Accessibility regularizer for power-law experts

Apply the regularizer to the exponent parameters of the Newton-envelope layer, not to ordinary unconstrained MLP weights. Parameterize a_j=softplus(alpha_j) and b_j=softplus(beta_j) so the intended nonnegative-exponent assumption holds. During each training step, draw K fixed or freshly sampled positive directions p_k,q_k from log-uniform values in [0.25,4], optionally normalize each pair by p_k+q_k because the condition is homogeneous. Compute h_k=max_j(p_k*a_j+q_k*b_j), v_k=h_k-2*min(p_k,q_k), and add lambda_acc/K times softplus(tau*v_k)/tau to the task loss. Include the balanced shortcut v_bal=max_j(a_j+b_j)-2 for a cheap always-on penalty. Start with lambda_acc in {1e-4,1e-3,1e-2} and tau=10; anneal lambda from zero over the first 10% of training so the model first discovers useful exponents. The exact support maximum and accessibility threshold come from the paper; K, direction sampling, lambda, and softplus smoothing are engineering choices. First test on a synthetic near-corner regression task with train points at moderate radii and test points closer to x=y=0, comparing no regularization, balanced-only regularization, and directional regularization. Track extrapolation error, maximum predicted magnitude, gradient norm, and learned exponents. Success means improved near-corner extrapolation and fewer exploding gradients at equal in-domain error; reject the method if it simply biases the model toward underfitting or materially worsens ordinary-domain accuracy.