1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
|
"""
Generate the snapshot-evolution figure(s) for the paper from existing JSONs.
Produces:
- figure_snapshot_resmlp.pdf : ResMLP with vs without out_ln, ||h_L|| and ||g||
over epochs for BP and DFA
- figure_snapshot_vit.pdf : ViT-Mini ||h_L|| and ||g|| over epochs for BP/DFA
Usage:
python experiments/figure_snapshot_evolution.py
"""
import os, sys, json
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
def load_log(path, log_key):
if not os.path.exists(path):
return None
with open(path) as f:
return json.load(f).get(log_key)
def trajectory(log, metric):
"""Extract a per-epoch trajectory for the given metric."""
eps = [r['epoch'] for r in log]
if metric == 'h_L':
# last hidden norm — handles both ResMLP (hidden_norms) and ViT (hidden_norms_cls)
values = []
for r in log:
if 'hidden_norms_cls' in r:
values.append(r['hidden_norms_cls'][-1])
else:
values.append(r['hidden_norms'][-1])
elif metric == 'g_2':
values = []
for r in log:
key = 'bp_grad_per_sample_l2_med' if 'bp_grad_per_sample_l2_med' in r else 'bp_grad_norms_per_sample_med'
values.append(r[key][2])
elif metric == 'acc':
values = [r['acc_eval'] for r in log]
elif metric == 'gamma_dfa':
values = [r.get('gamma_dfa', float('nan')) for r in log]
else:
return None, None
return np.array(eps), np.array(values)
def make_resmlp_figure(out_path):
fig, axes = plt.subplots(2, 2, figsize=(10, 7), sharex=True)
runs = {
'with_out_ln_s42': 'results/snapshot_evolution_v2/snapshot_evolution_s42.json',
'no_out_ln_s42': 'results/snapshot_no_outln_v1/snapshot_noLN_s42.json',
'no_out_ln_s123': 'results/snapshot_no_outln_v1/snapshot_noLN_s123.json',
'no_out_ln_s456': 'results/snapshot_no_outln_v1/snapshot_noLN_s456.json',
}
runs_loaded = {k: (load_log(v, 'bp_log'), load_log(v, 'dfa_log')) for k, v in runs.items()}
# Top row: with out_ln
bp, dfa = runs_loaded['with_out_ln_s42']
ax = axes[0, 0]
e, v = trajectory(bp, 'h_L'); ax.plot(e, v, 'b-', label='BP', lw=2)
e, v = trajectory(dfa, 'h_L'); ax.plot(e, v, 'r-', label='DFA', lw=2)
ax.set_yscale('log'); ax.set_ylabel(r'$\|h_L\|_2$ (median)')
ax.set_title('ResMLP with terminal LayerNorm (s42)')
ax.legend(); ax.grid(True, alpha=0.3)
ax = axes[0, 1]
e, v = trajectory(bp, 'g_2'); ax.plot(e, v, 'b-', label='BP', lw=2)
e, v = trajectory(dfa, 'g_2'); ax.plot(e, v, 'r-', label='DFA', lw=2)
ax.set_yscale('log'); ax.set_ylabel(r'$\|\nabla_{h_2} L\|_2$ (BP grad, median)')
ax.set_title('ResMLP with terminal LayerNorm (s42)')
ax.legend(); ax.grid(True, alpha=0.3)
# Bottom row: no out_ln, mean ± std across 3 seeds
no_ln_bp_h = []; no_ln_bp_g = []; no_ln_dfa_h = []; no_ln_dfa_g = []
for k in ['no_out_ln_s42', 'no_out_ln_s123', 'no_out_ln_s456']:
bp, dfa = runs_loaded[k]
if bp is None or dfa is None: continue
e_bp, h_bp = trajectory(bp, 'h_L'); _, g_bp = trajectory(bp, 'g_2')
e_dfa, h_dfa = trajectory(dfa, 'h_L'); _, g_dfa = trajectory(dfa, 'g_2')
no_ln_bp_h.append(h_bp); no_ln_bp_g.append(g_bp)
no_ln_dfa_h.append(h_dfa); no_ln_dfa_g.append(g_dfa)
if no_ln_bp_h:
eps = e_bp
bp_h_arr = np.array(no_ln_bp_h)
bp_g_arr = np.array(no_ln_bp_g)
dfa_h_arr = np.array(no_ln_dfa_h)
dfa_g_arr = np.array(no_ln_dfa_g)
ax = axes[1, 0]
ax.plot(eps, np.mean(bp_h_arr, 0), 'b-', label='BP', lw=2)
ax.fill_between(eps, np.mean(bp_h_arr, 0)-np.std(bp_h_arr, 0), np.mean(bp_h_arr, 0)+np.std(bp_h_arr, 0), color='b', alpha=0.2)
ax.plot(eps, np.mean(dfa_h_arr, 0), 'r-', label='DFA', lw=2)
ax.fill_between(eps, np.mean(dfa_h_arr, 0)-np.std(dfa_h_arr, 0), np.mean(dfa_h_arr, 0)+np.std(dfa_h_arr, 0), color='r', alpha=0.2)
ax.set_yscale('log'); ax.set_xlabel('epoch'); ax.set_ylabel(r'$\|h_L\|_2$ (median)')
ax.set_title(f'ResMLP WITHOUT terminal LayerNorm (mean ± std, n={len(no_ln_bp_h)})')
ax.legend(); ax.grid(True, alpha=0.3)
ax = axes[1, 1]
ax.plot(eps, np.mean(bp_g_arr, 0), 'b-', label='BP', lw=2)
ax.fill_between(eps, np.mean(bp_g_arr, 0)-np.std(bp_g_arr, 0), np.mean(bp_g_arr, 0)+np.std(bp_g_arr, 0), color='b', alpha=0.2)
ax.plot(eps, np.mean(dfa_g_arr, 0), 'r-', label='DFA', lw=2)
ax.fill_between(eps, np.mean(dfa_g_arr, 0)-np.std(dfa_g_arr, 0), np.mean(dfa_g_arr, 0)+np.std(dfa_g_arr, 0), color='r', alpha=0.2)
ax.set_yscale('log'); ax.set_xlabel('epoch'); ax.set_ylabel(r'$\|\nabla_{h_2} L\|_2$ (BP grad, median)')
ax.set_title(f'ResMLP WITHOUT terminal LayerNorm (mean ± std, n={len(no_ln_bp_h)})')
ax.legend(); ax.grid(True, alpha=0.3)
plt.suptitle('Snapshot evolution: residual stream + BP grad over training\n(top: with terminal LN — DFA explodes; bottom: no terminal LN — DFA still grows but BP grad does NOT collapse)', y=1.02)
plt.tight_layout()
plt.savefig(out_path, bbox_inches='tight', dpi=150)
print(f"Saved {out_path}")
plt.close()
def make_vit_figure(out_path):
fig, axes = plt.subplots(1, 2, figsize=(11, 4))
runs = sorted([
f for f in os.listdir('results/snapshot_vit_v1')
if f.startswith('snapshot_vit_s') and f.endswith('.json')
])
if not runs:
print("No ViT snapshot JSONs found")
return
bp_h_list = []; bp_g_list = []; dfa_h_list = []; dfa_g_list = []
eps = None
for r in runs:
path = f'results/snapshot_vit_v1/{r}'
bp = load_log(path, 'bp_log')
dfa = load_log(path, 'dfa_log')
if bp is None or dfa is None: continue
e_bp, h_bp = trajectory(bp, 'h_L'); _, g_bp = trajectory(bp, 'g_2')
e_dfa, h_dfa = trajectory(dfa, 'h_L'); _, g_dfa = trajectory(dfa, 'g_2')
bp_h_list.append(h_bp); bp_g_list.append(g_bp)
dfa_h_list.append(h_dfa); dfa_g_list.append(g_dfa)
eps = e_bp
bp_h_arr = np.array(bp_h_list); bp_g_arr = np.array(bp_g_list)
dfa_h_arr = np.array(dfa_h_list); dfa_g_arr = np.array(dfa_g_list)
ax = axes[0]
ax.plot(eps, np.mean(bp_h_arr, 0), 'b-', label='BP', lw=2)
if len(bp_h_list) > 1:
ax.fill_between(eps, np.mean(bp_h_arr, 0)-np.std(bp_h_arr, 0), np.mean(bp_h_arr, 0)+np.std(bp_h_arr, 0), color='b', alpha=0.2)
ax.plot(eps, np.mean(dfa_h_arr, 0), 'r-', label='DFA', lw=2)
if len(dfa_h_list) > 1:
ax.fill_between(eps, np.mean(dfa_h_arr, 0)-np.std(dfa_h_arr, 0), np.mean(dfa_h_arr, 0)+np.std(dfa_h_arr, 0), color='r', alpha=0.2)
ax.set_yscale('log'); ax.set_xlabel('epoch'); ax.set_ylabel(r'$\|h_L^{cls}\|_2$ (median)')
ax.set_title(f'ViT-Mini, terminal LayerNorm (n={len(bp_h_list)})')
ax.legend(); ax.grid(True, alpha=0.3)
ax = axes[1]
ax.plot(eps, np.mean(bp_g_arr, 0), 'b-', label='BP', lw=2)
if len(bp_g_list) > 1:
ax.fill_between(eps, np.mean(bp_g_arr, 0)-np.std(bp_g_arr, 0), np.mean(bp_g_arr, 0)+np.std(bp_g_arr, 0), color='b', alpha=0.2)
ax.plot(eps, np.mean(dfa_g_arr, 0), 'r-', label='DFA', lw=2)
if len(dfa_g_list) > 1:
ax.fill_between(eps, np.mean(dfa_g_arr, 0)-np.std(dfa_g_arr, 0), np.mean(dfa_g_arr, 0)+np.std(dfa_g_arr, 0), color='r', alpha=0.2)
ax.set_yscale('log'); ax.set_xlabel('epoch'); ax.set_ylabel(r'$\|\nabla_{h_2} L\|_2$ (BP grad, median)')
ax.set_title(f'ViT-Mini, terminal LayerNorm (n={len(bp_g_list)})')
ax.legend(); ax.grid(True, alpha=0.3)
plt.tight_layout()
plt.savefig(out_path, bbox_inches='tight', dpi=150)
print(f"Saved {out_path}")
plt.close()
if __name__ == '__main__':
os.makedirs('results/figures', exist_ok=True)
make_resmlp_figure('results/figures/figure_snapshot_resmlp.pdf')
make_vit_figure('results/figures/figure_snapshot_vit.pdf')
|
