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Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/algorithmic_structure/out.txt ADDED
@@ -0,0 +1,409 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ ======================================================================
2
+ ALGORITHMIC STRUCTURE ANALYSIS (H25–H27)
3
+ ======================================================================
4
+
5
+ Loading results...
6
+
7
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=div]_[int=False].pt: 10000 results for $->/
8
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=minus]_[int=False].pt: 10000 results for $->-
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=mod]_[int=False].pt: 10000 results for $->%
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=mul]_[int=False].pt: 10000 results for $->*
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=plus]_[int=False].pt: 10000 results for $->+
12
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=concat]_[int=False].pt: 10000 results for /->$
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=minus]_[int=False].pt: 10000 results for /->-
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=mod]_[int=False].pt: 10000 results for /->%
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=mul]_[int=False].pt: 10000 results for /->*
16
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=plus]_[int=False].pt: 10000 results for /->+
17
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=concat]_[int=False].pt: 10000 results for -->$
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=mod]_[int=False].pt: 10000 results for -->%
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=minus]_[int=False].pt: 10000 results for %->-
25
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26
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=plus]_[int=False].pt: 10000 results for %->+
27
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=concat]_[int=False].pt: 10000 results for *->$
28
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=div]_[int=False].pt: 10000 results for *->/
29
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=minus]_[int=False].pt: 10000 results for *->-
30
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=mod]_[int=False].pt: 10000 results for *->%
31
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=plus]_[int=False].pt: 10000 results for *->+
32
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=concat]_[int=False].pt: 10000 results for +->$
33
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=div]_[int=False].pt: 10000 results for +->/
34
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=minus]_[int=False].pt: 10000 results for +->-
35
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=mod]_[int=False].pt: 10000 results for +->%
36
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=mul]_[int=False].pt: 10000 results for +->*
37
+ $->/: 10000 prompts
38
+ $->-: 10000 prompts
39
+ $->%: 10000 prompts
40
+ $->*: 10000 prompts
41
+ $->+: 10000 prompts
42
+ /->$: 10000 prompts
43
+ /->-: 10000 prompts
44
+ /->%: 10000 prompts
45
+ /->*: 10000 prompts
46
+ /->+: 10000 prompts
47
+ -->$: 10000 prompts
48
+ -->/: 10000 prompts
49
+ -->%: 10000 prompts
50
+ -->*: 10000 prompts
51
+ -->+: 10000 prompts
52
+ %->$: 10000 prompts
53
+ %->/: 10000 prompts
54
+ %->-: 10000 prompts
55
+ %->*: 10000 prompts
56
+ %->+: 10000 prompts
57
+ *->$: 10000 prompts
58
+ *->/: 10000 prompts
59
+ *->-: 10000 prompts
60
+ *->%: 10000 prompts
61
+ *->+: 10000 prompts
62
+ +->$: 10000 prompts
63
+ +->/: 10000 prompts
64
+ +->-: 10000 prompts
65
+ +->%: 10000 prompts
66
+ +->*: 10000 prompts
67
+ Layers: [0, 1, 2]
68
+
69
+ Running H25 (multiplication vs addition)...
70
+
71
+ Running H26 (generalization gap)...
72
+
73
+
74
+ Running H27 (subtraction as a + (−b))...
75
+ H25: Addition → Multiplication probe transfer
76
+ ┏━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━┓
77
+ ┃ Layer ┃ R²(add) ┃ R²(mul) ┃ add→mul ┃ mul→add ┃ cos-sim(matched) ┃
78
+ ┡━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━┩
79
+ │ L0 │ 0.747 │ 0.703 │ -1.308 │ -7078803.500 │ 0.505 │
80
+ ├───────┼─────────┼─────────┼─────────┼──────────────┼──────────────────┤
81
+ │ L1 │ 0.937 │ 0.844 │ -1.286 │ -564492.250 │ 0.324 │
82
+ ├───────┼─────────┼─────────┼─────────┼──────────────┼──────────────────┤
83
+ │ L2 │ 0.864 │ 0.707 │ -1.296 │ -264654.000 │ 0.075 │
84
+ └───────┴─────────┴─────────┴─────────┴──────────────┴──────────────────┘
85
+ H26: Generalization gap — $->/
86
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
87
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
88
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
89
+ │ L0 │ 0.996 │ 0.996 │ 0.000 │ generalize │
90
+ ├───────┼──────────┼────────────┼────────┼────────────┤
91
+ │ L1 │ 0.997 │ 0.997 │ -0.000 │ generalize │
92
+ ├───────┼──────────┼────────────┼────────┼────────────┤
93
+ │ L2 │ 0.988 │ 0.989 │ -0.000 │ generalize │
94
+ └───────┴──────────┴���───────────┴────────┴────────────┘
95
+ H26: Generalization gap — $->-
96
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
97
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
98
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
99
+ │ L0 │ 0.996 │ 0.996 │ 0.000 │ generalize │
100
+ ├───────┼──────────┼────────────┼────────┼────────────┤
101
+ │ L1 │ 0.997 │ 0.997 │ 0.000 │ generalize │
102
+ ├───────┼──────────┼────────────┼────────┼────────────┤
103
+ │ L2 │ 0.988 │ 0.988 │ -0.000 │ generalize │
104
+ └───────┴──────────┴────────────┴────────┴────────────┘
105
+ H26: Generalization gap — $->%
106
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
107
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
108
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
109
+ │ L0 │ 0.996 │ 0.996 │ 0.000 │ generalize │
110
+ ├───────┼──────────┼────────────┼────────┼────────────┤
111
+ │ L1 │ 0.997 │ 0.997 │ -0.000 │ generalize │
112
+ ├───────┼──────────┼────────────┼────────┼────────────┤
113
+ │ L2 │ 0.988 │ 0.989 │ -0.000 │ generalize │
114
+ └───────┴──────────┴────────────┴────────┴────────────┘
115
+ H26: Generalization gap — $->*
116
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
117
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
118
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
119
+ │ L0 │ 0.996 │ 0.996 │ 0.000 │ generalize │
120
+ ├───────┼──────────┼────────────┼────────┼────────────┤
121
+ │ L1 │ 0.997 │ 0.997 │ 0.000 │ generalize │
122
+ ├───────┼──────────┼────────────┼────────┼────────────┤
123
+ │ L2 │ 0.988 │ 0.988 │ -0.000 │ generalize │
124
+ └───────┴──────────┴────────────┴────────┴────────────┘
125
+ H26: Generalization gap — $->+
126
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
127
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
128
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
129
+ │ L0 │ 0.996 │ 0.996 │ 0.000 │ generalize │
130
+ ├───────┼──────────┼────────────┼────────┼────────────┤
131
+ │ L1 │ 0.997 │ 0.997 │ 0.000 │ generalize │
132
+ ├───────┼──────────┼────────────┼────────┼────────────┤
133
+ │ L2 │ 0.988 │ 0.988 │ -0.000 │ generalize │
134
+ └───────┴──────────┴────────────┴────────┴────────────┘
135
+ H26: Generalization gap — /->$
136
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
137
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
138
+ ┡━━━━━━━╇��━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
139
+ │ L0 │ 0.286 │ 0.328 │ -0.041 │ generalize │
140
+ ├───────┼──────────┼────────────┼────────┼────────────┤
141
+ │ L1 │ 0.595 │ 0.650 │ -0.055 │ generalize │
142
+ ├───────┼──────────┼────────────┼────────┼────────────┤
143
+ │ L2 │ 0.449 │ 0.477 │ -0.028 │ generalize │
144
+ └───────┴──────────┴────────────┴────────┴────────────┘
145
+ H26: Generalization gap — /->-
146
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
147
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
148
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
149
+ │ L0 │ 0.286 │ 0.328 │ -0.041 │ generalize │
150
+ ├───────┼──────────┼────────────┼────────┼────────────┤
151
+ │ L1 │ 0.595 │ 0.650 │ -0.055 │ generalize │
152
+ ├───────┼──────────┼────────────┼────────┼────────────┤
153
+ │ L2 │ 0.449 │ 0.477 │ -0.028 │ generalize │
154
+ └───────┴──────────┴────────────┴────────┴────────────┘
155
+ H26: Generalization gap — /->%
156
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
157
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
158
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
159
+ │ L0 │ 0.286 │ 0.328 │ -0.041 │ generalize │
160
+ ├───────┼──────────┼────────────┼────────┼────────────┤
161
+ │ L1 │ 0.595 │ 0.650 │ -0.055 │ generalize │
162
+ ├───────┼──────────┼────────────┼────────┼────────────┤
163
+ │ L2 │ 0.449 │ 0.477 │ -0.028 │ generalize │
164
+ └───────┴──────────┴────────────┴────────┴────────────┘
165
+ H26: Generalization gap — /->*
166
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
167
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
168
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
169
+ │ L0 │ 0.286 │ 0.328 │ -0.041 │ generalize │
170
+ ├───────┼──────────┼────────────┼────────┼────────────┤
171
+ │ L1 │ 0.595 │ 0.650 │ -0.055 │ generalize │
172
+ ├───────┼──────────┼────────────┼────────┼────────────┤
173
+ │ L2 │ 0.449 │ 0.477 │ -0.028 │ generalize │
174
+ └───────┴──────────┴────────────┴────────┴────────────┘
175
+ H26: Generalization gap — /->+
176
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
177
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
178
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
179
+ │ L0 │ 0.286 │ 0.328 │ -0.041 │ generalize │
180
+ ├───────┼──────────┼────────────┼────────┼────────────┤
181
+ │ L1 │ 0.595 │ 0.650 │ -0.055 │ generalize │
182
+ ├───────┼──────────┼────────────┼────────┼────────────┤
183
+ │ L2 │ 0.449 │ 0.477 │ -0.028 │ generalize │
184
+ └───────┴──────────┴────────────┴────────┴────────────┘
185
+ H26: Generalization gap — -->$
186
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
187
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
188
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
189
+ │ L0 │ 0.747 │ 0.745 │ 0.001 │ generalize │
190
+ ├───────┼──────────┼────────────┼───────┼────────────┤
191
+ │ L1 │ 0.976 │ 0.976 │ 0.000 │ generalize │
192
+ ├───────┼──────────┼────────────┼───────┼────────────┤
193
+ │ L2 │ 0.955 │ 0.955 │ 0.000 │ generalize │
194
+ └───────┴──────────┴────────────┴───────┴────────────┘
195
+ H26: Generalization gap — -->/
196
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
197
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
198
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
199
+ │ L0 │ 0.736 │ 0.738 │ -0.001 │ generalize │
200
+ ├───────┼──────────┼────────────┼────────┼────────────┤
201
+ │ L1 │ 0.975 │ 0.975 │ -0.000 │ generalize │
202
+ ├───────┼──────────┼────────────┼────────┼────────────┤
203
+ │ L2 │ 0.954 │ 0.954 │ -0.000 │ generalize │
204
+ └───────┴──────────┴────────────┴────────┴────────────┘
205
+ H26: Generalization gap — -->%
206
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
207
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
208
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
209
+ │ L0 │ 0.736 │ 0.738 │ -0.001 │ generalize │
210
+ ├───────┼──────────┼────────────┼────────┼────────────┤
211
+ │ L1 │ 0.975 │ 0.975 │ -0.000 │ generalize │
212
+ ├───────┼──────────┼────────────┼────────┼────────────┤
213
+ │ L2 │ 0.954 │ 0.954 │ -0.000 │ generalize │
214
+ └───────┴──────────┴────────────┴────────┴────────────┘
215
+ H26: Generalization gap — -->*
216
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
217
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
218
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
219
+ │ L0 │ 0.747 │ 0.745 │ 0.001 │ generalize │
220
+ ├───────┼──────────┼────────────┼───────┼────────────┤
221
+ │ L1 │ 0.976 │ 0.976 │ 0.000 │ generalize │
222
+ ├───────┼──────────┼────────────┼───────┼────────────┤
223
+ │ L2 │ 0.955 │ 0.955 │ 0.000 │ generalize │
224
+ └───────┴──────────┴────────────┴───────┴────────────┘
225
+ H26: Generalization gap — -->+
226
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
227
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
228
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
229
+ │ L0 │ 0.747 │ 0.745 │ 0.001 │ generalize │
230
+ ├───────┼──────────┼────────────┼───────┼────────────┤
231
+ │ L1 │ 0.976 │ 0.976 │ 0.000 │ generalize │
232
+ ├───────┼──────────┼────────────┼───────┼────────────┤
233
+ │ L2 │ 0.955 │ 0.955 │ 0.000 │ generalize │
234
+ └───────┴──────────┴────────────┴───────┴────────────┘
235
+ H26: Generalization gap — %->$
236
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
237
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
238
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
239
+ │ L0 │ 0.335 │ 0.338 │ -0.003 │ generalize │
240
+ ├───────┼──────────┼────────────┼────────┼────────────┤
241
+ │ L1 │ 0.768 │ 0.771 │ -0.002 │ generalize │
242
+ ├───────┼──────────┼────────────┼────────┼────────────┤
243
+ │ L2 │ 0.863 │ 0.863 │ 0.000 │ generalize │
244
+ └───────┴──────────┴────────────┴────────┴────────────┘
245
+ H26: Generalization gap — %->/
246
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
247
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
248
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
249
+ │ L0 │ 0.335 │ 0.338 │ -0.003 │ generalize │
250
+ ├───────┼──────────┼────────────┼────────┼────────────┤
251
+ │ L1 │ 0.768 │ 0.771 │ -0.002 │ generalize │
252
+ ├───────┼──────────┼────────────┼────────┼────────────┤
253
+ │ L2 │ 0.863 │ 0.863 │ 0.000 │ generalize │
254
+ └───────┴──────────┴────────────┴────────┴────────────┘
255
+ H26: Generalization gap — %->-
256
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
257
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
258
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
259
+ │ L0 │ 0.335 │ 0.338 │ -0.003 │ generalize │
260
+ ├───────┼──────────┼────────────┼────────┼────────────┤
261
+ │ L1 │ 0.768 │ 0.771 │ -0.002 │ generalize │
262
+ ├───────┼──────────┼────────────┼────────┼────────────┤
263
+ │ L2 │ 0.863 │ 0.863 │ 0.000 │ generalize │
264
+ └───────┴──────────┴────────────┴────────┴────────────┘
265
+ H26: Generalization gap — %->*
266
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
267
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
268
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
269
+ │ L0 │ 0.335 │ 0.338 │ -0.003 │ generalize │
270
+ ├───────┼──────────┼────────────┼────────┼────────────┤
271
+ │ L1 │ 0.768 │ 0.771 │ -0.002 │ generalize │
272
+ ├───────┼──────────┼────────────┼────────┼────────────┤
273
+ │ L2 │ 0.863 │ 0.863 │ 0.000 │ generalize │
274
+ └───────┴──────────┴────────────┴────────┴────────────┘
275
+ H26: Generalization gap — %->+
276
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
277
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
278
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
279
+ │ L0 │ 0.335 │ 0.338 │ -0.003 │ generalize │
280
+ ├───────┼──────────┼────────────┼────────┼────────────┤
281
+ │ L1 │ 0.768 │ 0.771 │ -0.002 │ generalize │
282
+ ├───────┼──────────┼────────────┼────────┼────────────┤
283
+ │ L2 │ 0.863 │ 0.863 │ 0.000 │ generalize │
284
+ └───────┴──────────┴────────────┴────────┴────────────┘
285
+ H26: Generalization gap — *->$
286
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
287
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
288
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
289
+ │ L0 │ 0.701 │ 0.682 │ 0.018 │ generalize │
290
+ ├───────┼──────────┼────────────┼───────┼────────────┤
291
+ │ L1 │ 0.834 │ 0.833 │ 0.001 │ generalize │
292
+ ├───────┼──────────┼────────────┼───────┼────────────┤
293
+ │ L2 │ 0.697 │ 0.697 │ 0.000 │ generalize │
294
+ └───────┴──────────┴────────────┴───────┴────────────┘
295
+ H26: Generalization gap — *->/
296
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
297
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
298
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
299
+ │ L0 │ 0.714 │ 0.713 │ 0.001 │ generalize │
300
+ ├───────┼──────────┼────────────┼────────┼────────────┤
301
+ │ L1 │ 0.844 │ 0.843 │ 0.001 │ generalize │
302
+ ├───────┼──────────┼────────────┼────────┼────────────┤
303
+ │ L2 │ 0.706 │ 0.706 │ -0.000 │ generalize │
304
+ └───────┴──────────┴────────────┴────────┴────────────┘
305
+ H26: Generalization gap — *->-
306
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
307
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
308
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
309
+ │ L0 │ 0.701 │ 0.682 │ 0.018 │ generalize │
310
+ ├───────┼──────────┼────────────┼───────┼────────────┤
311
+ │ L1 │ 0.834 │ 0.833 │ 0.001 │ generalize │
312
+ ├───────┼──────────┼────────────┼───────┼────────────┤
313
+ │ L2 │ 0.697 │ 0.697 │ 0.000 │ generalize │
314
+ └───────┴──────────┴────────────┴───────┴────────────┘
315
+ H26: Generalization gap — *->%
316
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
317
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
318
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
319
+ │ L0 │ 0.714 │ 0.713 │ 0.001 │ generalize │
320
+ ├───────┼──────────┼────────────┼────────┼────────────┤
321
+ │ L1 │ 0.844 │ 0.843 │ 0.001 │ generalize │
322
+ ├───────┼──────────┼────────────┼────────┼────────────┤
323
+ │ L2 │ 0.706 │ 0.706 │ -0.000 │ generalize │
324
+ └───────┴──────────┴────────────┴────────┴────────────┘
325
+ H26: Generalization gap — *->+
326
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
327
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
328
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
329
+ │ L0 │ 0.701 │ 0.682 │ 0.018 │ generalize │
330
+ ├───────┼──────────┼────────────┼───────┼────────────┤
331
+ │ L1 │ 0.834 │ 0.833 │ 0.001 │ generalize │
332
+ ├───────┼──────────┼────────────┼───────┼────────────┤
333
+ │ L2 │ 0.697 │ 0.697 │ 0.000 │ generalize │
334
+ └───────┴──────────┴────────────┴───────┴────────────┘
335
+ H26: Generalization gap — +->$
336
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
337
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
338
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
339
+ │ L0 │ 0.749 │ 0.750 │ -0.001 │ generalize │
340
+ ├───────┼──────────┼────────────┼────────┼────────────┤
341
+ │ L1 │ 0.932 │ 0.931 │ 0.000 │ generalize │
342
+ ├───────┼──────────┼────────────┼────────┼────────────┤
343
+ │ L2 │ 0.857 │ 0.857 │ 0.000 │ generalize │
344
+ └───────┴──────────┴────────────┴────────┴────────────┘
345
+ H26: Generalization gap — +->/
346
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
347
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
348
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
349
+ │ L0 │ 0.759 │ 0.758 │ 0.002 │ generalize │
350
+ ├───────┼──────────┼────────────┼───────┼────────────┤
351
+ │ L1 │ 0.936 │ 0.935 │ 0.001 │ generalize │
352
+ ├───────┼──────────┼────────────┼───────┼────────────┤
353
+ │ L2 │ 0.863 │ 0.862 │ 0.000 │ generalize │
354
+ └───────┴──────────┴────────────┴───────┴────────────┘
355
+ H26: Generalization gap — +->-
356
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
357
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
358
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
359
+ │ L0 │ 0.749 │ 0.750 │ -0.001 │ generalize │
360
+ ├───────┼──────────┼────────────┼────────┼────────────┤
361
+ │ L1 │ 0.932 │ 0.931 │ 0.000 │ generalize │
362
+ ├───────┼──────────┼────────────┼────────┼────────────┤
363
+ │ L2 │ 0.857 │ 0.857 │ 0.000 │ generalize │
364
+ └───────┴──────────┴────────────┴────────┴────────────┘
365
+ H26: Generalization gap — +->%
366
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━┳━━━━━━━━━━━━┓
367
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
368
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━╇━━━━━━━━━━━━┩
369
+ │ L0 │ 0.759 │ 0.758 │ 0.002 │ generalize │
370
+ ├───────┼──────────┼────────────┼───────┼────────────┤
371
+ │ L1 │ 0.936 │ 0.935 │ 0.001 │ generalize │
372
+ ├───────┼──────────┼────────────┼───────┼────────────┤
373
+ │ L2 │ 0.863 │ 0.862 │ 0.000 │ generalize │
374
+ └───────┴──────────┴────────────┴───────┴────────────┘
375
+ H26: Generalization gap — +->*
376
+ ┏━━━━━━━┳━━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━┳━━━━━━━━━━━━┓
377
+ ┃ Layer ┃ R²(seen) ┃ R²(unseen) ┃ Gap ┃ Verdict ┃
378
+ ┡━━━━━━━╇━━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━╇━━━━━━━━━━━━┩
379
+ │ L0 │ 0.749 │ 0.750 │ -0.001 │ generalize │
380
+ ├───────┼──────────┼────────────┼────────┼────────────┤
381
+ │ L1 │ 0.932 │ 0.931 │ 0.000 │ generalize │
382
+ ├───────┼──────────┼────────────┼────────┼────────────┤
383
+ │ L2 │ 0.857 │ 0.857 │ 0.000 │ generalize │
384
+ └───────┴──────────┴────────────┴────────┴────────────┘
385
+ H27: Subtraction as a + (−b)? (eq_sign residuals)
386
+ ┏━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┳━━━━━━━━━━┓
387
+ ┃ Layer ┃ cos-sim(sub vs add) ┃ R²(sub within) ┃ R²(add → sub) ┃ Verdict ┃
388
+ ┡━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━╇━━━━━━━━━━┩
389
+ │ L0 │ 0.721 │ 0.740 │ -25.561 │ distinct │
390
+ ├───────┼─────────────────────┼────────────────┼───────────────┼──────────┤
391
+ │ L1 │ 0.463 │ 0.977 │ -10.411 │ distinct │
392
+ ├───────┼─────────────────────┼────────────────┼───────────────┼──────────┤
393
+ │ L2 │ 0.309 │ 0.957 │ -6.337 │ distinct │
394
+ └───────┴─────────────────────┴────────────────┴───────────────┴──────────┘
395
+
396
+ Generating plots...
397
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/algorithmic_structure/h25_multiplication_vs_addition.png
398
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/algorithmic_structure/h26_generalization_gap.png
399
+
400
+ Saved:
401
+ results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1
402
+ 024I/analysis/algorithmic_structure/metrics.json
403
+
404
+ ======================================================================
405
+ Algorithmic structure analysis complete.
406
+ Output:
407
+ results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1
408
+ 024I/analysis/algorithmic_structure
409
+ ======================================================================
Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/answer_construction/f20_answer_decodability_by_layer.png ADDED

Git LFS Details

  • SHA256: 53d8c9b284464b7f66ee6b484aa60dd3fe0086cad1ce076510d5762867d05b30
  • Pointer size: 131 Bytes
  • Size of remote file: 757 kB
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Git LFS Details

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  • Pointer size: 130 Bytes
  • Size of remote file: 64.2 kB
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1
+ ======================================================================
2
+ ATTENTION HEAD ANALYSIS (E16–E18)
3
+ ======================================================================
4
+
5
+ NOTE: Raw attention weight matrices are not stored in the current
6
+ inference pipeline. This script analyzes per-head OUTPUT vectors
7
+ (value-weighted outputs before o_proj), which reveals WHAT each head
8
+ computes but not WHICH tokens it attends to.
9
+ To get token-level attention patterns, inference.py would need to store
10
+ the full attention weight matrices during generation.
11
+
12
+ Loading results...
13
+
14
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=div]_[int=False].pt: 10000 results for $->/
15
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=minus]_[int=False].pt: 10000 results for $->-
16
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=mod]_[int=False].pt: 10000 results for $->%
17
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=mul]_[int=False].pt: 10000 results for $->*
18
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=plus]_[int=False].pt: 10000 results for $->+
19
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=concat]_[int=False].pt: 10000 results for /->$
20
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=minus]_[int=False].pt: 10000 results for /->-
21
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=mod]_[int=False].pt: 10000 results for /->%
22
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=mul]_[int=False].pt: 10000 results for /->*
23
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=plus]_[int=False].pt: 10000 results for /->+
24
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=concat]_[int=False].pt: 10000 results for -->$
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+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=div]_[int=False].pt: 10000 results for -->/
26
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=mod]_[int=False].pt: 10000 results for -->%
27
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=mul]_[int=False].pt: 10000 results for -->*
28
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=plus]_[int=False].pt: 10000 results for -->+
29
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=concat]_[int=False].pt: 10000 results for %->$
30
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=div]_[int=False].pt: 10000 results for %->/
31
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=minus]_[int=False].pt: 10000 results for %->-
32
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=mul]_[int=False].pt: 10000 results for %->*
33
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=plus]_[int=False].pt: 10000 results for %->+
34
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=concat]_[int=False].pt: 10000 results for *->$
35
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=div]_[int=False].pt: 10000 results for *->/
36
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=minus]_[int=False].pt: 10000 results for *->-
37
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=mod]_[int=False].pt: 10000 results for *->%
38
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=plus]_[int=False].pt: 10000 results for *->+
39
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=concat]_[int=False].pt: 10000 results for +->$
40
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=div]_[int=False].pt: 10000 results for +->/
41
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=minus]_[int=False].pt: 10000 results for +->-
42
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=mod]_[int=False].pt: 10000 results for +->%
43
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=mul]_[int=False].pt: 10000 results for +->*
44
+ $->/: 10000 prompts
45
+ $->-: 10000 prompts
46
+ $->%: 10000 prompts
47
+ $->*: 10000 prompts
48
+ $->+: 10000 prompts
49
+ /->$: 10000 prompts
50
+ /->-: 10000 prompts
51
+ /->%: 10000 prompts
52
+ /->*: 10000 prompts
53
+ /->+: 10000 prompts
54
+ -->$: 10000 prompts
55
+ -->/: 10000 prompts
56
+ -->%: 10000 prompts
57
+ -->*: 10000 prompts
58
+ -->+: 10000 prompts
59
+ %->$: 10000 prompts
60
+ %->/: 10000 prompts
61
+ %->-: 10000 prompts
62
+ %->*: 10000 prompts
63
+ %->+: 10000 prompts
64
+ *->$: 10000 prompts
65
+ *->/: 10000 prompts
66
+ *->-: 10000 prompts
67
+ *->%: 10000 prompts
68
+ *->+: 10000 prompts
69
+ +->$: 10000 prompts
70
+ +->/: 10000 prompts
71
+ +->-: 10000 prompts
72
+ +->%: 10000 prompts
73
+ +->*: 10000 prompts
74
+ Layers: [0, 1, 2]
75
+
76
+ Running E16a (head activity)...
77
+
78
+ num_heads=4
79
+
80
+ Running E16b/E17 (head context similarity)...
81
+
82
+ Running E18 (head operation specialization)...
83
+ E16a: Mean head output norm (mean across pairs, both
84
+ contexts)
85
+
86
+ Layer-Head opA opB op = ans
87
+ ─────────────────────────────────────────────────────
88
+ L0-H0 0.998 1.044 1.126 3.241 1.373
89
+ L0-H1 2.055 1.945 2.606 3.284 2.407
90
+ L0-H2 1.174 1.185 1.048 2.749 1.412
91
+ L0-H3 1.747 1.649 2.143 2.425 2.722
92
+ L1-H0 4.948 4.208 3.687 3.309 3.387
93
+ L1-H1 4.751 3.517 3.795 3.283 3.565
94
+ L1-H2 5.925 4.701 3.194 3.182 4.009
95
+ L1-H3 3.809 4.116 2.978 3.789 3.536
96
+ L2-H0 2.134 2.101 2.216 5.146 5.749
97
+ L2-H1 5.776 4.906 4.451 5.466 4.540
98
+ L2-H2 2.353 9.365 2.642 5.249 5.263
99
+ L2-H3 2.773 2.902 11.921 3.893 4.651
100
+
101
+ E16b/E17: Head activity cosine sim (std vs over,
102
+ mean across pairs)
103
+
104
+ Layer opA opB op = ans
105
+ ───────────────────────────────────────────────
106
+ L0 0.999 0.999 0.963 0.969 0.964
107
+ L1 0.990 0.966 0.959 0.957 0.964
108
+ L2 0.999 0.998 0.996 0.945 0.961
109
+
110
+ E18: Head specialization by semantic operation (mean norm at
111
+ eq_sign)
112
+
113
+ Layer-Head addition multiplication subtraction unknown
114
+ ────────────────────────────────────────────────────────────────
115
+ L0-H0 3.223 3.150 3.859 3.073
116
+ L0-H1 3.343 3.259 3.203 3.300
117
+ L0-H2 2.741 2.732 2.751 2.757
118
+ L0-H3 1.147 2.124 3.214 2.688
119
+ L1-H0 2.915 4.007 2.710 3.407
120
+ L1-H1 2.676 3.624 3.197 3.401
121
+ L1-H2 3.041 3.432 2.625 3.331
122
+ L1-H3 5.877 3.312 4.727 2.939
123
+ L2-H0 6.302 3.293 4.962 5.439
124
+ L2-H1 5.360 5.599 5.488 5.450
125
+ L2-H2 4.558 4.889 6.675 5.124
126
+ L2-H3 2.129 2.521 2.881 5.276
127
+
128
+
129
+ Generating plots...
130
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/attention/e16a_head_activity_std.png
131
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/attention/e16a_head_activity_over.png
132
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/attention/e16b_head_context_similarity.png
133
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/attention/e18_head_operation_specialization.png
134
+
135
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/attention/metrics.json
136
+
137
+ ======================================================================
138
+ Attention head analysis complete.
139
+ Output: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/attention
140
+ ======================================================================
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697
+ "operand_a": {
698
+ "carry": 0.8247820675002838,
699
+ "tens_carry": 0.8206571090012902,
700
+ "borrow": null,
701
+ "tens_borrow": null
702
+ },
703
+ "operand_b": {
704
+ "carry": 0.9985097471577549,
705
+ "tens_carry": 0.9886136965650609,
706
+ "borrow": null,
707
+ "tens_borrow": null
708
+ },
709
+ "operator": {
710
+ "carry": 0.8234614979159571,
711
+ "tens_carry": 0.8144208569666487,
712
+ "borrow": null,
713
+ "tens_borrow": null
714
+ },
715
+ "eq_sign": {
716
+ "carry": 1.0,
717
+ "tens_carry": 0.9355093746026444,
718
+ "borrow": null,
719
+ "tens_borrow": null
720
+ }
721
+ }
722
+ },
723
+ "+->*": {
724
+ "0": {
725
+ "operand_a": {
726
+ "carry": 0.8306957209208555,
727
+ "tens_carry": 0.8215367938311445,
728
+ "borrow": null,
729
+ "tens_borrow": null
730
+ },
731
+ "operand_b": {
732
+ "carry": 0.9312294306823613,
733
+ "tens_carry": 0.97123294109647,
734
+ "borrow": null,
735
+ "tens_borrow": null
736
+ },
737
+ "operator": {
738
+ "carry": 0.5650423921861929,
739
+ "tens_carry": 0.5671711045399409,
740
+ "borrow": null,
741
+ "tens_borrow": null
742
+ },
743
+ "eq_sign": {
744
+ "carry": 0.6868074366957989,
745
+ "tens_carry": 0.7903447131024179,
746
+ "borrow": null,
747
+ "tens_borrow": null
748
+ }
749
+ },
750
+ "1": {
751
+ "operand_a": {
752
+ "carry": 0.82797117897859,
753
+ "tens_carry": 0.8242006178055602,
754
+ "borrow": null,
755
+ "tens_borrow": null
756
+ },
757
+ "operand_b": {
758
+ "carry": 0.9987845432275947,
759
+ "tens_carry": 0.9884640961768657,
760
+ "borrow": null,
761
+ "tens_borrow": null
762
+ },
763
+ "operator": {
764
+ "carry": 0.8270680308050465,
765
+ "tens_carry": 0.8205897853080678,
766
+ "borrow": null,
767
+ "tens_borrow": null
768
+ },
769
+ "eq_sign": {
770
+ "carry": 0.8812714294183254,
771
+ "tens_carry": 0.9561700055300497,
772
+ "borrow": null,
773
+ "tens_borrow": null
774
+ }
775
+ },
776
+ "2": {
777
+ "operand_a": {
778
+ "carry": 0.8245663143103105,
779
+ "tens_carry": 0.8226390037510338,
780
+ "borrow": null,
781
+ "tens_borrow": null
782
+ },
783
+ "operand_b": {
784
+ "carry": 0.9984881762890641,
785
+ "tens_carry": 0.9882340941068468,
786
+ "borrow": null,
787
+ "tens_borrow": null
788
+ },
789
+ "operator": {
790
+ "carry": 0.8262881145983936,
791
+ "tens_carry": 0.819147972331751,
792
+ "borrow": null,
793
+ "tens_borrow": null
794
+ },
795
+ "eq_sign": {
796
+ "carry": 1.0,
797
+ "tens_carry": 0.934987614888534,
798
+ "borrow": null,
799
+ "tens_borrow": null
800
+ }
801
+ }
802
+ }
803
+ }
804
+ }
Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/carry_borrow/out.txt ADDED
@@ -0,0 +1,272 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ ======================================================================
2
+ CARRY AND BORROW ANALYSIS (C10–C12)
3
+ ======================================================================
4
+
5
+ Loading results...
6
+
7
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=div]_[int=False].pt: 10000 results for $->/
8
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=minus]_[int=False].pt: 10000 results for $->-
9
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=mod]_[int=False].pt: 10000 results for $->%
10
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=mul]_[int=False].pt: 10000 results for $->*
11
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=concat]_[oop=plus]_[int=False].pt: 10000 results for $->+
12
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=concat]_[int=False].pt: 10000 results for /->$
13
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=minus]_[int=False].pt: 10000 results for /->-
14
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=mod]_[int=False].pt: 10000 results for /->%
15
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=mul]_[int=False].pt: 10000 results for /->*
16
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=div]_[oop=plus]_[int=False].pt: 10000 results for /->+
17
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=concat]_[int=False].pt: 10000 results for -->$
18
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=div]_[int=False].pt: 10000 results for -->/
19
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=mod]_[int=False].pt: 10000 results for -->%
20
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=mul]_[int=False].pt: 10000 results for -->*
21
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=minus]_[oop=plus]_[int=False].pt: 10000 results for -->+
22
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=concat]_[int=False].pt: 10000 results for %->$
23
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=div]_[int=False].pt: 10000 results for %->/
24
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=minus]_[int=False].pt: 10000 results for %->-
25
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=mul]_[int=False].pt: 10000 results for %->*
26
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mod]_[oop=plus]_[int=False].pt: 10000 results for %->+
27
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=concat]_[int=False].pt: 10000 results for *->$
28
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=div]_[int=False].pt: 10000 results for *->/
29
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=minus]_[int=False].pt: 10000 results for *->-
30
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=mod]_[int=False].pt: 10000 results for *->%
31
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=mul]_[oop=plus]_[int=False].pt: 10000 results for *->+
32
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=concat]_[int=False].pt: 10000 results for +->$
33
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=div]_[int=False].pt: 10000 results for +->/
34
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=minus]_[int=False].pt: 10000 results for +->-
35
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=mod]_[int=False].pt: 10000 results for +->%
36
+ ✓ Loaded [m=arithmetic-circuit-overloading--Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I]_[p=10000]_[fs=8]_[rv=True]_[pz=True]_[op=plus]_[oop=mul]_[int=False].pt: 10000 results for +->*
37
+ $->/: 10000 prompts
38
+ $->-: 10000 prompts
39
+ $->%: 10000 prompts
40
+ $->*: 10000 prompts
41
+ $->+: 10000 prompts
42
+ /->$: 10000 prompts
43
+ /->-: 10000 prompts
44
+ /->%: 10000 prompts
45
+ /->*: 10000 prompts
46
+ /->+: 10000 prompts
47
+ -->$: 10000 prompts
48
+ -->/: 10000 prompts
49
+ -->%: 10000 prompts
50
+ -->*: 10000 prompts
51
+ -->+: 10000 prompts
52
+ %->$: 10000 prompts
53
+ %->/: 10000 prompts
54
+ %->-: 10000 prompts
55
+ %->*: 10000 prompts
56
+ %->+: 10000 prompts
57
+ *->$: 10000 prompts
58
+ *->/: 10000 prompts
59
+ *->-: 10000 prompts
60
+ *->%: 10000 prompts
61
+ *->+: 10000 prompts
62
+ +->$: 10000 prompts
63
+ +->/: 10000 prompts
64
+ +->-: 10000 prompts
65
+ +->%: 10000 prompts
66
+ +->*: 10000 prompts
67
+ Layers: [0, 1, 2]
68
+
69
+ Collecting carry/borrow data (addition and subtraction pairs only)...
70
+
71
+
72
+ Running C10/C11...
73
+
74
+ C10/C11: -->$ — units-borrow AUROC (per layer ×
75
+ position)
76
+
77
+ Layer operand_a operand_b operator eq_sign
78
+ ────────────────────────────────────────────────────
79
+ L0 0.825 0.915 0.615 0.665
80
+ L1 0.822 1.000 0.818 0.919
81
+ L2 0.819 1.000 0.812 1.000
82
+
83
+ C10/C11: -->$ — tens-borrow AUROC (per layer ×
84
+ position)
85
+
86
+ Layer operand_a operand_b operator eq_sign
87
+ ────────────────────────────────────────────────────
88
+ L0 0.819 0.980 0.658 0.760
89
+ L1 0.822 0.991 0.807 0.968
90
+ L2 0.821 0.995 0.782 0.978
91
+
92
+ C10/C11: -->/ — units-borrow AUROC (per layer ×
93
+ position)
94
+
95
+ Layer operand_a operand_b operator eq_sign
96
+ ────────────────────────────────────────────────────
97
+ L0 0.826 0.916 0.605 0.664
98
+ L1 0.824 1.000 0.819 0.913
99
+ L2 0.822 1.000 0.813 1.000
100
+
101
+ C10/C11: -->/ — tens-borrow AUROC (per layer ×
102
+ position)
103
+
104
+ Layer operand_a operand_b operator eq_sign
105
+ ────────────────────────────────────────────────────
106
+ L0 0.825 0.981 0.659 0.755
107
+ L1 0.827 0.990 0.815 0.969
108
+ L2 0.823 0.994 0.781 0.977
109
+
110
+ C10/C11: -->% — units-borrow AUROC (per layer ×
111
+ position)
112
+
113
+ Layer operand_a operand_b operator eq_sign
114
+ ────────────────────────────────────────────────────
115
+ L0 0.826 0.916 0.605 0.664
116
+ L1 0.824 1.000 0.819 0.913
117
+ L2 0.822 1.000 0.813 1.000
118
+
119
+ C10/C11: -->% — tens-borrow AUROC (per layer ×
120
+ position)
121
+
122
+ Layer operand_a operand_b operator eq_sign
123
+ ────────────────────────────────────────────────────
124
+ L0 0.825 0.981 0.659 0.755
125
+ L1 0.827 0.990 0.815 0.969
126
+ L2 0.823 0.994 0.781 0.977
127
+
128
+ C10/C11: -->* — units-borrow AUROC (per layer ×
129
+ position)
130
+
131
+ Layer operand_a operand_b operator eq_sign
132
+ ────────────────────────────────────────────────────
133
+ L0 0.825 0.915 0.615 0.665
134
+ L1 0.822 1.000 0.818 0.919
135
+ L2 0.819 1.000 0.812 1.000
136
+
137
+ C10/C11: -->* — tens-borrow AUROC (per layer ×
138
+ position)
139
+
140
+ Layer operand_a operand_b operator eq_sign
141
+ ────────────────────────────────────────────────────
142
+ L0 0.819 0.980 0.658 0.760
143
+ L1 0.822 0.991 0.807 0.968
144
+ L2 0.821 0.995 0.782 0.978
145
+
146
+ C10/C11: -->+ — units-borrow AUROC (per layer ×
147
+ position)
148
+
149
+ Layer operand_a operand_b operator eq_sign
150
+ ────────────────────────────────────────────────────
151
+ L0 0.825 0.915 0.615 0.665
152
+ L1 0.822 1.000 0.818 0.919
153
+ L2 0.819 1.000 0.812 1.000
154
+
155
+ C10/C11: -->+ — tens-borrow AUROC (per layer ×
156
+ position)
157
+
158
+ Layer operand_a operand_b operator eq_sign
159
+ ────────────────────────────────────────────────────
160
+ L0 0.819 0.980 0.658 0.760
161
+ L1 0.822 0.991 0.807 0.968
162
+ L2 0.821 0.995 0.782 0.978
163
+
164
+ C10/C11: +->$ — units-carry AUROC (per layer ×
165
+ position)
166
+
167
+ Layer operand_a operand_b operator eq_sign
168
+ ────────────────────────────────────────────────────
169
+ L0 0.831 0.931 0.565 0.687
170
+ L1 0.828 0.999 0.827 0.881
171
+ L2 0.825 0.998 0.826 1.000
172
+
173
+ C10/C11: +->$ — tens-carry AUROC (per layer ×
174
+ position)
175
+
176
+ Layer operand_a operand_b operator eq_sign
177
+ ────────────────────────────────────────────────────
178
+ L0 0.822 0.971 0.567 0.790
179
+ L1 0.824 0.988 0.821 0.956
180
+ L2 0.823 0.988 0.819 0.935
181
+
182
+ C10/C11: +->/ — units-carry AUROC (per layer ×
183
+ position)
184
+
185
+ Layer operand_a operand_b operator eq_sign
186
+ ────────────────────────────────────────────────────
187
+ L0 0.829 0.931 0.565 0.687
188
+ L1 0.828 0.999 0.825 0.884
189
+ L2 0.825 0.999 0.823 1.000
190
+
191
+ C10/C11: +->/ — tens-carry AUROC (per layer ×
192
+ position)
193
+
194
+ Layer operand_a operand_b operator eq_sign
195
+ ──────────────��─────────────────────────────────────
196
+ L0 0.821 0.972 0.586 0.789
197
+ L1 0.824 0.989 0.821 0.957
198
+ L2 0.821 0.989 0.814 0.936
199
+
200
+ C10/C11: +->- — units-carry AUROC (per layer ×
201
+ position)
202
+
203
+ Layer operand_a operand_b operator eq_sign
204
+ ────────────────────────────────────────────────────
205
+ L0 0.831 0.931 0.565 0.687
206
+ L1 0.828 0.999 0.827 0.881
207
+ L2 0.825 0.998 0.826 1.000
208
+
209
+ C10/C11: +->- — tens-carry AUROC (per layer ×
210
+ position)
211
+
212
+ Layer operand_a operand_b operator eq_sign
213
+ ────────────────────────────────────────────────────
214
+ L0 0.822 0.971 0.567 0.790
215
+ L1 0.824 0.988 0.821 0.956
216
+ L2 0.823 0.988 0.819 0.935
217
+
218
+ C10/C11: +->% — units-carry AUROC (per layer ×
219
+ position)
220
+
221
+ Layer operand_a operand_b operator eq_sign
222
+ ────────────────────────────────────────────────────
223
+ L0 0.829 0.931 0.565 0.687
224
+ L1 0.828 0.999 0.825 0.884
225
+ L2 0.825 0.999 0.823 1.000
226
+
227
+ C10/C11: +->% — tens-carry AUROC (per layer ×
228
+ position)
229
+
230
+ Layer operand_a operand_b operator eq_sign
231
+ ────────────────────────────────────────────────────
232
+ L0 0.821 0.972 0.586 0.789
233
+ L1 0.824 0.989 0.821 0.957
234
+ L2 0.821 0.989 0.814 0.936
235
+
236
+ C10/C11: +->* — units-carry AUROC (per layer ×
237
+ position)
238
+
239
+ Layer operand_a operand_b operator eq_sign
240
+ ────────────────────────────────────────────────────
241
+ L0 0.831 0.931 0.565 0.687
242
+ L1 0.828 0.999 0.827 0.881
243
+ L2 0.825 0.998 0.826 1.000
244
+
245
+ C10/C11: +->* — tens-carry AUROC (per layer ×
246
+ position)
247
+
248
+ Layer operand_a operand_b operator eq_sign
249
+ ────────────────────────────────────────────────────
250
+ L0 0.822 0.971 0.567 0.790
251
+ L1 0.824 0.988 0.821 0.956
252
+ L2 0.823 0.988 0.819 0.935
253
+
254
+ C12: Carry vs borrow across layers (at
255
+ eq_sign)
256
+
257
+ Layer Carry (mean) Borrow (mean)
258
+ ──────────────────────────────────────
259
+ L0 0.687 0.665
260
+ L1 0.882 0.917
261
+ L2 1.000 1.000
262
+
263
+
264
+ Generating plots...
265
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/carry_borrow/c12_carry_borrow_by_layer.png
266
+
267
+ Saved: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/carry_borrow/metrics.json
268
+
269
+ ======================================================================
270
+ Carry and borrow analysis complete.
271
+ Output: results/Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/carry_borrow
272
+ ======================================================================
Llama-3.3-70B-Instruct-v2-3d-5M-500K-0.1-reverse-padzero-99-256D-3L-4H-1024I/analysis/information_flow/i28_answer_refinement_by_layer.png ADDED

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