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The dataset generation failed
Error code: DatasetGenerationError
Exception: CastError
Message: Couldn't cast
model: string
probe: string
target: string
produced: bool
induced: bool
actual_tokens: list<item: string>
child 0, item: string
canonical_tokens: list<item: string>
child 0, item: string
non_canonical: bool
excluded: bool
text: string
seed: int64
temperature: double
domain: string
generated_ids: list<item: int64>
child 0, item: int64
canonical_ids: list<item: int64>
child 0, item: int64
prompt: string
exclude_reason: string
spans: list<item: struct<surface: string, actual: list<item: string>, canonical: list<item: string>>>
child 0, item: struct<surface: string, actual: list<item: string>, canonical: list<item: string>>
child 0, surface: string
child 1, actual: list<item: string>
child 0, item: string
child 2, canonical: list<item: string>
child 0, item: string
to
{'model': Value('string'), 'domain': Value('string'), 'prompt': Value('string'), 'seed': Value('int64'), 'temperature': Value('float64'), 'excluded': Value('bool'), 'non_canonical': Value('bool'), 'generated_ids': List(Value('int64')), 'canonical_ids': List(Value('int64')), 'text': Value('string'), 'spans': List({'surface': Value('string'), 'actual': List(Value('string')), 'canonical': List(Value('string'))}), 'exclude_reason': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1816, in _prepare_split_single
for key, table in generator:
^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 613, in wrapped
for item in generator(*args, **kwargs):
~~~~~~~~~^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
model: string
probe: string
target: string
produced: bool
induced: bool
actual_tokens: list<item: string>
child 0, item: string
canonical_tokens: list<item: string>
child 0, item: string
non_canonical: bool
excluded: bool
text: string
seed: int64
temperature: double
domain: string
generated_ids: list<item: int64>
child 0, item: int64
canonical_ids: list<item: int64>
child 0, item: int64
prompt: string
exclude_reason: string
spans: list<item: struct<surface: string, actual: list<item: string>, canonical: list<item: string>>>
child 0, item: struct<surface: string, actual: list<item: string>, canonical: list<item: string>>
child 0, surface: string
child 1, actual: list<item: string>
child 0, item: string
child 2, canonical: list<item: string>
child 0, item: string
to
{'model': Value('string'), 'domain': Value('string'), 'prompt': Value('string'), 'seed': Value('int64'), 'temperature': Value('float64'), 'excluded': Value('bool'), 'non_canonical': Value('bool'), 'generated_ids': List(Value('int64')), 'canonical_ids': List(Value('int64')), 'text': Value('string'), 'spans': List({'surface': Value('string'), 'actual': List(Value('string')), 'canonical': List(Value('string'))}), 'exclude_reason': Value('string')}
because column names don't match
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1369, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
~~~~~~~~~~~~~~~~~~~~~~~~~^
builder, max_dataset_size_bytes=max_dataset_size_bytes
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 948, in stream_convert_to_parquet
builder._prepare_split(split_generator=splits_generators[split], file_format="parquet")
~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1683, in _prepare_split
for job_id, done, content in self._prepare_split_single(
~~~~~~~~~~~~~~~~~~~~~~~~~~^
gen_kwargs=gen_kwargs, job_id=job_id, **_prepare_split_args
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
):
^
File "/usr/local/lib/python3.14/site-packages/datasets/builder.py", line 1869, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
model string | domain string | prompt string | seed int64 | temperature float64 | excluded bool | non_canonical bool | generated_ids list | canonical_ids list | text string | spans list | exclude_reason string |
|---|---|---|---|---|---|---|---|---|---|---|---|
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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279,
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141... | To compute the sum of 48251 and 39987 digit by digit, we start adding each column from right to left, starting with the units place, and move to the left. If a column's sum is 10 or more, we carry the tens digit to the next column.
1. Units place: 1 + 7 = 8
2. Tens place: 5 + 8 = 13 (we write down 3 and carry 1)
3. Hu... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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488,
220,
22,
... | Sure, let's compute \( 48251 + 39987 \) digit by digit.
Starting from the rightmost digit:
1. **Units place**: \( 1 + 7 = 8 \).
2. **Tens place**: \( 5 + 8 = 13 \), write down \( 3 \) and carry \( 1 \) to the next place.
3. **Hundreds place**: \( 2 + 9 = 11 \), write down \( 1 \) and carry \( 1 \) to the next place.
... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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320... | [
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5109,
553,
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11,
5916,
504,
279,
1290,
3562,
15723,
320... | Sure! Let's break it down step by step. The addition problem is:
48251
+ 39987
We'll add these numbers by column, starting from the rightmost digit (units place):
```
48251
+ 39987
-------
```
Working from right to left:
1. Units place: \( 1 + 7 = 8 \)
2. Tens place: \( 5 + 8 = 13 \). Write down 3, carry over 1.... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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25,
17767,
220,
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488,
220,
22,
284,
220,
23,
1124,
4292,
17,
13,... | Certainly! Let's compute \( 48251 + 39987 \) digit by digit.
1. Start with the ones place: \( 1 + 7 = 8 \).
2. Move to the tens place: \( 5 + 8 = 13 \). Write down 3 and carry over 1.
3. Move to the hundreds place: \( 2 + 9 + 1 = 12 \). Write down 2 and carry over 1.
4. Move to the thousands place: \( 8 + 3 + 1 = 12 \... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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279,
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3562,
18509,
320,
25643,
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8,
323,
975,
1039,
... | Certainly! Let's compute the sum of **48251 + 39987** digit by digit. We'll add the numbers starting from the rightmost digits (units place) and work our way to the leftmost digits (thousands place) step by step.
### Digit-by-Digit Addition:
1. **First, align the numbers by place values:**
```
48251
+ 39987... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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16... | [
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1447,
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3070,
26314,
1992,
66963,
220,
16... | Sure, I can assist with that. Let's compute \(48251 + 39987\) digit by digit.
Starting from the rightmost digits:
1. **Units place:** 1 + 7 = 8
2. **Tens place:** 5 + 8 = 13 (write down 3, carry over 1)
3. **Hundreds place:** 2 + 9 + 1 (carry over) = 12 (write down 2, carry over 1)
4. **Thousands place:** 8 + 9 + 1 (... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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8,
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311,
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14822... | [
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3562,
15723,
320,
25643,
1992,
8,
323,
7218,
311,
279,
2115,
382,
14374,
14822... | To compute 48251 + 39987 digit by digit, we'll follow the process of addition starting from the rightmost digit (units place) and moving to the left.
### Step-by-step Addition
1. **Units place**:
- 1 + 7 = 8
2. **Tens place**:
- 5 + 8 = 13
- Since we have a carry over (1), we write 3 and carry over 1 to the... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
1249,
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28447,
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24... | [
1249,
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24,
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22,
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28447,
13874,
19324,
24... | To compute 48251 + 39987 digit by digit, we proceed as follows:
```
48251
+ 39987
---------
```
Starting from the rightmost digit:
1. 1 + 7 = 8
2. 5 + 8 = 13 (write down 3, carry 1)
3. 1 + 9 + 1 (carried) = 11 (write down 1, carry 1)
4. 8 + 8 + 1 (carried) = 17 (write down 7, carry 1)
5. 3 + 4 (carried) = 7
So:
... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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481,... | [
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724,
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1019,
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481,
220,
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488,
220,
23,
481,... | Sure, I'll work through this digit by digit:
1. **Units Column:**
- 1 + 7 = 8
2. **Tens Column:**
- 1 + 8 - 2 carrying over (from the previous units sum)
1 + 8 = 9
9 - 2 = 7
- (Remember, we need to borrow from the hundreds column)
3. **Hundreds Column:**
- 2 - 1 carried over (from the previous ... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
10061,
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553,
3019,
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13874,
... | [
10061,
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20,
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198,
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220,
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24,
24,
23,
22,
198,
13874,
... | Let's add the two numbers step by step:
**Step 1: Align the numbers vertically by their place values.**
```
48251
+ 39987
```
**Step 2: Start adding from the rightmost digit (the units place).**
```
48251
+ 39987
------
1
```
So, the sum of 48251 and 39987 is 88238. | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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... | [
1249,
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24,
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5692,
594,
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432,
594,
2814,
1447,
16,
13,
3070,
26314,
1992,
95518,
... | To compute 48251 + 39987 digit by digit, we start with the ones place and move to the left. Here's how it's done:
1. **Units place**: 1 + 7 = 8
2. **Tens place**: 5 + 8 = 13 (write down 3 and carry over 1)
3. **Hundreds place**: 2 + 9 = 11 (write down 1 and carry over 1)
4. **Thousands place**: 8 + 3 = 11 (write down ... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Compute 48251 + 39987 and show your work digit by digit. | 31 | 1 | false | false | [
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510,
256,
41233,
414,
220,
19,
23,
17,
20,
16,
198,
262,
488,
220,
18,
24,
24,
23,
22,
198,
256,
99... | Certainly! Here are the steps to add these two numbers digit by digit:
1. **Align the numbers vertically**:
```
48251
+ 39987
```
2. **Add the units (ones) column**:
```
1
+ 7
______
8
```
3. **Move to the tens column**:
```
5
+ 8
______
9
```
4. **Next,... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | true | [
1249,
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1447,
14374,
14822,
220,
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510,
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11,
5285,
279,
5109,
50935,
11,
... | [
1249,
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23,
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220,
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19,
16,
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1447,
14374,
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16,
510,
5338,
11,
5285,
279,
5109,
50935,
11,
... | To calculate \(7823 \times 941\), we can use the standard multiplication method. Here’s the step-by-step process:
### Step 1:
First, align the numbers vertically, making sure the last digits (ones place) are aligned:
```
7823
× 941
------
```
### Step 2:
Multiply each digit of 7823 by 1 (units place of 941):
```
... | [
{
"surface": " ",
"actual": [
" ",
" "
],
"canonical": [
" "
]
}
] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
1249,
11047,
17767,
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23,
17,
18,
1124,
15136,
220,
24,
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16,
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803,... | [
1249,
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23,
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16,
553,
220,
22,
320,
11284,
220,
22,
23,
17,
18,
374,
264,
2699,
803,... | To calculate \(7823 \times 941\), you can break it down into more manageable steps by first multiplying 941 by 7 (since 7823 is a bit more than 7800, you can do a rough estimation using 7800 for simplicity):
\[ 7800 \times 941 = 7313800 \]
Next, do the actual multiplication for the difference from the part above whic... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
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0,
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... | [
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369,
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22,
23,
17,
18,
646,
387,
10865,
1495,
438,
... | Certainly! Let's solve 7823 * 941 step by step.
### Step 1: Break down the larger number into components for easier multiplication.
7823 can be broken down as:
- 7800 (700 * 11)
- 80 (8 * 10)
- 20 (2 * 10)
- 3 (3 * 1)
So, 7823 = 7800 + 80 + 20 + 3
### Step 2: Break down the smaller number into components for easier... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
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1... | [
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220,
1... | To perform the multiplication of 7823 and 941, we can break it down into a series of simpler multiplications. Here's how you can do it step by step:
### Step 1: Break Down Multiplication
- First, break the multiplication down into additions: \(7823 \times 941 = 7823 \times (900 + 40 + 1)\).
### Step 2: Add the Multip... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
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1... | [
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1... | Sure, let's break down the multiplication of 7823 by 941 into several steps.
**Step 1: Writing the Multiplication**
\[ 7823 \times 941 \]
**Step 2: Horizontal (column) multiplication**
1. Multiply the number in the ones place of 941 (1) by each digit of 7823, starting from the right:
- \(1 \times 3 = 3\)
- \(... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
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71059,
220,
22,
... | Certainly! Let's work through the multiplication step by step:
### First, let's outline the multiplication:
\[ 7823 \times 941 \]
### Step 1: Multiply 7823 by 1 (941 * 1).
```
7823
x 941
---------
```
The multiplication of any number by 1 remains the same number. So:
```
7823
x 941
---------
7823
```
... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
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35181,
71465,
... | [
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70028,
7354,
382,
14374,
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220,
16,
25,
71059,
279,
35181,
71465,
... | To calculate \( 7823 \times 941 \), we can use the standard multiplication algorithm. We'll break it down into manageable steps.
### Step 1: Multiply the Units Digit
First, we multiply the units digit of 7823 by the tens digit of 941:
- The units digit of 7823 is 3, and the tens digit of 941 is 1 (implied by placement... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
1249,
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5297,
5486,
1447,
... | [
1249,
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1667,
264,
5297,
5486,
1447,
... | To multiply a three-digit number by a two-digit number, you can break down the process into simpler steps. I will explain the multiplication of 7823 by 941 using a standard approach:
**1)** First multiply 7823 by 0:
```
7823
*0
----------
0
```
**2)** Now, multiply 7823 by 9:
```
7823
* 9
---
6845
```
**3)** Next... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
1249,
30270,
220,
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18,
553,
220,
24,
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11,
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30270,
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553,
220,
19... | [
1249,
30270,
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22,
23,
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24,
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24,
15,
15,
11,
323,
1221,
30270,
220,
22,
23,
17,
18,
553,
220,
19... | To multiply 7823 by 941, we can break it down into two steps: first, multiply 7823 by 900, and then multiply 7823 by 40 (since 941 = 900 + 41), and then add the two results together. However, a simpler approach is to multiply directly.
Let's perform the multiplication step by step:
1. Multiply 7823 by 940 (900 + 40):... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
1249,
11047,
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23,
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18,
1124,
15136,
220,
24,
19,
16,
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8661,
21937,
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1492,
13,
43... | [
1249,
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22,
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16,
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2578,
1492,
13,
43... | To calculate \(7823 \times 941\), we can break it down into simpler steps. Since both numbers are relatively large, breaking them into smaller numbers for easier calculation might help. However, in this case, we'll use a straightforward multiplication:
Let's multiply each digit of 7823 by each digit of 941 and then ad... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
1249,
11047,
220,
22,
23,
17,
18,
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220,
24,
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11,
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70028,
5479,
166... | [
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5479,
166... | To calculate 7823 * 941, it's not necessary to perform a full multiplication of such large numbers at once. Instead, you can break down the calculation into smaller, more manageable parts using the distributive property of multiplication, also known as the FOIL method when dealing with binomials, or by using simpler de... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | What is 7823 * 941? Work through it step by step. | 31 | 1 | false | false | [
95456,
0,
6771,
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220,
22,
23,
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70028,
5479,
... | [
95456,
0,
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279,
5109,
198,
1654,
646,
1438,
1817,
1372,
1495,
1119,
803,
70028,
5479,
... | Certainly! Let's calculate \( 7823 \times 941 \) step by step.
### Step 1: Break down the numbers
We can break each number down into more manageable parts:
\[ 7823 = 7000 + 800 + 20 + 3 \]
\[ 941 = 9000 + 400 + 1 \]
### Step 2: Distribute the multiplication
Now, we distribute the multiplication by \( 941 \) to each p... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
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481,
220,
24,
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24,
24,
24,
24,
24,
198,
256,
48... | Certainly! Let's add the numbers step by step:
1. Start with the rightmost digits of each number.
2. Adding the last digits:
- 9 from 199999
- 2 from 800002
- 8 from 45678
- Result: 9 + 2 + 8 = 19
3. Write down the last digit 9 and carry over 1 to the next column.
4. Now add the next digits along with t... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
95456,
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220,
19,
20,
11,
21,
22,
23,
271,
8304,
220,
16,
25,
40580,
279,
5... | Certainly! Let's add the numbers step by step:
Given numbers: 199,999, 800,002, and 45,678
Step 1: Arrange the numbers vertically:
```
199,999
800,002
45,678
---------
```
Step 2: Add the numbers column by column from right to left, starting with the units place:
1. Add the units: 3 + 2 + 8 = 13
Write dow... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
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382,
14374,
14822,
220,
16,
25,
49472,
279,
5109,
50935,
553,
1992,
897,
510,
13874,
3989,
220,
220... | Sure, I'll add these numbers step by step. Let's break down the addition into easier steps and compute the result.
### Step 1: Align the numbers vertically by place value:
```
199999
+ 800002
+ 45678
---------
```
### Step 2: Start adding from the rightmost digit (units place):
```
199999
+ 800002
+ 45678
-... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
1249,
11625,
279,
5256,
3491,
17767,
16,
24,
24,
24,
24,
24,
488,
220,
23,
15,
15,
15,
15,
17,
488,
220,
19,
20,
21,
22,
23,
59,
701,
582,
3278,
1438,
432,
1495,
1119,
7354,
1447,
8304,
220,
16,
25,
49472,
279,
5109,
553,
862,... | [
1249,
11625,
279,
5256,
3491,
17767,
16,
24,
24,
24,
24,
24,
488,
220,
23,
15,
15,
15,
15,
17,
488,
220,
19,
20,
21,
22,
23,
59,
701,
582,
3278,
1438,
432,
1495,
1119,
7354,
1447,
8304,
220,
16,
25,
49472,
279,
5109,
553,
862,... | To solve the addition problem \(199999 + 800002 + 45678\), we'll break it down into steps:
Step 1: Align the numbers by their place values:
\[
\begin{array}{cccccc}
& 1 & 9 & 9 & 9 & 9 & \\
& 8 & 0 & 0 & 0 & 0 & 2 \\
+ & 4 & 5 & 6 & 7 & 8 & \\
\hline
\end{array}
\]
Step 2: Add the numbers starting from the rightmos... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
39814,
11,
358,
3278,
1438,
1495,
419,
5256,
3491,
1119,
7354,
1447,
16,
8,
5512,
11,
1077,
594,
738,
705,
279,
3491,
438,
264,
16202,
5256,
3491,
510,
256,
220,
16,
24,
24,
24,
24,
24,
198,
10,
23,
15,
15,
15,
15,
17,
198,
10... | [
39814,
11,
358,
3278,
1438,
1495,
419,
5256,
3491,
1119,
7354,
1447,
16,
8,
5512,
11,
1077,
594,
738,
705,
279,
3491,
438,
264,
16202,
5256,
3491,
510,
256,
220,
16,
24,
24,
24,
24,
24,
198,
10,
23,
15,
15,
15,
15,
17,
198,
10... | Sure, I'll break down this addition problem into steps:
1) First, let's set up the problem as a horizontal addition problem:
199999
+800002
+ 45678
__________
2) Now, we'll add from right to left:
9+8+2=29
So now we have 0 (carried over) and 9+0=9
3) Moving left:
9+0+5=14
So now we have 4 and carry o... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
1249,
912,
279,
5109,
220,
16,
24,
24,
24,
24,
24,
11,
220,
23,
15,
15,
15,
15,
17,
11,
323,
220,
19,
20,
21,
22,
23,
3019,
14319,
29208,
11,
1795,
1493,
7354,
1447,
16,
13,
49472,
279,
5109,
553,
862,
1992,
2750,
510,
256,
... | [
1249,
912,
279,
5109,
220,
16,
24,
24,
24,
24,
24,
11,
220,
23,
15,
15,
15,
15,
17,
11,
323,
220,
19,
20,
21,
22,
23,
3019,
14319,
29208,
11,
1795,
1493,
7354,
1447,
16,
13,
49472,
279,
5109,
553,
862,
1992,
2750,
510,
256,
... | To add the numbers 199999, 800002, and 45678 step-by-step, follow these steps:
1. Align the numbers by their place values:
```
199999
800002
+ 45678
```
2. Add the digits in the ten millions place:
```
1 (from the first number)
+ 8 (from the second number)
- - - - - - - - - - - -
... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
912,
279,
5109,
3019,
553,
3019,
1447,
1654,
614,
510,
16,
24,
24,
24,
24,
24,
488,
220,
23,
15,
15,
15,
15,
17,
488,
220,
19,
20,
21,
22,
23,
271,
16,
13,
5512,
11,
1077,
594,
5285,
279,
5109,
553,
862,... | [
95456,
0,
6771,
594,
912,
279,
5109,
3019,
553,
3019,
1447,
1654,
614,
510,
16,
24,
24,
24,
24,
24,
488,
220,
23,
15,
15,
15,
15,
17,
488,
220,
19,
20,
21,
22,
23,
271,
16,
13,
5512,
11,
1077,
594,
5285,
279,
5109,
553,
862,... | Certainly! Let's add the numbers step by step:
We have:
199999 + 800002 + 45678
1. First, let's align the numbers by their place values:
```
199999
+ 800002
+ 45678
```
2. Now, we'll add from right to left, starting with the units place.
3. Units place:
9 + 2 + 8 = 29
Write down 9 and carry over 2 to the te... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
39814,
11,
1077,
594,
912,
1493,
5109,
3019,
14319,
29208,
1447,
16,
13,
5512,
11,
1077,
594,
30893,
279,
5109,
1447,
256,
220,
16,
24,
24,
24,
24,
24,
198,
256,
488,
220,
23,
15,
15,
15,
15,
17,
198,
256,
488,
220,
19,
20,
21... | [
39814,
11,
1077,
594,
912,
1493,
5109,
3019,
14319,
29208,
1447,
16,
13,
5512,
11,
1077,
594,
30893,
279,
5109,
1447,
256,
220,
16,
24,
24,
24,
24,
24,
198,
256,
488,
220,
23,
15,
15,
15,
15,
17,
198,
256,
488,
220,
19,
20,
21... | Sure, let's add these numbers step-by-step:
1. First, let's arrange the numbers:
199999
+ 800002
+ 45678
2. Now, it's easier to align them by place value:
199999
+ 800002
+ 45678
------
245677
3. Let's see how it adds up step by step:
- Start from the rightmost digits: 9... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | true | [
1249,
912,
279,
5109,
220,
16,
24,
24,
24,
24,
24,
11,
220,
23,
15,
15,
15,
15,
17,
11,
323,
220,
19,
20,
21,
22,
23,
3019,
14319,
29208,
11,
1795,
1493,
7354,
1447,
14374,
14822,
220,
16,
25,
49472,
279,
5109,
553,
862,
1992,... | [
1249,
912,
279,
5109,
220,
16,
24,
24,
24,
24,
24,
11,
220,
23,
15,
15,
15,
15,
17,
11,
323,
220,
19,
20,
21,
22,
23,
3019,
14319,
29208,
11,
1795,
1493,
7354,
1447,
14374,
14822,
220,
16,
25,
49472,
279,
5109,
553,
862,
1992,... | To add the numbers 199999, 800002, and 45678 step-by-step, follow these steps:
### Step 1: Align the numbers by their place values
Write the numbers one below the other, aligning them by the digit groups:
```
199999
800002
+ 45678
```
### Step 2: Add the rightmost digit
Add the digits in the ones place:
```
19... | [
{
"surface": " ",
"actual": [
" ",
" "
],
"canonical": [
" "
]
}
] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
1438,
1495,
279,
5256,
3019,
553,
3019,
1447,
16,
13,
3070,
4562,
10771,
95518,
220,
24,
488,
220,
17,
488,
220,
23,
198,
256,
481,
220,
24,
488,
220,
17,
284,
220,
16,
16,
198,
256,
481,
2691,
220,
16,
311,... | [
95456,
0,
6771,
594,
1438,
1495,
279,
5256,
3019,
553,
3019,
1447,
16,
13,
3070,
4562,
10771,
95518,
220,
24,
488,
220,
17,
488,
220,
23,
198,
256,
481,
220,
24,
488,
220,
17,
284,
220,
16,
16,
198,
256,
481,
2691,
220,
16,
311,... | Certainly! Let's break down the addition step by step:
1. **Unit Place**: 9 + 2 + 8
- 9 + 2 = 11
- Add 1 to the unit place. Now we have 0 + 0 + 1 (the leftover 1).
- Result: Let's add this result to the next place.
2. **Ten's Place**: 9 + 0 + 2 + 7 (carry over from unit place) = 18
- 18 is more than 10, s... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
39814,
11,
1077,
594,
912,
1493,
2326,
5109,
3019,
14319,
29208,
1447,
14374,
14822,
220,
16,
25,
49472,
279,
5109,
50935,
198,
13874,
3989,
220,
220,
16,
24,
24,
24,
24,
24,
198,
10,
220,
23,
15,
15,
15,
15,
17,
198,
10,
220,
2... | [
39814,
11,
1077,
594,
912,
1493,
2326,
5109,
3019,
14319,
29208,
1447,
14374,
14822,
220,
16,
25,
49472,
279,
5109,
50935,
198,
13874,
3989,
220,
220,
16,
24,
24,
24,
24,
24,
198,
10,
220,
23,
15,
15,
15,
15,
17,
198,
10,
220,
2... | Sure, let's add these three numbers step-by-step:
### Step 1: Align the numbers vertically
```
199999
+ 800002
+ 45678
```
### Step 2: Add the numbers starting from the rightmost digit:
#### 1. Ones place:
```
+ 9
+ 2
+ 8
```
Adding these together:
```
199999
+ 800002
+ 45678
------
9
```
#### ... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Add these: 199999 + 800002 + 45678. Show each step. | 31 | 1 | false | false | [
39814,
11,
1077,
594,
912,
1493,
5109,
3019,
553,
3019,
1447,
16,
13,
3070,
2212,
279,
1156,
1378,
5109,
25,
1019,
256,
1124,
9640,
256,
220,
16,
24,
24,
24,
24,
24,
488,
220,
23,
15,
15,
15,
15,
17,
284,
17607,
256,
1124,
2533,... | [
39814,
11,
1077,
594,
912,
1493,
5109,
3019,
553,
3019,
1447,
16,
13,
3070,
2212,
279,
1156,
1378,
5109,
25,
1019,
256,
1124,
9640,
256,
220,
16,
24,
24,
24,
24,
24,
488,
220,
23,
15,
15,
15,
15,
17,
284,
17607,
256,
1124,
2533,... | Sure, let's add these numbers step by step:
1. **Add the first two numbers:**
\[
199999 + 800002 = ?
\]
First, align the numbers by their place values:
\[
\begin{array}{c@{}c@{}c}
& 1 & 9 & 9 & 9 & 9 \\
+ & 8 & 0 & 0 & 0 & 2 \\
\end{array}
\]
Add the units place: \(9 + 2 = 11\) (w... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
2736,
279,
1293,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
382,
13874,
3989,
981,
220,
16,
17,
18,
19,
198,
256,
24768,
220,
20,
21,
22,
23,
198,
256,
32671,
12924,
256,
220,
24,
17,
22,
... | [
95456,
0,
6771,
594,
2736,
279,
1293,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
382,
13874,
3989,
981,
220,
16,
17,
18,
19,
198,
256,
24768,
220,
20,
21,
22,
23,
198,
256,
32671,
12924,
256,
220,
24,
17,
22,
... | Certainly! Let's perform the long multiplication of 1234 by 5678.
```
1234
× 5678
_______
92752 (1234 × 8)
91708 (1234 × 7, bring down a decimal point)
61700 (1234 × 6, multiply by 10, then add the previous 91708)
12340 (1234 × 5, multiply by 10, then add the previous 61700)
_________
70741... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
279,
1293,
46444,
1714,
382,
8420,
594,
279,
3019,
14319,
29208,
1882,
1447,
13874,
3989,
257,
220,
16,
17,
18,
19,
198,
87,
220,
220,
20,
21,
22,
... | [
95456,
0,
6771,
594,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
279,
1293,
46444,
1714,
382,
8420,
594,
279,
3019,
14319,
29208,
1882,
1447,
13874,
3989,
257,
220,
16,
17,
18,
19,
198,
87,
220,
220,
20,
21,
22,
... | Certainly! Let's multiply 1234 by 5678 using the long multiplication method.
Here's the step-by-step process:
```
1234
x 5678
==========
10072 (1234 x 8)
800120 (1234 x 60, shift one place to the left)
670800 (1234 x 500, shift two places to the left)
7170200 (1234 x 100, shift thr... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
279,
1293,
46444,
1714,
382,
14374,
14822,
220,
16,
25,
2573,
705,
279,
46444,
198,
59,
9640,
59,
7265,
90,
1653,
15170,
81,
532,
16,
17,
18,
19,
... | [
95456,
0,
6771,
594,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
279,
1293,
46444,
1714,
382,
14374,
14822,
220,
16,
25,
2573,
705,
279,
46444,
198,
59,
9640,
59,
7265,
90,
1653,
15170,
81,
532,
16,
17,
18,
19,
... | Certainly! Let's multiply 1234 by 5678 using the long multiplication method.
### Step 1: Set up the multiplication
\[
\begin{array}{r}
1234 \\
\times 5678 \\
\end{array}
\]
### Step 2: Multiply 1234 by 8 (the last digit of 5678)
\[
1234 \times 8 = 9872
\]
Bring down this number.
\[
\begin{array}{r}
1234 \\
\sqrt{ \p... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
1249,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
11,
1795,
1493,
7354,
1447,
16,
13,
9645,
279,
8131,
1372,
389,
1909,
323,
279,
9155,
1372,
3685,
11,
5285,
287,
279,
18509,
320,
29280,
287,
429,
220,
16,
17,
18,
19,
... | [
1249,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
11,
1795,
1493,
7354,
1447,
16,
13,
9645,
279,
8131,
1372,
389,
1909,
323,
279,
9155,
1372,
3685,
11,
5285,
287,
279,
18509,
320,
29280,
287,
429,
220,
16,
17,
18,
19,
... | To multiply 1234 by 5678, follow these steps:
1. Write the larger number on top and the smaller number below, aligning the digits (remembering that 1234 has 4 digits and 5678 has 5 digits).
```
1234
× 5678
_________
```
2. Multiply 1234 by 8 (the units digit of 5678).
```
1234
× 8
------
... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
2736,
279,
1293,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
3019,
553,
3019,
382,
13874,
3989,
257,
220,
16,
17,
18,
19,
198,
220,
24768,
256,
220,
20,
21,
22,
23,
198,
220,
32671,
5973,
19... | [
95456,
0,
6771,
594,
2736,
279,
1293,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
3019,
553,
3019,
382,
13874,
3989,
257,
220,
16,
17,
18,
19,
198,
220,
24768,
256,
220,
20,
21,
22,
23,
198,
220,
32671,
5973,
19... | Certainly! Let's perform the long multiplication of 1234 by 5678 step by step.
```
1234
× 5678
_________
10232 (1234 × 8)
73628 (1234 × 70, shifted one position to the left)
61682 (1234 × 600, shifted two positions to the left)
12340 (1234 × 5000, shifted thre... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | true | [
39814,
11,
1077,
594,
728,
1526,
279,
1293,
46444,
1882,
369,
84192,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
13,
12090,
315,
9027,
264,
9124,
3019,
14319,
29208,
1293,
46444,
11,
358,
3278,
4936,
21101,
279,
1882,
1447,
16,
... | [
39814,
11,
1077,
594,
728,
1526,
279,
1293,
46444,
1882,
369,
84192,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
13,
12090,
315,
9027,
264,
9124,
3019,
14319,
29208,
1293,
46444,
11,
358,
3278,
4936,
21101,
279,
1882,
1447,
16,
... | Sure, let's go through the long multiplication process for multiplying 1234 by 5678. Instead of showing a visual step-by-step long multiplication, I'll simply outline the process:
1. Write the numbers vertically, spacing them apart:
```
1234
x 5678
```
2. Multiply 1234 by 8 (the ones digit of 5678)... | [
{
"surface": " -----\n",
"actual": [
" ----",
"-\n"
],
"canonical": [
" -----\n"
]
}
] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
2014,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
11,
358,
3278,
19869,
279,
1293,
46444,
1882,
3019,
553,
3019,
13,
5692,
594,
1246,
432,
594,
2814,
1447,
13874,
3989,
286,
220,
16,
220,
17,
220,
18,
220,
19... | [
95456,
0,
2014,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
11,
358,
3278,
19869,
279,
1293,
46444,
1882,
3019,
553,
3019,
13,
5692,
594,
1246,
432,
594,
2814,
1447,
13874,
3989,
286,
220,
16,
220,
17,
220,
18,
220,
19... | Certainly! To multiply 1234 by 5678, I'll demonstrate the long multiplication process step by step. Here's how it's done:
```
1 2 3 4
× 5 6 7 8
__________________
1 2 3 4 × 8 = 9 8 7 2
1 2 3 4 × 7 = 5 6 8 6
1 2 3 4 × 6 = 3 9 8 6
1 2 3 4 × 5 = 6 2 0 9
____________________... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
2014,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
1293,
46444,
11,
582,
1795,
1493,
7354,
1447,
13874,
3989,
286,
220,
16,
17,
18,
19,
198,
87,
220,
20,
21,
22,
23,
198,
771,
6913,
13874,
3989,
16,
13... | [
95456,
0,
2014,
30270,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
1293,
46444,
11,
582,
1795,
1493,
7354,
1447,
13874,
3989,
286,
220,
16,
17,
18,
19,
198,
87,
220,
20,
21,
22,
23,
198,
771,
6913,
13874,
3989,
16,
13... | Certainly! To multiply 1234 by 5678 using long multiplication, we follow these steps:
```
1234
x 5678
-----------------
```
1. **Multiply 1234 by 8 (the last digit of 5678):**
- \(1234 \times 8 = 9872\)
2. **Shift the result one position to the left (since we're multiplying by the next digit, remember to m... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
5724,
46444,
369,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
374,
438,
11017,
1447,
13874,
3989,
981,
220,
16,
17,
18,
19,
198,
257,
24768,
220,
220,
20,
21,
22,
23,
198,
262,
32671,
5973,
198,
981,
220,
16,
15,
... | [
95456,
0,
5724,
46444,
369,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
374,
438,
11017,
1447,
13874,
3989,
981,
220,
16,
17,
18,
19,
198,
257,
24768,
220,
220,
20,
21,
22,
23,
198,
262,
32671,
5973,
198,
981,
220,
16,
15,
... | Certainly! Long multiplication for 1234 by 5678 is as follows:
```
1234
× 5678
_________
10032 (1234 × 8)
8670 (1234 × 7, shift one place to the left)
61720 (1234 × 6, shift two places to the left)
617200 (1234 × 5, shift three places to the left)
_________
7040532
```
So... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
2736,
279,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
1293,
46444,
1447,
59,
9640,
59,
7265,
90,
1653,
15170,
81,
532,
257,
220,
16,
17,
18,
19,
90155,
4955,
1733,
220,
20,
21,
22,
23... | [
95456,
0,
6771,
594,
2736,
279,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
1667,
1293,
46444,
1447,
59,
9640,
59,
7265,
90,
1653,
15170,
81,
532,
257,
220,
16,
17,
18,
19,
90155,
4955,
1733,
220,
20,
21,
22,
23... | Certainly! Let's perform the multiplication of 1234 by 5678 using long multiplication:
\[
\begin{array}{r}
1234 \\
\times 5678 \\
\hline
1234 \quad (1 \times 1234) \\
8330 \quad (2 \times 1234) \\
41620 \quad (3 \times 1234) \\
61700 \quad (4 \times 1234) \\
\hline
4522552
\end{array}
\]
Here’s how... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
6771,
594,
1191,
553,
6243,
705,
279,
1293,
46444,
315,
17767,
16,
17,
18,
19,
57758,
553,
17767,
20,
21,
22,
23,
59,
568,
1205,
1184,
311,
30270,
1817,
15723,
315,
825,
1372,
553,
1817,
15723,
315,
2441,
382,
8420,
594,
... | [
95456,
0,
6771,
594,
1191,
553,
6243,
705,
279,
1293,
46444,
315,
17767,
16,
17,
18,
19,
57758,
553,
17767,
20,
21,
22,
23,
59,
568,
1205,
1184,
311,
30270,
1817,
15723,
315,
825,
1372,
553,
1817,
15723,
315,
2441,
382,
8420,
594,
... | Certainly! Let's start by setting up the long multiplication of \(1234\) by \(5678\). We need to multiply each digit of one number by each digit of another.
Here's the multiplication:
```
1234
× 5678
=
```
Now let's multiply each digit of \(1234\) by each digit of \(5678\) from right to left, remem... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Multiply 1234 by 5678, showing the long multiplication. | 31 | 1 | false | false | [
95456,
0,
5692,
374,
279,
1293,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
11,
9027,
1817,
3019,
9355,
1447,
13874,
3989,
981,
220,
16,
17,
18,
19,
198,
256,
24768,
256,
220,
20,
21,
22,
23,
198,
220,
32671,
59... | [
95456,
0,
5692,
374,
279,
1293,
46444,
315,
220,
16,
17,
18,
19,
553,
220,
20,
21,
22,
23,
11,
9027,
1817,
3019,
9355,
1447,
13874,
3989,
981,
220,
16,
17,
18,
19,
198,
256,
24768,
256,
220,
20,
21,
22,
23,
198,
220,
32671,
59... | Certainly! Here is the long multiplication of 1234 by 5678, showing each step clearly:
```
1234
× 5678
_________
10072 (1234 × 8)
82708 (1234 × 70, shift one position to the left)
314848 (1234 × 60, shift two positions to the left)
1221520 (1234 × 500, shift three positions to the left)... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
264,
14806,
14257,
504,
279,
5888,
315,
34784,
4013,
1447,
785,
2629,
17767,
328,
1124,
8,
315,
279,
1156,
17767,
308,
1124,
8,
5810,
5109,
374,
2661,
5... | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
264,
14806,
14257,
504,
279,
5888,
315,
34784,
4013,
1447,
785,
2629,
17767,
328,
1124,
8,
315,
279,
1156,
17767,
308,
1124,
8,
5810,
5109,
374,
2661,
5... | To sum the numbers from 1 to 100, we can use a formula derived from the properties of arithmetic series:
The sum \( S \) of the first \( n \) natural numbers is given by:
\[ S = \frac{n(n + 1)}{2} \]
For \( n = 100 \):
\[ S = \frac{100 \times 101}{2} \]
Now, let's calculate the partial sums step by step to show ho... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
279,
1156,
17767,
308,
1124,
8,
5810,
5109,
13,
576,
14806,
374,
1447,
78045,
328,
284,
1124,
37018,
91362,
1445,
10,
1... | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
279,
1156,
17767,
308,
1124,
8,
5810,
5109,
13,
576,
14806,
374,
1447,
78045,
328,
284,
1124,
37018,
91362,
1445,
10,
1... | To sum the numbers from 1 to 100, we can use the formula for the sum of the first \( n \) natural numbers. The formula is:
\[ S = \frac{n(n+1)}{2} \]
For \( n = 100 \), the sum \( S \) is:
\[ S = \frac{100(100+1)}{2} = \frac{100 \times 101}{2} = \frac{10100}{2} = 5050 \]
To see the partial sums, we can look at the ... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
1477,
279,
2629,
315,
279,
5109,
504,
220,
16,
1526,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
11,
892,
374,
1447,
78045,
328,
1089,
284,
1124,
37018,
91362,
2877,
62,
16,
488,
26... | [
1249,
1477,
279,
2629,
315,
279,
5109,
504,
220,
16,
1526,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
11,
892,
374,
1447,
78045,
328,
1089,
284,
1124,
37018,
91362,
2877,
62,
16,
488,
26... | To find the sum of the numbers from 1 through 100, we can use the formula for the sum of an arithmetic series, which is:
\[ S_n = \frac{n(a_1 + a_n)}{2} \]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms,
- \( a_1 \) is the first term,
- \( a_n \) is the last term.
For the ... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
13,
576,
14806,
374,
510,
78045,
328,
1089,
284,
1124,
37018,
91362,
15170,
17,
92,
320,
64,
488,
293... | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
13,
576,
14806,
374,
510,
78045,
328,
1089,
284,
1124,
37018,
91362,
15170,
17,
92,
320,
64,
488,
293... | To sum the numbers from 1 to 100, we can use the formula for the sum of an arithmetic series. The formula is:
\[ S_n = \frac{n}{2} (a + b) \]
where:
- \( S_n \) is the sum of the first \( n \) terms,
- \( n \) is the number of terms,
- \( a \) is the first term,
- \( b \) is the last term.
In this case, \( a = 1 \), \... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
279,
1156,
17767,
308,
1124,
8,
5810,
5109,
11,
892,
374,
510,
59,
9640,
50,
1089,
284,
1124,
37018,
91362,
1445,
10,
... | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
279,
1156,
17767,
308,
1124,
8,
5810,
5109,
11,
892,
374,
510,
59,
9640,
50,
1089,
284,
1124,
37018,
91362,
1445,
10,
... | To sum the numbers from 1 to 100, we can use the formula for the sum of the first \( n \) natural numbers, which is:
\[
S_n = \frac{n(n+1)}{2}
\]
Here, \( n = 100 \). Plugging in this value, we have:
\[
S_{100} = \frac{100 \times 101}{2} = 5050
\]
To verify this by summing the numbers directly, we can use the fact tha... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
13,
576,
14806,
374,
1447,
78045,
328,
1089,
284,
1124,
37018,
91362,
2877,
62,
16,
488,
264,
1089,
9... | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
13,
576,
14806,
374,
1447,
78045,
328,
1089,
284,
1124,
37018,
91362,
2877,
62,
16,
488,
264,
1089,
9... | To sum the numbers from 1 to 100, we can use the formula for the sum of an arithmetic series. The formula is:
\[ S_n = \frac{n(a_1 + a_n)}{2} \]
where:
- \( n \) is the number of terms,
- \( a_1 \) is the first term,
- \( a_n \) is the last term.
In this case:
- \( n = 100 \) (since we are summing from 1 to 100),
- ... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
279,
1156,
308,
5810,
5109,
11,
892,
374,
2661,
553,
1447,
78045,
328,
284,
1124,
37018,
91362,
1445,
488,
220,
16,
913... | [
1249,
2629,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
11,
582,
646,
990,
279,
14806,
369,
279,
2629,
315,
279,
1156,
308,
5810,
5109,
11,
892,
374,
2661,
553,
1447,
78045,
328,
284,
1124,
37018,
91362,
1445,
488,
220,
16,
913... | To sum the numbers from 1 to 100, we can use the formula for the sum of the first n natural numbers, which is given by:
\[ S = \frac{n(n + 1)}{2} \]
In this case, \( n = 100 \), so the formula becomes:
\[ S = \frac{100(100 + 1)}{2} = \frac{100 \times 101}{2} = \frac{10100}{2} = 5050 \]
If we want to demonstrate the... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
39814,
0,
576,
2629,
315,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
646,
387,
16588,
1667,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
11,
892,
374,
2661,
553,
1447,
78045,
328,
284,
1124,
37018,
91362,
2877,
62,
16,
4... | [
39814,
0,
576,
2629,
315,
279,
5109,
504,
220,
16,
311,
220,
16,
15,
15,
646,
387,
16588,
1667,
279,
14806,
369,
279,
2629,
315,
458,
34784,
4013,
11,
892,
374,
2661,
553,
1447,
78045,
328,
284,
1124,
37018,
91362,
2877,
62,
16,
4... | Sure! The sum of the numbers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series, which is given by:
\[ S = \frac{n(a_1 + a_n)}{2} \]
where:
- \( S \) is the sum of the series,
- \( n \) is the number of terms,
- \( a_1 \) is the first term,
- \( a_n \) is the last term.
For the ser... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
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5... | Sure, I can help you sum the numbers 1 through 100. You'll notice that this sum is an example of a harmonic series, which is the sum of the reciprocals of the natural numbers.
Starting with 1:
```
Sum = 1
```
Adding the next number, 2:
```
Sum = 1 + 2 = 3
```
Adding the next number, 3:
```
Sum = 3 + 3 = 6
```
Co... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
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1445... | To sum the numbers from 1 to 100, we can use the formula for the sum of the first \( n \) positive integers, which is given by:
\[
S = \frac{n(n + 1)}{2}
\]
Here, \( n = 100 \). Plugging in this value, we get:
\[
S = \frac{100(100 + 1)}{2} = \frac{100 \times 101}{2} = \frac{10100}{2} = 5050
\]
So, the sum of the nu... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
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... | Here are the partial sums as you go through the numbers from 1 to 100:
1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
.
.
.
.
100 + 100 = 200
200 + 100 = 300
--------------------------------------------------------------------------------------------------
1 + 2 + 3 + 4 + 5 + ... + 99 + 100 = 5050 | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | arithmetic | Sum the numbers 1 through 100, showing partial sums as you go. | 31 | 1 | false | false | [
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9139... | To sum the numbers from 1 to 100, we can use the formula for the sum of the first \( n \) natural numbers:
\[
S_n = \frac{n(n + 1)}{2}
\]
Given \( n = 100 \):
\[
S_{100} = \frac{100(100 + 1)}{2} = \frac{100 \times 101}{2} = \frac{10100}{2} = 5050
\]
So, the sum of the numbers from 1 to 100 is \( 5050 \).
To verify... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | false | [
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1... | Madrid, ciudad capital de España y uno de los núcleos más reinfostrados de la península ibérica, tiene una historia que remonta a más de 1.000 años atrás. Fundada como el castillo de Medinaceli, abandonado en 407, durante las guerras napoleónicas y llevado por los invasores franceses, y reconstruida en 1830. Este trans... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | true | [
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Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | false | [
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Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | false | [
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Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | true | [
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Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | false | [
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Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | false | [
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Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | true | [
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1370,
409,
83115,
1187,
4734,
12842,
409,
5141,
9039,
57147,
37072,
... | [
59642,
43360,
511,
3046,
64,
662,
5093,
74327,
409,
326,
27004,
11058,
5006,
66549,
11,
2804,
16948,
13,
6485,
274,
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11,
7437,
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11,
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2062,
1370,
409,
83115,
1187,
4734,
12842,
409,
5141,
9039,
57147,
37072,
... | Esta respuesta se basa en una aplicación de lenguaje automático, qwen. Lo siento, sin embargo, puedo no ser capaz de validar la exactitud de las respuestas lingüísticas generadas, ya que no tengo un amplio conocimiento sobre el historial poblacional o gubernamental de Madrid. Sin embargo, logré recuperar mis conocimien... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Escribe un párrafo en español sobre la historia de Madrid. | 31 | 1 | false | false | [
37036,
1869,
1531,
5093,
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39357,
49375,
7924,
11,
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2584,
662,
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379,
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409,
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13,
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78,
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409,
1187,
39357,
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3802,
2123,
4154,
1674,
21470,
704,
29668,
409,
... | [
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... | Madrid es una importante ciudad española, ubicada en la provincia de Madrid y la región de Madrid. El núcleo medieval de la ciudad fue fundado por Alfonso VI de León y Castilla en 1082. En la época de la Edad Media, hablaba precisamente el castellano madrileño. Poco más tarde, el comienzo de nuestra historia como ciuda... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | true | [
27515,
3375,
650,
5473,
3193,
24267,
662,
54367,
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1887,
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45,
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11,
... | [
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650,
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321,
11,
9765,
99064,
20007,
265,
1187,
1887,
4386,
45,
3083,
11,
12962,
560... | Voici un court poème en français sur la mer :
Mouvement sauvage, menace et charmant,
Oceanique jeuil, tu vois montre la main ;
Nuit, fleuve qui traverse le ciel stratiostrophique,
Thème mélancolique de ta face pâle.
Placeur, gigantesque toile d'astrologique,
Moment d'existence à toi, lumière et silence.
Matin, soleil... | [
{
"surface": " menace",
"actual": [
" men",
"ace"
],
"canonical": [
" menace"
]
},
{
"surface": "Ocean",
"actual": [
"O",
"cean"
],
"canonical": [
"Ocean"
]
},
{
"surface": " jeuil",
"actual": [
" je",
"uil"
... | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | false | [
27515,
3375,
650,
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662,
54367,
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84334,
11,
75320,
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13,
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334,
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11,
... | [
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11,
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334,
26789,
12445,
1723,
11,
... | Voici un poème en français qui rend hommage à la mer :
**Petite mer, grande mer,
Jour et nuit, toi nous enserras.**
**Éscaleurs, bergeries, noéts
Polynesia conduis, sur nos pas bras dessus dessous.**
**Idylles, pélerins, ouvertures
Vous vous enfermez sur vos partons.**
**Et sur votre saule-taureau vous ridesz... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | false | [
27515,
3375,
650,
5473,
3193,
24267,
662,
54367,
1729,
1187,
4704,
14512,
1912,
37915,
11,
2303,
53,
5525,
34074,
11,
274,
480,
308,
580,
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1842,
12422,
84,
274,
485,
258,
11,
2303,
55999,
6021,
274,
97179,
2900,
662,
29770,
483,
... | [
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650,
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84,
274,
485,
258,
11,
2303,
55999,
6021,
274,
97179,
2900,
662,
29770,
483,
... | Voici un court poème en français sur la mer :
De là,
Vaste horizon, sable nacré et bleu serein,
Ta route s'impose en bouillonnante gaieté,
Absolutité de l'océan, sereine.
Miroitante et murmure aux teintes iridescentes,
Tu transcends ton aigle-toit de ciel;
Récit presque secret des bancs de poissons.
Cours... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | false | [
8747,
8755,
11,
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41525,
20286,
198,
73123,
8766,
17796,
963,
276,
11,
1187,
17098,
274,
6,
19667,
1003,
345,
10197,
396,
552,
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326,
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11,
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301,
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345,
55848,
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382,
45,
... | [
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345,
55848,
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29417,
7888,
409,
70481,
382,
45,
... | La Mer, immensément Large
Dans ton océan, la vie s'écrit,
Peinture sur l'eau, ciel sur mer,
Une histoire traversée de champs.
Nuit et jour, tes vastes bras sont vides,
Chez les berges sous les larmes,
Dans les flots des vents s'engouffrent,
Où sur la glace s'aoive Jules de Brunn.
Ira oceanique, qui diversifie,
Détour... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | false | [
53,
2253,
424,
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12068,
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512,
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301,
294,
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345,
69451,
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564,
266,
296,
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577,
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37731,
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324,
624,
55999,
2081,
1371,
39534,
1842,
1013,
396,
7888,
409,
68170,
324,
34... | [
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294,
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324,
624,
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1371,
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1842,
1013,
396,
7888,
409,
68170,
324,
34... | Voyage éphémère sous le ciel d'eau,
Ton éclat m'aide à retrouver mon bonheur.
Ta courbe obscure et teintée de vapeur,
Brille que je puisse te toucher sans chérir.
Je te donne le plus pur de moi,
Si cela m'en veut de te quitter.
Ne te regrette pas pas tu soleil,
Je me rends toi mère oiseau et ami.
Omer, cet océan jalo... | [] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | true | [
27515,
3375,
650,
3193,
24267,
15491,
89759,
662,
54367,
1729,
1187,
4704,
11,
108648,
87267,
85106,
33126,
104715,
104034,
11,
99999,
100431,
104927,
110121,
113460,
1447,
8747,
4704,
345,
67,
596,
512,
11825,
301,
12422,
84,
4132,
6591,
3... | [
27515,
3375,
650,
3193,
24267,
15491,
89759,
662,
54367,
1729,
1187,
4704,
11,
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87267,
85106,
33126,
104715,
104034,
11,
31838,
87752,
27091,
104927,
110121,
113460,
1447,
8747,
4704,
345,
67,
596,
512,
11825,
301,
12422,
84,
4132,
6... | Voici un poème simplifié en français sur la mer,的传统可能需要更专业的训练,所以下面是我尽力所提供的:
La mer,
dans le ciel bleu infini,
elle est comme un peintre,
tout un tableau d'aventures.
Le vent souffle, et roule,
les ondulations se détachent,
la plage, ses murs dorés.
La mer, le temps de passer.
Illustrant le Pouvoir des Flots,
le voya... | [
{
"surface": "所以下面",
"actual": [
"所以",
"下面"
],
"canonical": [
"所",
"以下",
"面"
]
}
] | null |
Qwen/Qwen2.5-1.5B-Instruct | multilingual_latin | Écris un court poème en français sur la mer. | 31 | 1 | false | true | [
27515,
3375,
650,
5473,
3193,
24267,
662,
54367,
1729,
1187,
4704,
14512,
8747,
4704,
11,
37783,
259,
13725,
15510,
1875,
345,
35,
69654,
662,
21162,
31492,
1187,
326,
2886,
624,
1925,
348,
1263,
939,
59304,
6866,
3541,
348,
13488,
345,
... | [
27515,
3375,
650,
5473,
3193,
24267,
662,
54367,
1729,
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4704,
14512,
8747,
4704,
11,
37783,
259,
13725,
15510,
1875,
345,
38025,
325,
662,
21162,
31492,
1187,
326,
2886,
624,
1925,
348,
1263,
939,
59304,
6866,
3541,
348,
13488,
345,
... | Voici un court poème en français sur la mer :
La mer, immense tapis sans fin,
Danse en silence sous la lune.
On vole des enfants dans les vagues,
Dans ce passe-temps décontracté.
Ces mers couchées au bleu criard,
Laissent entrevoir les fonds bruns,
Jardinés de drowned albies,
Du sens d'étourneaux rares.
On pêche, l'... | [
{
"surface": "Danse",
"actual": [
"D",
"anse"
],
"canonical": [
"Dan",
"se"
]
}
] | null |
End of preview.
Non-canonical tokenization in LLM generations
Per-generation records from seven language models, capturing the token IDs each model actually emitted alongside the canonical re-encoding of its own output.
Tokenization is many-to-one: many token sequences decode to the same string, but re-encoding that string recovers only the canonical sequence. So storing a transcript as text and re-tokenizing it preserves the string while silently changing the segmentation — and any analysis that operates on positions (logit lens, probes, per-position attribution, serial-depth accounting) then runs on positions the model never produced.
This dataset exists so that the rates reported in the accompanying writeup can be recomputed on CPU, without re-running generation.
Models
| model | tokenizer lineage | dtype (as released) |
|---|---|---|
gpt2 |
GPT-2 BPE | fp32 |
meta-llama/Llama-3.2-1B-Instruct |
tiktoken-derived | bf16 |
meta-llama/Llama-3.2-3B-Instruct |
tiktoken-derived | bf16 |
meta-llama/Llama-3.1-8B-Instruct |
tiktoken-derived | bf16 |
Qwen/Qwen2.5-1.5B-Instruct |
Qwen BBPE | bf16 |
google/gemma-2-2b |
SentencePiece | fp32 |
openai/gpt-oss-20b |
o200k (OpenAI) | bf16* |
*gpt-oss ships MXFP4, whose kernels need Hopper; this ran bf16-dequantized on an A100. The only model not at as-released precision.
Generation settings: temperature 1.0, pure sampling (top_k=0, top_p=1.0, repetition_penalty=1.0 — pinned explicitly, not inherited from each repo's
generation_config.json), 200 max new tokens, seed 31, transformers 4.57.6,
clean_up_tokenization_spaces=False.
Schema
One JSON object per generation (<model>.jsonl):
| field | meaning |
|---|---|
model |
model id |
domain |
english, arithmetic, code, multilingual_latin, multilingual_cyrillic, multilingual_cjk |
prompt |
the user prompt |
seed, temperature |
generation config |
generated_ids |
the token IDs the model actually emitted |
canonical_ids |
encode(decode(generated_ids)) — what a stored-as-text transcript becomes |
text |
decoded output |
non_canonical |
whether canonical_ids != generated_ids |
spans |
per differing region: surface, actual tokens, canonical tokens |
excluded, exclude_reason |
rounds trips that can't be measured (replacement_char for truncated UTF-8, non_nfc for Qwen's NFC normalizer) |
induce_<model>.jsonl holds the prompted-induction trials, with probe,
target, produced, induced, actual_tokens, canonical_tokens.
Verifying
import json
from transformers import AutoTokenizer
rows = [json.loads(l) for l in open("meta-llama_Llama-3.2-1B-Instruct.jsonl")]
tok = AutoTokenizer.from_pretrained(rows[0]["model"])
bad = tot = 0
for r in rows:
if r["excluded"]:
continue
ids = r["generated_ids"]
text = tok.decode(ids, skip_special_tokens=False,
clean_up_tokenization_spaces=False)
canon = tok.encode(text, add_special_tokens=False) # recompute, don't trust the flag
if canon != ids:
bad += sum(i2 - i1 for op, i1, i2, _, _ in __import__("difflib")
.SequenceMatcher(a=ids, b=canon, autojunk=False).get_opcodes()
if op != "equal")
tot += len(ids)
print(f"non-canonical tokens: {bad/tot:.2%}")
Or use the repo's verifier, which does this across every file and checks the recomputed values against the stored flags:
uv run python -m experiments.retok.phase2_verify *.jsonl
Gotchas if you measure this yourself
- Pin the sampling parameters. HF inherits anything unset from the model
repo's
generation_config.json, and these differ per model. Off-canonical tokens live in the distribution tail, so top-k/top-p truncation suppresses the metric — unevenly across models. - Disable
clean_up_tokenization_spaces. It shipsTruefor Llama-3.x andFalsefor GPT-2/Qwen, and destructively rewrites" ." → "."," 's" → "'s"and eight more, producing spurious non-canonical detections for one family only. - Report the dtype. This is a tail-sampling measurement and precision moves it: GPT-2 at bf16 rather than native fp32 shifts its Cyrillic rate 0.43% → 1.09%.
- Exclude unmeasurable round trips: outputs containing U+FFFD (truncated UTF-8 can't re-encode) and, for Qwen, non-NFC text (its tokenizer normalizes on encode).
Source
Code, full run log and writeup: https://github.com/brendanlong/experiments
(experiments/retok/).
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