A New Era of Advancement
Leschik’s Law : A Comprehensive Guide to Understanding AI’s Exponential Growth & The End of Moore’s Law.
Introduction
Leschik’s Law states that the performance of AI models doubles every N months, while the cost of training and deploying them decreases by half, adjusted for the speed, scalability, and ethical barriers busted by AI & ML.
Updated Formulas
Performance Doubling with Ethical Adjustment
Performance=Performance0×2(t/n)×(Speedup_Factor)t×Ethical_Factor
Cost Halving with Scalability Adjustment
Cost=Cost0×0.5(t/n)×(Speedup_Factor)t×Scalability_FactorCost
Parameters Explained
- Performance and Cost: These are the performance and cost metrics at a given time t, respectively.
- Performance₀ and Cost₀: These are the initial performance and cost metrics.
- t: This is the time in months.
- N: This is the number of months in which performance doubles, allowing for more granularity.
- Speedup Factor: This is the factor by which AI & ML technologies double the speed.
- Ethical Factor: This is a multiplier that accounts for ethical considerations like fairness, transparency, and data privacy.
- Scalability Factor: This is a multiplier that accounts for the scalability of the AI model, including data storage and parallel processing capabilities.
Leschik’s Law in Python
import math
def calculate_leschiks_law(t, N, Performance_0, Cost_0, Speedup_Factor, Ethical_Factor, Scalability_Factor):
# Calculate Performance
Performance = Performance_0 * math.pow(2, (t / N)) * math.pow(Speedup_Factor, t) * Ethical_Factor
# Calculate Cost
Cost = Cost_0 * math.pow(0.5, (t / N)) * math.pow(Speedup_Factor, t) * Scalability_Factor
return Performance, Cost
# Example usage
t = 24 # Time in months
N = 12 # Performance doubles every 12 months
Performance_0 = 1 # Initial performance
Cost_0 = 100 # Initial cost
Speedup_Factor = 1.1 # 10% speedup every month
Ethical_Factor = 0.9 # 10% reduction due to ethical considerations
Scalability_Factor = 1.05 # 5% improvement in scalability
Performance, Cost = calculate_leschiks_law(t, N, Performance_0, Cost_0, Speedup_Factor, Ethical_Factor, Scalability_Factor)
print(f"Performance after {t} months: {Performance}")
print(f"Cost after {t} months: {Cost}")Updated for 20 Year Application (1/1/2024)
import numpy as np
import matplotlib.pyplot as plt
# Time frame in years
years = np.arange(2024, 2044)
# Moore's Law: Computing power doubles every 2 years in the semiconductor industry
moore_law_semiconductor = np.array([2**(year/2) for year in range(len(years))])
# Leschik’s Law applied to AI/ML in the semiconductor industry
# Assuming AI/ML leads to a significant increase in efficiency and production
leschik_law_semiconductor = np.array([2**(year) for year in range(len(years))])
# Plotting
plt.figure(figsize=(15, 7))
# Moore's Law Impact on Semiconductor Industry
plt.subplot(1, 2, 1)
plt.plot(years, moore_law_semiconductor, label='Moore\'s Law Impact', color='blue')
plt.title('Semiconductor Industry: Moore\'s Law')
plt.xlabel('Year')
plt.ylabel('Computing Power Growth')
plt.legend()
# Leschik’s Law Impact on Semiconductor Industry with AI/ML Integration
plt.subplot(1, 2, 2)
plt.plot(years, leschik_law_semiconductor, label='Leschik’s Law with AI/ML', color='green')
plt.title('Semiconductor Industry: Leschik’s Law with AI/ML')
plt.xlabel('Year')
plt.ylabel('Efficiency and Production Growth')
plt.legend()
plt.tight_layout()
plt.show()
PROOF OF WORK
To prove Leschik’s Law in Python, we can use the following steps:
- Define the initial performance and cost metrics (Performance₀ and Cost₀).
- Define the number of months in which performance doubles (N).
- Define the Speedup Factor, Ethical Factor, and Scalability Factor.
- Calculate the Performance and Cost at a given time t using the following formulas:
Python
Performance=Performance0×2(t/n)×(Speedup_Factor)t×Ethical_Factor
Cost=Cost0×0.5(t/n)×(Speedup_Factor)t×Scalability_FactorUse code with caution. Learn more
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- Verify that the Performance and Cost at a given time t are consistent with Leschik’s Law.
Theoretical Charts and Breakdowns
Comparing Leschik’s Law with Moore’s Law
Moore’s Law states that the number of transistors on a microchip doubles approximately every two years, leading to an increase in computing power and a decrease in cost per transistor. However, it doesn’t account for factors like speed, scalability, and ethical considerations, which are crucial in the AI & ML domain.
Here’s a theoretical comparison:
Why Leschik’s Law is More Relevant
1. Speed Factor: Leschik’s Law considers the speedup factor, which is crucial for real-time AI applications.
2. Ethical Factor: It incorporates ethical considerations, making it more aligned with responsible AI development.
3. Scalability Factor: It takes into account the scalability of AI models, which is essential for large-scale deployments.
4. Granularity: It allows for more granularity by letting you define the number of months in which performance doubles (N).
Leschik’s Law in Python: Proof and Enhancements
Updated Python Code with Plotting
To visualize the law, we can plot the performance and cost over time. I’ll use `matplotlib` for plotting.
import math
import matplotlib.pyplot as plt
import numpy as np
def calculate_leschiks_law(t, N, Performance_0, Cost_0, Speedup_Factor, Ethical_Factor, Scalability_Factor):
Performance = Performance_0 * math.pow(2, (t / N)) * math.pow(Speedup_Factor, t) * Ethical_Factor
Cost = Cost_0 * math.pow(0.5, (t / N)) * math.pow(Speedup_Factor, t) * Scalability_Factor
return Performance, Cost
# Parameters
t_values = np.linspace(0, 24, 100) # Time from 0 to 24 months
N = 12
Performance_0 = 1
Cost_0 = 100
Speedup_Factor = 1.1
Ethical_Factor = 0.9
Scalability_Factor = 1.05
# Calculate and Plot
Performance_values = []
Cost_values = []
for t in t_values:
Performance, Cost = calculate_leschiks_law(t, N, Performance_0, Cost_0, Speedup_Factor, Ethical_Factor, Scalability_Factor)
Performance_values.append(Performance)
Cost_values.append(Cost)
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.plot(t_values, Performance_values, label='Performance')
plt.title('Performance Over Time')
plt.xlabel('Time (months)')
plt.ylabel('Performance')
plt.legend()
plt.subplot(1, 2, 2)
plt.plot(t_values, Cost_values, label='Cost', color='r')
plt.title('Cost Over Time')
plt.xlabel('Time (months)')
plt.ylabel('Cost')
plt.legend()
plt.tight_layout()
plt.show()PROOF
To prove Leschik’s Law, you can:
- Use historical data to fit the model and validate the parameters (N, Speedup_Factor, Ethical_Factor, Scalability_Factor).
2. Use statistical tests to confirm the goodness of fit.
3. Run simulations to see if the model predicts future performance and cost accurately.
VALIDITY TEST
# Import necessary libraries
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
# Load the historical data
data = pd.read_csv('leschik_law_data.csv')
# Define the model parameters
N = 12 # Performance doubles every 12 months
Speedup_Factor = 1.1 # 10% speedup every month
Ethical_Factor = 0.9 # 10% reduction due to ethical considerations
Scalability_Factor = 1.05 # 5% improvement in scalability
# Create the model
model = LinearRegression()
# Fit the model to the data
model.fit(data[['Time']], data[['Performance']])
# Make predictions
predictions = model.predict(np.array([[25]]))
# Print the predictions
print('Predicted performance after 25 months:', predictions[0])By doing this, you can empirically validate Leschik’s Law and its parameters.
