Add memory centering, grid search experiments, and energy visualizationsHEADmaster

- Add centering support to MemoryBank (center_query, apply_centering, mean
  persistence in save/load) to remove centroid attractor in Hopfield dynamics
- Add center flag to MemoryBankConfig, device field to PipelineConfig
- Grid search scripts: initial (β≤8), residual, high-β, and centered grids
  with dedup-based LLM caching (89-91% call savings)
- Energy landscape visualization: 2D contour, 1D profile, UMAP, PCA heatmap
  comparing centered vs uncentered dynamics
- Experiment log (note.md) documenting 4 rounds of results and root cause
  analysis of centroid attractor problem
- Key finding: β_critical ≈ 37.6 for centered memory; best configs beat
  FAISS baseline by +3-4% F1

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

1 files changed, 313 insertions, 0 deletions

diff --git a/scripts/eval_centered_grid.py b/scripts/eval_centered_grid.py
new file mode 100644
index 0000000..4581251
--- /dev/null
+++ b/scripts/eval_centered_grid.py
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+"""Evaluate centered Hopfield on 100 questions.
+
+Memory bank is mean-centered (M̃ = M - μ), query is centered (q̃ = q - μ).
+β_critical = 37.6: below it origin is stable attractor, above it dynamics escape.
+
+Grid: β spanning both sides of β_critical, iter = [0, 1, 2, 3, 5, 8].
+No residual — pure Hopfield update on centered space.
+
+Usage:
+    CUDA_VISIBLE_DEVICES=1 nohup python -u scripts/eval_centered_grid.py \
+        --memory-bank data/processed/hotpotqa_memory_bank.pt \
+        --questions data/processed/hotpotqa_questions.jsonl \
+        --device cuda --max-samples 100 \
+        > data/processed/centered_grid.log 2>&1 &
+"""
+
+import argparse
+import json
+import logging
+import sys
+import time
+from pathlib import Path
+from typing import Dict, List, Tuple
+
+import numpy as np
+import torch
+import torch.nn.functional as F
+import yaml
+
+from hag.config import EncoderConfig, GeneratorConfig, MemoryBankConfig
+from hag.energy import compute_attention_entropy
+from hag.encoder import Encoder
+from hag.generator import Generator
+from hag.memory_bank import MemoryBank
+from hag.metrics import exact_match, f1_score
+from hag.retriever_faiss import FAISSRetriever
+
+logging.basicConfig(
+    level=logging.INFO,
+    format="%(asctime)s %(levelname)s %(name)s: %(message)s",
+    stream=sys.stdout,
+)
+logger = logging.getLogger(__name__)
+
+
+def load_questions(path: str, max_samples: int) -> Tuple[List[str], List[str]]:
+    questions, gold_answers = [], []
+    with open(path) as f:
+        for line in f:
+            r = json.loads(line)
+            questions.append(r["question"])
+            gold_answers.append(r["answer"])
+            if len(questions) >= max_samples:
+                break
+    return questions, gold_answers
+
+
+@torch.no_grad()
+def hopfield_retrieve_centered(
+    query: torch.Tensor,
+    memory_centered: torch.Tensor,
+    mean: torch.Tensor,
+    beta: float,
+    max_iter: int,
+    top_k: int,
+) -> Tuple[torch.Tensor, float]:
+    """Pure Hopfield retrieval on centered memory bank.
+
+    Args:
+        query: (batch, d) raw query embeddings
+        memory_centered: (d, N) centered memory bank (M̃ = M - μ)
+        mean: (d,) memory bank mean
+        beta, max_iter, top_k: Hopfield params
+
+    Returns:
+        (top_k_indices (batch, top_k), avg_entropy)
+    """
+    # Center the query
+    q = query - mean.unsqueeze(0)  # (batch, d)
+
+    for _ in range(max_iter):
+        logits = beta * (q @ memory_centered)  # (batch, N)
+        alpha = torch.softmax(logits, dim=-1)  # (batch, N)
+        q = alpha @ memory_centered.T  # (batch, d)
+
+    # Final attention
+    logits = beta * (q @ memory_centered)
+    alpha = torch.softmax(logits, dim=-1)
+    _, indices = torch.topk(alpha, top_k, dim=-1)
+    entropy = compute_attention_entropy(alpha)
+    return indices, entropy
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description="Centered Hopfield grid evaluation")
+    parser.add_argument("--config", type=str, default="configs/hotpotqa.yaml")
+    parser.add_argument("--memory-bank", type=str, required=True)
+    parser.add_argument("--questions", type=str, required=True)
+    parser.add_argument("--device", type=str, default="cpu")
+    parser.add_argument("--max-samples", type=int, default=100)
+    parser.add_argument("--output", type=str, default="data/processed/centered_grid_results.json")
+    parser.add_argument("--top-k", type=int, default=5)
+    args = parser.parse_args()
+
+    with open(args.config) as f:
+        cfg = yaml.safe_load(f)
+
+    # Grid: span β_critical ≈ 37.6
+    betas = [10.0, 20.0, 30.0, 38.0, 40.0, 45.0, 50.0, 60.0, 75.0, 100.0, 150.0, 200.0]
+    max_iters_list = [0, 1, 2, 3, 5, 8]
+    top_k = args.top_k
+
+    total_configs = len(betas) * len(max_iters_list)
+    logger.info("=" * 60)
+    logger.info("Centered Hopfield Grid Search")
+    logger.info("  β_critical ≈ 37.6")
+    logger.info("  betas: %s", betas)
+    logger.info("  max_iters: %s", max_iters_list)
+    logger.info("  total configs: %d", total_configs)
+    logger.info("=" * 60)
+
+    t_start = time.time()
+
+    questions, gold_answers = load_questions(args.questions, args.max_samples)
+    n = len(questions)
+    logger.info("Loaded %d questions", n)
+
+    # Load memory bank (uncentered)
+    mb = MemoryBank(MemoryBankConfig(**cfg.get("memory", {})))
+    mb.load(args.memory_bank, device=args.device)
+    M_raw = mb.embeddings  # (d, N)
+    d, N = M_raw.shape
+    logger.info("Memory bank: %d passages, dim=%d", N, d)
+
+    # Center the memory bank
+    mu = M_raw.mean(dim=1)  # (d,)
+    M_cent = M_raw - mu.unsqueeze(1)  # (d, N)
+    logger.info("Centered memory bank. ‖μ‖=%.4f, ‖M̃·1/N‖=%.2e",
+                mu.norm().item(), M_cent.mean(dim=1).norm().item())
+
+    # Compute β_critical
+    S = torch.linalg.svdvals(M_cent)
+    lambda_max_C = (S[0].item() ** 2) / N
+    beta_crit = 1.0 / lambda_max_C
+    logger.info("β_critical = %.2f (λ_max(C)=%.4f, σ_max=%.4f)", beta_crit, lambda_max_C, S[0].item())
+
+    encoder = Encoder(EncoderConfig(**cfg.get("encoder", {})), device=args.device)
+    generator = Generator(GeneratorConfig(**cfg.get("generator", {})), device=args.device)
+
+    logger.info("Encoding questions...")
+    all_embs = []
+    batch_size = cfg.get("encoder", {}).get("batch_size", 64)
+    for i in range(0, n, batch_size):
+        all_embs.append(encoder.encode(questions[i : i + batch_size]))
+    Q = torch.cat(all_embs, dim=0)  # (n, d)
+    logger.info("Encoded, shape=%s", Q.shape)
+
+    # FAISS baseline (on raw embeddings)
+    logger.info("Running FAISS baseline...")
+    emb_np = M_raw.T.cpu().numpy().astype(np.float32)
+    faiss_ret = FAISSRetriever(top_k=top_k)
+    faiss_ret.build_index(emb_np, mb.passages)
+
+    faiss_indices: Dict[int, Tuple[int, ...]] = {}
+    llm_cache: Dict[Tuple[int, frozenset], str] = {}
+
+    for i in range(n):
+        q_np = Q[i].cpu().numpy().astype(np.float32)
+        result = faiss_ret.retrieve(q_np)
+        idx_tuple = tuple(sorted(result.indices.tolist()))
+        faiss_indices[i] = idx_tuple
+        cache_key = (i, frozenset(idx_tuple))
+        answer = generator.generate(questions[i], result.passages)
+        llm_cache[cache_key] = answer
+        if (i + 1) % 20 == 0:
+            ems = [exact_match(llm_cache[(j, frozenset(faiss_indices[j]))], gold_answers[j]) for j in range(i + 1)]
+            f1s = [f1_score(llm_cache[(j, frozenset(faiss_indices[j]))], gold_answers[j]) for j in range(i + 1)]
+            logger.info("  FAISS %d/%d: EM=%.3f F1=%.3f", i + 1, n, np.mean(ems), np.mean(f1s))
+
+    faiss_em = np.mean([exact_match(llm_cache[(i, frozenset(faiss_indices[i]))], gold_answers[i]) for i in range(n)])
+    faiss_f1 = np.mean([f1_score(llm_cache[(i, frozenset(faiss_indices[i]))], gold_answers[i]) for i in range(n)])
+    logger.info("FAISS baseline: EM=%.4f F1=%.4f", faiss_em, faiss_f1)
+
+    # Phase 2: Retrieve all configs (centered)
+    logger.info("Phase 2: Retrieving all %d configs (centered)...", total_configs)
+    t_ret = time.time()
+
+    retrieval_data: Dict[str, List[Tuple[Tuple[int, ...], float]]] = {}
+
+    for beta in betas:
+        for max_iter in max_iters_list:
+            config_key = f"β={beta}_iter={max_iter}"
+            indices_batch, entropy = hopfield_retrieve_centered(
+                Q, M_cent, mu, beta=beta, max_iter=max_iter, top_k=top_k,
+            )
+            per_q = []
+            for i in range(n):
+                idx_tuple = tuple(sorted(indices_batch[i].tolist()))
+                per_q.append((idx_tuple, entropy))
+            retrieval_data[config_key] = per_q
+
+    logger.info("Retrieval done in %.1fs, %d configs", time.time() - t_ret, len(retrieval_data))
+
+    # Phase 3: Dedup + generate
+    needed: Dict[Tuple[int, frozenset], Tuple[int, Tuple[int, ...]]] = {}
+    for key, per_q in retrieval_data.items():
+        for i, (idx_tuple, _) in enumerate(per_q):
+            cache_key = (i, frozenset(idx_tuple))
+            if cache_key not in llm_cache and cache_key not in needed:
+                needed[cache_key] = (i, idx_tuple)
+
+    logger.info("Unique LLM calls needed: %d (cache has %d)", len(needed), len(llm_cache))
+
+    t_gen = time.time()
+    for call_idx, (cache_key, (q_idx, idx_tuple)) in enumerate(needed.items()):
+        passages = mb.get_passages_by_indices(torch.tensor(list(idx_tuple), dtype=torch.long))
+        answer = generator.generate(questions[q_idx], passages)
+        llm_cache[cache_key] = answer
+        if (call_idx + 1) % 50 == 0:
+            elapsed = time.time() - t_gen
+            rate = (call_idx + 1) / elapsed
+            logger.info("  Generated %d/%d (%.1f/s, ~%.0fs left)",
+                        call_idx + 1, len(needed), rate, (len(needed) - call_idx - 1) / rate)
+    logger.info("Generation done: %d calls in %.1fs", len(needed), time.time() - t_gen)
+
+    # Phase 4: Evaluate
+    logger.info("Phase 4: Evaluating...")
+    results = []
+    for config_key, per_q in retrieval_data.items():
+        ems, f1s, overlaps = [], [], []
+        for i, (idx_tuple, ent) in enumerate(per_q):
+            cache_key = (i, frozenset(idx_tuple))
+            answer = llm_cache[cache_key]
+            ems.append(exact_match(answer, gold_answers[i]))
+            f1s.append(f1_score(answer, gold_answers[i]))
+            overlaps.append(len(set(idx_tuple) & set(faiss_indices[i])) / top_k)
+
+        em, f1 = np.mean(ems), np.mean(f1s)
+        # Parse beta from config_key
+        beta_val = float(config_key.split("_")[0].split("=")[1])
+        iter_val = int(config_key.split("_")[1].split("=")[1])
+        r = {
+            "config": config_key,
+            "beta": beta_val,
+            "max_iter": iter_val,
+            "em": round(em, 4),
+            "f1": round(f1, 4),
+            "avg_faiss_overlap": round(np.mean(overlaps), 4),
+            "avg_entropy": round(per_q[0][1], 4),
+            "above_beta_crit": beta_val > beta_crit,
+        }
+        results.append(r)
+
+    results.sort(key=lambda x: x["f1"], reverse=True)
+
+    # Count how many beat FAISS
+    n_beat = sum(1 for r in results if r["f1"] > faiss_f1)
+    logger.info("\n%d/%d configs beat FAISS F1=%.3f", n_beat, len(results), faiss_f1)
+
+    # Log top 20
+    logger.info("\nTop 20 configs:")
+    for i, r in enumerate(results[:20]):
+        marker = " ***" if r["f1"] > faiss_f1 else ""
+        crit = ">" if r["above_beta_crit"] else "<"
+        logger.info("  %2d. %-25s EM=%.3f F1=%.3f overlap=%.3f H=%.2f β%sβ_c%s",
+                    i + 1, r["config"], r["em"], r["f1"], r["avg_faiss_overlap"],
+                    r["avg_entropy"], crit, marker)
+
+    # Summary by β: best iter for each β
+    logger.info("\nBest iter per β:")
+    for beta in betas:
+        beta_results = [r for r in results if r["beta"] == beta]
+        if beta_results:
+            best = beta_results[0]
+            crit = ">" if best["above_beta_crit"] else "<"
+            logger.info("  β=%6.1f (β%sβ_c): best iter=%d EM=%.3f F1=%.3f overlap=%.3f",
+                        beta, crit, best["max_iter"], best["em"], best["f1"], best["avg_faiss_overlap"])
+
+    t_total = time.time() - t_start
+    output = {
+        "meta": {
+            "n_questions": n,
+            "total_configs": len(retrieval_data),
+            "unique_llm_calls": len(needed),
+            "total_time_s": round(t_total, 1),
+            "beta_critical": round(beta_crit, 2),
+        },
+        "faiss_baseline": {"em": round(faiss_em, 4), "f1": round(faiss_f1, 4)},
+        "grid_results": results,
+        "best_config": results[0],
+        "top10": results[:10],
+    }
+
+    Path(args.output).parent.mkdir(parents=True, exist_ok=True)
+    with open(args.output, "w") as f:
+        json.dump(output, f, indent=2)
+
+    logger.info("=" * 60)
+    logger.info("RESULTS SUMMARY")
+    logger.info("  FAISS: EM=%.4f F1=%.4f", faiss_em, faiss_f1)
+    logger.info("  β_critical = %.2f", beta_crit)
+    logger.info("  Configs beating FAISS: %d/%d", n_beat, len(results))
+    logger.info("  Top 5:")
+    for i, r in enumerate(results[:5]):
+        logger.info("    %d. %-25s EM=%.3f F1=%.3f overlap=%.3f",
+                    i + 1, r["config"], r["em"], r["f1"], r["avg_faiss_overlap"])
+    logger.info("  Total time: %.1fs", t_total)
+    logger.info("  Saved to: %s", args.output)
+    logger.info("=" * 60)
+
+
+if __name__ == "__main__":
+    main()