// multi-utility computation suite · offline · instant · precise
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│ [c] calcalyst_ │
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sci.gradient-descent-step Calculator
Calculates one gradient descent step for a scalar function and estimates steps to convergence: n ≈ log(ε_initial/ε_target)/log(1/(1−αλ)) for quadratic. Gradient descent converges linearly (constant error reduction per step) near a quadratic minimum — Newton's method uses the Hessian for quadratic convergence.
Inputs
W Current
Rate of charge flow (A). I = V/R. Above ~100 mA through the body can be lethal. Fuses protect against overcurrent.
Gradient
Reference formula or conversion factor shown for context.
Learning Rate
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
Momentum
Reference formula or conversion factor shown for context.
Prev Velocity
Speed in a specified direction (m/s). Required for momentum, kinetic energy, and wave calculations.
Results
new weight (SGD)
The computed weight (gravitational force) or mass.
new weight (with momentum)
Product of mass and velocity (kg·m/s). Conserved in all collisions — total momentum before equals total after. More mass or more speed makes stopping harder.
velocity v_new
Sample size or count used in the calculation.
effective learning rate (momentum)
Product of mass and velocity (kg·m/s). Conserved in all collisions — total momentum before equals total after. More mass or more speed makes stopping harder.
w_t+1 = w_t - η·∇L
Reference formula or conversion factor shown for context.
Adam optimizer
Reference formula or conversion factor shown for context.