counting the number of times the covered code has been executed provides a more fine-grained view of program behavior than only "covered/not covered" binary code coverage.**
   - **Analysis:** This statement is correct. While binary code coverage only tells you whether a particular part of the code has been executed, counting the number of times each part of the code is executed (also known as edge or path coverage) provides deeper insights into the program's behavior. This finer granularity can help the fuzzer prioritize certain inputs that might lead to new or interesting behaviors.

3. **Due to the coverage feedback, a small random perturbation of a seed can have a significant impact on further exploration.**
   - **Analysis:** This statement is also correct. Coverage-guided fuzzers utilize feedback about which parts of the code are executed to guide their exploration. Even a small change in input can lead to different execution paths being taken, which may uncover new code that wasn't reached with the original seed. As such, small perturbations can indeed have a large impact on the exploration of the input space.

4. **Fuzzers that have higher code coverage always find more bugs.**
   - **Analysis:** This statement is misleading and generally false. While higher code coverage can increase the likelihood of finding bugs, it does not guarantee that more bugs will be found. Some parts of the code may be covered but not contain any bugs, while other areas might have bugs that are difficult to reach, regardless of coverage. Thus, while there is a correlation between coverage and bug discovery, it is not a strict rule that higher coverage will always lead to more bugs being found.

Based on this analysis, the correct statements about coverage-guided fuzzing are:

- **1. True**
- **2. True**
- **3. True**
- **4. False**

In summary, statements 1, 2, and 3 are correct, while statement 4 is not.
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_precision@10, cosine_recall@1, cosine_recall@3, cosine_recall@5, cosine_recall@10, cosine_ndcg@10, cosine_mrr@10, cosine_map@100
model-index: name: BGE base Financial Matryoshka
results: task: type: information-retrieval
name: Information Retrieval
dataset: name: dim 768
type: dim_768
metrics: type: cosine_accuracy@1
value: 0.7480314960629921
name: Cosine Accuracy@1
verified: no, type: cosine_accuracy@3
value: 0.9133858267716536
name: Cosine Accuracy@3
verified: no, type: cosine_accuracy@5
value: 0.9291338582677166
name: Cosine Accuracy@5
verified: no, type: cosine_accuracy@10
value: 0.952755905511811
name: Cosine Accuracy@10
verified: no, type: cosine_precision@1
value: 0.7480314960629921
name: Cosine Precision@1
verified: no, type: cosine_precision@3
value: 0.30446194225721795
name: Cosine Precision@3
verified: no, type: cosine_precision@5
value: 0.18582677165354328
name: Cosine Precision@5
verified: no, type: cosine_precision@10
value: 0.0952755905511811
name: Cosine Precision@10
verified: no, type: cosine_recall@1
value: 0.7480314960629921
name: Cosine Recall@1
verified: no, type: cosine_recall@3
value: 0.9133858267716536
name: Cosine Recall@3
verified: no, type: cosine_recall@5
value: 0.9291338582677166
name: Cosine Recall@5
verified: no, type: cosine_recall@10
value: 0.952755905511811
name: Cosine Recall@10
verified: no, type: cosine_ndcg@10
value: 0.8627260553527355
name: Cosine Ndcg@10
verified: no, type: cosine_mrr@10
value: 0.832564679415073
name: Cosine Mrr@10
verified: no, type: cosine_map@100
value: 0.8333418602723881
name: Cosine Map@100
verified: no, task: type: information-retrieval
name: Information Retrieval
dataset: name: dim 512
type: dim_512
metrics: type: cosine_accuracy@1
value: 0.7637795275590551
name: Cosine Accuracy@1
verified: no, type: cosine_accuracy@3
value: 0.905511811023622
name: Cosine Accuracy@3
verified: no, type: cosine_accuracy@5
value: 0.9291338582677166
name: Cosine Accuracy@5
verified: no, type: cosine_accuracy@10
value: 0.9448818897637795
name: Cosine Accuracy@10
verified: no, type: cosine_precision@1
value: 0.7637795275590551
name: Cosine Precision@1
verified: no, type: cosine_precision@3
value: 0.3018372703412075
name: Cosine Precision@3
verified: no, type: cosine_precision@5
value: 0.18582677165354328
name: Cosine Precision@5
verified: no, type: cosine_precision@10
value: 0.09448818897637794
name: Cosine Precision@10
verified: no, type: cosine_recall@1
value: 0.7637795275590551
name: Cosine Recall@1
verified: no, type: cosine_recall@3
value: 0.905511811023622
name: Cosine Recall@3
verified: no, type: cosine_recall@5
value: 0.9291338582677166
name: Cosine Recall@5
verified: no, type: cosine_recall@10
value: 0.9448818897637795
name: Cosine Recall@10
verified: no, type: cosine_ndcg@10
value: 0.865873424380728
name: Cosine Ndcg@10
verified: no, type: cosine_mrr@10
value: 0.8393888263967003
name: Cosine Mrr@10
verified: no, type: cosine_map@100
value: 0.8408348815035829
name: Cosine Map@100
verified: no, task: type: information-retrieval
name: Information Retrieval
dataset: name: dim 256
type: dim_256
metrics: type: cosine_accuracy@1
value: 0.7322834645669292
name: Cosine Accuracy@1
verified: no, type: cosine_accuracy@3
value: 0.905511811023622
name: Cosine Accuracy@3
verified: no, type: cosine_accuracy@5
value: 0.9133858267716536
name: Cosine Accuracy@5
verified: no, type: cosine_accuracy@10
value: 0.9448818897637795
name: Cosine Accuracy@10
verified: no, type: cosine_precision@1
value: 0.7322834645669292
name: Cosine Precision@1
verified: no, type: cosine_precision@3
value: 0.3018372703412075
name: Cosine Precision@3
verified: no, type: cosine_precision@5
value: 0.1826771653543307
name: Cosine Precision@5
verified: no, type: cosine_precision@10
value: 0.09448818897637794
name: Cosine Precision@10
verified: no, type: cosine_recall@1
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name: Cosine Recall@1
verified: no, type: cosine_recall@3
value: 0.905511811023622
name: Cosine Recall@3
verified: no, type: cosine_recall@5
value: 0.9133858267716536
name: Cosine Recall@5
verified: no, type: cosine_recall@10
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name: Cosine Recall@10
verified: no, type: cosine_ndcg@10
value: 0.8491570192812045
name: Cosine Ndcg@10
verified: no, type: cosine_mrr@10
value: 0.8173322084739407
name: Cosine Mrr@10
verified: no, type: cosine_map@100
value: 0.8184315799994355
name: Cosine Map@100
verified: no, task: type: information-retrieval
name: Information Retrieval
dataset: name: dim 128
type: dim_128
metrics: type: cosine_accuracy@1
value: 0.7244094488188977
name: Cosine Accuracy@1
verified: no, type: cosine_accuracy@3
value: 0.889763779527559
name: Cosine Accuracy@3
verified: no, type: cosine_accuracy@5
value: 0.9133858267716536
name: Cosine Accuracy@5
verified: no, type: cosine_accuracy@10
value: 0.937007874015748
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verified: no, type: cosine_recall@1
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verified: no, type: cosine_recall@3
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name: Cosine Recall@5
verified: no, type: cosine_recall@10
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verified: no, type: cosine_ndcg@10
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name: Cosine Ndcg@10
verified: no, type: cosine_mrr@10
value: 0.8044619422572177
name: Cosine Mrr@10
verified: no, type: cosine_map@100
value: 0.8060220619275738
name: Cosine Map@100
verified: no, task: type: information-retrieval
name: Information Retrieval
dataset: name: dim 64
type: dim_64
metrics: type: cosine_accuracy@1
value: 0.6929133858267716
name: Cosine Accuracy@1
verified: no, type: cosine_accuracy@3
value: 0.8661417322834646
name: Cosine Accuracy@3
verified: no, type: cosine_accuracy@5
value: 0.9133858267716536
name: Cosine Accuracy@5
verified: no, type: cosine_accuracy@10
value: 0.9291338582677166
name: Cosine Accuracy@10
verified: no, type: cosine_precision@1
value: 0.6929133858267716
name: Cosine Precision@1
verified: no, type: cosine_precision@3
value: 0.28871391076115493
name: Cosine Precision@3
verified: no, type: cosine_precision@5
value: 0.18267716535433068
name: Cosine Precision@5
verified: no, type: cosine_precision@10
value: 0.09291338582677164
name: Cosine Precision@10
verified: no, type: cosine_recall@1
value: 0.6929133858267716
name: Cosine Recall@1
verified: no, type: cosine_recall@3
value: 0.8661417322834646
name: Cosine Recall@3
verified: no, type: cosine_recall@5
value: 0.9133858267716536
name: Cosine Recall@5
verified: no, type: cosine_recall@10
value: 0.9291338582677166
name: Cosine Recall@10
verified: no, type: cosine_ndcg@10
value: 0.8202429021089767
name: Cosine Ndcg@10
verified: no, type: cosine_mrr@10
value: 0.7840082489688789
name: Cosine Mrr@10
verified: no, type: cosine_map@100
value: 0.7859411642894073
name: Cosine Map@100
verified: no
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Created: 2025-06-10 10:45:35