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