Datasets:
row_uid stringlengths 16 16 | source stringclasses 3
values | task stringclasses 3
values | question stringlengths 398 809 | options stringlengths 23 76 ⌀ | answer stringclasses 40
values | num_input_images int32 1 1 | num_steps int32 1 4 | input_image_0 imagewidth (px) 430 512 | thought_0 stringlengths 139 3.03k | target_image_0 imagewidth (px) 430 727 | thought_1 stringlengths 91 2.15k ⌀ | target_image_1 imagewidth (px) 430 512 ⌀ | thought_2 stringlengths 85 1.59k ⌀ | target_image_2 imagewidth (px) 430 512 ⌀ | thought_3 stringlengths 253 1.11k ⌀ | target_image_3 imagewidth (px) 512 512 ⌀ | thought_4 stringclasses 0
values | target_image_4 imagewidth (px) | thought_5 stringlengths 9 2.02k | split stringclasses 1
value | license stringclasses 1
value | source_scene_corpus stringclasses 2
values | est_tokens int32 5.59k 18k | filter_flags stringclasses 7
values |
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1e99fb86df98edf9 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its initial position and trajectory. The red ball is located on the left side of the square arena, and the green arrow indicates it is moving upward and slightly to the left. Given its proximity to the left wall and the steep angle of the arrow, it ... | As observed in the previous step, the ball strikes the left wall. According to the rules of ideal reflection, the component of velocity perpendicular to the wall is reversed while the parallel component remains unchanged. In this case, the ball was moving left and up; after reflecting off the vertical left wall, it wil... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Following the reflected path, the ball travels diagonally upward and to the right. Looking at the destination of this trajectory, it heads directly toward the top boundary of the arena where the holes are located. The path intersects the top boundary within the section labeled "1". Since there are no further walls to s... | train | mit | procedural_grid | 10,185 | S5.replay_unsupported,S8.phash_near_but_distinct | |||
281d48703f70fae4 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | To begin our analysis, we observe the initial state of the environment. We have a square arena bounded by solid walls on the left, right, and bottom, while the top boundary contains five distinct rectangular holes numbered 1 through 5 from left to right. A red ball is positioned in the lower-right quadrant of the arena... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the newly generated trajectory line, we can see that the ball travels across the arena without encountering the left, right, or bottom walls. The path is a direct line from the starting point to the top edge of the play area. By carefully examining where the solid black line terminates at the top boundary, we... | train | mit | procedural_grid | 9,000 | S5.replay_unsupported | ||
41f5c14cc201fd58 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. Observing the initial image, the red ball is located in the lower-right quadrant of the square enclosure. A green arrow points diagonally upward and to the right, indicating the ball's initial direction ... | The ball strikes the right wall at a point roughly one-third of the way up from the bottom. Following the rules of ideal reflection, the component of velocity perpendicular to the wall (the horizontal component) is reversed, while the vertical component remains unchanged. This causes the ball to bounce back toward the ... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | As we trace this reflected path, the ball travels diagonally across the upper portion of the arena. The trajectory heads directly toward the top wall where the holes are located. By following the straight line from the right wall, the ball reaches the top boundary at a position within the leftmost section. Specifically... | train | mit | procedural_grid | 10,340 | S5.replay_unsupported,S8.phash_near_but_distinct | |||
abac1aabcb37692a | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 2 | To determine which hole the red ball will enter, we must first observe its initial state. In the provided image, the red ball is positioned in the lower-right quadrant of a square arena. A green arrow indicates its starting direction, pointing diagonally downward and to the left. Based on this vector, the ball's first ... | Observing the trajectory from the first step, the ball has struck the bottom wall at a point slightly to the right of the center line. According to the rules of ideal reflection, the ball's angle of incidence must equal its angle of reflection. Since it hit the bottom wall while moving downward and to the left, it will... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Following the reflected path from the bottom wall, the ball travels in a straight diagonal line across the arena. It bypasses the left wall entirely and heads directly toward the top boundary. By observing the destination of this second leg of the journey, the ball reaches the top horizontal line within the section cle... | train | mit | procedural_grid | 10,224 | S5.replay_unsupported,S8.phash_near_but_distinct | |||
d3e3d32e868a3287 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 1 | Upon observing the initial setup, we see a red ball positioned in the central upper region of a square enclosure. At the top of this enclosure, there are three distinct rectangular openings labeled 1, 2, and 3 from left to right. A green arrow originates from the red ball, pointing diagonally toward the upper-left dire... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Reviewing the visual evidence in the updated image, the ball's path has been clearly traced. The solid black line shows a direct, uninterrupted path from the starting position to the upper boundary. The red dot, representing the ball's position upon reaching the top, is located on the horizontal line that separates the... | train | mit | procedural_grid | 9,047 | S5.replay_unsupported | ||
8568eae8ea7cf982 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 4 | To determine which hole the red ball will enter, we must carefully track its trajectory based on the laws of ideal reflection. Initially, we observe the red ball positioned in the upper-right quadrant of the field. A green arrow indicates it is moving diagonally downward and to the right. Based on this vector, the ball... | Upon hitting the right wall, the ball undergoes reflection. The horizontal component of its velocity is reversed, while the vertical component remains downward. This sends the ball on a new diagonal path towards the bottom-left. Following this trajectory, the ball travels across the lower section of the enclosure until... | After bouncing off the bottom wall, the ball's vertical motion is reversed from downward to upward, while it continues to move toward the left. This diagonal path leads it directly toward the left wall. To visualize this, I will draw a solid black line from the bottom wall to the left boundary. At the point of contact,... | From the left wall, the ball reflects once more. Its leftward horizontal velocity is reversed to the right, and its upward vertical velocity is maintained. The ball now travels diagonally upward and to the right. By extending this final path, we can see it heading toward the top boundary where the numbered holes are lo... | null | Not supported with pagination yet | By tracing the final path to the top of the image, the ball makes contact with the upper boundary. Looking at the numbered segments, the ball lands precisely within the area designated as Hole 3. After three distinct bounces off the right, bottom, and left walls, the ball concludes its motion.
The red ball enters Hole... | train | mit | procedural_grid | 17,099 | S5.replay_unsupported,S8.phash_near_but_distinct | |||||
d8b83abada4e8b45 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. In the provided image, the red ball is located in the lower-left quadrant of the square arena. A green arrow points diagonally upward and to the left, indicating the ball's initial direction of motion. T... | Observing the first auxiliary image, we see that the ball has struck the left wall at the coordinates (0.00, 6.73). According to the rules of ideal reflection, the component of velocity perpendicular to the wall is reversed, while the parallel component remains the same. Since the ball hit a vertical wall while moving ... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | In this second step, the reflected path leads the ball directly toward the top boundary. By tracing the line, we can see that the ball reaches the top wall at the position (1.21, 10.00). Looking at the layout of the holes at the top, this coordinate falls squarely within the boundaries of the first rectangular opening.... | train | mit | procedural_grid | 10,283 | S5.replay_unsupported | |||
1165374ed44472bd | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 3 | To determine which hole the red ball will enter, we must first observe its starting position and initial trajectory. In the original image, the red ball is located in the lower-left quadrant of the square arena. A green arrow points diagonally upward and to the left, indicating the ball's initial direction of travel to... | Upon hitting the left wall, the ball undergoes an ideal reflection. Since the wall is vertical, the horizontal component of the ball's velocity is reversed, while the upward vertical component remains constant. This causes the ball to bounce off the wall and move diagonally upward and to the right. We need to track thi... | Now, the ball has reached the right wall. Following the rules of ideal reflection once again, the horizontal velocity is reversed from rightward to leftward, while the ball continues its upward motion. This reflection directs the ball toward the top of the arena, where the numbered holes are located. By extending a sol... | null | Not supported with pagination yet | null | Not supported with pagination yet | By carefully tracing the ball's path, we observed it bounce twice: first off the left wall and then off the right wall. Following the second reflection, the ball travels upward and to the left, crossing the top boundary within the region labeled as Hole 3. Therefore, the ball will enter Hole 3 first.
The red ball ente... | train | mit | procedural_grid | 13,700 | S5.replay_unsupported | ||||
ce6ecbff2f9e2203 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 3 | The initial state shows a red ball positioned in the lower-right quadrant of a square arena. A green arrow points diagonally downward and to the left, indicating the ball's starting trajectory. At the top of the arena, there are four numbered holes (1, 2, 3, and 4) separated by thin vertical lines. To predict which hol... | Reflecting off the bottom wall, the ball's downward vertical velocity is reversed to upward, while its leftward horizontal velocity remains constant. This means the ball now travels diagonally upward and to the left. Given the angle of reflection, the ball will continue across the arena until it encounters the left wal... | Upon striking the left wall, the ball undergoes its second reflection. This time, the leftward horizontal velocity is reversed to rightward, while the upward vertical velocity remains unchanged. The ball is now moving diagonally upward and to the right. Projecting this path forward from the point of impact on the left ... | null | Not supported with pagination yet | null | Not supported with pagination yet | By carefully tracing the ball's path through two reflections—first off the bottom wall and then off the left wall—it becomes clear that the ball's trajectory leads it straight into the second opening. The final position of the ball at the top boundary falls between the markers for Hole 2.
The red ball will enter hole ... | train | mit | procedural_grid | 13,653 | S5.replay_unsupported | ||||
0114e260ea95f328 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | In the initial image, we observe a red ball positioned in the upper-left quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and toward the right. This arrow defines the ball's initial trajectory. Above the enclosure, there are five numbered holes, 1 through 5, arranged ho... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the updated image, the black line represents the ball's first leg of travel. The line starts at the original red ball position and proceeds straight to the top wall. Upon reaching the top boundary, the red dot indicates the point of contact. By examining the horizontal position of this contact point relative ... | train | mit | procedural_grid | 8,930 | S5.replay_unsupported | ||
27b1f75af6e1688b | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | Looking at the initial setup, we have a red ball positioned in the upper-left quadrant of a square enclosure. A green arrow indicates the ball's starting trajectory, pointing steeply upward and slightly to the right. The top boundary of this area is divided into five distinct target zones, labeled 1 through 5 from left... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Following the projected path, the ball moves straight from its origin toward the top wall without hitting any side walls first. The line clearly terminates at a point on the top boundary. By looking at the numbered segments at the top, I can observe that the intersection point falls directly within the boundaries of th... | train | mit | procedural_grid | 8,817 | S5.replay_unsupported | ||
edfda5e7816ad30e | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. By observing the initial image, the red ball is positioned in the upper-right quadrant of the square arena. A green arrow indicates its initial direction, pointing slightly upwards and to the right. Give... | As seen in the first auxiliary image, the ball moves from its starting coordinates toward the right wall. It travels along a straight path and strikes the vertical right wall at a point roughly four-fifths of the way up the wall's total height. Following the rules of reflection, the horizontal component of the ball's v... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | In the second auxiliary image, we can observe the result of this reflection. The ball travels from the right wall toward the top edge of the arena. By tracing this diagonal line, we see it crosses the space below the numbered holes. The path leads directly to the top boundary, specifically hitting the area designated a... | train | mit | procedural_grid | 10,305 | S5.replay_unsupported | |||
1bc3dd33b400aa7d | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. In the provided image, a red ball is positioned in the center-right area of a square enclosure. A green arrow points diagonally downward and to the left, indicating the ball's initial path. By observing ... | Upon hitting the bottom wall, the ball undergoes an ideal reflection. According to the rules of physics provided, the component of velocity perpendicular to the wall is reversed, while the parallel component remains the same. This means the ball will bounce upward at the same angle it arrived, continuing its leftward p... | The ball has now reached the left wall. Applying the reflection rules once more, the leftward horizontal velocity is reversed to the right, while the upward vertical velocity is maintained. This sends the ball on a new path, moving diagonally upward and toward the right.
Looking at the enclosure, the top boundary cont... | null | Not supported with pagination yet | null | Not supported with pagination yet | By following the completed trajectory, we observe that after two bounces—first off the bottom wall and then off the left wall—the ball travels directly into the area marked as Hole 2. The ball reaches the top boundary at a position clearly within the boundaries of the second rectangular slot.
In summary, the ball ente... | train | mit | procedural_grid | 13,747 | S5.replay_unsupported | ||||
bde0547b452a44ab | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. The ball is positioned in the center-left area of the field, and the green arrow indicates a downward-left movement. Specifically, the ball starts at coordinates (3.42, 5.75) with an initial angle of app... | Observing the first bounce, the ball hits the bottom wall at position (0.66, 0.00). According to the rules of ideal reflection, the component of velocity perpendicular to the wall (the vertical component) is reversed, while the horizontal component remains constant. This means the ball will now travel upward and contin... | The ball strikes the left wall at position (0.00, 1.37). Following the same reflection principles, the horizontal velocity component is now reversed (changing from leftward to rightward), while the upward vertical velocity remains unchanged. The ball is now set on a path moving toward the top-right area of the field.
... | null | Not supported with pagination yet | null | Not supported with pagination yet | By extending this final trajectory, we can see that the ball travels diagonally across the field and reaches the top wall at position (4.14, 10.00). Looking at the numbered holes at the top, the position 4.14 falls within the boundaries of the third rectangular hole. Therefore, after two bounces—first off the bottom wa... | train | mit | procedural_grid | 13,731 | S5.replay_unsupported | ||||
30400afc47fd81a7 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 1 | In the initial image, we observe a square arena with a red ball positioned on the left side. A green arrow points diagonally upward and to the right, indicating the ball's starting velocity. At the top of the arena, there are three numbered rectangular holes: 1, 2, and 3. Our objective is to determine which of these ho... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | As we can see from the newly drawn trajectory, the ball moves diagonally across the space. It does not hit the left or right walls. Instead, it travels directly toward the top boundary. The path ends precisely at the top wall, marked by the red dot. By observing the position of this dot relative to the numbered holes, ... | train | mit | procedural_grid | 8,821 | S5.replay_unsupported | ||
579b6294ffdb34ec | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | Looking at the initial image, we see a red ball positioned in the middle-lower section of a square enclosure. A green arrow points diagonally upward and to the right, indicating the ball's starting trajectory. At the top of the enclosure, there are three numbered holes: Hole 1 on the left, Hole 2 in the center, and Hol... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | As shown in the auxiliary image, the ball follows a straight trajectory from its starting coordinates toward the top wall. The path does not intersect with the side walls, meaning no reflections are necessary for this segment. The black line terminates at the boundary between the main area and the scoring holes. By obs... | train | mit | procedural_grid | 8,929 | S5.replay_unsupported | ||
3f44901babe64722 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 1 | Looking at the initial setup, we have a red ball positioned in the lower-right quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally toward the upper-left corner. This enclosure is bounded by solid walls on the left, right, and bottom, while the top boundary contains four distinct ... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the trajectory drawn in the first step, we can see that the ball moves in a straight path from its starting point directly toward the top boundary. Because of the specific angle and the ball's proximity to the center-right, the path is steep enough that it does not encounter the left wall before reaching the ... | train | mit | procedural_grid | 8,981 | S5.replay_unsupported | ||
a84c08059f2674cc | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 3 | To determine which hole the red ball will enter, we must carefully track its trajectory based on its initial position and direction, applying the laws of ideal reflection whenever it strikes a wall. Looking at the initial image, we see a red ball located in the lower-left quadrant of a square enclosure. A green arrow p... | The ball strikes the bottom wall at position (0.32, 0.00). According to the rules of ideal reflection, the horizontal component of its velocity remains the same, while the vertical component is reversed. This causes the ball to bounce upward and continue its leftward progression. It is now heading toward the left verti... | The ball travels a short distance before hitting the left wall at position (0.00, 0.63). At this point, another reflection occurs: the vertical velocity remains upward, but the horizontal velocity is reversed from left to right. The ball is now moving diagonally upward and to the right across the main area of the enclo... | null | Not supported with pagination yet | null | Not supported with pagination yet | Following this path, the ball travels across the enclosure and reaches the top wall at position (4.84, 10.00). By observing the layout of the holes at the top—numbered 1, 2, and 3 from left to right—we can see that the contact point (4.84) falls within the boundaries of the middle hole. Consequently, the ball enters Ho... | train | mit | procedural_grid | 13,702 | S5.replay_unsupported | ||||
b492591b0889b98a | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its starting position and the direction indicated by the green arrow. The ball is positioned in the middle-left area of the square enclosure. The green arrow points diagonally upward and to the left, suggesting the ball will initially travel toward ... | Observing the first trajectory segment, we see that the ball moves from its starting point at approximately (2.38, 5.03) and hits the left wall. The point of impact on the left wall is located at (0.00, 6.67). At this point, the ball must reflect. According to the laws of physics provided, the horizontal velocity compo... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Following the reflected path, the ball travels across the upper portion of the enclosure. By extending this line, we can see it intersects the top boundary. The intersection point occurs at (4.83, 10.00). Looking at the layout of the holes at the top, numbered 1 through 4 from left to right, we can see that this specif... | train | mit | procedural_grid | 10,143 | S5.replay_unsupported | |||
fb4d2bedf88a0338 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 4 | 1 | 1 | Looking at the initial setup, we have a red ball positioned in the upper-middle section of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the right. This arrow defines the ball's starting trajectory. Above the main enclosure, there are five numbered rectangular holes (1 th... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | By drawing the trajectory, we can see that the red ball moves in a straight path directly from its starting point toward the top edge. The line crosses the horizontal boundary of the holes at a point clearly within the segment labeled "4". There are no walls or obstacles in this direct path to cause a reflection, meani... | train | mit | procedural_grid | 8,897 | S5.replay_unsupported | ||
182975dbdea131e1 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | Looking at the initial image, we see a red ball positioned in the lower-right quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the right, which indicates the ball's starting trajectory. At the top of the enclosure, there are three distinct holes labeled 1, 2, and... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the trajectory drawn in the auxiliary image, the black line extends directly from the starting point to the top edge of the enclosure without striking the right-side wall first. The path terminates at a point on the top wall that falls within the boundaries of the section labeled "3". Because the ball reaches... | train | mit | procedural_grid | 8,804 | S5.replay_unsupported | ||
62112b51013e1b60 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 4 | 1 | 2 | To determine which hole the red ball will enter, we must first observe its starting position and the direction indicated by the green arrow. The ball is located in the lower-right quadrant of the square arena. The green arrow points diagonally upward and to the right, suggesting an initial trajectory that will take it ... | Now that the ball has hit the right wall, we must apply the rules of ideal reflection. The horizontal component of its velocity will be reversed, while the vertical component remains the same. Since the ball was moving up and to the right, it will now move up and to the left. The angle of incidence equals the angle of ... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the final trajectory, the ball reflects off the right wall and travels a short distance leftward and upward. It strikes the top boundary within the section labeled as Hole 4. Because the first bounce occurred so high up on the right wall, the ball did not have enough horizontal space to travel across to any o... | train | mit | procedural_grid | 10,347 | S5.replay_unsupported | |||
dffd82f3013298be | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 2 | To begin our analysis, we observe the initial state of the environment. We have a red ball located in the lower-left quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the left at approximately a 135-degree angle from the positive x-axis. Above the main enclosure, ... | The ball has now struck the left wall. According to the laws of ideal reflection provided in the rules, the component of velocity perpendicular to the wall is reversed, while the parallel component remains the same. Since the ball hit a vertical wall, its horizontal direction changes from leftward to rightward, while i... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | The trajectory shows the ball traveling across the width of the enclosure and moving upward. It strikes the top boundary at a position that falls within the segment labeled "3". Specifically, the path crosses the boundary line between the main area and the holes, landing squarely in the third rectangular opening from t... | train | mit | procedural_grid | 10,400 | S5.replay_unsupported | |||
8c736de8a10ce0ff | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. Observing the initial image, the red ball is located in the lower-right quadrant of the square enclosure. A green arrow points upwards and to the right, indicating its initial direction of motion toward ... | The ball has now struck the right wall at position (10.00, 2.45). According to the rules of ideal reflection, the component of velocity perpendicular to the wall is reversed, while the parallel component remains the same. Since the ball hit a vertical wall, its horizontal direction will flip from rightward to leftward,... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Following the reflected path across the enclosure, the ball travels toward the upper-left. The trajectory is a straight diagonal line that crosses the majority of the field. By tracing this line accurately, we can see that it intersects the top boundary line. Specifically, the ball reaches the top wall at position (3.0... | train | mit | procedural_grid | 10,214 | S5.replay_unsupported,S8.phash_near_but_distinct | |||
4aae317d78c8eb87 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 5 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its initial position and velocity. The red ball is located in the lower-middle section of the square arena, and the green arrow indicates it is moving diagonally downward and to the right. Given the laws of ideal reflection, the ball will maintain i... | The ball has now struck the bottom wall at position (4.89, 0.00). According to the rules of reflection, the angle of incidence equals the angle of reflection. Since the ball was moving down and to the right, it will now bounce upward while continuing its rightward progress. The trajectory remains a straight line until ... | The ball has reached the right-side wall at position (10.00, 9.06). At this point, the horizontal component of its velocity will be reversed (moving from right-to-left), while the upward vertical component remains unchanged. This reflection will send the ball on a steep upward path toward the top boundary where the num... | null | Not supported with pagination yet | null | Not supported with pagination yet | By observing the final trajectory, the ball strikes the top boundary at position (9.47, 10.00). Looking at the horizontal layout of the holes at the top of the frame, this position falls squarely within the boundaries of the rightmost hole. The holes are numbered 1 through 5 from left to right, and the ball has clearly... | train | mit | procedural_grid | 13,919 | S5.replay_unsupported | ||||
20466289a131fde6 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | In the initial image, we observe a red ball located in the lower-left quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the right. This arrow indicates the ball's initial velocity vector. At the top of the enclosure, there are five numbered rectangular holes, labe... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the newly drawn trajectory in the image above, we can see the path of the ball more clearly. The straight line begins at the initial coordinates of the red ball and travels diagonally across the empty space. Because the path is aimed directly at the top wall and does not encounter the left, right, or bottom w... | train | mit | procedural_grid | 8,906 | S5.replay_unsupported | ||
61c30a9d2f54bc11 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 4 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its initial state. The red ball is positioned in the center-left area of the square enclosure. A green arrow points diagonally downward and to the right, indicating the ball's starting trajectory. Given the rules of ideal reflection, the ball will t... | The ball has now completed its first leg of travel, hitting the bottom wall slightly to the right of the center. Following the law of reflection—where the angle of incidence equals the angle of reflection—the ball will now bounce upward and continue its motion toward the right. Since it was moving down and to the right... | The ball has struck the right wall at a point roughly two-thirds of the way up the side. Because it hit a vertical wall, its horizontal velocity component will reverse, while its upward vertical component remains unchanged. This means the ball will now travel diagonally upward and to the left.
To complete the trajecto... | null | Not supported with pagination yet | null | Not supported with pagination yet | By tracing the final segment of the trajectory, we can see that the ball moves from the right wall toward the top edge of the enclosure. The path concludes as the ball crosses the boundary of the top wall. Looking at the horizontal positions of the holes, the ball lands clearly within the boundaries of the fourth recta... | train | mit | procedural_grid | 13,835 | S5.replay_unsupported | ||||
862b26485adcd0e3 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 1 | Looking at the initial image, we see a red ball positioned in the upper half of a square enclosure. A green arrow is attached to the ball, pointing diagonally upward and to the left. This arrow defines the ball's starting trajectory. At the top of the enclosure, there are three distinct sections labeled 1, 2, and 3, wh... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | By drawing the trajectory, we can see that the ball travels upward and slightly to the left. The path is a straight line that intersects the top boundary. Upon inspection of the intersection point, the red dot representing the ball's arrival at the wall falls within the boundaries of the middle section. This section is... | train | mit | procedural_grid | 8,851 | S5.replay_unsupported | ||
fc5cf4dbc6ced801 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its initial state. The red ball is located in the lower-right quadrant of the square arena. A green arrow points diagonally downwards and to the right, indicating the ball's starting trajectory. Given the rules of ideal reflection, where the angle o... | Observing the first bounce, the ball has struck the right wall at a point roughly one-sixth of the way up from the bottom. According to the law of reflection, the horizontal component of its velocity will reverse, while the vertical component remains downward. This means the ball will now move diagonally down and to th... | After hitting the bottom wall, the ball's vertical velocity is reversed, causing it to travel upwards, while its horizontal velocity continues to carry it to the left. The ball is now on a long diagonal path heading toward the top of the arena, where the numbered holes are located.
To visualize this final leg of the ... | null | Not supported with pagination yet | null | Not supported with pagination yet | By following the completed trajectory, we can see that the ball moves from the bottom wall across the width of the arena. It crosses under the regions for Hole 3 and Hole 2 before finally reaching the top boundary. The red dot clearly indicates that the ball enters the region labeled "1". The ball successfully reached ... | train | mit | procedural_grid | 13,804 | S5.replay_unsupported | ||||
2923743a24d4cef4 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 1 | In the initial image, we observe a red ball positioned in the lower-right quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the left, indicating its starting velocity and direction. At the top of the enclosure, there are three distinct target zones or holes, numbe... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Following the projection of the ball's path, we can see that the trajectory is quite steep. The black line drawn from the starting position extends upward and to the left, crossing a significant portion of the horizontal space. Upon reaching the top boundary, the line terminates within the segment labeled "1". The ball... | train | mit | procedural_grid | 8,814 | S5.replay_unsupported | ||
2bf189b7414f2882 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 1 | Looking at the initial setup, we observe a red ball positioned in the upper-middle section of a square enclosure. A green arrow points upwards and slightly to the right, establishing the ball's initial trajectory. At the top of the enclosure, four distinct holes are labeled 1 through 4 from left to right. To determine ... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the newly drawn trajectory, the black line proceeds straight from the ball's initial position and makes contact with the top boundary. By examining the point of contact marked by the red dot at the end of the line, we can see it lands at approximately the coordinate (4.97, 10.00). This point is located just t... | train | mit | procedural_grid | 8,921 | S5.replay_unsupported | ||
6637e1f3c71111a2 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory within the square enclosure. The ball begins at a central-right position, roughly at the coordinates (4.95, 4.78). A green arrow indicates it is moving downwards and slightly to the left, at an angle of a... | Upon reaching the bottom wall at position (3.33, 0.00), the ball undergoes an ideal reflection. According to the rules, the vertical component of its velocity is reversed while the horizontal component remains the same. This causes the ball to bounce upward and continue its leftward progress. Looking at the steep angle... | The ball strikes the left wall at position (0.00, 9.87). This point is very high up on the wall, nearly at the corner where the side wall meets the top boundary. Following the laws of reflection, the ball's horizontal velocity component is reversed, sending it toward the right, while its upward vertical velocity remain... | null | Not supported with pagination yet | null | Not supported with pagination yet | The ball reaches the top wall almost immediately after its second bounce, hitting at position (0.04, 10.00). This location is at the extreme left end of the top boundary. By observing the layout of the numbered holes at the top, we can see that Hole 1 occupies the leftmost section of the top edge. Therefore, the ball p... | train | mit | procedural_grid | 13,751 | S5.replay_unsupported | ||||
7df2d723cf52ea4a | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its initial state and environment. The ball is located in the lower-right quadrant of the square arena. A green arrow points diagonally downwards and to the left, establishing the initial trajectory. At the top of the arena, there are four numbered ... | The ball has completed its first segment, striking the bottom wall at a point roughly one-third of the way from the left corner. According to the laws of reflection, the ball's downward vertical velocity is now reversed to an upward direction, while its leftward horizontal velocity remains constant. This means the ball... | The ball has now hit the left wall at a point slightly below the vertical midpoint of the arena. This second collision reverses the horizontal component of the ball's velocity from leftward to rightward, while the upward vertical component remains unchanged. Consequently, the ball will now move diagonally up and to the... | null | Not supported with pagination yet | null | Not supported with pagination yet | By following the reflected path, we can see that the ball travels from the left wall across the arena toward the top. The trajectory clearly intersects the top boundary within the section labeled "3". The ball passes the boundaries of holes 1 and 2 and enters the third hole from the left.
In summary, the ball reflects... | train | mit | procedural_grid | 13,791 | S5.replay_unsupported | ||||
41960af55af42f8d | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 1 | In the initial image, we observe a red ball located in the lower-left quadrant of a square arena. A green arrow originates from the ball, pointing diagonally upward and to the right. This arrow defines the ball's initial trajectory. At the top of the arena, there are four distinct rectangular openings or "holes," numbe... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the newly drawn trajectory, the black line proceeds straight from the ball's starting point to the top edge without hitting the right-hand wall first. The line terminates at a point on the top boundary that falls within the width of a specific hole. By examining the horizontal segments at the top, we can see ... | train | mit | procedural_grid | 9,007 | S5.replay_unsupported | ||
f411bf4782fc5099 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 1 | Looking at the initial setup, we have a red ball located in the lower-left quadrant of a square enclosure. A green arrow indicates the ball's starting trajectory, pointing diagonally upward and to the right. At the top of the enclosure, there are three designated holes labeled 1, 2, and 3. My goal is to determine which... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the trajectory drawn in the auxiliary image, the black line proceeds straight from the starting point to the top edge of the enclosure. The path does not intersect the left or right walls, meaning there are no intermediate bounces required for this specific trajectory. The line terminates at a point on the to... | train | mit | procedural_grid | 8,975 | S5.replay_unsupported | ||
5fc7e02293d09fa5 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 4 | To determine which hole the red ball will enter, we must carefully track its trajectory within the square enclosure, accounting for reflections off the walls. We begin by observing the initial state: a red ball is positioned in the center-left area of the frame. A green arrow points diagonally downward and to the left,... | Upon hitting the left wall, the ball undergoes an ideal reflection. Since the wall is vertical, the horizontal component of the ball's velocity is reversed, while the vertical component remains unchanged. This causes the ball to bounce off the wall and travel diagonally downward and to the right. I will now extend the ... | The ball now strikes the bottom wall. In an ideal reflection against a horizontal surface, the vertical velocity component is reversed, while the horizontal velocity continues to the right. Consequently, the ball begins to move diagonally upward and to the right. I will trace this new path by drawing a solid black line... | After the third bounce, which occurs on the right wall, the horizontal velocity is reversed once more. The ball is now traveling diagonally upward and to the left. By projecting this path forward, we can see it heading toward the top boundary where the numbered holes are located. I will draw this final segment of the p... | null | Not supported with pagination yet | By examining the final position of the ball at the top boundary, we can see that it has crossed the line into the area labeled "2". The trajectory clearly shows the ball passing through the opening for Hole 2 after completing three reflections off the side and bottom walls.
In summary, the ball's path involves a refle... | train | mit | procedural_grid | 17,274 | S5.replay_unsupported | |||||
2734fdfe24d9d947 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 4 | 1 | 2 | To determine which hole the red ball will enter, we must first analyze its initial position and trajectory. Observing the starting image, the red ball is located in the upper-left quadrant of the square arena. A green arrow points diagonally downward and to the right, establishing the ball's initial direction. By exten... | The ball has now completed its first movement, striking the bottom wall at a point roughly below the boundary between holes 2 and 3. According to the laws of ideal reflection, the angle of incidence equals the angle of reflection. Since the ball was moving downward and to the right, it will now bounce upward while main... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | By tracing this reflected path, we can see that the ball travels diagonally across the right half of the arena. It continues its upward and rightward trajectory until it reaches the top edge of the square. The line concludes at the far right side of the top boundary, directly entering the opening designated as Hole 4. ... | train | mit | procedural_grid | 10,206 | S5.replay_unsupported | |||
68d898fff7d8b01b | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its starting position and initial movement. Looking at the initial image, the red ball is located in the lower-right quadrant of the square arena. A green arrow points downward and slightly to the right, indicating the ball's initial trajectory. Bas... | The ball has now struck the bottom wall. According to the rules of ideal reflection, the angle of incidence equals the angle of reflection. Since the ball was moving downward and to the right, it will now bounce upward while maintaining its rightward horizontal velocity component. Given the steepness of the initial ang... | After hitting the right wall, the ball's horizontal velocity is reversed, meaning it will now travel to the left. However, its upward vertical velocity remains unchanged. The ball is now on a direct path toward the top of the arena, where the numbered holes are located. By tracing this final diagonal segment, we can se... | null | Not supported with pagination yet | null | Not supported with pagination yet | By observing the final trajectory, the ball crosses the top boundary within the section labeled "3". The path shows that after bouncing off the bottom wall and then the right wall, the ball's upward and leftward momentum carries it directly into the third hole from the left.
The ball enters Hole 3.
\boxed{3} | train | mit | procedural_grid | 13,744 | S5.replay_unsupported | ||||
cc2e56529b11586f | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 1 | To determine which hole the red ball will enter, we must first analyze the starting conditions provided in the initial image. We see a red ball located in the lower-left quadrant of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the right. This arrow defines the ball's ini... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Looking at the visualized path, the ball travels in a straight line from its starting coordinates toward the upper section of the container. The trajectory does not hit the left or right side walls before reaching the top. By tracing the line carefully, we can see it crosses the horizontal line that separates the main ... | train | mit | procedural_grid | 8,842 | S5.replay_unsupported,S14.sampled_qa | ||
684fabd92f4899fe | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 3 | The initial state shows a red ball positioned in the lower-left quadrant of a square arena. A green arrow points diagonally downward and to the left, indicating the ball's starting trajectory. To determine which hole the ball will eventually enter, we must trace its path, accounting for reflections off the solid black ... | The ball has now struck the bottom wall. According to the rules of ideal reflection, the vertical component of its velocity is reversed while the horizontal component remains the same. This causes the ball to bounce upward and further to the left. I need to plan the next segment of the trajectory. I will draw a solid b... | Upon hitting the left wall, the ball's horizontal velocity component is reversed, sending it toward the right, while its upward vertical velocity continues unchanged. This reflection directs the ball diagonally upward and to the right, aiming toward the top boundary where the holes are located. I will now draw the fina... | null | Not supported with pagination yet | null | Not supported with pagination yet | By tracing this final reflection, we can see that the ball crosses the top boundary. The point of intersection is located within the middle section of the top edge. Looking at the labels provided at the start, this section corresponds to Hole 2. After two bounces—one off the bottom wall and one off the left wall—the ba... | train | mit | procedural_grid | 13,624 | S5.replay_unsupported | ||||
f448307faa8ee6d4 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 4 | 1 | 1 | To determine which hole the red ball will enter, we must first analyze its starting position and the direction of its initial movement. Observing the initial image, the red ball is located in the upper right quadrant of the square arena. A green arrow points diagonally upward and to the left, indicating the ball's traj... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | As shown in the auxiliary image, the projected path of the ball is a straight line that moves directly toward the top boundary without hitting the right or left walls first. The red dot placed at the end of the black line indicates the point of contact with the upper edge. By observing the position of this contact poin... | train | mit | procedural_grid | 8,797 | S5.replay_unsupported | ||
c7223e8465006a7f | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 2 | 1 | 2 | In the initial setup, we observe a red ball located in the lower-middle section of a square enclosure. A green arrow originates from the ball, pointing diagonally upward and to the left at an angle of approximately 135 degrees. This indicates the ball's starting velocity. At the top of the enclosure, there are four tar... | The ball has now reached the left wall. According to the rules of ideal reflection, the component of velocity perpendicular to the wall is reversed, while the parallel component remains the same. This means the ball, which was moving up and to the left, will now bounce and move up and to the right. The angle of reflect... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | By carefully following the ball's path, we have traced its motion from the starting point to its first collision with the left wall, and then its subsequent reflection toward the top boundary. The ball's trajectory concludes as it crosses into the region labeled Hole 2. No further reflections occur as the ball has reac... | train | mit | procedural_grid | 10,308 | S5.replay_unsupported | |||
9e857e97fe93ca34 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 5 | 1 | 1 | In the initial image, we observe a red ball located in the lower-right quadrant of a square arena. A green arrow originates from the ball, pointing sharply upward and slightly to the right. This arrow defines the ball's initial trajectory. At the top of the arena, there are five numbered holes, 1 through 5, arranged fr... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the newly drawn trajectory, the black line proceeds straight from the ball's origin toward the top wall. Because the angle is so steep and the ball is already positioned quite far to the right, the path does not intersect the right-side vertical wall. Instead, the line terminates exactly at the top boundary l... | train | mit | procedural_grid | 8,994 | S5.replay_unsupported | ||
c880ebb5de3ab42a | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 2 | To determine which hole the red ball will enter, we first observe its initial state. The ball is located in the upper-left quadrant of the square enclosure. A green arrow indicates its initial trajectory, pointing upwards and to the left. Based on this vector, the ball is moving toward the left wall at a steep upward a... | Upon hitting the left wall, the ball follows the law of reflection: the angle of incidence equals the angle of reflection. Since the wall is vertical, the vertical component of the ball's velocity remains unchanged (it continues moving upward), while the horizontal component is reversed, causing it to move toward the r... | null | Not supported with pagination yet | null | Not supported with pagination yet | null | Not supported with pagination yet | Observing the point where the ball reaches the top boundary, it lands squarely within the section labeled "1". The ball has successfully traveled from its starting point, bounced once off the left wall, and headed straight into the first available opening. There are no further walls to reflect off of once it enters the... | train | mit | procedural_grid | 10,179 | S5.replay_unsupported | |||
6bed23f87820dd3c | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 3 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its initial state and environment. The ball is positioned in the upper right quadrant of a square container, specifically at coordinates (5.39, 7.79). A green arrow indicates its starting trajectory, pointing downwards and slightly to the right at a... | The ball has completed its first leg, hitting the bottom wall at position (8.62, 0.00). According to the rules of ideal reflection, the vertical component of its velocity reverses while the horizontal component remains the same. This causes the ball to bounce upward and continue its rightward progress. Looking at the g... | The second reflection occurs at the right wall at position (10.00, 3.34). At this stage, the horizontal velocity component reverses, sending the ball toward the left, while it continues to travel upward. Given the steepness of the angle and the current position, the ball is now heading directly toward the top boundary ... | null | Not supported with pagination yet | null | Not supported with pagination yet | The ball reaches the top boundary at position (7.24, 10.00). By observing the horizontal layout of the holes at the top of the frame, we can see that Hole 1, Hole 2, Hole 3, and Hole 4 are arranged from left to right. The coordinate (7.24, 10.00) falls squarely within the boundaries of the third rectangular opening. Af... | train | mit | procedural_grid | 13,782 | S5.replay_unsupported | ||||
d1f3258a93db2ef5 | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 3 | In the initial setup, we observe a red ball positioned in the right half of a square enclosure. A green arrow points from the ball toward the right wall at a shallow upward angle, approximately 20.67 degrees above the horizontal. Above the main enclosure, there are three numbered rectangular holes: Hole 1 on the left, ... | The ball has now hit the right wall at a point slightly above its starting height. According to the rules of ideal reflection, the component of velocity perpendicular to the wall is reversed, while the parallel component remains the same. This means the ball will now travel toward the left wall while continuing its upw... | Upon reaching the left wall, the ball is now much higher than it was at the previous bounce. Observing the trajectory, the ball hits the left boundary just below the top edge of the enclosure. Following the same law of reflection, the horizontal velocity is reversed again, meaning the ball will now move toward the righ... | null | Not supported with pagination yet | null | Not supported with pagination yet | As the ball travels from the left wall toward the right, it immediately crosses the plane of the top boundary. By extending the path, we can see that the ball reaches the top wall at a position corresponding to the first hole. Specifically, the trajectory places the ball well within the horizontal boundaries of Hole 1.... | train | mit | procedural_grid | 13,856 | S5.replay_unsupported | ||||
3a502ec7d34f2b8a | motif_ball_tracking | ball_tracking_naive | **Rules:**
1. There is a red ball and a green arrow; the arrow indicates the ball's initial direction of motion;
2. At the top of the image, there are several rectangular holes arranged horizontally, numbered from left to right starting at 1;
3. The black boundaries of the image represent solid walls. When the ball hit... | null | 1 | 1 | 3 | To determine which hole the red ball will enter, we must first analyze its starting position and initial trajectory. The ball is located in the right half of the square enclosure, and a green arrow points upward and to the right. This indicates that the ball's first movement will be a straight line toward the right-han... | The ball has hit the right wall. According to the rules of ideal reflection, the angle of incidence equals the angle of reflection. Since the ball was moving up and to the right, it will now reflect and travel up and to the left. The vertical component of its velocity remains unchanged, so it continues to ascend while ... | Upon striking the left wall, the ball undergoes another reflection. Having been moving up and to the left, the reversal of its horizontal velocity component means it will now move up and to the right. The angle of this new path will mirror its previous approach relative to the wall's normal.
I will now visualize the f... | null | Not supported with pagination yet | null | Not supported with pagination yet | By observing the final trajectory, we can see that the red ball strikes the top boundary within the section labeled "1". The path shows the ball traveled from the right wall to the left wall, and then reflected perfectly into the first hole.
In summary, the ball followed a clear path: it bounced off the right wall, tr... | train | mit | procedural_grid | 13,704 | S5.replay_unsupported |
Spatial MMCoT v1 · motif
MoTiF (OpenRaiser/MoTiF), the naive arm of its procedurally generated multi-step tasks: ball_tracking_naive, manipulation_naive, maze_naive (manipulation shows MoTiF's own CLEVR-style 3D renders of solids, not images from the CLEVR dataset). Each step has its own target image. The reflexion arm, which pairs each problem with a deliberately corrupted frame, is not included. sokoban_naive is excluded (7,997 upstream rows, S0.task_excluded): its eight numeric options are generated from the answer, so the correct option is the largest option minus 7 on almost every row, and the task can be answered from the option text without looking at the board. Manipulation can be partly answered without the image, in two ways: count questions ('how many ...') offer four consecutive integers and the correct count is never the largest of them, and for 'what is the object ...' questions the option named last in the operation list, and not in the question, is often right. Report manipulation scores next to the text-only baselines, with count questions scored separately (numbers under Known issues). VisWorld-Eval (thuml/VisWorld-Eval) ballgame uses the same rule text and question as ball_tracking_naive, so it is in-domain; VisWorld-Eval multihop asks the same kind of question as manipulation_naive (numbered place, swap, change and remove operations on CLEVR-style rendered scenes, then where an object is or which object is where); its wording is paraphrased and S11 found no shared images, so it is near-domain. Do not report either as out-of-distribution for a model trained on this source. Every read-back ends with a \boxed{} that holds the <answer> key (rows with no box were refused at conversion, S0.no_boxed_answer). On 12 rows upstream boxed the option's value instead of its key; that box was rewritten to the key (flag S0.boxed_value_to_key), so those read-backs are not verbatim.
Supervision kind (supervision_kind in meta): full_interleaved on every row: the upstream trace itself interleaves text and target images (drawn or rendered states on most sources; the source note above says which), and the read-back comes after the target image it reads. The text is upstream's and was not checked against the images.
Upstream: OpenRaiser/MoTiF. Licence: mit.
Known issues
Rows with a measured per-row problem are listed in reports/known_issues/, one TSV per issue (a # <description> line, then row_uid<TAB>split<TAB>detail lines), so they can be filtered out. They are still in this release: no row was removed for these issues.
| issue | rows | train | validation | what | how it was found | file |
|---|---|---|---|---|---|---|
count_options_give_answer |
147 | 144 | 3 | Count questions offer four consecutive integers and the correct count is never the largest; when the smallest option is above 0 the answer is always the second largest (options 1-4 mean 3, options 2-5 mean 4), so these rows can be answered from the options alone. | task manipulation_naive, a 'how many' question whose four options are consecutive integers with the smallest above 0; measured 2026-10-01; known_issues.py sha1 b2249331; export b3fa1b9 rows 49ce42f4/07653074 | reports/known_issues/count_options_give_answer.tsv |
To leave the listed rows out (the snippet in the loader section downloads reports/known_issues/ with the data):
import glob, os
root = "<root>/motif"
drop = {line.split("\t")[0] for f in glob.glob(os.path.join(root, "reports/known_issues/*.tsv"))
for line in open(f) if line.strip() and not line.startswith(("#", "row_uid\t"))}
# keep a row when its row_uid (a column of train/, meta/ and preview/) is not in drop
Measured caveats
Measured on this release by the pre-publication review (2026-09-25): problems that cannot be listed row by row (a shortcut in the options, a label convention, an upstream labelling scheme) and what the review found around the lists above. Where a caveat counts listed rows ("listed as ..."), the count is the table's, read from reports/known_issues/summary.json. Its other numbers are the review's own measurements, which no file carries: they hold for exactly these rows and are not re-measured automatically. Items marked Training-signal defect are problems in what the rows teach, not only in how they are described; no row was removed for them.
- All 2,094 rows S4c quarantined are
manipulation_naiverows. The read-back states its answer in words and then boxes the option letter ('... the answer is the blue cylinder. The final answer is \boxed{D}'); the check compares the first 30 characters after 'answer is' or 'Answer:' with the letter and could not match those words. Re-read against the upstream text, 2,090 of them each name the labelled option, name it with another option (6) or state no option (8), and none names a different one; the other 4 were not re-read. They are 26.2% of the task's 7,980 convertible rows, and the loss falls unevenly: 32.6% of 'what is the object ...' questions (1,697 of 5,199), 11.9% of 'how many' (242 of 2,031) and 20.6% of 'where' questions (151 of 734). The released manipulation rows are therefore 59.4% object, 30.8% count and 9.9% 'where' questions, against 65.3% / 25.5% / 9.2% upstream. - Training-signal defect. Count questions in
manipulation_naive('how many ...', 1,743 training and 41 validation rows) can be answered from the option list: the four options are consecutive integers and the correct count is never the largest (0 of 1,743 train, 0 of 41 validation). Options 1-4 always mean 3 and options 2-5 always mean 4: the 147 rows (144 train, 3 validation; listed ascount_options_give_answer) whose smallest option is above 0 are answered by their options alone. On options 0-3 the answer is 1 on 774 of 1,599 training rows (48.4%). A rule that reads only the option list scores 918 of 1,743 = 0.527 on the training count rows, against 0.25 chance. S13's rank cap did not run on these rows, because the manipulation group mixes numeric and object options; rank 1 holds 44.4% of the count rows.
Size
| split | rows | target image slots | distinct target images |
|---|---|---|---|
| train | 20,429 | 43,209 | 43,177 |
| validation | 636 | 1,349 | 1,349 |
A slot is one target position in one row; rows can share a target image (same scene or same intermediate state), and a row can repeat one of its own targets, so there are fewer distinct images (by content hash) than slots.
| task | train | validation |
|---|---|---|
| ball_tracking_naive | 7,753 | 232 |
| manipulation_naive | 5,629 | 168 |
| maze_naive | 7,047 | 236 |
Input images per row: 1. Target images per row (the images the model is trained to generate): 1 to 4.
Image corpus (source_scene_corpus): procedural_grid 15,268, blender_clevr 5,797. procedural_grid is this pipeline's label for any procedurally generated synthetic image (2D grid puzzles and simple 3D renders of primitive objects alike); the source note above says what the images show.
Row format
One row is: input image(s) and a question, then K rounds of thought → target image (the target is the source's own ground-truth image, which the model is trained to generate), then a final thought (normally a read-back of the last target; where a source's final thought is something else, or often leaves out the answer, the source note or Known issues says so) and the answer; here K is 1 to 4. In the train config:
image_list list<binary> inputs first, then the K target images in order
num_input_images int64 how many of image_list are inputs
instruction_list list<string> one element: system prompt + question, + options on 5,797 of 21,065 rows
output_text_list list<string> K+1 elements:
[0] <think>plan 1</think><image_start>
[j] <image_end><think>plan j+1</think><image_start>
[K] <image_end><think>read-back</think><answer>answer</answer>
row_uid string join key to `meta` and `preview`
Every image is a JPEG, and no input image is larger than 512 px on its long edge (measured on this release, 2026-09-25); the size each target was stored at is target_px in meta.
<answer> holds what the model is trained to emit. On 15,268 of 21,065 rows it equals meta.answer_value; on the other 5,797 (answer type mcq_letter 5,797) it holds the option key (a letter for mcq_letter), while meta.answer_value (the answer column of preview) holds that option's text. Map the key through the options listed in the question before comparing the two, and score model output against <answer>.
The system prompt is ThinkMorph's VLM_THINK_SYSTEM_PROMPT from its inferencer.py, verbatim (GEN_THINK_SYSTEM_PROMPT there has the same text), including its leading and trailing newline. The markers are plain strings, not tokenizer special tokens; the prompt writes </image_end> and the data writes <image_end>, exactly as the ThinkMorph-7B checkpoint was trained.
preview shows the same rows with one column per slot: input_image_i for the inputs; for each of the K = num_steps rounds, the plan thought_j and its target target_image_j, both empty for K <= j < 5; and the read-back in thought_5 on every row.
meta holds the per-row sidecar: task, scene_id and geometry_uid (the scene and geometry keys; the split key is named in the split paragraph below), trajectory_id (a camera-path or sample label, empty where the source has none), num_steps, num_input_images, answer_type, answer_value, majority_class_rate, target_image_kind, target_px, est_tokens, licence, split (train / validation, the Hub split names), supervision_kind (full_interleaved / visual_aux / visual_only) and filter_flags. majority_class_rate is the share of the task's most frequent answer_value among its training rows: it measures answer skew and is not a guessing baseline (where a task mixes question types or each row has its own options it can be far below chance); compare scores with the text-only baselines below.
Per-row license in meta: mit 21,065.
Flags on released rows (filter_flags in meta and preview, comma-separated):
| flag | rows | meaning |
|---|---|---|
S5.replay_unsupported |
21,065 | no solver re-derives this task's answer from the trace, so S5 did not replay it |
S8.phash_near_but_distinct |
10,272 | a target's perceptual hash is within 6 bits of an input image's, but its pixels differ, so it is not a copy; kept |
S14.sampled_qa |
200 | chosen for the S14 human spot-check (reports/s14_sample.tsv) |
S0.boxed_value_to_key |
12 | upstream boxed the option's value; the read-back's \boxed{} was rewritten to the option key |
S0.row_uid_salted |
3 | the content-derived row_uid repeated within the build and was re-derived |
Training with a BAGEL-family loader
Every row here has one input image (num_input_images is 1), so the stock ThinkMorph UnifiedEditIterableDataset (https://github.com/ThinkMorph/ThinkMorph: image_list[0] as input, image_list[j+1] after output_text_list[j]) and the IPT release's version (which reads num_input_images) both read it as intended. Mixed with a source whose rows have more than one input image, only a loader that reads num_input_images is correct.
The stock BAGEL edit loader (ByteDance-Seed/Bagel) cannot train these rows: it never reads output_text_list and expects each instruction_list element to be a list of paraphrases.
parquet_info.json keys each training chunk as <source>/<split>/<file>, here motif/train/chunk_00000.parquet, with row-group counts read from the parquet footers. The loader matches a chunk only when its key equals the path it builds, os.path.join(data_dir, file), and skips a chunk with no key without a warning: a source that is alone in its group then fails with IndexError: list index out of range, and in a mixed group it adds no rows. Download into a directory named after the source, not after the repository:
from huggingface_hub import snapshot_download
snapshot_download("yrlyrl/spatial-mmcot-motif", repo_type="dataset", local_dir="<root>/motif",
allow_patterns=["train/*", "validation/*", "parquet_info.json", "reports/known_issues/*"])
Then either run from <root> with data_dir: motif/train and parquet_info_path: motif/parquet_info.json, or rebuild the index with absolute keys and use an absolute data_dir:
import json, os
root = "/abs/path/to/root" # the directory that holds motif/
info = json.load(open(os.path.join(root, "motif", "parquet_info.json")))
info = {os.path.join(root, k): v for k, v in info.items()}
json.dump(info, open(os.path.join(root, "motif", "parquet_info_abs.json"), "w"))
# data_dir = os.path.join(root, "motif", "train") (spelled exactly so, no trailing slash)
# parquet_info_path = os.path.join(root, "motif", "parquet_info_abs.json")
The Hugging Face cache (.../snapshots/<hash>/train/) or a folder named spatial-mmcot-motif matches no key.
num_used_data counts chunk files, not rows: the loader repeats this source's file list up to that number, lists every (file, row group) pair, and deals whole row groups out, floor(R / world_size) to each rank and floor(that / num_workers) to each DataLoader worker. The remainder is never read. This source has 1 training chunk file holding 160 row groups of up to 128 rows, so keep num_used_data large, e.g. the 128 of ThinkMorph's interleaved_reasoning.yaml (upstream's example.yaml asks for more than GPUs x workers); every row group is then read. In a run that mixes sources, give each source the same multiple of its own training chunk-file count, e.g. 128 per file (128 here): the file list is repeated up to num_used_data entries, so a flat 128 for every source would read a two-file source's rows half as often as a one-file source's.
How the rows were chosen
| stage | rows |
|---|---|
| upstream rows read | 31,362 |
refused before conversion (S0raw; each reason is in the table below) |
8,092 |
| quarantined at S4c (an automatic check could not match the read-back's conclusion to the label) | 2,094 |
| dropped at S5 (the text contains a phrase from S5's self-contradiction list, e.g. 'does not make sense', 'discrepancy', 'there must be a mistake'; a keyword match, not a comparison with the images, so it also removes some sound rows) | 37 |
| dropped at S8 (a target was removed as a copy of an input, as transparent or as too small, and the row had no target left or was a multi-step chain that cannot lose a state) | 70 |
| after conversion and per-row filters | 21,069 |
| removed by S10 (3 exact duplicates; 1 near duplicate) | 4 |
| removed by answer-prior balancing (S13) | 0 |
| released | 21,065 |
Every removed row has one line, with its reason, in reports/:
| file | step | reason (the line's flag, or the field shown) |
rows |
|---|---|---|---|
build/dropped.jsonl |
S0raw | S0.task_excluded |
7,997 |
build/dropped.jsonl |
S0raw | S0.no_boxed_answer |
95 |
build/dropped.jsonl |
S5 | S5.self_contradiction |
37 |
build/dropped.jsonl |
S8 | S8.chain_broken |
70 |
build/quarantine.jsonl |
S4c | S4c.cot_label_conflict |
2,094 |
s10_dropped.jsonl |
S10 | level: exact |
3 |
s10_dropped.jsonl |
S10 | level: near |
1 |
S0raw lines in build/dropped.jsonl were refused before a release row existed, so their row_uid field holds the converter's key for the upstream record, not a 16-hex row_uid; lines from later steps carry the row_uid the row had. No removed row appears in meta or preview. For this source the key is built from upstream fields that repeat across rows (for most sources a hash of the question text), so it is not unique: the 95 S0.no_boxed_answer lines carry 22 distinct keys; the 7,997 S0.task_excluded lines carry 7,949 distinct keys. Those rows are counted with their reason but cannot be traced to individual upstream rows.
2,094 rows were quarantined rather than dropped (S4c): an automatic check could not match the read-back's stated conclusion to the stored label. 2,090 of them were re-read afterwards against the upstream text, and none of those is a wrong label (see Known issues).
S8.k_zero and S8.chain_broken name what happened to the row, not which check removed the image; the lines in this build do not record whether it was the size, transparency or copy check.
Per-step counters of the conversion
31,362 upstream rows were read; S0raw refused 8,092 before a row existed and passed 23,270 to the first step. S0 runs once more, last, on the final bytes. The reason for every refused, dropped or quarantined row is in the files above.
| step | in | out | dropped | quarantined | rejected | repaired |
|---|---|---|---|---|---|---|
| S0raw (refused before conversion) | 31,362 | 23,270 | 0 | 0 | 8,092 | 0 |
| S4 | 23,270 | 23,270 | 0 | 0 | 0 | 0 |
| S4c | 23,270 | 21,176 | 0 | 2,094 | 0 | 0 |
| S5 | 21,176 | 21,139 | 37 | 0 | 0 | 0 |
| S8 | 21,139 | 21,069 | 70 | 0 | 0 | 0 |
| S9 | 21,069 | 21,069 | 0 | 0 | 0 | 0 |
| S0 (final structural check, after S9) | 21,069 | 21,069 | 0 | 0 | 0 | 0 |
The train/validation split keeps rows sharing a scene_id in meta on one side, and the assignment is frozen (splits/ in the summary repository). MoTiF has no scene ids: scene_id is the md5 of the upstream input image, so a key is one puzzle's starting image. S12 saw 21,065 rows under 21,040 keys; 17 rows joined another key because they share an input image. No validation input image has the content of a training input image, and none is a pixel-level near-copy of one. S12 does not record per source whether that test ran, but it skips it only for a source whose spec sets split_leak_pixels: false, and no spec does; over all sources it compared 21,661 candidate pairs (perceptual hash within 6 bits) pixel by pixel and found no near-copy (checked 2026-09-25). Target images are not covered by that check: 1 target-image slot in validation rows holds an image with the same content as a training target image (S12 compares a 64x64 greyscale hash and counts slots, so an image repeated in validation counts each time). These are states that other puzzles also reach, as a step or as their final state.
Answer-prior balancing (S13)
Each (task, split) group is checked separately. An answer is the answer value compared as lower-cased text without a trailing full stop, with 'farther' read as 'further' and 'nearer' as 'closer' (for multiple choice, the option text, not the letter; where the candidates are drawn in the image, as in zebra_jigsaw and zebra_tetris, the answer is the letter itself). An answer is real when it holds at least 5 rows and 2% of the group; k is the number of real answers. Answer step: the target is max(30%, 1/k) when k >= 2, and max(30%, 1/d) over the d distinct answers when k = 1; a validation group uses the larger of its own target and its task's train target. A group is cut only when k >= 1 and its most common answer holds more than the target plus 5 percentage points; every answer is then capped at one common count, chosen so that none exceeds the target, and smaller answers keep all their rows. At the answer step, a group at or below that trigger, or with no real answer (k = 0), is left as it is, so its most common answer can hold up to the target plus 5 percentage points. A task whose train group has exactly two real answers is instead cut, in every split, so that its two largest answers have equal counts, with no trigger. Rank and label steps: then, in a group where every option value of every row is a number, the rank of the correct option among the sorted values, and after it, in a group where every trained answer is an option label, the label, are each capped by the same cut-and-trigger rule on their own counts (own target, validation included): capped, never evened out, so two labels are cut only when one exceeds 55%, and then only down to 50%. These steps can also cut groups the answer step left whole, including k = 0 groups, and can raise an answer's final share above its target; the run fails if a real answer ends above the target plus 5 percentage points. A train group of at least 20 rows in which one answer holds 90% or more fails the run. PET (exact_cells_pet) instead cuts each (question type x turn direction) cell to equal counts of its two answers; a PET cell that shows only one answer is removed.
| task | split | pass | rule | rows in → out | real answers k | target | largest share, before → after | cut |
|---|---|---|---|---|---|---|---|---|
| ball_tracking_naive | train | answer | cap30[canon] |
7,753 → 7,753 | 5 | 30.0% | 28.6% → 28.6% | no |
| ball_tracking_naive | validation | answer | cap30[canon] |
232 → 232 | 5 | 30.0% | 32.8% → 32.8% | no |
| manipulation_naive | train | answer | cap30[canon] |
5,629 → 5,629 | 26 | 30.0% | 13.8% → 13.8% | no |
| manipulation_naive | train | letter | cap30[letter] |
5,629 → 5,629 | 4 | 30.0% | 26.5% → 26.5% | no |
| manipulation_naive | validation | answer | cap30[canon] |
168 → 168 | 17 | 30.0% | 8.3% → 8.3% | no |
| manipulation_naive | validation | letter | cap30[letter] |
168 → 168 | 4 | 30.0% | 29.2% → 29.2% | no |
| maze_naive | train | answer | cap30[canon] |
7,047 → 7,047 | 11 | 30.0% | 13.8% → 13.8% | no |
| maze_naive | validation | answer | cap30[canon] |
236 → 236 | 10 | 30.0% | 14.8% → 14.8% | no |
S13 removed no row from this source.
Text-only baselines
Accuracy of guessers that never see an image. For each task the released training rows are split into two fixed halves by a hash of row_uid; each guesser is fitted on one half and scored once on the other (one held-out half, not cross-validation; eval rows below). The reference is chance (the mean of 1 / number of options) where every row is multiple choice, and otherwise the eval-half accuracy of always giving the answer most common in the fit half (when a task's top answers are nearly tied, this need not be the task's most common answer; the line after the table gives that answer's validation score). Accuracies are recounted from the stored rates and eval rows, so they are exact. A task is flagged when a text-only guesser beats its reference by more than 0.15 (for a free-form task, a guesser other than the most common answer). A flagged task can be partly answered from the text alone; an unflagged task passed only these probes, which do not prove the text carries no answer. Report scores on every task next to this baseline.
Guessers: keywords: the most common answer per set of spatial words in the question; last_mentioned: the option named last in the question body; letter_prior: the most common answer letter; majority: the answer most common in the fit half; numeric_offset: where every option is a number, the smallest or largest option plus or minus the offset the correct one sat at most often (last_mentioned on the other rows); option_prior: the option text that won most often when shown; option_rank: where every option is a number, the option at the rank among the sorted values that the correct one held most often (last_mentioned on the other rows); template: the most common answer per question wording (numbers masked, object names kept).
| task | best text-only guesser | accuracy | reference | margin | eval rows | flagged |
|---|---|---|---|---|---|---|
| ball_tracking_naive | keywords |
0.249 | 0.249 (majority) | +0.000 | 3,888 | no |
| manipulation_naive | option_rank, rank 1 (0 = smallest) on the 842 numeric-option eval rows; last_mentioned on the other 1925; 0.448 on the 842 numeric-option rows |
0.467 | 0.250 (chance) | +0.217 | 2,767 | yes |
| maze_naive | keywords |
0.127 | 0.127 (majority) | +0.000 | 3,536 | no |
Always giving the most common training answer, scored on the validation split (the constant baseline to compare validation scores with): ball_tracking_naive: always answering 1 (28.6% of training rows) scores 0.328 (76/232); maze_naive: always answering 5 (13.8% of training rows) scores 0.114 (27/236).
For manipulation_naive the count questions alone can be answered from the option list far better than the pooled numbers above show (see Known issues); S13's rank step did not run on them, because the group mixes numeric and object options.
Spot-check (S14)
Pending. The S14 rows are chosen and flagged S14.sampled_qa in meta and preview; the human pass over them has not been signed off yet.
Citation
MoTiF's card gives no citation. Please credit the repository, OpenRaiser/MoTiF (MIT).
Provenance
The release files were written by our conversion code (the code repository is not public yet), scripts/convert/export.py at commit b3fa1b993ca9, from build motif_r3. The build was made by scripts/convert/run_source.py from the same repository at commit 76c78bd817c2. S10, S12 and S13 ran before the export; reports/export_manifest.json pins every input the export read by SHA-1 (build_manifest_sha1, s10_keep_sha1, s12_assignments_sha1, s13_balanced_keep_sha1).
Every row removed between upstream and this release has one line, with its reason, in reports/: build/dropped.jsonl (rows refused before conversion or dropped by a conversion step); build/quarantine.jsonl (rows set aside by S4c because an automatic check could not match the read-back's conclusion to the label); s10_dropped.jsonl (duplicates removed by S10); s10_label_conflicts.jsonl (rows S10 withheld because another row asks the identical question, options in the same order, of the same images with a different answer); s13_dropped.jsonl (rows removed by answer-prior balancing). known_issues/ lists rows with a measured problem (see Known issues); reports/ also holds the build manifest (absolute paths cut to basenames) and counters, the S14 sample list (s14_sample.tsv: row_uid, task, split) and export_manifest.json. In reports/build/manifest.json, spec.source_scene_corpus (procedural_grid) is only the converter's fallback for rows that carry no corpus of their own; it does not describe every row. Each row's corpus is source_scene_corpus in meta (procedural_grid 15,268, blender_clevr 5,797). Part of yrlyrl/spatial-mmcot.
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