RandomNumeric / New Layer

Generate random numbers following the standard normal distribution (also known as Z-distribution or bell curve). This is the most commonly used probability distribution in statistics and machine learning.

Mathematical form: $$f(x)=\frac{1}{\sqrt{2\pi }}{e}^{-\frac{x^2}{2}}$$ Key properties:

• Center (mean) at zero
• Spread (standard deviation) of 1
• About 68% of values fall between -1 and +1
• About 95% of values fall between -2 and +2
• About 99.7% of values fall between -3 and +3

Common uses: baseline random data, statistical testing, noise generation in ML.

Generate random numbers following a normal distribution (Gaussian distribution or bell curve) with customizable center and spread. This is useful for simulating natural phenomena, measurement errors, or any quantities that cluster around a central value. Mathematical form: $$f(x)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{(x-\mu {)}^2}{2{\sigma }^2}}$$ Where:

• Mean ($\mu$) sets the center point
• StdDev ($\sigma$) controls the spread

Similar to: np.random.normal(), rnorm() in R

Generate random numbers that are equally likely within a specified range. Like rolling a fair die or sampling from a range with no bias. Useful for simulations, random sampling, and generating test data. Mathematical form: $$f(x)=\{\begin{array}{ll}\frac{1}{b-a}& \text{for }a\le x\le b\\ 0& \text{otherwise}\end{array}$$ Where Low ($a$) and High ($b$) set the range. Similar to: np.random.uniform(), runif() in R

Use system-provided randomization. Each execution produces different boolean values. Suitable for security-sensitive applications, cryptographic operations, simulation, and cases where true randomness is required.

Generate reproducible random numbers using a seed value. Like using random.seed() in Python or set.seed() in R. Essential for:

• Reproducible scientific results
• Testing and debugging
• Sharing exact random sequences with others