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The dataset generation failed because of a cast error
Error code:   DatasetGenerationCastError
Exception:    DatasetGenerationCastError
Message:      An error occurred while generating the dataset

All the data files must have the same columns, but at some point there are 1 new columns ({'response_filtered'})

This happened while the json dataset builder was generating data using

hf://datasets/ceselder/cot-oracle-answer-trajectory/answer_trajectory_cleaned.jsonl (at revision f3894df13f791d79cd2f796485823020951f0157), [/tmp/hf-datasets-cache/medium/datasets/28683907771477-config-parquet-and-info-ceselder-cot-oracle-answe-c090a53b/hub/datasets--ceselder--cot-oracle-answer-trajectory/snapshots/f3894df13f791d79cd2f796485823020951f0157/answer_trajectory.jsonl (origin=hf://datasets/ceselder/cot-oracle-answer-trajectory@f3894df13f791d79cd2f796485823020951f0157/answer_trajectory.jsonl), /tmp/hf-datasets-cache/medium/datasets/28683907771477-config-parquet-and-info-ceselder-cot-oracle-answe-c090a53b/hub/datasets--ceselder--cot-oracle-answer-trajectory/snapshots/f3894df13f791d79cd2f796485823020951f0157/answer_trajectory_cleaned.jsonl (origin=hf://datasets/ceselder/cot-oracle-answer-trajectory@f3894df13f791d79cd2f796485823020951f0157/answer_trajectory_cleaned.jsonl)]

Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)
Traceback:    Traceback (most recent call last):
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1887, in _prepare_split_single
                  writer.write_table(table)
                File "/usr/local/lib/python3.12/site-packages/datasets/arrow_writer.py", line 675, in write_table
                  pa_table = table_cast(pa_table, self._schema)
                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
                  return cast_table_to_schema(table, schema)
                         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/table.py", line 2218, in cast_table_to_schema
                  raise CastError(
              datasets.table.CastError: Couldn't cast
              datapoint_type: string
              prompt: string
              target_response: string
              layer: int64
              layers: list<item: int64>
                child 0, item: int64
              num_positions: int64
              context_input_ids: list<item: int64>
                child 0, item: int64
              context_positions: list<item: int64>
                child 0, item: int64
              sent_idx: int64
              total_sentences: int64
              pct: int64
              final_answer: string
              response_filtered: string
              to
              {'datapoint_type': Value('string'), 'prompt': Value('string'), 'target_response': Value('string'), 'layer': Value('int64'), 'layers': List(Value('int64')), 'num_positions': Value('int64'), 'context_input_ids': List(Value('int64')), 'context_positions': List(Value('int64')), 'sent_idx': Value('int64'), 'total_sentences': Value('int64'), 'pct': Value('int64'), 'final_answer': Value('string')}
              because column names don't match
              
              During handling of the above exception, another exception occurred:
              
              Traceback (most recent call last):
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1347, in compute_config_parquet_and_info_response
                  parquet_operations = convert_to_parquet(builder)
                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 980, in convert_to_parquet
                  builder.download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 884, in download_and_prepare
                  self._download_and_prepare(
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 947, in _download_and_prepare
                  self._prepare_split(split_generator, **prepare_split_kwargs)
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1736, in _prepare_split
                  for job_id, done, content in self._prepare_split_single(
                                               ^^^^^^^^^^^^^^^^^^^^^^^^^^^
                File "/usr/local/lib/python3.12/site-packages/datasets/builder.py", line 1889, in _prepare_split_single
                  raise DatasetGenerationCastError.from_cast_error(
              datasets.exceptions.DatasetGenerationCastError: An error occurred while generating the dataset
              
              All the data files must have the same columns, but at some point there are 1 new columns ({'response_filtered'})
              
              This happened while the json dataset builder was generating data using
              
              hf://datasets/ceselder/cot-oracle-answer-trajectory/answer_trajectory_cleaned.jsonl (at revision f3894df13f791d79cd2f796485823020951f0157), [/tmp/hf-datasets-cache/medium/datasets/28683907771477-config-parquet-and-info-ceselder-cot-oracle-answe-c090a53b/hub/datasets--ceselder--cot-oracle-answer-trajectory/snapshots/f3894df13f791d79cd2f796485823020951f0157/answer_trajectory.jsonl (origin=hf://datasets/ceselder/cot-oracle-answer-trajectory@f3894df13f791d79cd2f796485823020951f0157/answer_trajectory.jsonl), /tmp/hf-datasets-cache/medium/datasets/28683907771477-config-parquet-and-info-ceselder-cot-oracle-answe-c090a53b/hub/datasets--ceselder--cot-oracle-answer-trajectory/snapshots/f3894df13f791d79cd2f796485823020951f0157/answer_trajectory_cleaned.jsonl (origin=hf://datasets/ceselder/cot-oracle-answer-trajectory@f3894df13f791d79cd2f796485823020951f0157/answer_trajectory_cleaned.jsonl)]
              
              Please either edit the data files to have matching columns, or separate them into different configurations (see docs at https://hf.co/docs/hub/datasets-manual-configuration#multiple-configurations)

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datapoint_type
string
prompt
string
target_response
string
layer
int64
layers
list
num_positions
int64
context_input_ids
list
context_positions
list
sent_idx
int64
total_sentences
int64
pct
int64
final_answer
string
cot_answer_trajectory
Activations from 33 positions across layers 9, 18, 27, representing sentence 2/149 (1%) of the model's chain of thought. What does the model currently think the answer is?
one of the options A to E. So, I need to figure out the relationship between 34 and 43, and then apply the same relationship to 25 to find the correct answer
9
[ 9, 18, 27 ]
33
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 71, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 71, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 71 ]
1
149
1
B
cot_answer_trajectory
Activations from 57 positions across layers 9, 18, 27, representing sentence 3/149 (2%) of the model's chain of thought. What does the model currently think the answer is?
one of the options A to E. Let me think about possible relationships between the numbers
9
[ 9, 18, 27 ]
57
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 112, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 112, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, ...
2
149
2
B
cot_answer_trajectory
Activations from 72 positions across layers 9, 18, 27, representing sentence 4/149 (2%) of the model's chain of thought. What does the model currently think the answer is?
either A, B, C, D, or E. Let me think about how 34 relates to 43. Maybe there's a mathematical operation that transforms 34 into 43. Let me check the difference first
9
[ 9, 18, 27 ]
72
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 8, 16, 2...
3
149
2
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 5/149 (3%) of the model's chain of thought. What does the model currently think the answer is?
likely to be one of the options given. Let me think about possible relationships
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
4
149
3
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 6/149 (4%) of the model's chain of thought. What does the model currently think the answer is?
C)36. But wait, let me check again. Maybe there's another pattern
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
5
149
4
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 7/149 (4%) of the model's chain of thought. What does the model currently think the answer is?
\boxed{C}
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
6
149
4
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 8/149 (5%) of the model's chain of thought. What does the model currently think the answer is?
43 - 34 = 9. So, the difference is 9. But then, if I apply that to 25, adding 9 would give 34. But 34 isn't one of the options
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
7
149
5
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 9/149 (6%) of the model's chain of thought. What does the model currently think the answer is?
25 + 9 = 34? Wait, but that would be 34, but 34 is already in the original pair. That doesn't make sense. Maybe not the difference
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
8
149
6
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 10/149 (6%) of the model's chain of thought. What does the model currently think the answer is?
25 plus 9, which is 34? Wait, but 34 is already in the original pair. That doesn't make sense. Maybe not the difference
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
9
149
6
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 11/149 (7%) of the model's chain of thought. What does the model currently think the answer is?
25 + 9 = 34? But 34 isn't one of the options. Wait, maybe I got the direction wrong. Maybe it's not adding 9, but something else
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
10
149
7
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 12/149 (8%) of the model's chain of thought. What does the model currently think the answer is?
34? But 34 isn't one of the options. Wait, the options are A)49, B)52, C)36, D)64, E)56. So that can't be
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
11
149
8
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 13/149 (8%) of the model's chain of thought. What does the model currently think the answer is?
not 34. So maybe that's not the right approach
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
12
149
8
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 14/149 (9%) of the model's chain of thought. What does the model currently think the answer is?
not 34. So maybe that's not the right approach
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
13
149
9
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 15/149 (10%) of the model's chain of thought. What does the model currently think the answer is?
C)36. Wait, but let me check again. Maybe there's another relationship. Let me think about the digits. 34 and 43. If you reverse the digits of 34, you get 43
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
14
149
10
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 16/149 (10%) of the model's chain of thought. What does the model currently think the answer is?
C)36. Wait, but why?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
15
149
10
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 17/149 (11%) of the model's chain of thought. What does the model currently think the answer is?
36. Wait, but why? Let me check
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
16
149
11
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 18/149 (12%) of the model's chain of thought. What does the model currently think the answer is?
the reverse of 25. Let's check: 25 reversed is 52. And 52 is option B. That seems possible. But let me check if there's another pattern
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
17
149
12
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 19/149 (12%) of the model's chain of thought. What does the model currently think the answer is?
the reverse of 25. Let's check: 25 reversed is 52. And 52 is option B. So maybe the answer is B)52?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
18
149
12
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 20/149 (13%) of the model's chain of thought. What does the model currently think the answer is?
the reverse of 25. Let's check: 25 reversed is 52. And 52 is option B. So maybe the answer is B)52?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
19
149
13
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 21/149 (14%) of the model's chain of thought. What does the model currently think the answer is?
the reverse of 25. Let's check: 25 reversed is 52. And 52 is option B. So maybe the answer is B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
20
149
14
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 22/149 (14%) of the model's chain of thought. What does the model currently think the answer is?
B)52. Let me check if that makes sense
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
21
149
14
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 23/149 (15%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But wait, let me make sure there isn't another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
22
149
15
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 24/149 (16%) of the model's chain of thought. What does the model currently think the answer is?
B?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
23
149
16
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 25/149 (16%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check if there's another possible relationship to make sure
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
24
149
16
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 26/149 (17%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But wait, let me check if there's another possible relationship. For example, maybe adding the digits? Let's see. 3 + 4 = 7, and 4 + 3 = 7. So
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
25
149
17
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 27/149 (18%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again. Let me think if there's another possible relationship. For example, maybe adding the digits? 3 + 4 = 7, and 4 + 3 = 7. So the
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
26
149
18
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 28/149 (18%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again. Let me think of other possibilities
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
27
149
18
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 29/149 (19%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again. Let me think if there's another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
28
149
19
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 30/149 (20%) of the model's chain of thought. What does the model currently think the answer is?
a number whose digits add up to 7? But 25's digits add up to 7 as well (2 + 5 = 7). So then, the answer would be a number with digits adding to 7. Let's
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
29
149
20
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 31/149 (20%) of the model's chain of thought. What does the model currently think the answer is?
a number whose digits add up to 7. Let's check the options
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
30
149
20
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 32/149 (21%) of the model's chain of thought. What does the model currently think the answer is?
a number where the digits add up to 7. Let's check the options:
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
31
149
21
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 33/149 (22%) of the model's chain of thought. What does the model currently think the answer is?
a number whose digits add up to 7. Let's check the options:
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
32
149
22
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 34/149 (22%) of the model's chain of thought. What does the model currently think the answer is?
a number whose digits add up to 7. Let's check the options:
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
33
149
22
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 35/149 (23%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
34
149
23
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 36/149 (24%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
35
149
24
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 37/149 (24%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check if there's another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
36
149
24
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 38/149 (25%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again if there's another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
37
149
25
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 39/149 (26%) of the model's chain of thought. What does the model currently think the answer is?
B)52? But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
38
149
26
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 40/149 (26%) of the model's chain of thought. What does the model currently think the answer is?
B)52? But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
39
149
26
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 41/149 (27%) of the model's chain of thought. What does the model currently think the answer is?
52, which is B. But let me check again if there's another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
40
149
27
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 42/149 (28%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But wait, let me check if there's another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
41
149
28
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 43/149 (28%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But wait, earlier I thought reversing the digits would also give 52. So both the digit sum and reversing the digits lead to 52. So that's a good sign. Let me check if there's another
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
42
149
28
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 44/149 (29%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again if there's another possible relationship. For example, maybe 34 and 43 are related by some mathematical operation. Let me think. 34 + 9 = 43
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
43
149
29
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 45/149 (30%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
44
149
30
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 46/149 (30%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
45
149
30
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 47/149 (31%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
46
149
31
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 48/149 (32%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
47
149
32
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 49/149 (32%) of the model's chain of thought. What does the model currently think the answer is?
B)52. Let me check again. Let me think if there's another possible relationship. For example, maybe multiplying digits? 3*4=12, 4*3=12. So same product. Then for
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
48
149
32
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 50/149 (33%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
49
149
33
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 51/149 (34%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
50
149
34
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 52/149 (34%) of the model's chain of thought. What does the model currently think the answer is?
25 + 9 = 34, but 34 isn't an option. Wait, but maybe the difference is 9, but then 25 + 9 = 34, which is not an option. Alternatively
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
51
149
34
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 53/149 (35%) of the model's chain of thought. What does the model currently think the answer is?
25 + 9 = 34. But 34 isn't an option. Wait, but maybe the difference is 9, but the next number is 25 + something else?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
52
149
35
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 54/149 (36%) of the model's chain of thought. What does the model currently think the answer is?
34? But 34 isn't an option. Wait, but the options are A)49, B)52, C)36, D)64, E)56. So that doesn't fit
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
53
149
36
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 55/149 (36%) of the model's chain of thought. What does the model currently think the answer is?
not that. Alternatively, maybe multiplying? 34 * something equals 43? 43 divided by 34 is roughly 1.26, which doesn't seem helpful. Maybe squares or cubes? 34 is not
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
54
149
36
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 56/149 (37%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
55
149
37
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 57/149 (38%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
56
149
38
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 58/149 (38%) of the model's chain of thought. What does the model currently think the answer is?
not straightforward. Alternatively, maybe squares or cubes?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
57
149
38
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 59/149 (39%) of the model's chain of thought. What does the model currently think the answer is?
not straightforward. But since reversing digits gives 52, which is an option, and the sum of digits also gives 52, that seems to be the answer
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
58
149
39
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 60/149 (40%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
59
149
40
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 61/149 (40%) of the model's chain of thought. What does the model currently think the answer is?
likely B)52. But let me check again. Let me think if there's another possible relationship. For example, maybe squares or cubes? 34 is not a square, 43 isn't either. 25 is
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
60
149
40
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 62/149 (41%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
61
149
41
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 63/149 (42%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
62
149
42
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 64/149 (42%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
63
149
42
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 65/149 (43%) of the model's chain of thought. What does the model currently think the answer is?
likely B)52, since reversing the digits of 34 gives 43, and reversing 25 gives 52. Also, the sum of digits is same. So both patterns lead to B. So I think the answer
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
64
149
43
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 66/149 (44%) of the model's chain of thought. What does the model currently think the answer is?
52? Because reversing digits gives 52, and digits sum to 7. So both patterns point to B)52. Let me check the options again. The options are A)49, B)52, C
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
65
149
44
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 67/149 (44%) of the model's chain of thought. What does the model currently think the answer is?
36 (6 squared) or 49 (7 squared) or 64 (8 squared). Let's check the options. C)36, A)49, D)64. But 25 is
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
66
149
44
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 68/149 (45%) of the model's chain of thought. What does the model currently think the answer is?
52? Wait, 52 is not a square. 49 is 7 squared, which is option A. 64 is 8 squared, option D. So if the relationship is that 25 is a square
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
67
149
45
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 69/149 (46%) of the model's chain of thought. What does the model currently think the answer is?
49? But then, how does that relate to 34 and 43?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
68
149
46
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 70/149 (46%) of the model's chain of thought. What does the model currently think the answer is?
either A or C. But earlier, we saw that B)52 is the answer if we reverse digits or sum digits. So which is it?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
69
149
46
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 71/149 (47%) of the model's chain of thought. What does the model currently think the answer is?
one of those. But 25 is 5 squared. If the relationship is square numbers, then maybe 25 is 5², and the next square is 6²=36 (option C) or 7²=
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
70
149
47
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 72/149 (48%) of the model's chain of thought. What does the model currently think the answer is?
7 squared (49), 6 squared (36), 8 squared (64), etc. But how does that relate to 34 and 43?
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
71
149
48
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 73/149 (48%) of the model's chain of thought. What does the model currently think the answer is?
49? But then why is 34 and 43 related? Maybe not. Alternatively, maybe the numbers are related to their squares. Let me think. 34 and 43. 34 is 5^
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
72
149
48
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 74/149 (49%) of the model's chain of thought. What does the model currently think the answer is?
not directly about squares. Unless there's another pattern
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
73
149
49
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 75/149 (50%) of the model's chain of thought. What does the model currently think the answer is?
B)52, since reversing digits and sum of digits both lead to that. Let me check again. If the relationship is reversing digits, then 34 becomes 43, so 25 becomes 52. If the relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
74
149
50
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 76/149 (51%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
75
149
51
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 77/149 (51%) of the model's chain of thought. What does the model currently think the answer is?
B)52. Because reversing digits gives 52, and the sum of digits is same. So I think B is the answer. Let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
76
149
51
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 78/149 (52%) of the model's chain of thought. What does the model currently think the answer is?
likely B)52, since reversing the digits of 34 gives 43, and reversing 25 gives 52. Also, the sum of digits is same. So both patterns lead to B. So I think the answer
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
77
149
52
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 79/149 (53%) of the model's chain of thought. What does the model currently think the answer is?
B)52, since reversing the digits of 34 gives 43, and reversing 25 gives 52. Also, the sum of digits is same. So both patterns lead to B. So I think the answer is
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
78
149
53
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 80/149 (53%) of the model's chain of thought. What does the model currently think the answer is?
B)52, since reversing the digits of 34 gives 43, and reversing 25 gives 52. Also, the sum of digits is same. So both patterns lead to B. So I think the answer is
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
79
149
53
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 81/149 (54%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check if there's another possible relationship
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
80
149
54
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 82/149 (55%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
81
149
55
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 83/149 (55%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
82
149
55
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 84/149 (56%) of the model's chain of thought. What does the model currently think the answer is?
B
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
83
149
56
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 85/149 (57%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
84
149
57
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 86/149 (57%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
85
149
57
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 87/149 (58%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
86
149
58
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 88/149 (59%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
87
149
59
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 89/149 (59%) of the model's chain of thought. What does the model currently think the answer is?
25 + 9 = 34, but 34 isn't an option. Wait, but maybe the difference is 9, but in another way. For example, 34 + 9 = 43. If
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
88
149
59
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 90/149 (60%) of the model's chain of thought. What does the model currently think the answer is?
34? But 34 isn't an option. Wait, but maybe the difference is multiplied? Or something else. Alternatively, maybe the difference between the digits? Let's see, 34: 4 - 3 =
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
89
149
60
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 91/149 (61%) of the model's chain of thought. What does the model currently think the answer is?
not that. Alternatively, maybe 34 + 43 = 77. Not sure. 25 + ? = something? Not sure
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
90
149
61
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 92/149 (61%) of the model's chain of thought. What does the model currently think the answer is?
B)52. So I think the answer is B
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
91
149
61
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 93/149 (62%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
92
149
62
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 94/149 (63%) of the model's chain of thought. What does the model currently think the answer is?
25 + 9 = 34, but that's not an option. Wait, but maybe the difference is 9, but in the other direction? 34 + 9 = 43. So if we take
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
93
149
63
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 95/149 (63%) of the model's chain of thought. What does the model currently think the answer is?
B)52
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
94
149
63
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 96/149 (64%) of the model's chain of thought. What does the model currently think the answer is?
B)52. Because reversing the digits of 34 gives 43, and reversing 25 gives 52. Also, the sum of digits is same. So both patterns point to B. So I think the answer is
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
95
149
64
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 97/149 (65%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
96
149
65
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 98/149 (65%) of the model's chain of thought. What does the model currently think the answer is?
B)52. But let me check again. If the relationship is reversing digits, then 25 becomes 52. If the relationship is digit sum, then 25 (sum 7) needs a number with sum 7
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
97
149
65
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 99/149 (66%) of the model's chain of thought. What does the model currently think the answer is?
B)52. Since both the digit reversal and digit sum match. So I think the answer is B
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
98
149
66
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 100/149 (67%) of the model's chain of thought. What does the model currently think the answer is?
52, which is 5 and 2, adding to 7. So that's the same as the sum of digits. So that's another way to think about it
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
99
149
67
B
cot_answer_trajectory
Activations from 75 positions across layers 9, 18, 27, representing sentence 101/149 (67%) of the model's chain of thought. What does the model currently think the answer is?
a number whose digits add to 7. Which is 52. So that's B
9
[ 9, 18, 27 ]
75
[ 151644, 872, 198, 18, 19, 549, 220, 19, 18, 3504, 220, 17, 20, 549, 1939, 32, 8, 19, 24, 198, 33, 8, 20, 17, 198, 34, 8, 18, 21, 198, 35, 8, 21, 19, 198, 36, 8, 20, 21, 271, 16141, 448, 279, 6524, 13, 151645, 198, 151644, ...
[ 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 8, 16, 25, 33, 41, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, ...
100
149
67
B
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