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This commit is contained in:
gaojie
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"""
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Reacher trajectory distribution analysis figures.
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Produces two figures for the paper:
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1. Scatter grid: stationary marginal + per-delta 2D transition differences
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and per-dim (z_t, z_{t+delta}) scatters, annotated with R² and rho.
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2. rho-vs-SIGReg scatter: three panels (z_0, z_1, joint), colored by R²,
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showing the dual constraint that identifiability requires both
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rho off from 1 and approximately-Gaussian transition shape.
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Usage:
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python -m analysis.make_reacher_distributions \
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--results_dir results/reacher \
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--data_path data/reacher.h5 \
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--out_dir figures/reacher
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"""
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import argparse
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import json
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from collections import defaultdict
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from pathlib import Path
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import matplotlib
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matplotlib.use("Agg")
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import matplotlib.pyplot as plt
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import numpy as np
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import torch
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from scipy.stats import pearsonr
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DELTAS = [1, 2, 4, 8, 16, 32, 64]
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DEVICE = "cuda" if torch.cuda.is_available() else "cpu"
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N_MAX = 100_000
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# ═════════════════════════════════════════════════════════════════════════════
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# SIGReg (Epps–Pulley) — matches LeJEPA Algorithm 1
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# ═════════════════════════════════════════════════════════════════════════════
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def _sigreg_nd(x, num_slices=64, n_knots=17, seed=0, device=DEVICE):
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"""EP via random slicing on (N, K)."""
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x = torch.as_tensor(np.asarray(x), dtype=torch.float32, device=device)
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if x.dim() == 1:
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x = x[:, None]
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N, K = x.shape
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g = torch.Generator(device=device).manual_seed(seed)
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A = torch.randn(K, num_slices, generator=g, device=device)
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A = A / A.norm(p=2, dim=0)
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t = torch.linspace(-5, 5, n_knots, device=device)
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phi = torch.exp(-0.5 * t ** 2)
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zt = (x @ A).unsqueeze(2) * t
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cm, sm = torch.cos(zt).mean(0), torch.sin(zt).mean(0)
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err = ((cm - phi) ** 2 + sm ** 2) * phi
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return (torch.trapz(err, t, dim=1) * N).mean().item()
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def _sigreg_1d(x, n_knots=17, device=DEVICE):
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"""EP directly on 1D (no slicing)."""
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x = torch.as_tensor(np.asarray(x).reshape(-1), dtype=torch.float32, device=device)
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N = x.shape[0]
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t = torch.linspace(-5, 5, n_knots, device=device)
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phi = torch.exp(-0.5 * t ** 2)
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zt = x.unsqueeze(1) * t
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cm, sm = torch.cos(zt).mean(0), torch.sin(zt).mean(0)
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err = ((cm - phi) ** 2 + sm ** 2) * phi
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return (torch.trapz(err, t) * N).item()
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def _zscore(x):
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return (x - x.mean(0, keepdims=True)) / (x.std(0, keepdims=True) + 1e-8)
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def measure(x, n_draws=20, N_max=N_MAX, num_slices=64):
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"""
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SIGReg raw + zscored for joint (K-d) and per-dim marginals.
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Averages over n_draws random subsamples / projections.
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Returns dict mapping key -> (mean, std) over draws.
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"""
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x = np.asarray(x)
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if x.ndim == 1:
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x = x[:, None]
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N, K = x.shape
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rng = np.random.default_rng(0)
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keys = ["joint_raw", "joint_zs"]
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keys += [f"marg_{k}_raw" for k in range(K)]
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keys += [f"marg_{k}_zs" for k in range(K)]
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buf = {k: [] for k in keys}
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for s in range(n_draws):
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xs = x if N <= N_max else x[rng.choice(N, N_max, replace=False)]
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xz = _zscore(xs)
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buf["joint_raw"].append(_sigreg_nd(xs, num_slices, seed=s))
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buf["joint_zs"].append(_sigreg_nd(xz, num_slices, seed=s))
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for k in range(K):
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buf[f"marg_{k}_raw"].append(_sigreg_1d(xs[:, k]))
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buf[f"marg_{k}_zs"].append(_sigreg_1d(xz[:, k]))
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return {k: (np.mean(v), np.std(v)) for k, v in buf.items()}
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# ═════════════════════════════════════════════════════════════════════════════
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# R² loading — per-seed best-lambda tuning, median across seeds
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# ═════════════════════════════════════════════════════════════════════════════
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def get_best_r2_per_delta(results_dir, agg="median"):
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"""
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For each (delta, seed), pick the lambda with best R²; aggregate seeds
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with median (robust to outliers) or mean.
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"""
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by_dls = defaultdict(list)
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for p in Path(results_dir).rglob("result.json"):
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r = json.load(open(p))
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if "delta" not in r or r.get("rho") is not None:
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continue
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by_dls[(r["delta"], r["lamb"], r.get("seed", 0))].append(r)
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deltas = sorted({k[0] for k in by_dls})
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lambs = sorted({k[1] for k in by_dls})
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seeds = sorted({k[2] for k in by_dls})
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agg_fn = np.median if agg == "median" else np.mean
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best = {}
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for delta in deltas:
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per_seed = {"r2": [], "d0": [], "d1": [], "lamb": []}
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for seed in seeds:
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best_lamb, best_r2 = None, -np.inf
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for lamb in lambs:
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runs = by_dls.get((delta, lamb, seed), [])
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if not runs:
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continue
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r2 = np.mean([r["r2_hz"] for r in runs])
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if r2 > best_r2:
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best_r2, best_lamb = r2, lamb
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if best_lamb is None:
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continue
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runs = by_dls[(delta, best_lamb, seed)]
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per_seed["r2"].append(np.mean([r["r2_hz"] for r in runs]))
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per_seed["d0"].append(np.mean([r["r2_hz_per_dim"][0] for r in runs]))
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per_seed["d1"].append(np.mean([r["r2_hz_per_dim"][1] for r in runs]))
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per_seed["lamb"].append(best_lamb)
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best[delta] = {
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"r2": agg_fn(per_seed["r2"]),
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"r2_dim0": agg_fn(per_seed["d0"]),
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"r2_dim1": agg_fn(per_seed["d1"]),
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"lamb": np.median(per_seed["lamb"]),
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"n_seeds": len(per_seed["r2"]),
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}
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return best
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def best_ou_rho(results_dir):
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"""Return the rho of the OU run with highest mean R² across seeds/lambdas."""
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grouped = defaultdict(list)
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for p in Path(results_dir).rglob("result.json"):
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r = json.load(open(p))
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if "rho" not in r or r.get("rho") is None:
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continue
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grouped[(r["rho"], r["lamb"])].append(r)
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if not grouped:
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return None
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best_rho, best_mean = None, -np.inf
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for (rho, lamb), runs in grouped.items():
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m = np.mean([r["r2_hz"] for r in runs])
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if m > best_mean:
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best_mean, best_rho = m, rho
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return best_rho
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# ═════════════════════════════════════════════════════════════════════════════
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# Figure 1: scatter grid
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# ═════════════════════════════════════════════════════════════════════════════
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def make_scatter_grid(episodes, r2_dict, save_path, sub=1, s=1e-4):
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"""
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Left column: stationary marginal scatter of (z_0, z_1).
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Top row, remaining columns: 2D transition-difference scatter per delta.
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Bottom row, remaining columns: per-dim (z_t, z_{t+delta}) scatter.
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Titles show R² and rho.
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"""
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fig = plt.figure(figsize=0.85 * np.array((1 + 3 * len(DELTAS), 5)))
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gs = fig.add_gridspec(2, 2 + len(DELTAS))
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# stationary marginal (spans both rows, first two cols)
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ax = fig.add_subplot(gs[:2, :2])
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ax.scatter(*episodes.reshape(-1, 2)[::sub].T, s=s * 10)
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ax.set_title("Marginal")
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ax.grid()
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ax.set_xlabel(r"$z_0$ (shoulder)")
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ax.set_ylabel(r"$z_1$ (wrist)")
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for i, delta in enumerate(DELTAS):
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# top row: 2D transition differences
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ax = fig.add_subplot(gs[0, 2 + i])
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transitions = episodes[:, delta:] - episodes[:, :-delta]
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ax.scatter(*transitions.reshape(-1, 2)[::sub].T, s=s)
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r2_d0 = r2_dict[delta]["r2_dim0"]
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r2_d1 = r2_dict[delta]["r2_dim1"]
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ax.set_title(r"$\Delta=$" + f"{delta}" + "\n"
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r"$R^2=(%.2f, %.2f)$" % (r2_d0, r2_d1))
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ax.grid()
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# bottom row: per-dim (z_t, z_{t+delta}) with rho
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ax = fig.add_subplot(gs[1, 2 + i])
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a = episodes[:, delta:, 0].flatten()[::sub]
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b = episodes[:, :-delta, 0].flatten()[::sub]
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rho0 = pearsonr(a, b)[0]
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ax.scatter(a, b, s=s)
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c = episodes[:, delta:, 1].flatten()[::sub]
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d = episodes[:, :-delta, 1].flatten()[::sub]
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rho1 = pearsonr(c, d)[0]
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ax.scatter(c, d, s=s)
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ax.set_title(r"$\rho=(%.2f, %.2f)$" % (rho0, rho1))
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ax.grid()
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if i == 0:
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ax.legend([r"$z_0$ (shoulder)", r"$z_1$ (wrist)"], loc="upper left")
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plt.tight_layout()
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plt.savefig(save_path, dpi=500, bbox_inches="tight")
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plt.close()
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print(f"Saved {save_path}")
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# ═════════════════════════════════════════════════════════════════════════════
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# Figure 2: rho vs SIGReg scatter (3 panels)
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# ═════════════════════════════════════════════════════════════════════════════
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def make_rho_vs_sigreg(trans, r2_dict, save_path, best_ou_rho_val=None,
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gaussian_floor=1.2):
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"""
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Three panels (z_0, z_1, joint) showing rho vs SIGReg(zscored),
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colored by R². Vertical line marks the best OU rho for reference.
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"""
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fig, axes = plt.subplots(1, 3, figsize=(16, 4.5))
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names = [r"$z_0$ (shoulder)", r"$z_1$ (wrist)", "joint (avg across dims)"]
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all_r2 = []
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for d in DELTAS:
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all_r2.append(r2_dict[d]["r2_dim0"])
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all_r2.append(r2_dict[d]["r2_dim1"])
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all_r2.append(r2_dict[d]["r2"])
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vmin, vmax = min(all_r2), max(all_r2)
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def _one(ax, rhos, sigs, errs, r2s, xlabel, ylabel, title):
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if best_ou_rho_val is not None:
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ax.axvline(best_ou_rho_val, color="crimson", lw=1.4, ls="--",
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alpha=0.8, label=fr"best OU $\rho={best_ou_rho_val:.2f}$",
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zorder=1)
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sc = ax.scatter(rhos, sigs, c=r2s, cmap="viridis", s=140,
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vmin=vmin, vmax=vmax,
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edgecolors="black", linewidths=0.8, zorder=3)
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ax.errorbar(rhos, sigs, yerr=errs, fmt="none", ecolor="gray",
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alpha=0.5, zorder=2)
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for d, r, s in zip(DELTAS, rhos, sigs):
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ax.annotate(f"Δ={d}", (r, s), xytext=(6, 6),
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textcoords="offset points", fontsize=9)
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ax.axhline(gaussian_floor, color="red", lw=1, ls=":", alpha=0.6,
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label="Gaussian floor")
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ax.set_yscale("log")
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ax.set_xlabel(xlabel)
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ax.set_ylabel(ylabel)
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ax.set_title(title)
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ax.grid(alpha=0.3, which="both")
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ax.legend(loc="lower left", fontsize=8)
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return sc
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# per-dim panels
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for k in range(2):
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rhos = np.array([trans[d]["rho"][k] for d in DELTAS])
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sigs = np.array([trans[d]["sig"][f"marg_{k}_zs"][0] for d in DELTAS])
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errs = np.array([trans[d]["sig"][f"marg_{k}_zs"][1] for d in DELTAS])
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r2s = np.array([r2_dict[d][f"r2_dim{k}"] for d in DELTAS])
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sc = _one(axes[k], rhos, sigs, errs, r2s,
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xlabel=r"auto-correlation $\rho$",
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ylabel="SIGReg (zscored, marginal)",
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title=names[k])
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plt.colorbar(sc, ax=axes[k], label=r"$R^2$")
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# joint panel
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rhos_avg = np.array([np.mean(trans[d]["rho"]) for d in DELTAS])
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sigs_j = np.array([trans[d]["sig"]["joint_zs"][0] for d in DELTAS])
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errs_j = np.array([trans[d]["sig"]["joint_zs"][1] for d in DELTAS])
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r2s_avg = np.array([r2_dict[d]["r2"] for d in DELTAS])
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sc = _one(axes[2], rhos_avg, sigs_j, errs_j, r2s_avg,
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xlabel=r"avg auto-correlation $\bar{\rho}$",
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ylabel="SIGReg (zscored, 2D joint)",
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title=names[2])
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plt.colorbar(sc, ax=axes[2], label=r"$R^2$ (avg)")
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plt.tight_layout()
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plt.savefig(save_path, dpi=300, bbox_inches="tight")
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plt.close()
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print(f"Saved {save_path}")
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# ═════════════════════════════════════════════════════════════════════════════
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# Measurement pipeline
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# ═════════════════════════════════════════════════════════════════════════════
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def compute_all_transitions(episodes, n_draws=20):
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"""
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For each delta, compute SIGReg stats and per-dim rho on the
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transition-difference distribution z(t+delta) - z(t).
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"""
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trans = {}
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for d in DELTAS:
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diffs = (episodes[:, d:] - episodes[:, :-d]).reshape(-1, 2)
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rho = np.array([
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pearsonr(episodes[:, d:, k].flatten(),
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episodes[:, :-d, k].flatten())[0]
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for k in range(2)
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])
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trans[d] = {"rho": rho, "sig": measure(diffs, n_draws=n_draws)}
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return trans
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# ═════════════════════════════════════════════════════════════════════════════
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# Main
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# ═════════════════════════════════════════════════════════════════════════════
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def main():
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parser = argparse.ArgumentParser()
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parser.add_argument("--results_dir", type=str, default="results/reacher",
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help="Directory with result.json files")
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parser.add_argument("--data_path", type=str,
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default="data/reacher.h5",
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help="HDF5 file with 'qpos' and 'ep_len' datasets "
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"(reshaped to (n_episodes, T, 2))")
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parser.add_argument("--out_dir", type=str, default="figures/reacher")
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parser.add_argument("--n_draws", type=int, default=20,
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help="Random subsamples for SIGReg stats")
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parser.add_argument("--agg", type=str, default="median",
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choices=["median", "mean"],
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help="How to aggregate R² across seeds")
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args = parser.parse_args()
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out_dir = Path(args.out_dir)
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out_dir.mkdir(parents=True, exist_ok=True)
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# load episodes (HDF5 with qpos + ep_len, matching notebook convention)
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import h5py
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with h5py.File(args.data_path, "r") as f:
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qpos = np.array(f["qpos"])
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ep_len = np.array(f["ep_len"])
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T = int(ep_len[0])
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episodes = qpos.reshape(-1, T, 2)
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print(f"Loaded {len(episodes)} episodes of length {T} from {args.data_path}")
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r2_dict = get_best_r2_per_delta(args.results_dir, agg=args.agg)
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print(f"Loaded R² for deltas: {sorted(r2_dict.keys())}")
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for d in DELTAS:
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v = r2_dict[d]
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print(f" Δ={d:2d} λ={v['lamb']:.0e} n={v['n_seeds']} "
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f"R²={v['r2']:.3f} dim0={v['r2_dim0']:.3f} "
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f"dim1={v['r2_dim1']:.3f}")
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ou_rho = best_ou_rho(args.results_dir)
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if ou_rho is not None:
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print(f"Best OU rho: {ou_rho}")
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# measure transitions
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print("Computing SIGReg on transitions...")
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trans = compute_all_transitions(episodes, n_draws=args.n_draws)
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# figures
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make_scatter_grid(episodes, r2_dict,
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save_path=out_dir / "distribution.png")
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make_rho_vs_sigreg(trans, r2_dict,
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save_path=out_dir / "rho_vs_sigreg.png",
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best_ou_rho_val=ou_rho)
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if __name__ == "__main__":
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main()
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Reference in New Issue
Block a user