#!/usr/bin/env python3 """ The Impossible Classification Test ===================================== If 9 methods x 4 layers = 36 features can't distinguish visual from gibberish, the subspace projections contain ZERO content info. CPU only. Loads data from scaled gibberish GPU checkpoint. Setup: !pip install -q scikit-learn scipy xgboost """ import json import numpy as np from pathlib import Path from sklearn.ensemble import GradientBoostingClassifier, RandomForestClassifier from sklearn.svm import SVC from sklearn.linear_model import LogisticRegression from sklearn.neural_network import MLPClassifier from sklearn.model_selection import cross_val_score, StratifiedKFold from sklearn.metrics import roc_auc_score, classification_report from sklearn.preprocessing import StandardScaler from scipy import stats as sp from google.colab import drive drive.mount("/content/drive", force_remount=False) print("=" * 65) print("The Impossible Classification Test") print("=" * 65) # ---- Load data from scaled gibberish checkpoint ---- CHECKPOINT = Path("/content/drive/MyDrive/topohd_scaled_gib/gpu_checkpoint.json") assert CHECKPOINT.exists(), "Run scaled_gibberish_gpu.py first!" with open(CHECKPOINT) as f: raw = json.load(f) # Parse keys: format is "prompttype|method|layer" TARGET_LAYERS = [8, 16, 24, 32] methods = set() for key in raw: if key.startswith("_"): continue parts = key.split("|") if len(parts) == 3: methods.add(parts[1]) methods.discard("random") methods = sorted(methods) print(f"\n Methods: {methods}") print(f" Layers: {TARGET_LAYERS}") print(f" Feature dimensions: {len(methods)} x {len(TARGET_LAYERS)} = {len(methods)*len(TARGET_LAYERS)}") # ---- Build feature matrix ---- # For each prompt index, build a feature vector from all (method, layer) combinations feature_names = [f"{m}_L{l}" for m in methods for l in TARGET_LAYERS] N_FEATURES = len(feature_names) # Get prompt counts n_visual = raw.get("_progress_visual", 0) n_gibberish = raw.get("_progress_gibberish", 0) print(f" Visual prompts: {n_visual}") print(f" Gibberish prompts: {n_gibberish}") N = min(n_visual, n_gibberish) print(f" Using {N} per class (balanced)") # Build matrices X_visual = np.zeros((N, N_FEATURES)) X_gibberish = np.zeros((N, N_FEATURES)) for fi, (m, l) in enumerate([(m, l) for m in methods for l in TARGET_LAYERS]): v_key = f"visual|{m}|{l}" g_key = f"gibberish|{m}|{l}" v_vals = raw.get(v_key, []) g_vals = raw.get(g_key, []) for i in range(min(N, len(v_vals))): X_visual[i, fi] = v_vals[i] for i in range(min(N, len(g_vals))): X_gibberish[i, fi] = g_vals[i] X = np.vstack([X_visual, X_gibberish]) y = np.array([1]*N + [0]*N) # 1=visual, 0=gibberish # Remove any rows with all zeros (missing data) valid = X.sum(axis=1) != 0 X = X[valid] y = y[valid] print(f" Valid samples: {len(X)} ({sum(y)} visual, {len(y)-sum(y)} gibberish)") # ---- Train classifiers ---- print(f"\n Training 5 classifiers with 10-fold stratified CV ...") print(f" (Chance level = 50%)") print(f"\n {'Classifier':<30} {'Accuracy':>10} {'Std':>8} {'AUROC':>8}") print(f" {'-'*56}") cv = StratifiedKFold(n_splits=10, shuffle=True, random_state=42) scaler = StandardScaler() X_scaled = scaler.fit_transform(X) classifiers = { "Logistic Regression": LogisticRegression(max_iter=1000, random_state=42), "SVM (RBF kernel)": SVC(kernel='rbf', probability=True, random_state=42), "Random Forest (100 trees)": RandomForestClassifier(n_estimators=100, random_state=42), "Gradient Boosted Trees": GradientBoostingClassifier( n_estimators=200, max_depth=4, random_state=42), "MLP (128-64-32)": MLPClassifier( hidden_layer_sizes=(128, 64, 32), max_iter=500, random_state=42), } all_results = {} for name, clf in classifiers.items(): # Accuracy acc_scores = cross_val_score(clf, X_scaled, y, cv=cv, scoring='accuracy') # AUROC auc_scores = cross_val_score(clf, X_scaled, y, cv=cv, scoring='roc_auc') mean_acc = acc_scores.mean() std_acc = acc_scores.std() mean_auc = auc_scores.mean() all_results[name] = dict(accuracy=float(mean_acc), std=float(std_acc), auroc=float(mean_auc)) marker = " <<<" if mean_acc > 0.55 else "" print(f" {name:<30} {mean_acc*100:>9.1f}% {std_acc*100:>7.1f}% " f"{mean_auc:>7.3f}{marker}") # ---- Statistical test: is the best classifier better than chance? ---- print(f"\n Statistical test: best classifier vs chance (50%)") best_name = max(all_results, key=lambda k: all_results[k]["accuracy"]) best_acc = all_results[best_name]["accuracy"] best_std = all_results[best_name]["std"] if "std" in all_results[best_name] else 0 # Re-run best classifier to get per-fold accuracies best_clf = classifiers[best_name] fold_accs = cross_val_score(best_clf, X_scaled, y, cv=cv, scoring='accuracy') # One-sample t-test: is mean accuracy > 0.50? t_stat, p_val = sp.ttest_1samp(fold_accs, 0.50) p_one_sided = p_val / 2 if t_stat > 0 else 1.0 print(f" Best: {best_name} ({best_acc*100:.1f}%)") print(f" Per-fold: {[f'{a*100:.1f}%' for a in fold_accs]}") print(f" t-test vs 50%: t={t_stat:.3f}, p={p_one_sided:.4f} (one-sided)") if p_one_sided > 0.05: print(f" >>> NOT SIGNIFICANT: best classifier ≈ chance <<<") else: print(f" >>> SIGNIFICANT: classifier beats chance (but check effect size) <<<") print(f" Effect: {(best_acc - 0.50)*100:+.1f}pp above chance") # ---- Feature importance (from gradient boosted) ---- print(f"\n Feature Importance (Gradient Boosted Trees):") gb = GradientBoostingClassifier(n_estimators=200, max_depth=4, random_state=42) gb.fit(X_scaled, y) importances = gb.feature_importances_ # Top 10 features top_idx = np.argsort(importances)[::-1][:10] print(f" {'Feature':<25} {'Importance':>12}") print(f" {'-'*37}") for idx in top_idx: print(f" {feature_names[idx]:<25} {importances[idx]:>12.4f}") # Check if any single feature is useful print(f"\n Max single-feature importance: {importances.max():.4f}") print(f" (Uniform = {1/N_FEATURES:.4f})") if importances.max() < 2/N_FEATURES: print(f" No feature is more important than chance → no signal exists") # ---- Also test with factual and math ---- print(f"\n Bonus: Can classifier distinguish visual from factual?") n_factual = raw.get("_progress_factual", 0) if n_factual > 0: X_factual = np.zeros((min(N, n_factual), N_FEATURES)) for fi, (m, l) in enumerate([(m, l) for m in methods for l in TARGET_LAYERS]): f_key = f"factual|{m}|{l}" f_vals = raw.get(f_key, []) for i in range(min(N, len(f_vals))): X_factual[i, fi] = f_vals[i] X_vf = np.vstack([X_visual[:min(N, n_factual)], X_factual]) y_vf = np.array([1]*min(N, n_factual) + [0]*min(N, n_factual)) valid_vf = X_vf.sum(axis=1) != 0 X_vf, y_vf = X_vf[valid_vf], y_vf[valid_vf] X_vf_s = scaler.transform(X_vf) gb_vf = GradientBoostingClassifier(n_estimators=200, max_depth=4, random_state=42) vf_scores = cross_val_score(gb_vf, X_vf_s, y_vf, cv=cv, scoring='accuracy') print(f" Visual vs Factual: {vf_scores.mean()*100:.1f}% ± {vf_scores.std()*100:.1f}%") print(f"\n Bonus: Can classifier distinguish visual from math?") n_math = raw.get("_progress_math", 0) if n_math > 0: X_math = np.zeros((min(N, n_math), N_FEATURES)) for fi, (m, l) in enumerate([(m, l) for m in methods for l in TARGET_LAYERS]): mk = f"math|{m}|{l}" m_vals = raw.get(mk, []) for i in range(min(N, len(m_vals))): X_math[i, fi] = m_vals[i] X_vm = np.vstack([X_visual[:min(N, n_math)], X_math]) y_vm = np.array([1]*min(N, n_math) + [0]*min(N, n_math)) valid_vm = X_vm.sum(axis=1) != 0 X_vm, y_vm = X_vm[valid_vm], y_vm[valid_vm] X_vm_s = scaler.transform(X_vm) gb_vm = GradientBoostingClassifier(n_estimators=200, max_depth=4, random_state=42) vm_scores = cross_val_score(gb_vm, X_vm_s, y_vm, cv=cv, scoring='accuracy') print(f" Visual vs Math: {vm_scores.mean()*100:.1f}% ± {vm_scores.std()*100:.1f}%") # ---- Verdict ---- print(f"\n{'='*65}") print("VERDICT") print(f"{'='*65}") all_at_chance = all(r["accuracy"] < 0.55 for r in all_results.values()) if all_at_chance: print(f""" >>> ZERO DISCRIMINATIVE INFORMATION <<< Five classifiers (logistic regression, SVM, random forest, gradient boosted trees, neural network) trained on the full {N_FEATURES}-dimensional subspace projection profile ({len(methods)} methods x {len(TARGET_LAYERS)} layers) cannot distinguish visual prompts from gibberish above chance level. The 'visual subspace' projections contain ZERO information about whether the input describes visual content or is random character sequences. This is not a limitation of any individual method — it is a fundamental property of how PCA/SVD extracts directions from transformer hidden states. """) else: above = {k: v for k, v in all_results.items() if v["accuracy"] >= 0.55} print(f"\n {len(above)} classifiers achieved >55% accuracy.") print(f" Some weak signal exists in the projection profiles.") for k, v in above.items(): print(f" {k}: {v['accuracy']*100:.1f}%") # Save OUT = Path("/content/drive/MyDrive/topohd_classification") OUT.mkdir(exist_ok=True, parents=True) with open(OUT / "classification_results.json", "w") as f: json.dump(all_results, f, indent=2) print(f"\n Saved to {OUT}/")