Approximating Hyperbolic Tangent
5 hours ago
- #Performance Optimization
- #Numerical Approximation
- #Activation Functions
- The hyperbolic tangent (tanh) function is used in neural networks and audio processing due to its bounded, non-linear S-shaped curve.
- Fast approximations of tanh are essential for high-performance applications like real-time inference and audio processing.
- Taylor series expansion provides a polynomial approximation but has limited accuracy beyond certain input ranges.
- Padé approximants use rational polynomials for greater accuracy but require division operations, making them more computationally intensive.
- Splines approximate tanh via piecewise polynomials, trading off accuracy for speed, and are suitable for neural network activation functions.
- K-TanH leverages IEEE-754 floating-point format with integer operations and a 512-bit lookup table, optimized for hardware and SIMD parallelism.
- Schraudolph's method approximates tanh by manipulating floating-point bit patterns, similar to the fast inverse square root hack.
- Schraudolph-NG improves accuracy by using error cancellation in exponential approximations, at the cost of extra operations.