| """ |
| Many seeds at N=4000, shorter Adam (50k), hard L-BFGS polish. |
| Save best solution's shape for analysis. |
| """ |
| import sys |
| import jax |
| import jax.numpy as jnp |
| import numpy as np |
| from scipy.optimize import minimize as scipy_minimize |
| import optax |
|
|
|
|
| def compute_c1_numpy(f_values, n_points): |
| dx = 0.5 / n_points |
| f_nn = np.maximum(f_values, 0.0) |
| autoconv = np.convolve(f_nn, f_nn, mode='full') * dx |
| integral_sq = (np.sum(f_nn) * dx) ** 2 |
| if integral_sq < 1e-12: |
| return 1e10 |
| return np.max(autoconv) / integral_sq |
|
|
|
|
| def run(): |
| N = 4000 |
| dx = 0.5 / N |
|
|
| @jax.jit |
| def obj_smooth(params, temp): |
| f = jnp.exp(jnp.clip(params, -8, 4)) |
| padded = jnp.zeros(2 * N) |
| padded = padded.at[:N].set(f) |
| fft_f = jnp.fft.rfft(padded) |
| conv = jnp.fft.irfft(fft_f * fft_f, n=2 * N) * dx |
| integral_sq = (jnp.sum(f) * dx) ** 2 |
| smooth_max = jax.nn.logsumexp(temp * conv) / temp |
| return smooth_max / integral_sq |
|
|
| @jax.jit |
| def obj_hard(params): |
| f = jnp.exp(jnp.clip(params, -8, 4)) |
| padded = jnp.zeros(2 * N) |
| padded = padded.at[:N].set(f) |
| fft_f = jnp.fft.rfft(padded) |
| conv = jnp.fft.irfft(fft_f * fft_f, n=2 * N) * dx |
| integral_sq = (jnp.sum(f) * dx) ** 2 |
| return jnp.max(conv) / integral_sq |
|
|
| grad_smooth = jax.jit(jax.grad(obj_smooth)) |
| grad_hard = jax.jit(jax.grad(obj_hard)) |
|
|
| best_c1_overall = float('inf') |
| best_f_overall = None |
|
|
| for seed in range(20): |
| np.random.seed(seed) |
| init_f = np.ones(N) * 0.5 + 0.02 * np.random.randn(N) |
| params = jnp.array(np.log(np.maximum(init_f, 1e-6))) |
|
|
| |
| lr_schedule = optax.warmup_cosine_decay_schedule( |
| init_value=0.0, peak_value=0.005, warmup_steps=2000, |
| decay_steps=48000, end_value=1e-6, |
| ) |
| optimizer = optax.adam(learning_rate=lr_schedule) |
| opt_state = optimizer.init(params) |
|
|
| best_c1 = float('inf') |
| best_params = params |
|
|
| for step in range(50000): |
| loss, grads = jax.value_and_grad(obj_smooth)(params, 300.0) |
| updates, opt_state = optimizer.update(grads, opt_state, params) |
| params = optax.apply_updates(params, updates) |
|
|
| if step == 49999: |
| hc = float(obj_hard(params)) |
| if hc < best_c1: |
| best_c1 = hc |
| best_params = params |
|
|
| |
| params_np = np.array(best_params, dtype=np.float64) |
|
|
| for temp in [1000.0, 10000.0]: |
| def scipy_obj(p): |
| p_jax = jnp.array(p) |
| val = float(obj_smooth(p_jax, temp)) |
| g = np.array(grad_smooth(p_jax, temp), dtype=np.float64) |
| return val, g |
| result = scipy_minimize( |
| scipy_obj, params_np, method='L-BFGS-B', jac=True, |
| options={'maxiter': 3000, 'ftol': 1e-15, 'gtol': 1e-14, 'maxcor': 50}, |
| ) |
| params_np = result.x |
|
|
| |
| def scipy_obj_hard(p): |
| p_jax = jnp.array(p) |
| val = float(obj_hard(p_jax)) |
| g = np.array(grad_hard(p_jax), dtype=np.float64) |
| return val, g |
| result = scipy_minimize( |
| scipy_obj_hard, params_np, method='L-BFGS-B', jac=True, |
| options={'maxiter': 10000, 'ftol': 1e-16, 'gtol': 1e-15, 'maxcor': 100}, |
| ) |
| params_np = result.x |
|
|
| f_final = np.exp(np.clip(params_np, -8, 4)) |
| c1_final = compute_c1_numpy(f_final, N) |
|
|
| sys.stdout.write(f"Seed {seed:2d}: C1={c1_final:.10f}") |
| sys.stdout.flush() |
|
|
| if c1_final < best_c1_overall: |
| best_c1_overall = c1_final |
| best_f_overall = f_final |
| sys.stdout.write(" ***") |
| |
| np.save('/workspace/best_f.npy', f_final) |
| sys.stdout.write("\n") |
| sys.stdout.flush() |
|
|
| sys.stdout.write(f"\nFinal C1: {best_c1_overall:.10f}\n") |
| sys.stdout.flush() |
| return best_f_overall, best_c1_overall, best_c1_overall, N |
|
|
