""" Representation Learning Dynamics Experiment ============================================ How does a model's internal representation respond to continued training on the same task vs. learning a new one? Experiment design: Phase 1: Train model on Task A (modular addition) until convergence Phase 2: Fork into two branches: Branch A→A: Continue training on Task A (same task, more data) Branch A→B: Switch to Task B (modular subtraction) Track: CKA, subspace angles, gradient alignment, attention entropy, representation variance explained, probing accuracy — all per layer, at every checkpoint. The key contrast reveals what "learning" looks like at the representation level vs. what "forgetting" looks like — and the precise moment they diverge. """ import torch import torch.nn as nn import torch.optim as optim import numpy as np import json import os import copy import time from pathlib import Path from collections import defaultdict from typing import Dict, List, Optional from model import SmallTransformer, TransformerConfig from tasks import ( ModularArithmeticDataset, get_probe_data, get_dataloaders, DEFAULT_P, NUM_SPECIAL ) from representation_tracker import ( linear_CKA, svcca, subspace_angles, mean_subspace_angle_degrees, gradient_alignment, attention_entropy, task_variance_explained, parameter_delta_cosine, weight_change_magnitude_per_layer, cka_heatmap ) def evaluate(model, dataloader, device) -> Dict[str, float]: """Evaluate accuracy and loss on a dataset.""" model.eval() total_loss = 0 total_correct = 0 total_count = 0 with torch.no_grad(): for batch in dataloader: input_ids = batch['input_ids'].to(device) labels = batch['labels'].to(device) out = model(input_ids, labels=labels) total_loss += out['loss'].item() * input_ids.shape[0] # Accuracy: check last position prediction preds = out['logits'][:, -1, :].argmax(dim=-1) targets = labels[:, -1] total_correct += (preds == targets).sum().item() total_count += input_ids.shape[0] return { 'loss': total_loss / total_count, 'accuracy': total_correct / total_count, } def collect_representations(model, probe_input_ids, device, token_position: int = -1) -> Dict: """ Collect all representation data from a single forward pass on probe data. Returns hidden states, attention patterns, MLP activations. """ model.eval() with torch.no_grad(): out = model(probe_input_ids.to(device), return_internals=True) # Extract at the answer position (last token) hidden_states = [hs[:, token_position, :].cpu() for hs in out['hidden_states']] attn_weights = [aw.cpu() for aw in out['attn_weights']] mlp_hidden = [mh[:, token_position, :].cpu() for mh in out['mlp_hidden']] return { 'hidden_states': hidden_states, 'attn_weights': attn_weights, 'mlp_hidden': mlp_hidden, } def compute_all_metrics( model, model_init_state, model_phase1_state, reps_current, reps_at_init, reps_at_phase1_end, probe_input_ids_a, probe_labels_a, probe_input_ids_b, probe_labels_b, device, config ) -> Dict: """ Compute the full suite of representation metrics at a single checkpoint. """ metrics = {} n_layers = config.n_layers + 1 # +1 for embedding layer # === Per-layer metrics === for layer_idx in range(n_layers): prefix = f'layer_{layer_idx}' curr = reps_current['hidden_states'][layer_idx] init = reps_at_init['hidden_states'][layer_idx] p1 = reps_at_phase1_end['hidden_states'][layer_idx] # CKA vs initialization (how far has the representation drifted?) metrics[f'{prefix}/cka_vs_init'] = linear_CKA(curr, init) # CKA vs end of Phase 1 (how much has Phase 2 changed things?) metrics[f'{prefix}/cka_vs_phase1'] = linear_CKA(curr, p1) # SVCCA for secondary comparison metrics[f'{prefix}/svcca_vs_phase1'] = svcca(curr, p1) # Subspace angle vs Phase 1 end k = min(10, curr.shape[0] // 2, curr.shape[1]) if k > 0: metrics[f'{prefix}/subspace_angle_vs_phase1'] = \ mean_subspace_angle_degrees(curr, p1, k=k) else: metrics[f'{prefix}/subspace_angle_vs_phase1'] = 0.0 # === Attention entropy per layer === for layer_idx, aw in enumerate(reps_current['attn_weights']): ent = attention_entropy(aw) metrics[f'layer_{layer_idx+1}/attn_entropy_mean'] = ent['mean_entropy'] for h, he in enumerate(ent['per_head_entropy']): metrics[f'layer_{layer_idx+1}/head_{h}_entropy'] = he # === Task A representation variance explained === for layer_idx in range(n_layers): curr = reps_current['hidden_states'][layer_idx] if len(set(probe_labels_a.tolist())) > 1: tve = task_variance_explained( curr, torch.tensor(probe_labels_a, dtype=torch.float), n_components=10 ) metrics[f'layer_{layer_idx}/task_a_var_explained'] = tve['weighted_r2'] # === Parameter-space: weight change magnitude === current_state = {k: v.cpu() for k, v in model.state_dict().items()} wc_from_init = weight_change_magnitude_per_layer(model_init_state, current_state) wc_from_p1 = weight_change_magnitude_per_layer(model_phase1_state, current_state) # Aggregate per block for block_idx in range(config.n_layers): init_total = sum(v for k, v in wc_from_init.items() if f'blocks.{block_idx}' in k) p1_total = sum(v for k, v in wc_from_p1.items() if f'blocks.{block_idx}' in k) metrics[f'block_{block_idx}/weight_change_from_init'] = init_total metrics[f'block_{block_idx}/weight_change_from_phase1'] = p1_total return metrics def train_phase( model, optimizer, dataloader, n_epochs: int, device, phase_name: str, # For metric collection model_init_state, model_phase1_state, reps_at_init, reps_at_phase1_end, probe_input_ids_a, probe_labels_a, probe_input_ids_b, probe_labels_b, eval_loaders: Dict, config: TransformerConfig, checkpoint_every: int = 50, # steps between metric collection output_dir: str = 'results', ) -> List[Dict]: """ Train for n_epochs, collecting representation metrics periodically. """ history = [] global_step = 0 os.makedirs(output_dir, exist_ok=True) for epoch in range(n_epochs): model.train() epoch_loss = 0 n_batches = 0 for batch in dataloader: input_ids = batch['input_ids'].to(device) labels = batch['labels'].to(device) out = model(input_ids, labels=labels) loss = out['loss'] optimizer.zero_grad() loss.backward() optimizer.step() epoch_loss += loss.item() n_batches += 1 global_step += 1 # Collect metrics at checkpoint intervals if global_step % checkpoint_every == 0: model.eval() # Get current representations on probe data reps_current = collect_representations( model, probe_input_ids_a, device ) # Compute all metrics step_metrics = compute_all_metrics( model, model_init_state, model_phase1_state, reps_current, reps_at_init, reps_at_phase1_end, probe_input_ids_a, probe_labels_a, probe_input_ids_b, probe_labels_b, device, config ) # Evaluate on all datasets for name, loader in eval_loaders.items(): eval_res = evaluate(model, loader, device) step_metrics[f'eval/{name}_loss'] = eval_res['loss'] step_metrics[f'eval/{name}_acc'] = eval_res['accuracy'] # Gradient alignment between tasks # Get one batch from each task batch_a = next(iter(eval_loaders['add_test'])) batch_b = next(iter(eval_loaders['subtract_test'])) def loss_fn(m, b): return m(b['input_ids'].to(device), labels=b['labels'].to(device))['loss'] try: ga = gradient_alignment(model, batch_a, batch_b, loss_fn) step_metrics['gradient_alignment_a_vs_b'] = ga except Exception: step_metrics['gradient_alignment_a_vs_b'] = 0.0 step_metrics['phase'] = phase_name step_metrics['epoch'] = epoch step_metrics['step'] = global_step step_metrics['train_loss'] = epoch_loss / n_batches history.append(step_metrics) print(f"[{phase_name}] Step {global_step} | " f"Loss: {epoch_loss/n_batches:.4f} | " f"Add acc: {step_metrics.get('eval/add_test_acc', 0):.3f} | " f"Sub acc: {step_metrics.get('eval/subtract_test_acc', 0):.3f} | " f"CKA(L1 vs P1): {step_metrics.get('layer_1/cka_vs_phase1', 0):.3f} | " f"Grad align: {step_metrics.get('gradient_alignment_a_vs_b', 0):.3f}") model.train() # End of epoch eval print(f"[{phase_name}] Epoch {epoch+1}/{n_epochs} complete, " f"avg loss: {epoch_loss/n_batches:.4f}") return history def run_experiment( p: int = DEFAULT_P, n_layers: int = 2, d_model: int = 128, n_heads: int = 4, d_mlp: int = 512, phase1_epochs: int = 100, phase2_epochs: int = 100, lr: float = 1e-3, weight_decay: float = 1.0, batch_size: int = 512, train_frac: float = 0.5, checkpoint_every: int = 50, output_dir: str = 'results', seed: int = 42, ): """ Run the full two-phase experiment. """ torch.manual_seed(seed) np.random.seed(seed) device = torch.device('cuda' if torch.cuda.is_available() else 'cpu') print(f"Using device: {device}") # === Setup === config = TransformerConfig( vocab_size=p + NUM_SPECIAL, n_layers=n_layers, d_model=d_model, n_heads=n_heads, d_mlp=d_mlp, max_seq_len=5, ) model = SmallTransformer(config).to(device) print(f"Model parameters: {model.count_parameters():,}") # Save initial state model_init_state = {k: v.cpu().clone() for k, v in model.state_dict().items()} # Dataloaders loaders = get_dataloaders(p=p, batch_size=batch_size, train_frac=train_frac, seed=seed) # Probe datasets (fixed subsets for consistent metric computation) ds_a = ModularArithmeticDataset('add', p=p, split='test', train_frac=train_frac, seed=seed) ds_b = ModularArithmeticDataset('subtract', p=p, split='test', train_frac=train_frac, seed=seed) probe_ids_a, probe_labels_a = get_probe_data(ds_a, n_samples=min(500, len(ds_a))) probe_ids_b, probe_labels_b = get_probe_data(ds_b, n_samples=min(500, len(ds_b))) # Initial representations reps_at_init = collect_representations(model, probe_ids_a, device) # =========================== # PHASE 1: Train on Task A # =========================== print("\n" + "=" * 60) print("PHASE 1: Training on Task A (Modular Addition)") print("=" * 60) optimizer = optim.AdamW(model.parameters(), lr=lr, weight_decay=weight_decay) # Dummy phase1 state for Phase 1 tracking (use init) phase1_history = train_phase( model=model, optimizer=optimizer, dataloader=loaders['add_train'], n_epochs=phase1_epochs, device=device, phase_name='phase1_add', model_init_state=model_init_state, model_phase1_state=model_init_state, # placeholder reps_at_init=reps_at_init, reps_at_phase1_end=reps_at_init, # placeholder probe_input_ids_a=probe_ids_a, probe_labels_a=probe_labels_a, probe_input_ids_b=probe_ids_b, probe_labels_b=probe_labels_b, eval_loaders=loaders, config=config, checkpoint_every=checkpoint_every, output_dir=output_dir, ) # Save Phase 1 endpoint model_phase1_state = {k: v.cpu().clone() for k, v in model.state_dict().items()} reps_at_phase1_end = collect_representations(model, probe_ids_a, device) phase1_final_eval = evaluate(model, loaders['add_test'], device) print(f"\nPhase 1 final — Add accuracy: {phase1_final_eval['accuracy']:.3f}") # Save Phase 1 checkpoint torch.save(model.state_dict(), os.path.join(output_dir, 'phase1_checkpoint.pt')) # =========================== # PHASE 2: Fork into A→A and A→B # =========================== # Branch A→A: Continue on same task print("\n" + "=" * 60) print("PHASE 2a: Branch A→A (Continue training on Addition)") print("=" * 60) model_aa = SmallTransformer(config).to(device) model_aa.load_state_dict(torch.load(os.path.join(output_dir, 'phase1_checkpoint.pt'), weights_only=True)) optimizer_aa = optim.AdamW(model_aa.parameters(), lr=lr, weight_decay=weight_decay) history_aa = train_phase( model=model_aa, optimizer=optimizer_aa, dataloader=loaders['add_train'], n_epochs=phase2_epochs, device=device, phase_name='phase2_aa', model_init_state=model_init_state, model_phase1_state=model_phase1_state, reps_at_init=reps_at_init, reps_at_phase1_end=reps_at_phase1_end, probe_input_ids_a=probe_ids_a, probe_labels_a=probe_labels_a, probe_input_ids_b=probe_ids_b, probe_labels_b=probe_labels_b, eval_loaders=loaders, config=config, checkpoint_every=checkpoint_every, output_dir=output_dir, ) # Branch A→B: Switch to new task print("\n" + "=" * 60) print("PHASE 2b: Branch A→B (Switch to Subtraction)") print("=" * 60) model_ab = SmallTransformer(config).to(device) model_ab.load_state_dict(torch.load(os.path.join(output_dir, 'phase1_checkpoint.pt'), weights_only=True)) optimizer_ab = optim.AdamW(model_ab.parameters(), lr=lr, weight_decay=weight_decay) history_ab = train_phase( model=model_ab, optimizer=optimizer_ab, dataloader=loaders['subtract_train'], n_epochs=phase2_epochs, device=device, phase_name='phase2_ab', model_init_state=model_init_state, model_phase1_state=model_phase1_state, reps_at_init=reps_at_init, reps_at_phase1_end=reps_at_phase1_end, probe_input_ids_a=probe_ids_a, probe_labels_a=probe_labels_a, probe_input_ids_b=probe_ids_b, probe_labels_b=probe_labels_b, eval_loaders=loaders, config=config, checkpoint_every=checkpoint_every, output_dir=output_dir, ) # =========================== # PHASE 3: Cross-model comparison # =========================== print("\n" + "=" * 60) print("PHASE 3: Cross-model representation comparison") print("=" * 60) reps_aa = collect_representations(model_aa, probe_ids_a, device) reps_ab = collect_representations(model_ab, probe_ids_a, device) cross_metrics = {} for layer_idx in range(config.n_layers + 1): ha = reps_aa['hidden_states'][layer_idx] hb = reps_ab['hidden_states'][layer_idx] hp1 = reps_at_phase1_end['hidden_states'][layer_idx] cross_metrics[f'layer_{layer_idx}/cka_aa_vs_ab'] = linear_CKA(ha, hb) cross_metrics[f'layer_{layer_idx}/cka_aa_vs_p1'] = linear_CKA(ha, hp1) cross_metrics[f'layer_{layer_idx}/cka_ab_vs_p1'] = linear_CKA(hb, hp1) cross_metrics[f'layer_{layer_idx}/subspace_angle_aa_vs_ab'] = \ mean_subspace_angle_degrees(ha, hb, k=min(10, ha.shape[0] // 2, ha.shape[1])) # CKA heatmaps heatmap_aa_vs_ab = cka_heatmap(reps_aa['hidden_states'], reps_ab['hidden_states']) heatmap_aa_vs_p1 = cka_heatmap(reps_aa['hidden_states'], reps_at_phase1_end['hidden_states']) heatmap_ab_vs_p1 = cka_heatmap(reps_ab['hidden_states'], reps_at_phase1_end['hidden_states']) # Parameter delta cosine params_init = [v for v in model_init_state.values()] params_aa = [v.cpu() for v in model_aa.state_dict().values()] params_ab = [v.cpu() for v in model_ab.state_dict().values()] params_p1 = [v for v in model_phase1_state.values()] cross_metrics['param_delta_cosine_aa_vs_ab'] = \ parameter_delta_cosine(params_p1, params_aa, params_ab) cross_metrics['param_delta_cosine_aa_vs_p1_from_init'] = \ parameter_delta_cosine(params_init, params_p1, params_aa) print("\n=== Cross-model metrics ===") for k, v in sorted(cross_metrics.items()): print(f" {k}: {v:.4f}") # =========================== # Save all results # =========================== results = { 'config': { 'p': p, 'n_layers': n_layers, 'd_model': d_model, 'n_heads': n_heads, 'd_mlp': d_mlp, 'phase1_epochs': phase1_epochs, 'phase2_epochs': phase2_epochs, 'lr': lr, 'weight_decay': weight_decay, 'batch_size': batch_size, 'train_frac': train_frac, 'seed': seed, 'n_parameters': model.count_parameters(), }, 'phase1_history': phase1_history, 'phase2_aa_history': history_aa, 'phase2_ab_history': history_ab, 'cross_metrics': cross_metrics, 'cka_heatmaps': { 'aa_vs_ab': heatmap_aa_vs_ab.tolist(), 'aa_vs_p1': heatmap_aa_vs_p1.tolist(), 'ab_vs_p1': heatmap_ab_vs_p1.tolist(), }, } results_path = os.path.join(output_dir, 'experiment_results.json') with open(results_path, 'w') as f: json.dump(results, f, indent=2, default=str) print(f"\nResults saved to {results_path}") # Save final models torch.save(model_aa.state_dict(), os.path.join(output_dir, 'model_aa_final.pt')) torch.save(model_ab.state_dict(), os.path.join(output_dir, 'model_ab_final.pt')) return results if __name__ == '__main__': import argparse parser = argparse.ArgumentParser() parser.add_argument('--p', type=int, default=DEFAULT_P) parser.add_argument('--n-layers', type=int, default=2) parser.add_argument('--d-model', type=int, default=128) parser.add_argument('--n-heads', type=int, default=4) parser.add_argument('--d-mlp', type=int, default=512) parser.add_argument('--phase1-epochs', type=int, default=100) parser.add_argument('--phase2-epochs', type=int, default=100) parser.add_argument('--lr', type=float, default=1e-3) parser.add_argument('--weight-decay', type=float, default=1.0) parser.add_argument('--batch-size', type=int, default=512) parser.add_argument('--train-frac', type=float, default=0.5) parser.add_argument('--checkpoint-every', type=int, default=50) parser.add_argument('--output-dir', type=str, default='results') parser.add_argument('--seed', type=int, default=42) args = parser.parse_args() run_experiment(**vars(args))