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# EVOLVE-BLOCK-START
"""
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)
N, F = X.shape
params = np.asarray(params)
if params.ndim == 1:
params = params[None, :] # (1, P)
T, P = params.shape
coeffs = params[:, :F] # (T, F)
exponents = params[:, F:2*F] # (T, F)
bias = params[:, -1] # (T,)
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)) # (N, F)
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) # (N, T)
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
# EVOLVE-BLOCK-END
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