import numpy as np import practice_check from practice_check import check, clear_progress, close, equal, fixture, fixtures, progress, shape, true from support import make_sine BUDGET = 1500 TARGET = 0.01 HELD_OUT_SEED = 70913 _runs = {} def train_data(): return make_sine(200, np.random.default_rng(0)) def held_out_x(): return np.random.default_rng(HELD_OUT_SEED).uniform(-np.pi, np.pi, size=2000) def fresh_run(sub, x, y, seed): saved = list(progress()) clear_progress() try: model = sub.train(x, y, np.random.default_rng(seed)) points = list(progress()) finally: clear_progress() practice_check._progress.extend(saved) return model, points def main_run(sub): key = id(sub) if key not in _runs: x, y = train_data() x_in, y_in = x.copy(), y.copy() clear_progress() model = sub.train(x_in, y_in, np.random.default_rng(1)) _runs[key] = {"model": model, "points": list(progress()), "x": x, "y": y, "x_in": x_in, "y_in": y_in} return _runs[key] def predictions(sub, model, x): out = np.asarray(sub.predict(model, x), dtype=float) shape(out, x.shape, what="the output of predict") return out def curve_mse(sub, model, x): return float(np.mean((predictions(sub, model, x) - np.sin(x)) ** 2)) @check("examples", "predict gives one value for each input", "predict returns a float array of shape (M,) for an input of shape (M,).") def example_shape(sub): run = main_run(sub) predictions(sub, run["model"], run["x"]) @check("examples", "the model fits the training points", "After training, the mean squared error against the noisy training targets must be at most 0.02. The noise alone gives about 0.01.") def example_train_mse(sub): run = main_run(sub) mse = float(np.mean((predictions(sub, run["model"], run["x"]) - run["y"]) ** 2)) true(mse <= 0.02, f"training mean squared error {mse:.5f} is above 0.02", "<= 0.02", mse) @check("properties", "training stays inside the step budget", "Call report(step, loss) once for each update step, with step = 0, 1, 2 and so on. Use at most 1500 steps.") def budget(sub): points = main_run(sub)["points"] true(len(points) >= 1, "train did not call report(step, loss)", "at least 1 call", 0) true(len(points) <= BUDGET, f"train used {len(points)} steps, the budget is {BUDGET}", f"<= {BUDGET}", len(points)) equal([point[0] for point in points], list(range(len(points))), what="the step numbers given to report") @check("properties", "the reported loss goes down", "Gradient descent must lower the loss. The mean of the last 10 reported losses must be below the first loss.") def loss_goes_down(sub): losses = np.array([point[1] for point in main_run(sub)["points"]]) true(losses.size >= 1 and np.all(np.isfinite(losses)), "a reported loss is NaN or infinite", "finite losses", losses) true(np.mean(losses[-10:]) < losses[0], "the loss did not go down", f"below {losses[0]:.4f}", float(np.mean(losses[-10:]))) @check("properties", "the same seed gives the same model", "Take every random number from the rng argument. Then two runs with the same seed give the same predictions.") def deterministic(sub): run = main_run(sub) x, y = train_data() model, points = fresh_run(sub, x, y, 1) x_test = held_out_x() equal(predictions(sub, model, x_test), predictions(sub, run["model"], x_test), what="the predictions of the second run") equal([point[1] for point in points], [point[1] for point in run["points"]], what="the losses of the second run") @check("properties", "the inputs are not changed", "Do not write into x or y and do not change their shape. Make a new array, for example with x.reshape(-1, 1).") def inputs_unchanged(sub): run = main_run(sub) equal(run["x_in"], run["x"], what="x after train") equal(run["y_in"], run["y"], what="y after train") @check("edge", "key points of the curve", "The fit must be close to sin(x) at 0, at plus and minus pi / 2 and at the ends of the range. Each error must be below 0.15.") def key_points(sub): x = np.array([-np.pi, -np.pi / 2, 0.0, np.pi / 2, np.pi]) close(predictions(sub, main_run(sub)["model"], x), np.sin(x), rtol=0, atol=0.15, what="the predictions at the key points") @check("edge", "predict on one input", "predict must work for one value and return shape (1,).") def one_input(sub): predictions(sub, main_run(sub)["model"], np.array([1.0])) @check("edge", "a smaller data set and a new seed", "Training must not depend on one lucky seed. With 100 points and another seed, the held-out error must also be at most 0.01.") def other_seed(sub): x, y = make_sine(100, np.random.default_rng(5)) model, _ = fresh_run(sub, x, y, 7) mse = curve_mse(sub, model, held_out_x()) true(mse <= TARGET, f"held-out mean squared error {mse:.5f} is above {TARGET}", f"<= {TARGET}", mse) @fixture("held_out") def reference_mse(ref): x, y = train_data() model = ref.train(x, y, np.random.default_rng(1)) x_test = held_out_x() yield {"target": TARGET}, float(np.mean((ref.predict(model, x_test) - np.sin(x_test)) ** 2)) @check("reference", "held-out error reaches the target", "The checks measure your model at 2000 new values of x from minus pi to pi. The mean squared error against the true curve sin(x) must be at most 0.01.") def held_out_mse(sub): (case, reference), = fixtures("held_out") mse = curve_mse(sub, main_run(sub)["model"], held_out_x()) true(mse <= case["target"], f"held-out mean squared error {mse:.5f} is above {case['target']}. The reference reaches {reference:.5f}", f"<= {case['target']}", mse)