ImplementCore implementation

Adam: one bias-corrected update step

Implement `run(m, v, g, t, beta1, beta2, lr, eps)` returning the Adam parameter step (delta) for one gradient g, given running first moment m and second moment v at timestep t. Update m <- beta1*m + (1-beta1)*g; v <- beta2*v + (1-beta2)*g^2; then delta = lr * m_hat / (sqrt(v_hat) + eps) with bias-corrected moments m_hat = m/(1-beta1^t), v_hat = v/(1-beta2^t). Return delta.

python15 mindifficulty 3/4

From Adam: A Method for Stochastic Optimization

Sample tests

run([0,0,1,1])→0.001
run([0,0,1,2])→0.000744136813

Hints

Adam tracks m_t (first moment) and v_t (second raw moment) with exponential averages.
Bias correction divides by (1 - beta^t) because the averages start at zero — crucial at small t.
Defaults beta1=0.9, beta2=0.999, eps=1e-8; the update is lr * m_hat / (sqrt(v_hat) + eps).
The sqrt(v_hat) term down-weights steps on coordinates with historically large gradients.

Hints

Code runs in an isolated sandbox on the OpenSandbox judge. No model key required.