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Speculative decoding is an advanced AI inference technique that is gaining traction in natural language processing (NLP) and other sequence generation tasks. It addresses one of the most significant challenges in deploying large-scale models: balancing computational efficiency with the quality of generated outputs. Models like GPT-3 and GPT-4 have set new benchmarks in AI capability but are computationally expensive, especially for real-time applications such as chatbots, translation systems, and interactive assistants. Speculative decoding offers a clever solution by introducing a two-model system: a smaller, faster draft model and a larger, more accurate target model. This approach reduces latency without compromising the quality of the generated sequences. At its core, speculative decoding is a two-step process. First, a lightweight draft model generates a sequence of tokens quickly. This model is typically a distilled version of the target model or another smaller model trained for speed. The draft model's output is not final but serves as a proposal. The second step involves the larger, more accurate target model, which evaluates the draft model’s tokens. The target model either accepts the proposed tokens if they meet a confidence threshold or refines them if they do not. This process allows the system to leverage the efficiency of the draft model while maintaining the precision of the target model. The reason speculative decoding is particularly appealing lies in its ability to reduce the computational burden of the larger model. By delegating the initial token generation to the draft model, the target model operates selectively, focusing only on validation or correction rather than generating every token from scratch. This division of labor significantly reduces inference latency and resource consumption, making it a preferred technique for real-time applications. The technique works well in scenarios where speed is critical, and the quality of generated outputs cannot be compromised. For instance, in chat-based applications, users expect near-instantaneous responses. Speculative decoding ensures that the system generates text quickly while retaining the nuanced understanding of the larger model. Similarly, in real-time translation systems, where delays can disrupt communication, speculative decoding provides a practical way to meet latency constraints. To understand speculative decoding more concretely, let us consider a code implementation. Below is an example that demonstrates how speculative decoding could be implemented using PyTorch and Hugging Face's Transformers library. This implementation involves a draft model (a smaller, faster version like DistilGPT-2) and a target model (a larger, more accurate model like GPT-2). from transformers import AutoModelForCausalLM, AutoTokenizer

# Load the draft (smaller) and target (larger) models

draft_model_name = "distilgpt2"  # Smaller, faster model 

target_model_name = "gpt2"      # Larger, more accurate model

draft_tokenizer = AutoTokenizer.from_pretrained(draft_model_name) draft_model = AutoModelForCausalLM.from_pretrained(draft_model_name)

target_tokenizer = AutoTokenizer.from_pretrained(target_model_name) target_model = AutoModelForCausalLM.from_pretrained(target_model_name)

def speculative_decode(prompt, max_length=50, threshold=0.9): """ Performs speculative decoding using a draft model and a target model.

Args:
    prompt (str): The input text to the model.
    max_length (int): The maximum length of the generated sequence.
    threshold (float): The confidence threshold for the target model to accept tokens.

Returns:
    str: The generated text sequence.
"""
# Step 1: Generate tokens using the draft model
draft_inputs = draft_tokenizer(prompt, return_tensors="pt")  # Tokenize the prompt
draft_outputs = draft_model.generate(draft_inputs.input_ids, max_length=max_length)  # Generate draft tokens
draft_tokens = draft_tokenizer.decode(draft_outputs[0], skip_special_tokens=True)  # Decode draft tokens to text

# Step 2: Verify tokens using the target model
target_inputs = target_tokenizer(draft_tokens, return_tensors="pt")  # Tokenize the draft output for the target model
target_logits = target_model(**target_inputs).logits  # Get logits (un-normalized probabilities) from the target model

# Step 3: Calculate confidence scores for each token
probs = target_logits.softmax(dim=-1)  # Convert logits to probabilities
confidence = probs.max(dim=-1).values.mean().item()  # Calculate the average confidence score across all tokens

# Step 4: Decide whether to accept or refine tokens
if confidence >= threshold:  # If confidence exceeds the threshold
    return draft_tokens  # Accept the draft tokens
else:  # Otherwise, refine the sequence using the target model
    refined_outputs = target_model.generate(target_inputs.input_ids, max_length=max_length)
    return target_tokenizer.decode(refined_outputs[0], skip_special_tokens=True)  # Return the refined sequence


prompt = "The future of AI is" output = speculative_decode(prompt, max_length=20) print(output) In this implementation, the speculative decoding process begins with the draft model generating a sequence of tokens. These tokens are then passed to the target model, which calculates the confidence for each token. If the average confidence exceeds a pre-defined threshold, the tokens are accepted as is. Otherwise, the target model refines the sequence to ensure output quality. This code includes detailed comments explaining each step, from tokenizing the input for the draft model to generating and validating tokens with the target model. The threshold parameter can be adjusted based on the application’s tolerance for speed versus accuracy trade-offs. One of the primary challenges in implementing speculative decoding is training the draft model. The draft model must align closely with the target model in terms of predictions, as significant discrepancies can reduce the efficiency of the process. For example, if the draft model frequently proposes incorrect tokens, the target model spends more time correcting them, negating the benefits of speculative decoding. Ensuring this alignment typically involves fine-tuning or distillation techniques that transfer knowledge from the target model to the draft model. Another critical aspect of speculative decoding is the confidence threshold used by the target model to accept or reject the draft model's tokens. If the threshold is too strict, the target model rejects too many tokens, increasing its workload and reducing efficiency. Conversely, if the threshold is too lenient, the system may accept suboptimal tokens, degrading output quality. Fine-tuning this parameter requires careful experimentation and may vary depending on the application. Speculative decoding can also integrate with parallel computation to further enhance efficiency. For example, while the target model processes one batch of tokens, the draft model can begin generating the next batch. This overlap reduces idle time for both models and maximizes throughput, making speculative decoding scalable for high-volume systems. While challenges like draft-target alignment and confidence threshold tuning exist, ongoing advancements in model training and inference techniques promise to make speculative decoding even more robust and accessible. This technique is poised to play a pivotal role in the future of AI deployment, particularly as demand for high-speed, high-quality systems continues to grow. The code above is publicly available in my github https://github.com/philhopkinsML Speculative decoding is an advanced AI inference technique that is gaining traction in natural language processing (NLP) and other sequence generation tasks. It addresses one of the most significant challenges in deploying large-scale models: balancing computational efficiency with the quality of generated outputs. Models like GPT-3 and GPT-4 have set new benchmarks in AI capability but are computationally expensive, especially for real-time applications such as chatbots, translation systems, and interactive assistants. Speculative decoding offers a clever solution by introducing a two-model system: a smaller, faster draft model and a larger, more accurate target model. This approach reduces latency without compromising the quality of the generated sequences. At its core, speculative decoding is a two-step process. First, a lightweight draft model generates a sequence of tokens quickly. This model is typically a distilled version of the target model or another smaller model trained for speed. The draft model's output is not final but serves as a proposal. The second step involves the larger, more accurate target model, which evaluates the draft model’s tokens. The target model either accepts the proposed tokens if they meet a confidence threshold or refines them if they do not. This process allows the system to leverage the efficiency of the draft model while maintaining the precision of the target model. The reason speculative decoding is particularly appealing lies in its ability to reduce the computational burden of the larger model. By delegating the initial token generation to the draft model, the target model operates selectively, focusing only on validation or correction rather than generating every token from scratch. This division of labor significantly reduces inference latency and resource consumption, making it a preferred technique for real-time applications. The technique works well in scenarios where speed is critical, and the quality of generated outputs cannot be compromised. For instance, in chat-based applications, users expect near-instantaneous responses. Speculative decoding ensures that the system generates text quickly while retaining the nuanced understanding of the larger model. Similarly, in real-time translation systems, where delays can disrupt communication, speculative decoding provides a practical way to meet latency constraints. To understand speculative decoding more concretely, let us consider a code implementation. Below is an example that demonstrates how speculative decoding could be implemented using PyTorch and Hugging Face's Transformers library. This implementation involves a draft model (a smaller, faster version like DistilGPT-2) and a target model (a larger, more accurate model like GPT-2). from transformers import AutoModelForCausalLM, AutoTokenizer

# Load the draft (smaller) and target (larger) models

draft_model_name = "distilgpt2"  # Smaller, faster model 

target_model_name = "gpt2"      # Larger, more accurate model

draft_tokenizer = AutoTokenizer.from_pretrained(draft_model_name) draft_model = AutoModelForCausalLM.from_pretrained(draft_model_name)

target_tokenizer = AutoTokenizer.from_pretrained(target_model_name) target_model = AutoModelForCausalLM.from_pretrained(target_model_name)

def speculative_decode(prompt, max_length=50, threshold=0.9): """ Performs speculative decoding using a draft model and a target model.

Args:
    prompt (str): The input text to the model.
    max_length (int): The maximum length of the generated sequence.
    threshold (float): The confidence threshold for the target model to accept tokens.

Returns:
    str: The generated text sequence.
"""
# Step 1: Generate tokens using the draft model
draft_inputs = draft_tokenizer(prompt, return_tensors="pt")  # Tokenize the prompt
draft_outputs = draft_model.generate(draft_inputs.input_ids, max_length=max_length)  # Generate draft tokens
draft_tokens = draft_tokenizer.decode(draft_outputs[0], skip_special_tokens=True)  # Decode draft tokens to text

# Step 2: Verify tokens using the target model
target_inputs = target_tokenizer(draft_tokens, return_tensors="pt")  # Tokenize the draft output for the target model
target_logits = target_model(**target_inputs).logits  # Get logits (un-normalized probabilities) from the target model

# Step 3: Calculate confidence scores for each token
probs = target_logits.softmax(dim=-1)  # Convert logits to probabilities
confidence = probs.max(dim=-1).values.mean().item()  # Calculate the average confidence score across all tokens

# Step 4: Decide whether to accept or refine tokens
if confidence >= threshold:  # If confidence exceeds the threshold
    return draft_tokens  # Accept the draft tokens
else:  # Otherwise, refine the sequence using the target model
    refined_outputs = target_model.generate(target_inputs.input_ids, max_length=max_length)
    return target_tokenizer.decode(refined_outputs[0], skip_special_tokens=True)  # Return the refined sequence


prompt = "The future of AI is" output = speculative_decode(prompt, max_length=20) print(output) from transformers import AutoModelForCausalLM, AutoTokenizer

# Load the draft (smaller) and target (larger) models

draft_model_name = "distilgpt2"  # Smaller, faster model 

target_model_name = "gpt2"      # Larger, more accurate model

draft_tokenizer = AutoTokenizer.from_pretrained(draft_model_name) draft_model = AutoModelForCausalLM.from_pretrained(draft_model_name)

target_tokenizer = AutoTokenizer.from_pretrained(target_model_name) target_model = AutoModelForCausalLM.from_pretrained(target_model_name)

def speculative_decode(prompt, max_length=50, threshold=0.9): """ Performs speculative decoding using a draft model and a target model.

Args:
    prompt (str): The input text to the model.
    max_length (int): The maximum length of the generated sequence.
    threshold (float): The confidence threshold for the target model to accept tokens.

Returns:
    str: The generated text sequence.
"""
# Step 1: Generate tokens using the draft model
draft_inputs = draft_tokenizer(prompt, return_tensors="pt")  # Tokenize the prompt
draft_outputs = draft_model.generate(draft_inputs.input_ids, max_length=max_length)  # Generate draft tokens
draft_tokens = draft_tokenizer.decode(draft_outputs[0], skip_special_tokens=True)  # Decode draft tokens to text

# Step 2: Verify tokens using the target model
target_inputs = target_tokenizer(draft_tokens, return_tensors="pt")  # Tokenize the draft output for the target model
target_logits = target_model(**target_inputs).logits  # Get logits (un-normalized probabilities) from the target model

# Step 3: Calculate confidence scores for each token
probs = target_logits.softmax(dim=-1)  # Convert logits to probabilities
confidence = probs.max(dim=-1).values.mean().item()  # Calculate the average confidence score across all tokens

# Step 4: Decide whether to accept or refine tokens
if confidence >= threshold:  # If confidence exceeds the threshold
    return draft_tokens  # Accept the draft tokens
else:  # Otherwise, refine the sequence using the target model
    refined_outputs = target_model.generate(target_inputs.input_ids, max_length=max_length)
    return target_tokenizer.decode(refined_outputs[0], skip_special_tokens=True)  # Return the refined sequence


prompt = "The future of AI is" output = speculative_decode(prompt, max_length=20) print(output) In this implementation, the speculative decoding process begins with the draft model generating a sequence of tokens. These tokens are then passed to the target model, which calculates the confidence for each token. If the average confidence exceeds a pre-defined threshold, the tokens are accepted as is. Otherwise, the target model refines the sequence to ensure output quality. This code includes detailed comments explaining each step, from tokenizing the input for the draft model to generating and validating tokens with the target model. The threshold parameter can be adjusted based on the application’s tolerance for speed versus accuracy trade-offs. One of the primary challenges in implementing speculative decoding is training the draft model. The draft model must align closely with the target model in terms of predictions, as significant discrepancies can reduce the efficiency of the process. For example, if the draft model frequently proposes incorrect tokens, the target model spends more time correcting them, negating the benefits of speculative decoding. Ensuring this alignment typically involves fine-tuning or distillation techniques that transfer knowledge from the target model to the draft model. Another critical aspect of speculative decoding is the confidence threshold used by the target model to accept or reject the draft model's tokens. If the threshold is too strict, the target model rejects too many tokens, increasing its workload and reducing efficiency. Conversely, if the threshold is too lenient, the system may accept suboptimal tokens, degrading output quality. Fine-tuning this parameter requires careful experimentation and may vary depending on the application. Speculative decoding can also integrate with parallel computation to further enhance efficiency. For example, while the target model processes one batch of tokens, the draft model can begin generating the next batch. This overlap reduces idle time for both models and maximizes throughput, making speculative decoding scalable for high-volume systems. While challenges like draft-target alignment and confidence threshold tuning exist, ongoing advancements in model training and inference techniques promise to make speculative decoding even more robust and accessible. This technique is poised to play a pivotal role in the future of AI deployment, particularly as demand for high-speed, high-quality systems continues to grow. The code above is publicly available in my github https://github.com/philhopkinsML https://github.com/philhopkinsML

Meet The AI Tag-Team Method That Reduces Latency in Your Model's Response

Authors:
(1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia;
(2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.3 Reinforcement Learning 7.4 Search-based Solutions 8 Experimental Setting 9 Related Work 10 Discussion and Conclusion, and References 5.3 Summary Given the complex configuration space and the diversity of workloads, employing pruning techniques to reduce workload running time and configuration search space emerges as a natural approach in addressing these complexities. In this section, we aim to provide direction for future practitioners and researchers on improving data collection efficiency and training efficiency through various pruning strategies. Specifically, we classify the pruning techniques into two levels: workload-level and configuration space. Regarding the workload level, we categorize it into two directions: eliminating redundant queries and workload feature reduction techniques. For the configuration level, we present the existing feature reduction methods applied in the state-of-the-art tuning methods, mainly focusing on feature projection, importance ranking, or feature clustering. Moreover, future researchers and practitioners can also try to explore different dimensionality reduction techniques tailored to specific data characteristics, as outlined in the survey by Hou et al. [31]. Furthermore, advancements in high-dimensional data technology offer opportunities to enhance the performance of feature pruning methods. For instance, Yang et al. [32] proposed an innovative variant of LASSO, named Efficient Tuning of Lasso (ET-Lasso), which focuses on ensuring feature selection consistency. This method has demonstrated effectiveness in efficiently selecting active features contributing to the response, achieved by integrating permuted features as pseudo-features within linear models. This paper is available on arxiv under CC BY 4.0 DEED. Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Authors: Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 2 Tuning Objectives 3 Overview of Tuning Framework 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 5.3 Summary 6 Knowledge from Experience 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.2 Neural Network 7.3 Reinforcement Learning 7.3 Reinforcement Learning 7.4 Search-based Solutions 7.4 Search-based Solutions 8 Experimental Setting 8 Experimental Setting 9 Related Work 9 Related Work 10 Discussion and Conclusion, and References 10 Discussion and Conclusion, and References 5.3 Summary Given the complex configuration space and the diversity of workloads, employing pruning techniques to reduce workload running time and configuration search space emerges as a natural approach in addressing these complexities. In this section, we aim to provide direction for future practitioners and researchers on improving data collection efficiency and training efficiency through various pruning strategies. Specifically, we classify the pruning techniques into two levels: workload-level and configuration space. Regarding the workload level, we categorize it into two directions: eliminating redundant queries and workload feature reduction techniques. For the configuration level, we present the existing feature reduction methods applied in the state-of-the-art tuning methods, mainly focusing on feature projection, importance ranking, or feature clustering. Moreover, future researchers and practitioners can also try to explore different dimensionality reduction techniques tailored to specific data characteristics, as outlined in the survey by Hou et al. [31]. Furthermore, advancements in high-dimensional data technology offer opportunities to enhance the performance of feature pruning methods. For instance, Yang et al. [32] proposed an innovative variant of LASSO, named Efficient Tuning of Lasso (ET-Lasso), which focuses on ensuring feature selection consistency. This method has demonstrated effectiveness in efficiently selecting active features contributing to the response, achieved by integrating permuted features as pseudo-features within linear models. This paper is available on arxiv under CC BY 4.0 DEED. This paper is available on arxiv under CC BY 4.0 DEED. available on arxiv

Pruning Techniques for Reducing Workload and Configuration Space Complexity

Authors:
(1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia;
(2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.3 Reinforcement Learning 7.4 Search-based Solutions 8 Experimental Setting 9 Related Work 10 Discussion and Conclusion, and References 5.2 Configuration-level Pruning Another approach to mitigating the optimization time required by machine learning-based methodologies is to reduce configuration space necessitating tuning. Configuration-level pruning endeavors to discern and prioritize the tuning of parameters that exert substantial influence on the DBMSs based on historical observations. • Spearman Rank Correlation Coefficient (SRCC) [26]: is a nonparametric measure of rank correlation on the strength of a monotonic relationship between paired data. It is defined as the Pearson correlation coefficient between the rank variables. By leveraging its capacity to gauge monotonic relationships, SRCC facilitates the identification and removal of redundant parameters, contributing to a more efficient and simplified configuration. LOCAT [7] calculates SRCC between each configuration parameter and the workload execution time to filter out some redundant configuration parameters and narrow down the parameter search space.” • Principal Component Analysis (PCA): is a dimensionality reduction method that transforms correlated variables into uncorrelated ones, known as principal components. It does so by calculating the covariance matrix, performing eigendecomposition, and selecting a subset of principal components based on their variance. After SRCC, LOCAT [7] applies Gaussian kernel Principal Component Analysis (KPCA) to further extract and form new lower-dimensional parameters derived after removal of redundant configuration parameters for subsequent optimal parameter searching. • Least Absolute Shrinkage and Selection Operator (LASSO) and Lasso Path Algorithm. In the context of linear regression, LASSO modifies this objective function by adding a L1 penalty term equals to λ times the sum of absolute values of the regression coefficients, where λ controls the strength of the penalty, and it helps to reduce the effect of irrelevant variables by penalizing models with large weights. A higher λ value results in more coefficients being pushed toward zero, thereby achieving interpretable, stable, and computationally efficient feature selection. OtterTune [8] uses the LASSO path algorithm to assess the importance of configuration parameters by gradually reducing the penalty term. The order in 6 which parameters are included during this process is then considered as the importance order, and OtterTune uses this information to prune less important parameters. • Random Forest (RF): is a supervised machine learning method to deal with classification and regression problems. It can be deemed a voting algorithm consisting of multiple decision trees, used to calculate the importance of features. In the study [27], the authors utilize Latin Hypercube Sampling (LHS) to select a subset of configurations. Subsequently, they employ Random Forests with 300 Classification and Regression Trees (CART) to ascertain the importance of each parameter. Their findings reveal that when employing the YCSB workload-A on Cassandra, optimizing just five parameters can yield performance levels comparable to 99% of the best configurations attained through extensive parameter tuning. HUNTER [13] adopt the RF classifier with CARTs and adopts the majority voting principle to determine the importance of the knobs. It then selects the top-20 knobs to reduce the configuration search space in its tuning framework. • Hashing-enhanced Subspace BO (HeSBO) [28]: is a randomized low-dimensional projection approach that operates by deducing the search space for Bayesian Optimization-based solutions (discussed in Section 7.1). By utilizing two uniform hash functions to construct the rows and signs of the random projection matrix, it performs a count-sketch projection to transform the original high-dimensional configuration space into lower-dimensional subspace. This process is intuitively designed to effectively preserve the characteristics, such as pairwise point distances, of the original high-dimensional space for the reduced (important) dimensions. LlamaTune [16] adopts it to perform a projection of the configuration space from all documentations to a lowerdimensional subspace and then use the Bayesian Optimization-based optimizer to tune this smaller subspace. • Alternative approaches: Due to the challenges of tuning in high-dimensional configuration spaces, the identification of parameters that significantly affect DBMS performance has gained considerable attention. Among them, Researchers in [29] propose Caver to select a subset of storage parameters. Given a set of initial parameters and configurations, Carver first employs LHS to select a small number of configurations for evaluation. Subsequently, it greedily selects the most important parameters based on their parameter importance values. The first parameter is determined by the highest importance value, after which Carver fixes its value and computes the parameter importance values for the remaining parameters. During this process, importance is calculated as the difference between the variance of the original set of configurations and the sum of variances within the subset when parameters take different values. The algorithm selects parameters with the maximum difference. Recently, OpAdviser [30] proposed constructing an effective configuration region that contains promising configurations. It leverages performance similarity among historical workloads to guide the construction process. Specifically, it extracts a relatively compact region based on similar workloads and a larger region based on less similar ones. Furthermore, OpAdviser constructs the target search space by employing a majority weighted voting strategy to aggregate suggestions from candidate tasks. This paper is available on arxiv under CC BY 4.0 DEED. Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Authors: Authors: (1) Limeng Zhang, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia; (2) M. Ali Babar, Centre for Research on Engineering Software Technologies (CREST), The University of Adelaide, Australia. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 1.1 Configuration Parameter Tuning Challenges and 1.2 Contributions 2 Tuning Objectives 2 Tuning Objectives 3 Overview of Tuning Framework 3 Overview of Tuning Framework 4 Workload Characterization and 4.1 Query-level Characterization 4 Workload Characterization and 4.1 Query-level Characterization 4.2 Runtime-based Characterization 4.2 Runtime-based Characterization 5 Feature Pruning and 5.1 Workload-level Pruning 5 Feature Pruning and 5.1 Workload-level Pruning 5.2 Configuration-level Pruning 5.2 Configuration-level Pruning 5.3 Summary 5.3 Summary 6 Knowledge from Experience 6 Knowledge from Experience 7 Configuration Recommendation and 7.1 Bayesian Optimization 7 Configuration Recommendation and 7.1 Bayesian Optimization 7.2 Neural Network 7.2 Neural Network 7.3 Reinforcement Learning 7.3 Reinforcement Learning 7.4 Search-based Solutions 7.4 Search-based Solutions 8 Experimental Setting 8 Experimental Setting 9 Related Work 9 Related Work 10 Discussion and Conclusion, and References 10 Discussion and Conclusion, and References 5.2 Configuration-level Pruning Another approach to mitigating the optimization time required by machine learning-based methodologies is to reduce configuration space necessitating tuning. Configuration-level pruning endeavors to discern and prioritize the tuning of parameters that exert substantial influence on the DBMSs based on historical observations. • Spearman Rank Correlation Coefficient (SRCC) [26]: is a nonparametric measure of rank correlation on the strength of a monotonic relationship between paired data. It is defined as the Pearson correlation coefficient between the rank variables. By leveraging its capacity to gauge monotonic relationships, SRCC facilitates the identification and removal of redundant parameters, contributing to a more efficient and simplified configuration. LOCAT [7] calculates SRCC between each configuration parameter and the workload execution time to filter out some redundant configuration parameters and narrow down the parameter search space.” • Principal Component Analysis (PCA): is a dimensionality reduction method that transforms correlated variables into uncorrelated ones, known as principal components. It does so by calculating the covariance matrix, performing eigendecomposition, and selecting a subset of principal components based on their variance. After SRCC, LOCAT [7] applies Gaussian kernel Principal Component Analysis (KPCA) to further extract and form new lower-dimensional parameters derived after removal of redundant configuration parameters for subsequent optimal parameter searching. • Least Absolute Shrinkage and Selection Operator (LASSO) and Lasso Path Algorithm. In the context of linear regression, LASSO modifies this objective function by adding a L1 penalty term equals to λ times the sum of absolute values of the regression coefficients, where λ controls the strength of the penalty, and it helps to reduce the effect of irrelevant variables by penalizing models with large weights. A higher λ value results in more coefficients being pushed toward zero, thereby achieving interpretable, stable, and computationally efficient feature selection. OtterTune [8] uses the LASSO path algorithm to assess the importance of configuration parameters by gradually reducing the penalty term. The order in 6 which parameters are included during this process is then considered as the importance order, and OtterTune uses this information to prune less important parameters. • Random Forest (RF): is a supervised machine learning method to deal with classification and regression problems. It can be deemed a voting algorithm consisting of multiple decision trees, used to calculate the importance of features. In the study [27], the authors utilize Latin Hypercube Sampling (LHS) to select a subset of configurations. Subsequently, they employ Random Forests with 300 Classification and Regression Trees (CART) to ascertain the importance of each parameter. Their findings reveal that when employing the YCSB workload-A on Cassandra, optimizing just five parameters can yield performance levels comparable to 99% of the best configurations attained through extensive parameter tuning. HUNTER [13] adopt the RF classifier with CARTs and adopts the majority voting principle to determine the importance of the knobs. It then selects the top-20 knobs to reduce the configuration search space in its tuning framework. • Hashing-enhanced Subspace BO (HeSBO) [28]: is a randomized low-dimensional projection approach that operates by deducing the search space for Bayesian Optimization-based solutions (discussed in Section 7.1). By utilizing two uniform hash functions to construct the rows and signs of the random projection matrix, it performs a count-sketch projection to transform the original high-dimensional configuration space into lower-dimensional subspace. This process is intuitively designed to effectively preserve the characteristics, such as pairwise point distances, of the original high-dimensional space for the reduced (important) dimensions. LlamaTune [16] adopts it to perform a projection of the configuration space from all documentations to a lowerdimensional subspace and then use the Bayesian Optimization-based optimizer to tune this smaller subspace. • Alternative approaches: Due to the challenges of tuning in high-dimensional configuration spaces, the identification of parameters that significantly affect DBMS performance has gained considerable attention. Among them, Researchers in [29] propose Caver to select a subset of storage parameters. Given a set of initial parameters and configurations, Carver first employs LHS to select a small number of configurations for evaluation. Subsequently, it greedily selects the most important parameters based on their parameter importance values. The first parameter is determined by the highest importance value, after which Carver fixes its value and computes the parameter importance values for the remaining parameters. During this process, importance is calculated as the difference between the variance of the original set of configurations and the sum of variances within the subset when parameters take different values. The algorithm selects parameters with the maximum difference. Recently, OpAdviser [30] proposed constructing an effective configuration region that contains promising configurations. It leverages performance similarity among historical workloads to guide the construction process. Specifically, it extracts a relatively compact region based on similar workloads and a larger region based on less similar ones. Furthermore, OpAdviser constructs the target search space by employing a majority weighted voting strategy to aggregate suggestions from candidate tasks. This paper is available on arxiv under CC BY 4.0 DEED. This paper is available on arxiv under CC BY 4.0 DEED. available on arxiv

How Configuration-level Pruning Reduces Optimization Time in DBMS Tuning

The WEF continues to be a propaganda arm for the Chinese Communist Party and its social credit system based on digital ID & CBDC: perspective. Communist China’s digital yuan serves as a model Central Bank Digital Currency (CBDC) to the world because it reduces reliance on physical cash while “democratizing access to banking services,” according to a World Economic Forum (WEF) report. Published on October 8, the report “Global Financial Inclusion Practices: Case Studies from China, India and the USA” heaps heavy praise on the communist regime for having implemented a programmable digital yuan that fosters what the authors call “financial inclusion” through the democratization of banking services. “By reducing reliance on physical cash and democratizing access to banking services, the digital yuan serves as a model for CBDC use to boost financial inclusion”
WEF, “Global Financial Inclusion Practices,” October 2024 If you’re wondering why the WEF is praising communist China for “democratizing” anything, it’s worth noting that the report was produced in collaboration with Beijing’s Tsinghua University Peoples Bank of China School of Finance, which was founded on March 29, 2012, as a joint venture between the University and the People’s Bank of China (PBC). In the report, there is no mention of the Chinese Communist Party (CCP) nor its social credit system and how it leverages digital ID and CBDC to incentivize, coerce, or otherwise manipulate human behavior. Instead, the report says: “The introduction of China’s digital yuan has played an important role in promoting financial inclusion by making financial services more accessible and affordable to underserved populations. “By reducing the reliance on physical cash and integrating the digital yuan into everyday transactions, even in areas with poor network connectivity, the e-CNY has helped to bring unbanked or underbanked individuals into the formal financial system.” Try telling that to the million or so Uighurs that have been sent to “re-education” camps, or try telling that to the millions of Chinese “netizens” who have been blacklisted by the social credit system. Under China’s social credit system, citizens are given a credit score based on their online and offline behavior. It’s a system that rewards “good” behavior like spending time with the elderly while punishing “bad” behavior like criticizing the government or spending too much time playing videogames. When “trust” is broken in one area, restrictions are placed everywhere — meaning citizens who commit even minor infractions can be blacklisted from traveling, going to restaurants, renting a home, or even having insurance. This has happened to over 30 million citizens, according to Chinese State-run propaganda channel CGTN. “The digital yuan has revolutionized Suzhou’s financial landscape, enhancing financial inclusion by providing broader and more convenient access to affordable services […] With thorough attention to infrastructure, regulation, technology and education, Suzhou’s approach offers a proven model for cities worldwide”
WEF, “Global Financial Inclusion Practices,” October 2024 Speaking of CCP propaganda, the WEF report highlights how China’s CBDC revolutionized the city of Suzhou’s financial landscape, stating that Suzhou is a proven model for cities worldwide. According to the report, “Suzhou, prominently featured in the [CBDC] pilot phases, stands out as a leader in the adoption of the digital yuan in China.” “The city has not only trialed traditional uses but also explored innovative applications by integrating the digital yuan with local transport and government services, enhancing its utility and acceptance among residents. “For example, users with a digital yuan wallet can touch their phone screen to the turnstile at metro stations, providing easy access to the station.” What the authors fail to mention in their example of a model city is that CBDCs cannot function without being linked to a person’s digital identity, and that both CBDC and digital ID are two of the three key components of Digital Public Infrastructure (DPI) that also includes massive data exchanges. In communist China, users with a low social credit score cannot use their digital yuan wallets on their phones to pass the turnstiles at the metro. And the CCP propagandists at the WEF have the gall to say that it’s a model system for the world! “The digital yuan enhances transaction efficiency and security, promoting public trust and providing a model for other CBDCs aimed at expanding financial inclusion globally”
WEF, “Global Financial Inclusion Practices,” October 2024 Three years ago the Center for a New American Security (CNAS) published a report detailing China’s ambitions for an authoritarian Digital Currency / Electronic Payment (DCEP) system in which the State aimed to process and support over 300,000 financial transactions per second, with the data feeding the Communist Party’s social credit system in real-time. According to the CNAS report, “This digital currency push is a major step in expanding the party’s digital authoritarianism, adding real-time financial data into the CCP’s strategy for technology-driven governance.” But it’s not just the financial transactions that the CCP is interested in — it’s about combining that financial data with data collected from the Internet of Things, smart homes, CCTV footage, and of course mobile phone usage, including citizens’ geolocation and browsing histories. According to CNAS, “The system will also enable the CCP to exercise greater control over private transactions, as well as to wield punitive power over Chinese citizens in tandem with the social credit system.” “In addition to basic information about users and transactions, it is possible that various metadata associated with users’ movements and devices could also be infused with such big data,” the CNAS reports states, adding, “The PBOC [People’s Bank of China] will become a possessor of a significant data trove to combine with its tools for censuring and surveilling individuals.” The WEF continues to be a propaganda arm of the Chinese Communist Party, calling its digital ID-based CBDC a model for the world despite it being used as a totalitarian tool for social credit. Tim Hinchliffe, Editor, The Sociable The WEF continues to be a propaganda arm for the Chinese Communist Party and its social credit system based on digital ID & CBDC: perspective. The WEF continues to be a propaganda arm for the Chinese Communist Party and its social credit system based on digital ID & CBDC: perspective. Communist China’s digital yuan serves as a model Central Bank Digital Currency ( CBDC ) to the world because it reduces reliance on physical cash while “democratizing access to banking services,” according to a World Economic Forum (WEF) report. CBDC Published on October 8, the report “ Global Financial Inclusion Practices: Case Studies from China, India and the USA ” heaps heavy praise on the communist regime for having implemented a programmable digital yuan that fosters what the authors call “financial inclusion” through the democratization of banking services. the report Global Financial Inclusion Practices: Case Studies from China, India and the USA “By reducing reliance on physical cash and democratizing access to banking services, the digital yuan serves as a model for CBDC use to boost financial inclusion” WEF, “Global Financial Inclusion Practices,” October 2024 “By reducing reliance on physical cash and democratizing access to banking services, the digital yuan serves as a model for CBDC use to boost financial inclusion” “By reducing reliance on physical cash and democratizing access to banking services, the digital yuan serves as a model for CBDC use to boost financial inclusion” “By reducing reliance on physical cash and democratizing access to banking services, the digital yuan serves as a model for CBDC use to boost financial inclusion” WEF, “ Global Financial Inclusion Practices ,” October 2024 Global Financial Inclusion Practices If you’re wondering why the WEF is praising communist China for “democratizing” anything, it’s worth noting that the report was produced in collaboration with Beijing’s Tsinghua University Peoples Bank of China School of Finance , which was founded on March 29, 2012, as a joint venture between the University and the People’s Bank of China (PBC). Tsinghua University Peoples Bank of China School of Finance In the report, there is no mention of the Chinese Communist Party (CCP) nor its social credit system and how it leverages digital ID and CBDC to incentivize, coerce, or otherwise manipulate human behavior. Instead, the report says: “The introduction of China’s digital yuan has played an important role in promoting financial inclusion by making financial services more accessible and affordable to underserved populations. “The introduction of China’s digital yuan has played an important role in promoting financial inclusion by making financial services more accessible and affordable to underserved populations. “The introduction of China’s digital yuan has played an important role in promoting financial inclusion by making financial services more accessible and affordable to underserved populations. “By reducing the reliance on physical cash and integrating the digital yuan into everyday transactions, even in areas with poor network connectivity, the e-CNY has helped to bring unbanked or underbanked individuals into the formal financial system.” “By reducing the reliance on physical cash and integrating the digital yuan into everyday transactions, even in areas with poor network connectivity, the e-CNY has helped to bring unbanked or underbanked individuals into the formal financial system.” “By reducing the reliance on physical cash and integrating the digital yuan into everyday transactions, even in areas with poor network connectivity, the e-CNY has helped to bring unbanked or underbanked individuals into the formal financial system.” Try telling that to the million or so Uighurs that have been sent to “re-education” camps, or try telling that to the millions of Chinese “netizens” who have been blacklisted by the social credit system. Uighurs Under China’s social credit system, citizens are given a credit score based on their online and offline behavior. It’s a system that rewards “good” behavior like spending time with the elderly while punishing “bad” behavior like criticizing the government or spending too much time playing videogames. When “trust” is broken in one area, restrictions are placed everywhere — meaning citizens who commit even minor infractions can be blacklisted from traveling, going to restaurants, renting a home, or even having insurance. This has happened to over 30 million citizens, according to Chinese State-run propaganda channel CGTN. “The digital yuan has revolutionized Suzhou’s financial landscape, enhancing financial inclusion by providing broader and more convenient access to affordable services […] With thorough attention to infrastructure, regulation, technology and education, Suzhou’s approach offers a proven model for cities worldwide” WEF, “Global Financial Inclusion Practices,” October 2024 “The digital yuan has revolutionized Suzhou’s financial landscape, enhancing financial inclusion by providing broader and more convenient access to affordable services […] With thorough attention to infrastructure, regulation, technology and education, Suzhou’s approach offers a proven model for cities worldwide” “The digital yuan has revolutionized Suzhou’s financial landscape, enhancing financial inclusion by providing broader and more convenient access to affordable services […] With thorough attention to infrastructure, regulation, technology and education, Suzhou’s approach offers a proven model for cities worldwide” “The digital yuan has revolutionized Suzhou’s financial landscape, enhancing financial inclusion by providing broader and more convenient access to affordable services […] With thorough attention to infrastructure, regulation, technology and education, Suzhou’s approach offers a proven model for cities worldwide” WEF, “ Global Financial Inclusion Practices ,” October 2024 Global Financial Inclusion Practices Speaking of CCP propaganda, the WEF report highlights how China’s CBDC revolutionized the city of Suzhou’s financial landscape, stating that Suzhou is a proven model for cities worldwide. According to the report, “ Suzhou, prominently featured in the [CBDC] pilot phases, stands out as a leader in the adoption of the digital yuan in China .” Suzhou, prominently featured in the [CBDC] pilot phases, stands out as a leader in the adoption of the digital yuan in China Suzhou, prominently featured in the [CBDC] pilot phases, stands out as a leader in the adoption of the digital yuan in China “ The city has not only trialed traditional uses but also explored innovative applications by integrating the digital yuan with local transport and government services, enhancing its utility and acceptance among residents . The city has not only trialed traditional uses but also explored innovative applications by integrating the digital yuan with local transport and government services, enhancing its utility and acceptance among residents The city has not only trialed traditional uses but also explored innovative applications by integrating the digital yuan with local transport and government services, enhancing its utility and acceptance among residents “ For example, users with a digital yuan wallet can touch their phone screen to the turnstile at metro stations, providing easy access to the station .” For example, users with a digital yuan wallet can touch their phone screen to the turnstile at metro stations, providing easy access to the station For example, users with a digital yuan wallet can touch their phone screen to the turnstile at metro stations, providing easy access to the station What the authors fail to mention in their example of a model city is that CBDCs cannot function without being linked to a person’s digital identity, and that both CBDC and digital ID are two of the three key components of Digital Public Infrastructure (DPI) that also includes massive data exchanges. Digital Public Infrastructure In communist China, users with a low social credit score cannot use their digital yuan wallets on their phones to pass the turnstiles at the metro. And the CCP propagandists at the WEF have the gall to say that it’s a model system for the world! “The digital yuan enhances transaction efficiency and security, promoting public trust and providing a model for other CBDCs aimed at expanding financial inclusion globally” WEF, “Global Financial Inclusion Practices,” October 2024 “The digital yuan enhances transaction efficiency and security, promoting public trust and providing a model for other CBDCs aimed at expanding financial inclusion globally” “The digital yuan enhances transaction efficiency and security, promoting public trust and providing a model for other CBDCs aimed at expanding financial inclusion globally” “The digital yuan enhances transaction efficiency and security, promoting public trust and providing a model for other CBDCs aimed at expanding financial inclusion globally” WEF, “ Global Financial Inclusion Practices ,” October 2024 Global Financial Inclusion Practices Three years ago the Center for a New American Security (CNAS) published a report detailing China’s ambitions for an authoritarian Digital Currency / Electronic Payment (DCEP) system in which the State aimed to process and support over 300,000 financial transactions per second, with the data feeding the Communist Party’s social credit system in real-time. published a report According to the CNAS report, “ This digital currency push is a major step in expanding the party’s digital authoritarianism, adding real-time financial data into the CCP’s strategy for technology-driven governance .” This digital currency push is a major step in expanding the party’s digital authoritarianism, adding real-time financial data into the CCP’s strategy for technology-driven governance This digital currency push is a major step in expanding the party’s digital authoritarianism, adding real-time financial data into the CCP’s strategy for technology-driven governance But it’s not just the financial transactions that the CCP is interested in — it’s about combining that financial data with data collected from the Internet of Things, smart homes, CCTV footage, and of course mobile phone usage, including citizens’ geolocation and browsing histories. According to CNAS, “ The system will also enable the CCP to exercise greater control over private transactions, as well as to wield punitive power over Chinese citizens in tandem with the social credit system .” The system will also enable the CCP to exercise greater control over private transactions, as well as to wield punitive power over Chinese citizens in tandem with the social credit system The system will also enable the CCP to exercise greater control over private transactions, as well as to wield punitive power over Chinese citizens in tandem with the social credit system “ In addition to basic information about users and transactions, it is possible that various metadata associated with users’ movements and devices could also be infused with such big data ,” the CNAS reports states, adding, “ The PBOC [People’s Bank of China] will become a possessor of a significant data trove to combine with its tools for censuring and surveilling individuals .” In addition to basic information about users and transactions, it is possible that various metadata associated with users’ movements and devices could also be infused with such big data In addition to basic information about users and transactions, it is possible that various metadata associated with users’ movements and devices could also be infused with such big data The PBOC [People’s Bank of China] will become a possessor of a significant data trove to combine with its tools for censuring and surveilling individuals The PBOC [People’s Bank of China] will become a possessor of a significant data trove to combine with its tools for censuring and surveilling individuals The WEF continues to be a propaganda arm of the Chinese Communist Party, calling its digital ID-based CBDC a model for the world despite it being used as a totalitarian tool for social credit. Tim Hinchliffe, Editor, The Sociable Tim Hinchliffe, Editor, The Sociable Tim Hinchliffe, Editor, The Sociable

China’s Digital Yuan: A CBDC Model Reducing Cash Dependency and Expanding Financial Access, Says WEF

China se digitale yuan: 'n CBDC-model wat kontantafhanklikheid verminder en finansiële toegang uitbrei, sê WEF

Кітайскі лічбавы юань: мадэль CBDC, якая зніжае залежнасць ад грашовых сродкаў і пашырае фінансавы доступ, кажа WEF

চীনের ডিজিটাল ইউয়ান: একটি CBDC মডেল নগদ নির্ভরতা হ্রাস করে এবং আর্থিক অ্যাক্সেস সম্প্রসারণ করে, WEF বলে

Kineski digitalni juan: CBDC model koji smanjuje ovisnost o gotovini i proširuje pristup finansijama, kaže WEF

El yuan digital chino: un modelo de CBDC que reduce la dependencia del efectivo y amplía el acceso financiero, afirma el WEF

चीन का डिजिटल युआन: नकदी निर्भरता को कम करने और वित्तीय पहुंच का विस्तार करने वाला एक सीबीडीसी मॉडल, WEF का कहना है

Yuan Digital Tiongkok: Model CBDC yang Mengurangi Ketergantungan Uang Tunai dan Memperluas Akses Keuangan, Kata WEF

中国のデジタル人民元：WEFによると、現金依存を減らし金融アクセスを拡大するCBDCモデル

चीनको डिजिटल युआन: नगद निर्भरता घटाउने र वित्तीय पहुँच विस्तार गर्ने CBDC मोडेल, WEF भन्छ

China's Digital Yuan: A CBDC Model Kuderedza Kutsamira Kwemari uye Kuwedzera Kuwanikwa Kwemari, inodaro WEF.

Кинески дигитални јуан: ЦБДЦ модел који смањује зависност од готовине и проширује финансијски приступ, каже ВЕФ

WEF'e göre Çin'in Dijital Yuanı: Nakit Bağımlılığını Azaltan ve Finansal Erişimi Genişleten Bir CBDC Modeli

As cloud adoption accelerates, so does the energy consumption of data centers, leading to a rising awareness of the environmental impact of IT infrastructures. A 2022 report by the International Energy Agency (IEA) noted that data centers now account for nearly 1% of the world's electricity use, with projections showing an even higher figure as cloud computing continues to grow. This has prompted companies, governments, and environmental groups to demand greener, more sustainable IT practices. DevOps, a field built on automation and infrastructure scaling, is at the center of these discussions, particularly as companies search for ways to reduce their environmental footprint while maintaining performance. Aliaksei Volski, a cloud engineer with years of experience working with sustainability-focused DevOps practices, brings invaluable insight into this field. Having spent the last several years optimizing cloud infrastructure with a strong focus on sustainability, Volski understands the intricate balance between technological advancement and environmental responsibility. “We’ve reached a point where the carbon footprint of our digital activities can’t be ignored,” Volski emphasizes. “Every company using cloud infrastructure should be thinking about how to reduce energy consumption and emissions through automation and smart resource management.” His recent work reflects a growing trend in the tech industry to reduce carbon footprints by embedding eco-friendly practices directly into DevOps processes. “Sustainability in DevOps isn’t just about reducing energy consumption,” Volski notes. “It’s about embedding efficiency into the automation process, ensuring that the infrastructure can scale without putting unnecessary strain on the environment.” One of the technologies often employed in sustainable DevOps strategies is Microsoft Azure, a cloud platform that has introduced several features to optimize energy efficiency. For instance, the Microsoft Sustainability Calculator enables organizations to monitor and visualize their carbon emissions across cloud resources, helping businesses identify areas for improvement. Furthermore, Microsoft has committed to making its data centers fully reliant on renewable energy by 2025, a move that will drastically reduce the environmental impact of cloud services. Leading companies like Microsoft, Google, and Amazon have taken notable steps toward reducing the carbon emissions associated with cloud infrastructure. Microsoft’s "Project Natick," for instance, focused on reducing energy consumption by submerging data centers underwater for natural cooling. Meanwhile, Google’s “Carbon-Free Energy” initiative aims to achieve 100% renewable energy in all its operations by 2030. Amazon’s “Sustainability in the Cloud” program emphasizes optimizing energy efficiency across its AWS data centers, incorporating green energy solutions and advanced cooling technologies. Volski’s broader experience in cloud infrastructure optimization underscores the growing need to balance business goals with ecological ones. His approach involves developing best practices for reducing the carbon footprint of cloud infrastructure, such as optimizing resource use and integrating automated monitoring systems to track energy consumption in real time. “One of the biggest wins we’ve had was through real-time monitoring,” Volski explains. “By setting up continuous tracking systems, we were able to identify when resources were being underutilized and then scale them down automatically. This not only saved on costs but also helped reduce our overall energy usage.” For example, a 2021 case study from Goldman Sachs highlighted how dynamic resource allocation via Kubernetes reduced energy consumption by 30% in its cloud infrastructure while maintaining high availability and performance. By adopting similar DevOps approaches, companies can make considerable gains in reducing their carbon footprint without compromising scalability or performance. Tools such as Terraform for infrastructure automation and Prometheus for monitoring provide robust frameworks that enable teams to efficiently scale their cloud environments while keeping energy usage in check. The push for greener DevOps practices is not just a passing trend but is increasingly becoming a competitive advantage for companies. A 2023 report from the Cloud Native Computing Foundation (CNCF) found that businesses implementing sustainable cloud practices saw a 15% reduction in operational costs on average. Furthermore, customers are beginning to demand eco-conscious initiatives from the brands they engage with. According to a 2022 survey by IBM, over 60% of consumers say they are more likely to purchase from companies that demonstrate environmentally friendly practices, highlighting the potential business benefits of adopting sustainable DevOps methodologies. Looking ahead, Volski emphasizes the need for a holistic approach that considers both technological advancements and sustainability. “It’s not enough to just optimize processes,” Volski says. “We need to integrate renewable energy wherever possible and encourage the adoption of practices like power-efficient coding and serverless architecture to further minimize the carbon impact of our systems.” Serverless computing, for instance, allows companies to run functions only when needed, drastically reducing the energy footprint by eliminating the need for always-on infrastructure. Another emerging trend in sustainable DevOps is the use of carbon-aware computing, where cloud operations are scheduled around periods of low carbon intensity in the energy grid. This concept allows cloud services to dynamically shift workloads to times when renewable energy is most available. According to a study by the University of Bristol, this strategy could reduce carbon emissions from cloud operations by as much as 20%. Volski sees this as a promising avenue for future developments: “Carbon-aware computing is one of those innovations that could have a huge impact. By adapting our operations to take advantage of cleaner energy sources, we’re not just improving our processes—we’re helping the planet.” By adopting sustainable practices in DevOps, companies have the opportunity to lead the charge in eco-friendly technology solutions. While the tech giants have made considerable headway, there’s still vast potential for businesses of all sizes to reduce their environmental impact. “DevOps professionals have the power to make a real difference,” Volski concludes. “With the right tools and mindset, we can ensure that the cloud revolution not only benefits business but also supports a healthier, more sustainable world.” As cloud adoption accelerates, so does the energy consumption of data centers, leading to a rising awareness of the environmental impact of IT infrastructures. A 2022 report by the International Energy Agency (IEA) noted that data centers now account for nearly 1% of the world's electricity use, with projections showing an even higher figure as cloud computing continues to grow. This has prompted companies, governments, and environmental groups to demand greener, more sustainable IT practices. DevOps, a field built on automation and infrastructure scaling, is at the center of these discussions, particularly as companies search for ways to reduce their environmental footprint while maintaining performance. Aliaksei Volski, a cloud engineer with years of experience working with sustainability-focused DevOps practices, brings invaluable insight into this field. Having spent the last several years optimizing cloud infrastructure with a strong focus on sustainability, Volski understands the intricate balance between technological advancement and environmental responsibility. “We’ve reached a point where the carbon footprint of our digital activities can’t be ignored,” Volski emphasizes. “Every company using cloud infrastructure should be thinking about how to reduce energy consumption and emissions through automation and smart resource management.” His recent work reflects a growing trend in the tech industry to reduce carbon footprints by embedding eco-friendly practices directly into DevOps processes. “Sustainability in DevOps isn’t just about reducing energy consumption,” Volski notes. “It’s about embedding efficiency into the automation process, ensuring that the infrastructure can scale without putting unnecessary strain on the environment.” One of the technologies often employed in sustainable DevOps strategies is Microsoft Azure, a cloud platform that has introduced several features to optimize energy efficiency. For instance, the Microsoft Sustainability Calculator enables organizations to monitor and visualize their carbon emissions across cloud resources, helping businesses identify areas for improvement. Furthermore, Microsoft has committed to making its data centers fully reliant on renewable energy by 2025, a move that will drastically reduce the environmental impact of cloud services. Leading companies like Microsoft, Google, and Amazon have taken notable steps toward reducing the carbon emissions associated with cloud infrastructure. Microsoft’s "Project Natick," for instance, focused on reducing energy consumption by submerging data centers underwater for natural cooling. Meanwhile, Google’s “Carbon-Free Energy” initiative aims to achieve 100% renewable energy in all its operations by 2030. Amazon’s “Sustainability in the Cloud” program emphasizes optimizing energy efficiency across its AWS data centers, incorporating green energy solutions and advanced cooling technologies. Volski’s broader experience in cloud infrastructure optimization underscores the growing need to balance business goals with ecological ones. His approach involves developing best practices for reducing the carbon footprint of cloud infrastructure, such as optimizing resource use and integrating automated monitoring systems to track energy consumption in real time. “One of the biggest wins we’ve had was through real-time monitoring,” Volski explains. “By setting up continuous tracking systems, we were able to identify when resources were being underutilized and then scale them down automatically. This not only saved on costs but also helped reduce our overall energy usage.” For example, a 2021 case study from Goldman Sachs highlighted how dynamic resource allocation via Kubernetes reduced energy consumption by 30% in its cloud infrastructure while maintaining high availability and performance. By adopting similar DevOps approaches, companies can make considerable gains in reducing their carbon footprint without compromising scalability or performance. Tools such as Terraform for infrastructure automation and Prometheus for monitoring provide robust frameworks that enable teams to efficiently scale their cloud environments while keeping energy usage in check. The push for greener DevOps practices is not just a passing trend but is increasingly becoming a competitive advantage for companies. A 2023 report from the Cloud Native Computing Foundation (CNCF) found that businesses implementing sustainable cloud practices saw a 15% reduction in operational costs on average. Furthermore, customers are beginning to demand eco-conscious initiatives from the brands they engage with. According to a 2022 survey by IBM, over 60% of consumers say they are more likely to purchase from companies that demonstrate environmentally friendly practices, highlighting the potential business benefits of adopting sustainable DevOps methodologies. Looking ahead, Volski emphasizes the need for a holistic approach that considers both technological advancements and sustainability. “It’s not enough to just optimize processes,” Volski says. “We need to integrate renewable energy wherever possible and encourage the adoption of practices like power-efficient coding and serverless architecture to further minimize the carbon impact of our systems.” Serverless computing, for instance, allows companies to run functions only when needed, drastically reducing the energy footprint by eliminating the need for always-on infrastructure. Another emerging trend in sustainable DevOps is the use of carbon-aware computing, where cloud operations are scheduled around periods of low carbon intensity in the energy grid. This concept allows cloud services to dynamically shift workloads to times when renewable energy is most available. According to a study by the University of Bristol, this strategy could reduce carbon emissions from cloud operations by as much as 20%. Volski sees this as a promising avenue for future developments: “Carbon-aware computing is one of those innovations that could have a huge impact. By adapting our operations to take advantage of cleaner energy sources, we’re not just improving our processes—we’re helping the planet.” By adopting sustainable practices in DevOps, companies have the opportunity to lead the charge in eco-friendly technology solutions. While the tech giants have made considerable headway, there’s still vast potential for businesses of all sizes to reduce their environmental impact. “DevOps professionals have the power to make a real difference,” Volski concludes. “With the right tools and mindset, we can ensure that the cloud revolution not only benefits business but also supports a healthier, more sustainable world.”

Greener DevOps: How Aliaksei Volski is Reducing Carbon Footprints in Cloud Infrastructure

Groener DevOps: hoe Aliaksei Volski koolstofvoetspore in wolkinfrastruktuur verminder

DevOps أكثر اخضرارًا: كيف يعمل Aliaksei Volski على تقليل البصمة الكربونية في البنية التحتية السحابية

Greener DevOps: Kunjams Aliaksei Volski jupax Infraestructura Cloud ukan Huellas de Carbono ukar jisk’achaski

DevOps más ecológico: cómo Aliaksei Volski reduce la huella de carbono en la infraestructura de la nube

Ավելի կանաչ DevOps. Ինչպես է Aliaksei Volski-ն նվազեցնում ածխածնի հետքերը Cloud ենթակառուցվածքում

より環境に優しい DevOps: Aliaksei Volski がクラウド インフラストラクチャの二酸化炭素排出量を削減する方法

Greener DevOps: Aliaksei Volski가 클라우드 인프라에서 탄소 발자국을 줄이는 방법

Greener DevOps: Jak Aliaksei Volski zmniejsza ślad węglowy w infrastrukturze chmurowej

DevOps ที่เป็นมิตรกับสิ่งแวดล้อม: Aliaksei Volski ลดรอยเท้าคาร์บอนในโครงสร้างพื้นฐานคลาวด์ได้อย่างไร

Greener DevOps: Aliaksei Volski ከመይ ጌሩ ኣብ ትሕተ ቅርጺ ደበና ኣሰር ካርቦን ይቕንሶ ኣሎ።

Greenaşyl DevOps: Aliaksei Wolski bulut infrastrukturasynda uglerod aýak yzlaryny nädip azaldar?

DevOps xanh hơn: Aliaksei Volski đang giảm lượng khí thải carbon trong cơ sở hạ tầng đám mây như thế nào

Table of Links Abstract and 1. Introduction 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution Literature Review
Methodology 3.1 Model Assumption 3.2 Theorems and Model Discussion Result Analysis
Conclusion and References 1.5 MONTE CARLO SIMULATION AND VARIANCE REDUCTION TECHNIQUES Monte Carlo simulation is a powerful computational technique used in various fields, including finance, engineering, physics, and statistics, to approximate complex systems and processes through repeated random sampling. It relies on the principles of randomness and statistical inference to estimate unknown quantities or simulate the behavior of systems that may be too intricate to model analytically. At its core, Monte Carlo simulation involves generating many random samples from a specified probability distribution, using these samples to simulate the system under consideration, and then analyzing the results to draw conclusions or make predictions [6]. One of the key challenges in Monte Carlo simulation is achieving accurate and efficient estimates while keeping computational costs manageable [7]. Variance reduction techniques are strategies employed to improve the efficiency and precision of Monte Carlo simulations by reducing the variability of the estimates obtained. Importance Sampling is a variance reduction technique that aims to improve the efficiency of Monte Carlo simulations by focusing the random samples on regions of the probability space where the integrand has the most significant contributions. Instead of sampling from the original distribution, importance sampling involves sampling from a modified distribution that places more emphasis on the relevant regions, thereby reducing the variance of the estimator [8][9]. Vector Random Variable technique is another variance reduction method commonly used in Monte Carlo simulations. It involves transforming correlated random variables into independent ones by utilizing techniques such as Cholesky decomposition or eigenvalue decomposition. By transforming the variables into an uncorrelated set, the variance of the estimator can be reduced, leading to more accurate results with fewer samples [10]. Antithetic Variates is a simple yet effective variance reduction technique that exploits negative correlation between pairs of random variables. It involves generating paired samples such that one sample is the negative of the other [11]. By averaging the results obtained from each pair, the variance of the estimator is reduced, resulting in more precise estimates with fewer random samples. Control Variates is a variance reduction technique that leverages known relationships between the variable of interest and another related variable, known as the control variate. By incorporating the control variate into the simulation, the variance of the estimator can be reduced, leading to more efficient estimates [12]. Control variates are chosen such that they are correlated with the variable of interest and have known expectations, facilitating the estimation process. Overall, variance reduction techniques play a crucial role in improving the accuracy and efficiency of Monte Carlo simulations. By implementing these techniques, practitioners can obtain more reliable estimates with fewer computational resources, making Monte Carlo simulation a valuable tool for decision-making and problem-solving in diverse fields. Authors:
(1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com);
(2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in);
(3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction Abstract and 1. Introduction 1.1 Option Pricing 1.1 Option Pricing 1.2 Asymptotic Notation (Big O) 1.2 Asymptotic Notation (Big O) 1.3 Finite Difference 1.3 Finite Difference 1.4 The Black-Schole Model 1.4 The Black-Schole Model 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.5 Monte Carlo Simulation and Variance Reduction Techniques 1.6 Our Contribution 1.6 Our Contribution Literature Review Methodology Literature Review Literature Review Literature Review Methodology Methodology 3.1 Model Assumption 3.1 Model Assumption 3.2 Theorems and Model Discussion 3.2 Theorems and Model Discussion Result Analysis Conclusion and References Result Analysis Result Analysis Result Analysis Conclusion and References Conclusion and References Conclusion and References 1.5 MONTE CARLO SIMULATION AND VARIANCE REDUCTION TECHNIQUES Monte Carlo simulation is a powerful computational technique used in various fields, including finance, engineering, physics, and statistics, to approximate complex systems and processes through repeated random sampling. It relies on the principles of randomness and statistical inference to estimate unknown quantities or simulate the behavior of systems that may be too intricate to model analytically. At its core, Monte Carlo simulation involves generating many random samples from a specified probability distribution, using these samples to simulate the system under consideration, and then analyzing the results to draw conclusions or make predictions [6]. One of the key challenges in Monte Carlo simulation is achieving accurate and efficient estimates while keeping computational costs manageable [7]. Variance reduction techniques are strategies employed to improve the efficiency and precision of Monte Carlo simulations by reducing the variability of the estimates obtained. Importance Sampling is a variance reduction technique that aims to improve the efficiency of Monte Carlo simulations by focusing the random samples on regions of the probability space where the integrand has the most significant contributions. Instead of sampling from the original distribution, importance sampling involves sampling from a modified distribution that places more emphasis on the relevant regions, thereby reducing the variance of the estimator [8][9]. Vector Random Variable technique is another variance reduction method commonly used in Monte Carlo simulations. It involves transforming correlated random variables into independent ones by utilizing techniques such as Cholesky decomposition or eigenvalue decomposition. By transforming the variables into an uncorrelated set, the variance of the estimator can be reduced, leading to more accurate results with fewer samples [10]. Antithetic Variates is a simple yet effective variance reduction technique that exploits negative correlation between pairs of random variables. It involves generating paired samples such that one sample is the negative of the other [11]. By averaging the results obtained from each pair, the variance of the estimator is reduced, resulting in more precise estimates with fewer random samples. Control Variates is a variance reduction technique that leverages known relationships between the variable of interest and another related variable, known as the control variate. By incorporating the control variate into the simulation, the variance of the estimator can be reduced, leading to more efficient estimates [12]. Control variates are chosen such that they are correlated with the variable of interest and have known expectations, facilitating the estimation process. Overall, variance reduction techniques play a crucial role in improving the accuracy and efficiency of Monte Carlo simulations. By implementing these techniques, practitioners can obtain more reliable estimates with fewer computational resources, making Monte Carlo simulation a valuable tool for decision-making and problem-solving in diverse fields. Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). Authors: Authors: (1) Agni Rakshit, Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, India (spiritualagnimath.statml@gmail.com); (2) Gautam Bandyopadhyay, Department of Management Studies, National Institute of Technology, Durgapur, Durgapur, India (gbandyopadhyay.dms@nitdgp.ac.in); (3) Tanujit Chakraborty, Department of Science and Engineering & Sorbonne Center for AI, Sorbonne University, Abu Dhabi, United Arab Emirates (tanujit.chakraborty@sorbonne.ae). This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv available on arxiv

Monte Carlo Simulation and Variance Reduction Techniques

Comparative Analysis of Option Pricing Methods: FDM, Monte Carlo Simulation, and Variance Reduction 

Authors:
(1) Seokil Ham, KAIST;
(2) Jungwuk Park, KAIST;
(3) Dong-Jun Han, Purdue University;
(4) Jaekyun Moon, KAIST. Table of Links Abstract and 1. Introduction 2. Related Works 3. Proposed NEO-KD Algorithm and 3.1 Problem Setup: Adversarial Training in Multi-Exit Networks 3.2 Algorithm Description 4. Experiments and 4.1 Experimental Setup 4.2. Main Experimental Results 4.3. Ablation Studies and Discussions 5. Conclusion, Acknowledgement and References A. Experiment Details B. Clean Test Accuracy and C. Adversarial Training via Average Attack D. Hyperparameter Tuning E. Discussions on Performance Degradation at Later Exits F. Comparison with Recent Defense Methods for Single-Exit Networks G. Comparison with SKD and ARD and H. Implementations of Stronger Attacker Algorithms 5 Conclusion In this paper, we proposed a new knowledge distillation based adversarial training strategy for robust multi-exit networks. Our solution, NEO-KD, reduces adversarial transferability in the network while guiding the output of the adversarial examples to closely follow the ensemble outputs of the neighbor exits of the clean data, significantly improving the overall adversarial test accuracy. Extensive experimental results on both anytime and budgeted prediction setups using various datasets confirmed the effectiveness of our method, compared to baselines relying on existing adversarial training or knowledge distillation techniques for multi-exit networks. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1I1A2A02061135), by the Center for Applied Research in Artificial Intelligence (CARAI) grant funded by DAPA and ADD (UD230017TD), and by IITP funds from MSIT of Korea (No. 2020-0-00626). References [1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In Computer Vision– ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XXIII, pages 484–501. Springer, 2020. [2] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 ieee symposium on security and privacy (sp), pages 39–57. Ieee, 2017. [3] Sihong Chen, Haojing Shen, Ran Wang, and Xizhao Wang. Towards improving fast adversarial training in multi-exit network. Neural Networks, 150:1–11, 2022. [4] Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive boundary attack. In International Conference on Machine Learning, pages 2196–2205. PMLR, 2020. [5] Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In International conference on machine learning, pages 2206–2216. PMLR, 2020. [6] Junhao Dong, Seyed-Mohsen Moosavi-Dezfooli, Jianhuang Lai, and Xiaohua Xie. The enemy of my enemy is my friend: Exploring inverse adversaries for improving adversarial training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24678–24687, 2023. [7] Yinpeng Dong, Ke Xu, Xiao Yang, Tianyu Pang, Zhijie Deng, Hang Su, and Jun Zhu. Exploring memorization in adversarial training. arXiv preprint arXiv:2106.01606, 2021. [8] Micah Goldblum, Liam Fowl, Soheil Feizi, and Tom Goldstein. Adversarially robust distillation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 3996–4003, 2020. [9] Dong-Jun Han, Jungwuk Park, Seokil Ham, Namjin Lee, and Jaekyun Moon. Improving lowlatency predictions in multi-exit neural networks via block-dependent losses. IEEE Transactions on Neural Networks and Learning Systems, 2023. [10] Mirazul Haque, Anki Chauhan, Cong Liu, and Wei Yang. Ilfo: Adversarial attack on adaptive neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14264–14273, 2020. [11] Sanghyun Hong, Yigitcan Kaya, Ionut,-Vlad Modoranu, and Tudor Dumitras. A panda? no, it’s a sloth: Slowdown attacks on adaptive multi-exit neural network inference. In International Conference on Learning Representations, 2020. [12] Ting-Kuei Hu, Tianlong Chen, Haotao Wang, and Zhangyang Wang. Triple wins: Boosting accuracy, robustness and efficiency together by enabling input-adaptive inference. In International Conference on Learning Representations, 2020. [13] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens Van Der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. arXiv preprint arXiv:1703.09844, 2017. [14] Hoki Kim. Torchattacks: A pytorch repository for adversarial attacks. arXiv preprint arXiv:2010.01950, 2020. [15] Alexandros Kouris, Stylianos I Venieris, Stefanos Laskaridis, and Nicholas Lane. Multi-exit semantic segmentation networks. In European Conference on Computer Vision, pages 330–349. Springer, 2022. [16] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. [17] Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7(7):3, 2015. [18] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998. [19] Sungyoon Lee, Hoki Kim, and Jaewook Lee. Graddiv: Adversarial robustness of randomized neural networks via gradient diversity regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. [20] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1891–1900, 2019. [21] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In International Conference on Learning Representations, 2018. [22] Tianyu Pang, Kun Xu, Chao Du, Ning Chen, and Jun Zhu. Improving adversarial robustness via promoting ensemble diversity. In International Conference on Machine Learning, pages 4970–4979. PMLR, 2019. [23] Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a defense to adversarial perturbations against deep neural networks. In 2016 IEEE symposium on security and privacy (SP), pages 582–597. IEEE, 2016. [24] Mary Phuong and Christoph H Lampert. Distillation-based training for multi-exit architectures. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1355– 1364, 2019. [25] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115:211–252, 2015. [26] Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern Recognition (ICPR), pages 2464–2469. IEEE, 2016. [27] Xinglu Wang and Yingming Li. Harmonized dense knowledge distillation training for multi-exit architectures. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 10218–10226, 2021. [28] Qunliang Xing, Mai Xu, Tianyi Li, and Zhenyu Guan. Early exit or not: Resource-efficient blind quality enhancement for compressed images. In European Conference on Computer Vision, pages 275–292. Springer, 2020. [29] Huanrui Yang, Jingyang Zhang, Hongliang Dong, Nathan Inkawhich, Andrew Gardner, Andrew Touchet, Wesley Wilkes, Heath Berry, and Hai Li. Dverge: diversifying vulnerabilities for enhanced robust generation of ensembles. Advances in Neural Information Processing Systems, 33:5505–5515, 2020. [30] Zhuolin Yang, Linyi Li, Xiaojun Xu, Shiliang Zuo, Qian Chen, Pan Zhou, Benjamin Rubinstein, Ce Zhang, and Bo Li. Trs: Transferability reduced ensemble via promoting gradient diversity and model smoothness. Advances in Neural Information Processing Systems, 34, 2021. [31] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan. Theoretically principled trade-off between robustness and accuracy. In International conference on machine learning, pages 7472–7482. PMLR, 2019. [32] Wangchunshu Zhou, Canwen Xu, Tao Ge, Julian McAuley, Ke Xu, and Furu Wei. Bert loses patience: Fast and robust inference with early exit. Advances in Neural Information Processing Systems, 33:18330–18341, 2020. [33] Jianing Zhu, Jiangchao Yao, Bo Han, Jingfeng Zhang, Tongliang Liu, Gang Niu, Jingren Zhou, Jianliang Xu, and Hongxia Yang. Reliable adversarial distillation with unreliable teachers. arXiv preprint arXiv:2106.04928, 2021. [34] Bojia Zi, Shihao Zhao, Xingjun Ma, and Yu-Gang Jiang. Revisiting adversarial robustness distillation: Robust soft labels make student better. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 16443–16452, 2021. This paper is available on arxiv under CC 4.0 license. Authors: (1) Seokil Ham, KAIST; (2) Jungwuk Park, KAIST; (3) Dong-Jun Han, Purdue University; (4) Jaekyun Moon, KAIST. Authors: Authors: (1) Seokil Ham, KAIST; (2) Jungwuk Park, KAIST; (3) Dong-Jun Han, Purdue University; (4) Jaekyun Moon, KAIST. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Related Works 2. Related Works 3. Proposed NEO-KD Algorithm and 3.1 Problem Setup: Adversarial Training in Multi-Exit Networks 3. Proposed NEO-KD Algorithm and 3.1 Problem Setup: Adversarial Training in Multi-Exit Networks 3.2 Algorithm Description 3.2 Algorithm Description 4. Experiments and 4.1 Experimental Setup 4. Experiments and 4.1 Experimental Setup 4.2. Main Experimental Results 4.2. Main Experimental Results 4.3. Ablation Studies and Discussions 4.3. Ablation Studies and Discussions 5. Conclusion, Acknowledgement and References 5. Conclusion, Acknowledgement and References A. Experiment Details A. Experiment Details B. Clean Test Accuracy and C. Adversarial Training via Average Attack B. Clean Test Accuracy and C. Adversarial Training via Average Attack D. Hyperparameter Tuning D. Hyperparameter Tuning E. Discussions on Performance Degradation at Later Exits E. Discussions on Performance Degradation at Later Exits F. Comparison with Recent Defense Methods for Single-Exit Networks F. Comparison with Recent Defense Methods for Single-Exit Networks G. Comparison with SKD and ARD and H. Implementations of Stronger Attacker Algorithms G. Comparison with SKD and ARD and H. Implementations of Stronger Attacker Algorithms 5 Conclusion In this paper, we proposed a new knowledge distillation based adversarial training strategy for robust multi-exit networks. Our solution, NEO-KD, reduces adversarial transferability in the network while guiding the output of the adversarial examples to closely follow the ensemble outputs of the neighbor exits of the clean data, significantly improving the overall adversarial test accuracy. Extensive experimental results on both anytime and budgeted prediction setups using various datasets confirmed the effectiveness of our method, compared to baselines relying on existing adversarial training or knowledge distillation techniques for multi-exit networks. Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1I1A2A02061135), by the Center for Applied Research in Artificial Intelligence (CARAI) grant funded by DAPA and ADD (UD230017TD), and by IITP funds from MSIT of Korea (No. 2020-0-00626). References [1] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: a query-efficient black-box adversarial attack via random search. In Computer Vision– ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part XXIII, pages 484–501. Springer, 2020. [2] Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017 ieee symposium on security and privacy (sp), pages 39–57. Ieee, 2017. [3] Sihong Chen, Haojing Shen, Ran Wang, and Xizhao Wang. Towards improving fast adversarial training in multi-exit network. Neural Networks, 150:1–11, 2022. [4] Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive boundary attack. In International Conference on Machine Learning, pages 2196–2205. PMLR, 2020. [5] Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In International conference on machine learning, pages 2206–2216. PMLR, 2020. [6] Junhao Dong, Seyed-Mohsen Moosavi-Dezfooli, Jianhuang Lai, and Xiaohua Xie. The enemy of my enemy is my friend: Exploring inverse adversaries for improving adversarial training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 24678–24687, 2023. [7] Yinpeng Dong, Ke Xu, Xiao Yang, Tianyu Pang, Zhijie Deng, Hang Su, and Jun Zhu. Exploring memorization in adversarial training. arXiv preprint arXiv:2106.01606, 2021. [8] Micah Goldblum, Liam Fowl, Soheil Feizi, and Tom Goldstein. Adversarially robust distillation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 3996–4003, 2020. [9] Dong-Jun Han, Jungwuk Park, Seokil Ham, Namjin Lee, and Jaekyun Moon. Improving lowlatency predictions in multi-exit neural networks via block-dependent losses. IEEE Transactions on Neural Networks and Learning Systems, 2023. [10] Mirazul Haque, Anki Chauhan, Cong Liu, and Wei Yang. Ilfo: Adversarial attack on adaptive neural networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14264–14273, 2020. [11] Sanghyun Hong, Yigitcan Kaya, Ionut,-Vlad Modoranu, and Tudor Dumitras. A panda? no, it’s a sloth: Slowdown attacks on adaptive multi-exit neural network inference. In International Conference on Learning Representations, 2020. [12] Ting-Kuei Hu, Tianlong Chen, Haotao Wang, and Zhangyang Wang. Triple wins: Boosting accuracy, robustness and efficiency together by enabling input-adaptive inference. In International Conference on Learning Representations, 2020. [13] Gao Huang, Danlu Chen, Tianhong Li, Felix Wu, Laurens Van Der Maaten, and Kilian Q Weinberger. Multi-scale dense networks for resource efficient image classification. arXiv preprint arXiv:1703.09844, 2017. [14] Hoki Kim. Torchattacks: A pytorch repository for adversarial attacks. arXiv preprint arXiv:2010.01950, 2020. [15] Alexandros Kouris, Stylianos I Venieris, Stefanos Laskaridis, and Nicholas Lane. Multi-exit semantic segmentation networks. In European Conference on Computer Vision, pages 330–349. Springer, 2022. [16] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. [17] Ya Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7(7):3, 2015. [18] Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278–2324, 1998. [19] Sungyoon Lee, Hoki Kim, and Jaewook Lee. Graddiv: Adversarial robustness of randomized neural networks via gradient diversity regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022. [20] Hao Li, Hong Zhang, Xiaojuan Qi, Ruigang Yang, and Gao Huang. Improved techniques for training adaptive deep networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1891–1900, 2019. [21] Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu. Towards deep learning models resistant to adversarial attacks. In International Conference on Learning Representations, 2018. [22] Tianyu Pang, Kun Xu, Chao Du, Ning Chen, and Jun Zhu. Improving adversarial robustness via promoting ensemble diversity. In International Conference on Machine Learning, pages 4970–4979. PMLR, 2019. [23] Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a defense to adversarial perturbations against deep neural networks. In 2016 IEEE symposium on security and privacy (SP), pages 582–597. IEEE, 2016. [24] Mary Phuong and Christoph H Lampert. Distillation-based training for multi-exit architectures. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 1355– 1364, 2019. [25] Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, et al. Imagenet large scale visual recognition challenge. International journal of computer vision, 115:211–252, 2015. [26] Surat Teerapittayanon, Bradley McDanel, and Hsiang-Tsung Kung. Branchynet: Fast inference via early exiting from deep neural networks. In 2016 23rd International Conference on Pattern Recognition (ICPR), pages 2464–2469. IEEE, 2016. [27] Xinglu Wang and Yingming Li. Harmonized dense knowledge distillation training for multi-exit architectures. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, pages 10218–10226, 2021. [28] Qunliang Xing, Mai Xu, Tianyi Li, and Zhenyu Guan. Early exit or not: Resource-efficient blind quality enhancement for compressed images. In European Conference on Computer Vision, pages 275–292. Springer, 2020. [29] Huanrui Yang, Jingyang Zhang, Hongliang Dong, Nathan Inkawhich, Andrew Gardner, Andrew Touchet, Wesley Wilkes, Heath Berry, and Hai Li. Dverge: diversifying vulnerabilities for enhanced robust generation of ensembles. Advances in Neural Information Processing Systems, 33:5505–5515, 2020. [30] Zhuolin Yang, Linyi Li, Xiaojun Xu, Shiliang Zuo, Qian Chen, Pan Zhou, Benjamin Rubinstein, Ce Zhang, and Bo Li. Trs: Transferability reduced ensemble via promoting gradient diversity and model smoothness. Advances in Neural Information Processing Systems, 34, 2021. [31] Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan. Theoretically principled trade-off between robustness and accuracy. In International conference on machine learning, pages 7472–7482. PMLR, 2019. [32] Wangchunshu Zhou, Canwen Xu, Tao Ge, Julian McAuley, Ke Xu, and Furu Wei. Bert loses patience: Fast and robust inference with early exit. Advances in Neural Information Processing Systems, 33:18330–18341, 2020. [33] Jianing Zhu, Jiangchao Yao, Bo Han, Jingfeng Zhang, Tongliang Liu, Gang Niu, Jingren Zhou, Jianliang Xu, and Hongxia Yang. Reliable adversarial distillation with unreliable teachers. arXiv preprint arXiv:2106.04928, 2021. [34] Bojia Zi, Shihao Zhao, Xingjun Ma, and Yu-Gang Jiang. Revisiting adversarial robustness distillation: Robust soft labels make student better. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 16443–16452, 2021. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

How NEO-KD Reduces Adversarial Transferability and Improves Accuracy

Reducing computational complexity has always been one of the primary goals of blockchain technology. One effective approach to achieving this is by reducing the bit width of the computation field. For example, SNARKs based on elliptic curves perform arithmetic operations in fields with bit widths of 256 or higher, while STARKs have evolved from using the 64-bit Goldilocks field to the 31-bit Mersenne31 and BabyBear fields. Beyond the efficiency of the prime numbers during modular operations, the significant reduction in bit width has led to Plonky2 being hundreds of times faster than its predecessor, Plonky. Following this trajectory, one might wonder: is it possible to set the field width to 1, specifically ${\mathbb{F}}_{2}$? The Ulvetanna (IRREDUCIBLE) team addressed this question in their research paper titled Succinct Arguments over Towers of Binary Fields [1], and implemented it in Rust with their project, Binius: a Hardware-Optimized SNARK [2][3]. Since its release, Binius has garnered significant attention in the ZK (Zero-Knowledge) community. The LambdaClass team has provided several technical analyses [4][5][6], and Vitalik Buterin offered a more accessible explanation [7]. In this article, we will explore the foundations of Binius, focusing on the Towers of Binary Fields, from both a technical and implementation perspective. Binary Fields The implementation of Binius is based on Binary Fields. In Binius, Binary Fields are constructed using towers of field extensions. The simplest Binary Field is ${{\mathbb{F}}{2}}$, which contains only two elements ${0,1}$, with operations performed modulo 2: addition corresponds to bitwise XOR, and multiplication corresponds to bitwise AND. By choosing an irreducible polynomial $m(x) = x^{2} + x + 1$ over ${{\mathbb{F}}{2}}$, we can form the field ${{\mathbb{F}}_{{2^{2}}}}$, where the elements are remainders of polynomials of degree at most 1, $r(x) = ax + b$ (with $a, b \in {0, 1}$). While one method to extend fields involves taking remainders using irreducible polynomials, Binius employs a more efficient approach: the use of Multilinear Lagrange polynomials as a basis for tower extensions. This method allows for recursive field extensions, where each extension field is nested within the previous one. The Specific Implementation of Tower Extensions is as Follows: First, ${{\tau }{0}} = {{\mathbb{F}}{2}}$; Then, ${{\tau }{1}} = \frac{{{\mathbb{F}}{2}}[{{x}{0}}]}{(x{0}^{2} + {{x}_{0}} + 1)}$; Next, ${{\tau }{k}} = \frac{{{\mathbb{F}}{2}}[{{x}{k-1}}]}{(x{k-1}^{2} + {{x}{k-1}}{{x}{k-2}} + 1)}$. From the construction process of the field extensions, it is clear that the extensions satisfy the following relationship: ${{\tau }{0}} \subset {{\tau }{1}} \subset {{\tau }{2}} \subset \cdots \subset {{\tau }{m}}$. For $k \ge 0$, the field extension can also be expressed in the direct form of a ring as: ${{\tau }{k}}={{{\mathbb{F}}{2}}[{{x}{0,}}\ldots ,{{x}{k-1}}]}/{\left( x_{0}^{2}+{{x}{0}}+1,\ldots ,x{k-1}^{2}+{{x}{k-2}}{{x}{k-1}}+1 \right)}$. Based on this implementation, different extensions can be obtained as follows: ${{\tau }_{0}}=\left{ 0,1 \right}$


${{\tau }{1}}=\left{ 0+0{{x}{0}},1+0{{x}{0}},0+1{{x}{0}},1+1{{x}{0}} \right}$, or ${{\tau }{1}}=\left{ {{\tau }{0}},0+1{{x}{0}},1+1{{x}_{0}} \right}$


$${{\tau }{2}}=\left{ \begin{align} & 0+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},1+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},0+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}}, \ & 1+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}x \ \end{align} \right}$$, Or ${{\tau }{2}}=\left{ {{\tau }{1}},0+0{{x}{0}}+1{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}{{x}{1}} \right}$ From the Elements Contained in the Extended Field It is evident that for an element ${{b}{0}}{{b}{1}}{{b}{2}}\ldots {{b}{{{2}^{k}}-1}}$ derived from ${{\tau }{k}}$, it can be decomposed into the sum of two parts: ${{b}{lo}} + {{x}{k-1}}{{b}{hi}}$ (where ${{b}{lo}}, {{b}{hi}} \in {{\tau }{k-1}}$). For example, $1100101010001111 = 11001010 + 1000111 \times {{x}{3}}$, where $11001010, 10001111 \in {{\tau }{2}}$. By iteratively decomposing, we can finally express: $$1100101010001111=1+{{x}{0}}+{{x}{2}}+{{x}{2}}{{x}{1}}+{{x}{3}}+{{x}{2}}{{x}{3}}+{{x}{0}}{{x}{2}}{{x}{3}}+{{x}{1}}{{x}{2}}{{x}{3}}+{{x}{0}}{{x}{1}}{{x}{2}}{{x}{3}}$$ Additionally, for $k > 0$, since $x_{k}^{2} = {{x}{k}}{{x}{k-1}} + 1$, addition and multiplication can be efficiently implemented in the binary extended field. Implementation of Binary Fields Irreducible provides the open-source Rust implementation of Binius [3]. The source code includes complete implementations and operations for the Tower of Binary Fields [8,9,10]. In [8], as shown in Figure 1, the implementation includes the complete definition of operations for binary fields and the construction of the Tower of Binary Fields. The Tower of Binary Fields, supporting up to a 128-bit binary field, is defined as follows: Additionally, [8] provides test and verification code for the Tower of Binary Fields and related operations. References [1] https://eprint.iacr.org/2023/1784 [2] https://www.irreducible.com/posts/binius-hardware-optimized-snark [3] https://gitlab.com/IrreducibleOSS/binius [4] SNARKs on binary fields: Binius - Part 1 (lambdaclass.com) [5] SNARKs on binary fields: Binius - Part 2 (lambdaclass.com) [6] How Binius is helping move the ZK industry forward (lambdaclass.com) [7] https://vitalik.eth.limo/general/2024/04/29/binius.html [8] binius/crates/field/src/binary_field.rs at main · IrreducibleOSS/binius · GitHub [9] binius/crates/field/src/binary_field_arithmetic.rs at main · IrreducibleOSS/binius · GitHub [10] binius/crates/field/src/extension.rs at main · IrreducibleOSS/binius · GitHub Reducing computational complexity has always been one of the primary goals of blockchain technology. One effective approach to achieving this is by reducing the bit width of the computation field. For example, SNARKs based on elliptic curves perform arithmetic operations in fields with bit widths of 256 or higher, while STARKs have evolved from using the 64-bit Goldilocks field to the 31-bit Mersenne31 and BabyBear fields. Beyond the efficiency of the prime numbers during modular operations, the significant reduction in bit width has led to Plonky2 being hundreds of times faster than its predecessor, Plonky. Following this trajectory, one might wonder: is it possible to set the field width to 1, specifically ${\mathbb{F}}_{2}$? The Ulvetanna (IRREDUCIBLE) team addressed this question in their research paper titled Succinct Arguments over Towers of Binary Fields [1] , and implemented it in Rust with their project, Binius: a Hardware-Optimized SNARK [2][3] . [1] [1] [2] [3] [2] [3] Since its release, Binius has garnered significant attention in the ZK (Zero-Knowledge) community. The LambdaClass team has provided several technical analyses [4][5][6], and Vitalik Buterin offered a more accessible explanation [7] . In this article, we will explore the foundations of Binius, focusing on the Towers of Binary Fields, from both a technical and implementation perspective. [7] [7] Binary Fields Binary Fields The implementation of Binius is based on Binary Fields. In Binius, Binary Fields are constructed using towers of field extensions. The simplest Binary Field is ${{\mathbb{F}}{2}}$ , which contains only two elements ${0,1}$ , with operations performed modulo 2: addition corresponds to bitwise XOR, and multiplication corresponds to bitwise AND. By choosing an irreducible polynomial $m(x) = x^{2} + x + 1$ over ${{\mathbb{F}}{2}}$ , we can form the field ${{\mathbb{F}}_{{2^{2}}}}$ , where the elements are remainders of polynomials of degree at most 1, $r(x) = ax + b$ (with $a, b \in {0, 1}$ ). ${{\mathbb{F}}{2}}$ ${0,1}$ $m(x) = x^{2} + x + 1$ over ${{\mathbb{F}}{2}}$ ${{\mathbb{F}}_{{2^{2}}}}$ $r(x) = ax + b$ (with $a, b \in {0, 1}$ While one method to extend fields involves taking remainders using irreducible polynomials, Binius employs a more efficient approach: the use of Multilinear Lagrange polynomials as a basis for tower extensions. This method allows for recursive field extensions, where each extension field is nested within the previous one. The Specific Implementation of Tower Extensions is as Follows: First, ${{\tau }{0}} = {{\mathbb{F}}{2}}$ ; Then, ${{\tau }{1}} = \frac{{{\mathbb{F}}{2}}[{{x}{0}}]}{(x{0}^{2} + {{x}_{0}} + 1)}$ ; Next, ${{\tau }{k}} = \frac{{{\mathbb{F}}{2}}[{{x}{k-1}}]}{(x{k-1}^{2} + {{x}{k-1}}{{x}{k-2}} + 1)}$. ${{\tau }{0}} = {{\mathbb{F}}{2}}$ ${{\tau }{1}} = \frac{{{\mathbb{F}}{2}}[{{x}{0}}]}{(x{0}^{2} + {{x}_{0}} + 1)}$ ${{\tau }{k}} = \frac{{{\mathbb{F}}{2}}[{{x}{k-1}}]}{(x{k-1}^{2} + {{x}{k-1}}{{x}{k-2}} + 1)}$. From the construction process of the field extensions, it is clear that the extensions satisfy the following relationship: ${{\tau }{0}} \subset {{\tau }{1}} \subset {{\tau }{2}} \subset \cdots \subset {{\tau }{m}}$ . For $k \ge 0$ , the field extension can also be expressed in the direct form of a ring as: ${{\tau }{k}}={{{\mathbb{F}}{2}}[{{x}{0,}}\ldots ,{{x}{k-1}}]}/{\left( x_{0}^{2}+{{x}{0}}+1,\ldots ,x{k-1}^{2}+{{x}{k-2}}{{x}{k-1}}+1 \right)}$. ${{\tau }{0}} \subset {{\tau }{1}} \subset {{\tau }{2}} \subset \cdots \subset {{\tau }{m}}$ $k \ge 0$ ${{\tau }{k}}={{{\mathbb{F}}{2}}[{{x}{0,}}\ldots ,{{x}{k-1}}]}/{\left( x_{0}^{2}+{{x}{0}}+1,\ldots ,x{k-1}^{2}+{{x}{k-2}}{{x}{k-1}}+1 \right)}$. Based on this implementation, different extensions can be obtained as follows: Based on this implementation, different extensions can be obtained as follows: ${{\tau }_{0}}=\left{ 0,1 \right}$ ${{\tau }{1}}=\left{ 0+0{{x}{0}},1+0{{x}{0}},0+1{{x}{0}},1+1{{x}{0}} \right}$, or ${{\tau }{1}}=\left{ {{\tau }{0}},0+1{{x}{0}},1+1{{x}_{0}} \right}$ $${{\tau }{2}}=\left{ \begin{align} & 0+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},1+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},0+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}}, \ & 1+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}x \ \end{align} \right}$$, Or ${{\tau }{2}}=\left{ {{\tau }{1}},0+0{{x}{0}}+1{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}{{x}{1}} \right}$ ${{\tau }_{0}}=\left{ 0,1 \right}$ ${{\tau }_{0}}=\left{ 0,1 \right}$ ${{\tau }_{0}}=\left{ 0,1 \right}$ ${{\tau }{1}}=\left{ 0+0{{x}{0}},1+0{{x}{0}},0+1{{x}{0}},1+1{{x}{0}} \right}$, or ${{\tau }{1}}=\left{ {{\tau }{0}},0+1{{x}{0}},1+1{{x}_{0}} \right}$ ${{\tau }{1}}=\left{ 0+0{{x}{0}},1+0{{x}{0}},0+1{{x}{0}},1+1{{x}{0}} \right}$, or ${{\tau }{1}}=\left{ {{\tau }{0}},0+1{{x}{0}},1+1{{x}_{0}} \right}$ ${{\tau }{1}}=\left{ 0+0{{x}{0}},1+0{{x}{0}},0+1{{x}{0}},1+1{{x}{0}} \right}$, or ${{\tau }{1}}=\left{ {{\tau }{0}},0+1{{x}{0}},1+1{{x}_{0}} \right}$ $${{\tau }{2}}=\left{ \begin{align} & 0+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},1+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},0+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}}, \ & 1+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}x \ \end{align} \right}$$, Or ${{\tau }{2}}=\left{ {{\tau }{1}},0+0{{x}{0}}+1{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}{{x}{1}} \right}$ $${{\tau }{2}}=\left{ \begin{align} & 0+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},1+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},0+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}}, \ & 1+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}x \ \end{align} \right}$$, Or ${{\tau }{2}}=\left{ {{\tau }{1}},0+0{{x}{0}}+1{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}{{x}{1}} \right}$ $${{\tau }{2}}=\left{ \begin{align} & 0+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},1+0{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},0+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}}, \ & 1+1{{x}{0}}+0{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}x \ \end{align} \right}$$, Or ${{\tau }{2}}=\left{ {{\tau }{1}},0+0{{x}{0}}+1{{x}{1}}+0{{x}{0}}{{x}{1}},\ldots ,1+1{{x}{0}}+1{{x}{1}}+1{{x}{0}}{{x}{1}} \right}$ From the Elements Contained in the Extended Field It is evident that for an element ${{b}{0}}{{b}{1}}{{b}{2}}\ldots {{b}{{{2}^{k}}-1}}$ derived from ${{\tau }{k}}$ , it can be decomposed into the sum of two parts: ${{b}{lo}} + {{x}{k-1}}{{b}{hi}}$ (where ${{b}{lo}}, {{b}{hi}} \in {{\tau }{k-1}}$) . For example, $1100101010001111 = 11001010 + 1000111 \times {{x}{3}}$, where $11001010, 10001111 \in {{\tau }{2}}$ . ${{b}{0}}{{b}{1}}{{b}{2}}\ldots {{b}{{{2}^{k}}-1}}$ ${{\tau }{k}}$ ${{b}{lo}} + {{x}{k-1}}{{b}{hi}}$ (where ${{b}{lo}}, {{b}{hi}} \in {{\tau }{k-1}}$) $1100101010001111 = 11001010 + 1000111 \times {{x}{3}}$, where $11001010, 10001111 \in {{\tau }{2}}$ . By iteratively decomposing, we can finally express: $$1100101010001111=1+{{x}{0}}+{{x}{2}}+{{x}{2}}{{x}{1}}+{{x}{3}}+{{x}{2}}{{x}{3}}+{{x}{0}}{{x}{2}}{{x}{3}}+{{x}{1}}{{x}{2}}{{x}{3}}+{{x}{0}}{{x}{1}}{{x}{2}}{{x}{3}}$$ $$1100101010001111=1+{{x}{0}}+{{x}{2}}+{{x}{2}}{{x}{1}}+{{x}{3}}+{{x}{2}}{{x}{3}}+{{x}{0}}{{x}{2}}{{x}{3}}+{{x}{1}}{{x}{2}}{{x}{3}}+{{x}{0}}{{x}{1}}{{x}{2}}{{x}{3}}$$ Additionally, for $k > 0$ , since $x_{k}^{2} = {{x}{k}}{{x}{k-1}} + 1$ , addition and multiplication can be efficiently implemented in the binary extended field. $k > 0$ $x_{k}^{2} = {{x}{k}}{{x}{k-1}} + 1$ Implementation of Binary Fields Implementation of Binary Fields Irreducible provides the open-source Rust implementation of Binius [3]. The source code includes complete implementations and operations for the Tower of Binary Fields [8,9,10]. In [8], as shown in Figure 1, the implementation includes the complete definition of operations for binary fields and the construction of the Tower of Binary Fields. The Tower of Binary Fields, supporting up to a 128-bit binary field, is defined as follows: Additionally, [8] provides test and verification code for the Tower of Binary Fields and related operations. References References [1] https://eprint.iacr.org/2023/1784 https://eprint.iacr.org/2023/1784 https://eprint.iacr.org/2023/1784 [2] https://www.irreducible.com/posts/binius-hardware-optimized-snark https://www.irreducible.com/posts/binius-hardware-optimized-snark https://www.irreducible.com/posts/binius-hardware-optimized-snark [3] https://gitlab.com/IrreducibleOSS/binius https://gitlab.com/IrreducibleOSS/binius https://gitlab.com/IrreducibleOSS/binius [4] SNARKs on binary fields: Binius - Part 1 (lambdaclass.com) [5] SNARKs on binary fields: Binius - Part 2 (lambdaclass.com) [6] How Binius is helping move the ZK industry forward (lambdaclass.com) [7] https://vitalik.eth.limo/general/2024/04/29/binius.html https://vitalik.eth.limo/general/2024/04/29/binius.html https://vitalik.eth.limo/general/2024/04/29/binius.html [8] binius/crates/field/src/binary_field.rs at main · IrreducibleOSS/binius · GitHub [9] binius/crates/field/src/binary_field_arithmetic.rs at main · IrreducibleOSS/binius · GitHub [10] binius/crates/field/src/extension.rs at main · IrreducibleOSS/binius · GitHub

How Binius Reduces Computational Complexity with Towers of Binary Fields

Как Binius намалява изчислителната сложност с кули от двоични полета

কিভাবে বিনিয়াস বাইনারি ফিল্ডের টাওয়ারের সাথে কম্পিউটেশনাল জটিলতা হ্রাস করে

Cómo Binius reduce la complejidad computacional con torres de campos binarios

Come Binius riduce la complessità computazionale con torri di campi binari

Binius がバイナリ フィールドのタワーを使用して計算の複雑さを軽減する方法

Binius가 이진 필드 타워로 계산 복잡성을 줄이는 방법

कसरी बिनियसले बाइनरी फिल्डहरूको टावरहरूसँग कम्प्युटेशनल जटिलता घटाउँछ

Cum reduce Binius complexitatea computațională cu turnuri de câmpuri binare

Maitiro eBinius Anoderedza Computational Complexity neTowers yeBinary Fields

Paano Binabawasan ng Binius ang Computational Complexity gamit ang Towers of Binary Fields

Як Binius зменшує обчислювальну складність за допомогою веж бінарних полів

Binius Giảm Độ Phức Tạp Tính Toán Như Thế Nào Với Các Tháp Trường Nhị Phân

September 9, 2024 - [Dubai, UAE] - Last week, Propchain announced the successful execution of its third proposal within the Propchain DAO, marking a significant milestone in its efforts to enhance the long-term value and sustainability of the $PROPC token ecosystem. The recently completed proposal focused on a strategic token burn initiative, reinforcing Propchain's commitment to community engagement and economic prudence. The initiative aimed to reinforce the economic foundation of the $PROPC token by reducing the total supply by approximately 25%, from 85 million to 64 million tokens. The token burn specifically targeted vested tokens, ensuring that unvested tokens remained unaffected. This approach was designed to decrease the monthly unvested token amount, effectively lowering the token's monthly inflation and fostering a more stable and sustainable economic environment. The token burn was conducted on a pro-rata basis, guaranteeing that each token holder's proportional ownership remained unchanged. For instance, a holder with 0.01% of the total supply before the burn would still maintain approximately 0.01% after the burn. This strategy ensured fairness for all holders while reducing the overall supply and increasing the percentage of tokens in circulation from approximately 24.4% to 32.4%. Such measures are essential for strengthening projects in the RWA space, where economic stability and long-term value creation are critical. By carefully managing token supply and reducing inflationary pressures, Propchain is ensuring that its platform remains appealing to both investors and users. This not only bolsters confidence in the $PROPC token but also sets a standard for responsible and sustainable growth within the RWA sector. The successful execution of this proposal is expected to greatly enhance the tokenomics of $PROPC by reducing inflationary pressures and enabling a healthier economic environment for the token. Propchain visualizes this achievement as a vital step forward in its ongoing token integration plans and in maintaining the integrity of its ecosystem. About Propchain Propchain leads the way in real estate investment platforms, placing consumer needs at the forefront by providing effortless access to tokenized assets and a user-friendly digital interface for asset management. It aims to revolutionize the real estate industry through the widespread adoption of blockchain technology, facilitating improved market dynamics, transparency, and long-term sustainability. Propchain's journey is marked by significant milestones, strategic focus, and innovative real estate strategies. With its dedication to digitally empowering the real estate value chain through investing and strategic positioning in the global market, Propchain is set to redefine the real estate investment landscape and continue its path of success. This story was distributed as a release by Btcwire under HackerNoon’s Business Blogging Program. Learn more about the program here. September 9, 2024 - [Dubai, UAE] - Last week, Propchain announced the successful execution of its third proposal within the Propchain DAO, marking a significant milestone in its efforts to enhance the long-term value and sustainability of the $PROPC token ecosystem. The recently completed proposal focused on a strategic token burn initiative, reinforcing Propchain's commitment to community engagement and economic prudence. The initiative aimed to reinforce the economic foundation of the $PROPC token by reducing the total supply by approximately 25%, from 85 million to 64 million tokens. The token burn specifically targeted vested tokens, ensuring that unvested tokens remained unaffected. This approach was designed to decrease the monthly unvested token amount, effectively lowering the token's monthly inflation and fostering a more stable and sustainable economic environment. The token burn was conducted on a pro-rata basis, guaranteeing that each token holder's proportional ownership remained unchanged. For instance, a holder with 0.01% of the total supply before the burn would still maintain approximately 0.01% after the burn. This strategy ensured fairness for all holders while reducing the overall supply and increasing the percentage of tokens in circulation from approximately 24.4% to 32.4%. Such measures are essential for strengthening projects in the RWA space, where economic stability and long-term value creation are critical. By carefully managing token supply and reducing inflationary pressures, Propchain is ensuring that its platform remains appealing to both investors and users. This not only bolsters confidence in the $PROPC token but also sets a standard for responsible and sustainable growth within the RWA sector. The successful execution of this proposal is expected to greatly enhance the tokenomics of $PROPC by reducing inflationary pressures and enabling a healthier economic environment for the token. Propchain visualizes this achievement as a vital step forward in its ongoing token integration plans and in maintaining the integrity of its ecosystem. About Propchain Propchain leads the way in real estate investment platforms, placing consumer needs at the forefront by providing effortless access to tokenized assets and a user-friendly digital interface for asset management. It aims to revolutionize the real estate industry through the widespread adoption of blockchain technology, facilitating improved market dynamics, transparency, and long-term sustainability. Propchain Propchain Propchain's journey is marked by significant milestones, strategic focus, and innovative real estate strategies. With its dedication to digitally empowering the real estate value chain through investing and strategic positioning in the global market, Propchain is set to redefine the real estate investment landscape and continue its path of success. This story was distributed as a release by Btcwire under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed as a release by Btcwire under HackerNoon’s Business Blogging Program. Learn more about the program here . here here

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