batch int64 | id string | index int64 | level int64 | subject string | outcome string | solved int64 | shard string | attempt int64 | steps int64 | start_rate float64 | thinking_tokens int64 | status string | cut int64 | cut_char int64 | cut_token int64 | rate_before float64 | rate_after float64 | threshold float64 | confirmed bool | lost_step string | cut_share float64 | saved_tokens int64 | problem string | answer string | source string | thinking string | step_starts list | step_labels list | thinking_before_cut string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | q5354_a5 | 5,354 | 4 | Number Theory | wrong | 5 | shard02 | 4 | 253 | 0.541667 | 12,453 | cut | 96 | 16,520 | 6,899 | 0.333333 | 0.166667 | 0.270833 | true | doubt | 0.554003 | 5,554 | A palindrome is a number that reads the same forward and backward. The largest possible 4-digit palindrome in base 3 can be expressed as a 3-digit palindrome in another base $b>2$. What is $b$? | 6 | test | Okay, so I have this problem here about palindromes in different bases. Let me try to understand what it's asking.
First, a palindrome is a number that reads the same forward and backward. For example, in base 10, 121 is a palindrome because reversing the digits gives the same number. The problem says that the largest... | [
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"doubt... | Okay, so I have this problem here about palindromes in different bases. Let me try to understand what it's asking.
First, a palindrome is a number that reads the same forward and backward. For example, in base 10, 121 is a palindrome because reversing the digits gives the same number. The problem says that the largest... |
1 | q4069_a2 | 4,069 | 5 | Precalculus | truncated | 5 | shard01 | 1 | 86 | 0.375 | 16,384 | cut | 76 | 39,150 | 14,392 | 0.208333 | 0.166667 | 0.1875 | true | conclude | 0.878418 | 1,992 | When every vector on the line $y = \frac{5}{2} x + 4$ is projected onto a certain vector $\mathbf{w},$ the result is always the vector $\mathbf{p}.$ Find the vector $\mathbf{p}.$ | \begin{pmatrix} -40/29 \\ 16/29 \end{pmatrix} | train | Alright, so I have this problem here: when every vector on the line \( y = \frac{5}{2}x + 4 \) is projected onto a certain vector \( \mathbf{w} \), the result is always the same vector \( \mathbf{p} \). I need to find the vector \( \mathbf{p} \).
Hmm, okay. Let me try to unpack this step by step. First, I know that pr... | [
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"verify... | Alright, so I have this problem here: when every vector on the line \( y = \frac{5}{2}x + 4 \) is projected onto a certain vector \( \mathbf{w} \), the result is always the same vector \( \mathbf{p} \). I need to find the vector \( \mathbf{p} \).
Hmm, okay. Let me try to unpack this step by step. First, I know that pr... |
1 | q4604_a6 | 4,604 | 5 | Prealgebra | wrong | 5 | shard08 | 5 | 108 | 0.375 | 11,891 | cut | 26 | 9,243 | 2,933 | 0.25 | 0.375 | 0.1875 | false | doubt | 0.246657 | 8,958 | "If altitude $CD$ is $\\sqrt3$ centimeters, what is the number of square centimeters in the area of (...TRUNCATED) | 2\sqrt{3} | train | "Okay, so I have this problem here where I need to find the area of triangle ABC. They've given me t(...TRUNCATED) | [0,1470,2080,2837,3581,3716,3799,4026,4209,4373,4617,5248,5404,5498,5643,5844,6045,6472,6812,7182,75(...TRUNCATED) | ["setup","self_correct","doubt","doubt","doubt","self_correct","doubt","doubt","doubt","self_correct(...TRUNCATED) | "Okay, so I have this problem here where I need to find the area of triangle ABC. They've given me t(...TRUNCATED) |
1 | q3791_a6 | 3,791 | 4 | Prealgebra | wrong | 6 | shard11 | 5 | 16 | 0.916667 | 1,278 | cut | 1 | 935 | 249 | 0.916667 | 0.291667 | 0.458333 | true | setup | 0.194836 | 1,029 | "My date tonight made reservations for us at his favorite Italian restaurant. He didn't know that I(...TRUNCATED) | \frac{1}{20} | train | "Okay, so my date made reservations at his favorite Italian restaurant, but he didn't know I'm a veg(...TRUNCATED) | [
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] | ["setup","conclude","verify","self_correct","self_correct","doubt","new_approach","conclude","conclu(...TRUNCATED) | "Okay, so my date made reservations at his favorite Italian restaurant, but he didn't know I'm a veg(...TRUNCATED) |
1 | q1129_a6 | 1,129 | 5 | Number Theory | truncated | 6 | shard01 | 5 | 799 | 0.958333 | 16,384 | cut | 52 | 13,429 | 4,914 | 0.375 | 0.375 | 0.479167 | false | self_correct | 0.299927 | 11,470 | "What is the least positive integer $n$ such that $n^2 - n$ is divisible by some but not all integer(...TRUNCATED) | 5 | train | "Alright, so I've got this math problem here: I need to find the least positive integer \\( n \\) su(...TRUNCATED) | [0,1500,2850,3330,3495,4058,4377,4631,4713,5185,5359,5520,5629,5666,5747,5978,6504,6762,6924,7053,71(...TRUNCATED) | ["setup","new_approach","doubt","doubt","self_correct","doubt","new_approach","doubt","doubt","self_(...TRUNCATED) | "Alright, so I've got this math problem here: I need to find the least positive integer \\( n \\) su(...TRUNCATED) |
1 | q5393_a1 | 5,393 | 4 | Prealgebra | truncated | 6 | shard05 | 0 | 189 | 0.75 | 16,384 | cut | 4 | 3,921 | 1,762 | 0.583333 | 0.125 | 0.375 | true | self_correct | 0.107544 | 14,622 | In writing the integers from 10 through 99 inclusive, how many times is the digit 6 written? | 19 | train | "Okay, so I have this problem here: \"In writing the integers from 10 through 99 inclusive, how many(...TRUNCATED) | [0,1883,2221,2622,3921,4150,5090,5287,5431,5519,5717,5827,6160,6678,6819,6904,7818,7959,8066,8249,84(...TRUNCATED) | ["setup","verify","self_correct","self_correct","self_correct","new_approach","self_correct","doubt"(...TRUNCATED) | "Okay, so I have this problem here: \"In writing the integers from 10 through 99 inclusive, how many(...TRUNCATED) |
1 | q2387_a8 | 2,387 | 5 | Precalculus | truncated | 5 | shard11 | 7 | 144 | 0.416667 | 16,384 | cut | 36 | 8,943 | 3,611 | 0.875 | 0.458333 | 0.208333 | false | doubt | 0.220398 | 12,773 | "If $5(\\cos a + \\cos b) + 4(\\cos a \\cos b + 1) = 0,$ then find all possible values of\n\\[\\tan (...TRUNCATED) | 3,-3 | train | "Okay, so I have this trigonometric equation: \\(5(\\cos a + \\cos b) + 4(\\cos a \\cos b + 1) = 0\\(...TRUNCATED) | [0,434,785,949,1168,1197,1312,1691,1786,2029,2131,2227,2387,2441,2657,2723,2921,3066,3459,3564,4382,(...TRUNCATED) | ["setup","doubt","new_approach","new_approach","doubt","doubt","new_approach","doubt","doubt","new_a(...TRUNCATED) | "Okay, so I have this trigonometric equation: \\(5(\\cos a + \\cos b) + 4(\\cos a \\cos b + 1) = 0\\(...TRUNCATED) |
1 | q1627_a8 | 1,627 | 5 | Geometry | wrong | 3 | shard07 | 7 | 294 | 0.041667 | 14,806 | cut | 78 | 12,730 | 4,877 | 0.208333 | 0.125 | 0.020833 | false | doubt | 0.329393 | 9,929 | "With all angles measured in degrees, the product $\\prod_{k=1}^{45} \\csc^2(2k-1)^\\circ=m^n$, wher(...TRUNCATED) | 91 | train | "Alright, so I have this problem here: I need to find the product of the cosecant squared of angles (...TRUNCATED) | [0,1132,1230,1492,2080,2344,2496,2702,2803,3078,3158,3292,3361,3528,3675,3834,3979,4105,4511,4566,47(...TRUNCATED) | ["setup","doubt","doubt","conclude","doubt","doubt","new_approach","new_approach","new_approach","ne(...TRUNCATED) | "Alright, so I have this problem here: I need to find the product of the cosecant squared of angles (...TRUNCATED) |
1 | q4354_a4 | 4,354 | 5 | Intermediate Algebra | truncated | 7 | shard10 | 3 | 102 | 0.541667 | 16,384 | cut | 63 | 15,304 | 7,383 | 0.416667 | 0.416667 | 0.270833 | false | doubt | 0.450623 | 9,001 | "Find all values of $x > 4$ which satisfy\n\\[\\sqrt{x - 4 \\sqrt{x - 4}} + 2 = \\sqrt{x + 4 \\sqrt{(...TRUNCATED) | [8,\infty) | train | "Okay, so I have this equation to solve: \n\n√(x - 4√(x - 4)) + 2 = √(x + 4√(x - 4)) - 2.\n\(...TRUNCATED) | [0,88,712,786,1403,2122,2234,2568,3022,4016,4130,4204,4332,4549,4707,5575,5792,5831,6320,6405,6665,6(...TRUNCATED) | ["setup","doubt","doubt","doubt","doubt","doubt","verify","verify","verify","doubt","conclude","self(...TRUNCATED) | "Okay, so I have this equation to solve: \n\n√(x - 4√(x - 4)) + 2 = √(x + 4√(x - 4)) - 2.\n\(...TRUNCATED) |
1 | q3600_a4 | 3,600 | 5 | Intermediate Algebra | truncated | 1 | shard00 | 3 | 290 | 0.041667 | 16,384 | cut | 145 | 26,836 | 10,682 | 0.083333 | 0.333333 | 0.020833 | false | new_approach | 0.651978 | 5,702 | "Find the number of ordered pairs of integers $(a,b)$ with $1 \\leq a \\leq 100$ and $b \\geq 0$ suc(...TRUNCATED) | 2600 | train | "Okay, so I have this problem here: I need to find the number of ordered pairs of integers (a, b) wh(...TRUNCATED) | [0,889,1390,1640,1985,2617,3007,3514,3990,4525,4784,5060,5491,6043,6271,6344,6383,6496,6506,7075,731(...TRUNCATED) | ["setup","doubt","conclude","doubt","self_correct","doubt","self_correct","doubt","doubt","conclude"(...TRUNCATED) | "Okay, so I have this problem here: I need to find the number of ordered pairs of integers (a, b) wh(...TRUNCATED) |
End of preview. Expand in Data Studio
THR cut points: DeepSeek-R1-Distill-Qwen-1.5B on MATH levels 4–5
Point-of-no-return labels for failed reasoning traces, built for Truncated Hindsight Refusal (THR): training a model to stop reasoning where its chance of success has collapsed, rather than at a fixed length.
How it was made
- Questions: 6,068 MATH level 4–5 problems (train + test splits, excluding MATH-500 and our 500-question dev set).
- Rollouts: DeepSeek-R1-Distill-Qwen-1.5B, 8 attempts per question, 16,384-token budget. We kept questions solved sometimes (1–7 of 8), and took one failed attempt (wrong answer or ran out of tokens) from each.
- Steps: each trace's reasoning is split into paragraphs. A new step starts at a turn word (Wait, Alternatively, Let me check, But, …). Each step is labelled setup, new_approach, self_correct, verify, doubt, conclude or format.
- Probing: we cut the trace at a step boundary and let the model continue from there with a fresh 8,192-token budget, sampling several times.
- The success rate from the empty prefix is the start rate (24 samples).
- A coarse grid (25/50/75/100%), then binary search (8 samples per point), finds the first step where success falls below 50% of the start rate.
- The steps either side of that boundary are then re-sampled 16 more times (confirmation).
- Two batches of 480 traces each, on disjoint questions (seeds 7 and 8).
Totals
| Batch 1 | Batch 2 | Both | |
|---|---|---|---|
| Traces | 480 | 480 | 960 |
| Cut found | 421 | 410 | 831 |
| Confirmed cut | 221 | 212 | 433 |
| No drop | 31 | 31 | 62 |
| Lost from the start | 28 | 39 | 67 |
Confirmed cuts: median at 38–39% of the trace (around token 3,000). Success just before the cut step is 46%, and 12% just after.
About two-thirds come before 6,000 tokens. The step where the drop happens is most often doubt.
Files
data/traces.jsonl: one row per trace (960 rows).probes/batch{1,2}.jsonl: every continuation probe: trace, step cut, sample count, outcomes.reports/batch{1,2}.md: summary report per batch.
Fields (data/traces.jsonl)
| Field | Meaning |
|---|---|
batch |
1 or 2 |
id |
q<question index>_a<attempt> |
index, level, subject, source |
MATH question index, level, subject, original split |
problem, answer |
question text and reference answer |
outcome |
how the original attempt failed: wrong or truncated (ran out of tokens) |
solved |
how many of the 8 original attempts were correct |
thinking |
full reasoning text of the failed attempt |
thinking_tokens |
its length in tokens |
steps, step_starts, step_labels |
number of steps, character offset of each step, label of each step |
status |
cut, no drop (never fell below the threshold) or lost from the start (start rate 0) |
start_rate |
success rate continuing from the empty prefix |
threshold |
0.5 × start_rate |
cut |
index of the step where the model got lost (the first step at or below the threshold) |
cut_char, cut_token |
where that step starts, in characters and tokens |
cut_share |
cut_token / thinking_tokens |
saved_tokens |
tokens after the cut |
rate_before, rate_after |
success continuing from just before / just after the lost step |
confirmed |
the drop held up under the extra confirmation samples |
lost_step |
label of the step where the drop happens |
thinking_before_cut |
thinking[:cut_char]: the reasoning to keep, before refusing |
Rows where status is not cut have no cut fields.
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