| |
| """ |
| Scaling law discovery for LLM finetuning scenarios |
| Initial program with a simple power law form that can be evolved |
| """ |
| import numpy as np |
| from scipy.optimize import minimize |
|
|
| def scaling_law_func(data_points, params): |
|
|
| X = np.atleast_2d(np.asarray(data_points)) |
| N, F = X.shape |
| params = np.asarray(params) |
|
|
| if params.ndim == 1: |
| params = params[None, :] |
| T, P = params.shape |
|
|
| coeffs = params[:, :F] |
| exponents = params[:, F:2*F] |
| bias = params[:, -1] |
|
|
| pred = (coeffs[None, :, :] * (X[:, None, :] ** exponents[None, :, :])).sum(axis=2) + bias[None, :] |
|
|
| return pred[:, 0] if pred.shape[1] == 1 else pred |
|
|
|
|
| def fit_scaling_law(data_points, loss_values): |
|
|
| X = np.atleast_2d(np.asarray(data_points)) |
| y = np.asarray(loss_values) |
| N, F = X.shape |
| P = 2 * F + 1 |
|
|
| if y.ndim == 1: |
| y2d = y[:, None] |
| else: |
| y2d = y |
| T = y2d.shape[1] |
|
|
| init = np.ones((T, P)) |
|
|
| def objective(flat_params): |
| params = flat_params.reshape(T, P) |
| pred = scaling_law_func(X, params) |
| mse = np.mean((pred - y2d) ** 2) |
| return mse |
|
|
| result = minimize(objective, init.ravel(), method='BFGS') |
| params_opt = result.x.reshape(T, P) if result.success else init |
|
|
| return params_opt[0] if T == 1 else params_opt |
| |
|
|
