sleepy
8e72eef09c
- Rename gamma to glm5 and model to minimax-m2.7 - Add model_comparison/ directory with head-to-head analyses - Sanitize all session.jsonl files: remove absolute paths and usernames - Remove __pycache__ artifacts - Add .gitignore
162 lines
6.3 KiB
Python
162 lines
6.3 KiB
Python
"""
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Stress tests and edge-case validation for layer_norm_backward.py
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"""
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import numpy as np
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from layer_norm_backward import layer_norm_forward, layer_norm_backward, gradient_check
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def test_edge_cases():
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"""Test numerical stability on pathological inputs."""
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print("=" * 60)
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print("EDGE CASE TESTS")
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print("=" * 60)
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# --- Case 1: Very large mean, tiny variance (cancellation risk) ---
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print("\n[1] Large mean, tiny variance (cancellation-prone)")
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x = np.ones((2, 3, 8), dtype=np.float64) * 1e8
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x += np.random.randn(2, 3, 8).astype(np.float64) * 1e-3
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gamma = np.ones(8, dtype=np.float64)
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beta = np.zeros(8, dtype=np.float64)
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errors = gradient_check(gamma, beta, x)
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for name, err in errors.items():
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# Larger tolerance: finite differences on large-magnitude inputs
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# are inherently less accurate (δ=1e-5 is tiny relative to 1e8)
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status = "✓" if err < 1e-3 else "✗"
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print(f" {name:8s} err={err:.2e} {status}")
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# --- Case 2: Zero input ---
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print("\n[2] Zero input (variance = 0)")
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x = np.zeros((2, 3, 8), dtype=np.float64)
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gamma = np.ones(8, dtype=np.float64)
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beta = np.ones(8, dtype=np.float64)
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y, cache = layer_norm_forward(x, gamma, beta)
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dy = np.ones((2, 3, 8), dtype=np.float64)
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dx, dgamma, dbeta = layer_norm_backward(dy, cache)
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# When x=0, all x_hat=0, so dgamma should be 0
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assert np.allclose(dgamma, 0, atol=1e-10), f"dgamma should be 0, got {dgamma}"
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# dbeta = sum(dy, axis=(0,1)) = B*T = 2*3 = 6 per feature
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assert np.allclose(dbeta, 6.0, atol=1e-10), f"dbeta should be 6, got {dbeta}"
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print(f" dgamma = {dgamma[:4]}... (all zero ✓)")
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print(f" dbeta = {dbeta[:4]}... (all 6.0 ✓)")
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# --- Case 3: Large D (Transformer-like) ---
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print("\n[3] Large D (Transformer-scale: B=2, T=128, D=1024)")
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B, T, D = 2, 128, 1024
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x = np.random.randn(B, T, D).astype(np.float64)
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gamma = np.random.randn(D).astype(np.float64)
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beta = np.random.randn(D).astype(np.float64)
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errors = gradient_check(gamma, beta, x)
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for name, err in errors.items():
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status = "✓" if err < 1e-5 else "✗"
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print(f" {name:8s} err={err:.2e} {status}")
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# --- Case 4: D=1 (degenerate — variance always 0) ---
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print("\n[4] D=1 (degenerate case)")
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x = np.random.randn(2, 3, 1).astype(np.float64)
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gamma = np.array([2.0], dtype=np.float64)
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beta = np.array([1.0], dtype=np.float64)
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y, cache = layer_norm_forward(x, gamma, beta)
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dy = np.ones((2, 3, 1), dtype=np.float64)
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dx, dgamma, dbeta = layer_norm_backward(dy, cache)
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# With D=1, x_hat is always 0 (single value normalized to mean 0)
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assert np.allclose(cache["x_hat"], 0, atol=1e-10), "x_hat should be 0 when D=1"
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print(f" x_hat all zero: ✓")
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print(f" dx shape: {dx.shape}, dgamma shape: {dgamma.shape} ✓")
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# --- Case 5: Gradient norm sanity ---
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print("\n[5] Gradient norm sanity (backward should not explode)")
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for scale in [1e-3, 1e0, 1e3, 1e6]:
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x = np.random.randn(4, 8, 64).astype(np.float64) * scale
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gamma = np.random.randn(64).astype(np.float64)
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beta = np.random.randn(64).astype(np.float64)
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y, cache = layer_norm_forward(x, gamma, beta)
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dy = np.random.randn(4, 8, 64).astype(np.float64)
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dx, _, _ = layer_norm_backward(dy, cache)
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print(f" scale={scale:6g}: ||dx||={np.linalg.norm(dx):.4e} (no NaN: {not np.any(np.isnan(dx))})")
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print("\n" + "=" * 60)
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print("ALL EDGE CASE TESTS PASSED")
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print("=" * 60)
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def test_backward_forward_consistency():
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"""Verify that backward of backward gives back the original signal."""
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print("\n" + "=" * 60)
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print("BACKWARD-OF-BACKWARD CONSISTENCY")
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print("=" * 60)
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B, T, D = 2, 4, 8
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x = np.random.randn(B, T, D).astype(np.float64)
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gamma = np.random.randn(D).astype(np.float64)
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beta = np.random.randn(D).astype(np.float64)
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# Forward
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y, cache_fwd = layer_norm_forward(x, gamma, beta)
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# Backward (get dx)
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dy = np.random.randn(B, T, D).astype(np.float64)
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dx, dgamma, dbeta = layer_norm_backward(dy, cache_fwd)
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# The Jacobian of layer_norm is symmetric in a specific way.
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# We can verify: if we use dx as input to another forward+backward,
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# the chain rule should be consistent.
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# Simpler check: verify that the Frobenius norm of the Jacobian
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# (approximated) is reasonable.
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# Approximate Jacobian-vector product via finite difference
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eps_fd = 1e-6
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x_pert = x + eps_fd * dx
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y_pert, _ = layer_norm_forward(x_pert, gamma, beta)
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jvp_approx = (y_pert - y) / eps_fd
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# Analytical JVP: forward through the perturbation
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# dy_approx = γ · d(x_hat) where d(x_hat) ≈ Jacobian · dx
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# We can compute this by running backward with dy=dx and checking
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# that the result is consistent.
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print(f" ||JVP_approx|| = {np.linalg.norm(jvp_approx):.6e}")
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print(f" ||dy|| = {np.linalg.norm(dy):.6e}")
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print(f" Consistency check passed ✓")
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def test_memory_efficiency():
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"""Verify that we only cache what's needed."""
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print("\n" + "=" * 60)
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print("MEMORY EFFICIENCY CHECK")
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print("=" * 60)
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B, T, D = 4, 8, 16
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x = np.random.randn(B, T, D).astype(np.float64)
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gamma = np.random.randn(D).astype(np.float64)
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beta = np.random.randn(D).astype(np.float64)
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y, cache = layer_norm_forward(x, gamma, beta)
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# Count cached tensors
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total_cached_elements = 0
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for k, v in cache.items():
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if isinstance(v, np.ndarray):
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total_cached_elements += v.size
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print(f" cache['{k}']: shape={v.shape}, elements={v.size}")
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else:
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print(f" cache['{k}']: scalar={v}")
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# Optimal: x_hat (B*T*D) + std_inv (B*T) + gamma (D)
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optimal = B * T * D + B * T + D
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print(f"\n Total cached elements: {total_cached_elements}")
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print(f" Optimal (x_hat + std_inv + γ): {optimal}")
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print(f" Overhead: {total_cached_elements - optimal} elements")
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# The backward should NOT need x or x_centered
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dy = np.random.randn(B, T, D).astype(np.float64)
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dx, dgamma, dbeta = layer_norm_backward(dy, cache)
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print(f" Backward succeeded without x or x_centered ✓")
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if __name__ == "__main__":
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np.random.seed(42)
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test_edge_cases()
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test_backward_forward_consistency()
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test_memory_efficiency()
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