# Disable progress bar for cleaner output logs import os os.environ["TQDM_DISABLE"] = "1" # Fixed parameters n, m, p = 2, 4, 5 # EVOLVE-BLOCK-START import numpy as np import jax import jax.numpy as jnp import optax from dataclasses import dataclass import tqdm # --- Straight-Through Estimator for Rounding --- @jax.custom_vjp def round_to_half_ste(x): """Forward pass: snaps values to the nearest half-integer.""" return jnp.round(x * 2) / 2 def round_ste_fwd(x): """Standard forward pass and identity for backward pass.""" return round_to_half_ste(x), None def round_ste_bwd(res, g): """Backward pass: Identity function, passes gradient straight through.""" return (g,) round_to_half_ste.defvjp(round_ste_fwd, round_ste_bwd) # --- End of STE definition --- # --- Loss Functions --- def weighted_l2_loss(reconstructed: jnp.ndarray, target: jnp.ndarray) -> jnp.ndarray: error = reconstructed - target weights = jnp.where(target != 0, 100.0, 1.0) return jnp.mean(weights * (error**2)) def l2_loss_real(x: jnp.ndarray, y: jnp.ndarray) -> jnp.ndarray: return jnp.mean((x - y) ** 2) # --- Hyperparameters --- @dataclass class Hyperparameters: rank: int = 55 # Phase 1: Continuous Search num_restarts: int = 10 phase1_steps: int = 80000 phase1_lr: float = 0.01 init_scale: float = 0.1 l1_strength: float = 1e-6 clamp_range: float = 4.0 # Phase 2: Discrete Fine-tuning phase2_steps: int = 20000 phase2_lr: float = 1e-4 # A much smaller learning rate for fine-tuning # --- Optimizer Classes --- class ContinuousOptimizer: """Finds a high-quality approximate continuous solution.""" def __init__(self, target_tensor: jnp.ndarray, hypers: Hyperparameters): self.target_tensor = target_tensor self.hypers = hypers self.opt = optax.adam(hypers.phase1_lr) def _get_constrained_decomposition(self, latent_decomposition: tuple) -> tuple: """Applies a scaled tanh to map latent parameters to the desired range.""" return jax.tree_util.tree_map( lambda x: self.hypers.clamp_range * jnp.tanh(x), latent_decomposition ) def _loss_fn(self, latent_decomposition: tuple) -> jnp.ndarray: constrained = self._get_constrained_decomposition(latent_decomposition) reconstructed = jnp.einsum("ir,jr,kr->ijk", *constrained) recon_loss = weighted_l2_loss(reconstructed, self.target_tensor) l1_penalty = sum(jnp.mean(jnp.abs(arr)) for arr in constrained) return recon_loss + self.hypers.l1_strength * l1_penalty class DiscreteOptimizer: """Refines a continuous solution into an exact discrete one using an STE.""" def __init__(self, target_tensor: jnp.ndarray, hypers: Hyperparameters): self.target_tensor = target_tensor self.hypers = hypers self.opt = optax.adam(hypers.phase2_lr) def _loss_fn(self, continuous_decomposition: tuple) -> jnp.ndarray: # Snap the continuous parameters to the discrete grid discrete_decomposition = jax.tree_util.tree_map(round_to_half_ste, continuous_decomposition) # Compute the loss using only these exact half-integer values reconstructed = jnp.einsum("ir,jr,kr->ijk", *discrete_decomposition) return l2_loss_real(reconstructed, self.target_tensor) # --- JIT-compatible Train Step --- def train_step(params, opt_state, optimizer, loss_fn): loss, grads = jax.value_and_grad(loss_fn)(params) updates, opt_state = optimizer.update(grads, opt_state, params) params = optax.apply_updates(params, updates) return params, opt_state, loss def get_matrix_multiplication_tensor(n, m, p): T = jnp.zeros((n * m, m * p, n * p)) for i, j, k in np.ndindex(n, m, p): T = T.at[i * m + j, j * p + k, k * n + i].set(1) return T def run(): hypers = Hyperparameters() target_tensor = get_matrix_multiplication_tensor(n, m, p) main_key = jax.random.PRNGKey(42) # --- PHASE 1: CONTINUOUS EXPLORATION --- print(f"\n{'='*20} PHASE 1: Continuous Exploration {'='*20}") best_loss_phase1 = float("inf") best_latent_decomp = None continuous_optimizer = ContinuousOptimizer(target_tensor, hypers) # JIT the train_step for the continuous phase jit_train_step_continuous = jax.jit(train_step, static_argnums=(2, 3)) for i in range(hypers.num_restarts): print(f"\n--- Restart {i+1}/{hypers.num_restarts} ---") main_key, restart_key = jax.random.split(main_key) init_fn = jax.nn.initializers.normal(stddev=hypers.init_scale) latent_decomp = ( init_fn(restart_key, (n * m, hypers.rank)), init_fn(restart_key, (m * p, hypers.rank)), init_fn(restart_key, (n * p, hypers.rank)), ) opt_state = continuous_optimizer.opt.init(latent_decomp) for _ in tqdm.tqdm(range(hypers.phase1_steps), desc="Continuous Search"): latent_decomp, opt_state, loss = jit_train_step_continuous( latent_decomp, opt_state, continuous_optimizer.opt, continuous_optimizer._loss_fn, ) final_loss = l2_loss_real( target_tensor, jnp.einsum( "ir,jr,kr->ijk", *continuous_optimizer._get_constrained_decomposition(latent_decomp), ), ) print(f"End of Trial | Final continuous loss: {final_loss:.8f}") if final_loss < best_loss_phase1: best_loss_phase1 = final_loss best_latent_decomp = latent_decomp # --- PHASE 2: DISCRETE FINE-TUNING --- print(f"\n{'='*20} PHASE 2: Discrete Fine-tuning (STE) {'='*20}") print(f"Starting with best continuous solution (loss: {best_loss_phase1:.8f})") continuous_params = continuous_optimizer._get_constrained_decomposition(best_latent_decomp) discrete_optimizer = DiscreteOptimizer(target_tensor, hypers) opt_state = discrete_optimizer.opt.init(continuous_params) # JIT the train_step for the discrete phase jit_train_step_discrete = jax.jit(train_step, static_argnums=(2, 3)) for step in tqdm.tqdm(range(hypers.phase2_steps), desc="Discrete Fine-tuning"): continuous_params, opt_state, loss = jit_train_step_discrete( continuous_params, opt_state, discrete_optimizer.opt, discrete_optimizer._loss_fn ) if (step + 1) % 2000 == 0: print(f"Step {step+1} | Discrete Loss: {loss:.8f}") if loss < 1e-7: print("\nFound a perfect solution!") break final_discrete_decomposition = jax.tree_util.tree_map(round_to_half_ste, continuous_params) final_loss = l2_loss_real( target_tensor, jnp.einsum("ir,jr,kr->ijk", *final_discrete_decomposition) ) print(f"Search complete. Final discrete loss: {final_loss:.8f}") final_decomposition_np = jax.tree_util.tree_map(np.array, final_discrete_decomposition) return final_decomposition_np, n, m, p, float(final_loss), hypers.rank # EVOLVE-BLOCK-END