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@@ -158,42 +158,37 @@ Best in bold. ‡ Scored over all 137 clips; every other row covers the same 135
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  ### Hand box metric: centroid hit fraction
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- We grade hand boxes one frame at a time. For every frame where a human drew a hand, we take the model's box for that same hand at that same moment and ask one question: does the center of the model's box land inside the human's box? Each yes is a hit. The score is the share of human (frame, hand) pairs the model hits, and any box the model draws outside the span where the human tracked that hand counts against it.
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- $$
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- \mathrm{CHF} = \frac{\big|\{(f,h)\in\mathcal G : \hat b_h(f)\ \text{defined} \wedge c(\hat b_h(f)) \in \operatorname{int} b_{f,h}\}\big|}{|\mathcal G| + |\mathcal E|},
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- \qquad c(b) = \Big(\tfrac{x_1+x_2}{2}, \tfrac{y_1+y_2}{2}\Big)
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- $$
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- Here $\hat b_h(f)$ is the predicted box track for hand $h$, $\mathcal G$ is the set of gold (frame, hand) pairs with gold box $b_{f,h}$, and $\mathcal E$ is the set of predicted boxes outside the time range of their hand's gold track.
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- Models don't all report boxes at 30 fps, so we don't make them. If a model gives us one box a second, we draw a straight line between its boxes and read off where its box would be on every frame in between. A model reporting at 1 fps scores the same as one at 30 fps as long as the hand moves in a straight line between its samples; it only loses credit where the hand actually went somewhere else.
 
 
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- We picked the centroid test over IoU on purpose. Two careful humans boxing the same hand agree on where the hand is far more than on exactly where its edges are, especially with spread fingers or a hand half out of frame. In the animation below, each predicted center is a dot on its own time slice: green if it lands inside the human box, red if it doesn't.
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  ![Centroid hit on one 2 s span: 107 of 120 frame-hands hit, a score of 0.89](assets/hand_box_metric_3d.gif)
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  ### Subtask, action, and hand caption metric: permissible subsegment Jaccard
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- While calibrating our annotators, we initially started with a metric similar to WGO-Bench's semantic F1, where we performed a bipartite matching of predicted clips to ground truth clips and scored their label mismatch with an LLM. Bipartite matching works very well for object boundaries, but not as well for actions over time, because two annotators may break up a timeline at different levels of granularity in ways that are equally valid. We found the same annotator may annotate the same clip at different levels of granularity at different sittings.
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- To remedy this, we developed permissible subsegment Jaccard:
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- $$
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- A(g,p) = \mathbb{1}\big[\,|g\cap p|>0 \;\wedge\; J(\ell_g,\ell_p)\,\big]
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- $$
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- $$
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- \mathrm{PSJ} = \frac{\displaystyle\sum_k\Big(\sum_{p\in P_k}\Big|\bigcup_{g:\,A(g,p)} g\cap p\Big| + \sum_{g\in G_k}\Big|\bigcup_{p:\,A(g,p)} g\cap p\Big|\Big)}{\displaystyle\sum_k\Big(\sum_{p\in P_k}|p| + \sum_{g\in G_k}|g|\Big)}
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- $$
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-
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- On each track $k$ (the subtask track, or each hand), $g$ is a human segment in $G$ and $p$ a model segment in $P$. $J$ is the LLM judge for subtasks and captions, and the Ego4D verb class for hand actions.
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- In words: a predicted segment and a human segment agree if they overlap in time and an LLM judge says they describe the same physical action, allowing for different wording and finer or coarser detail. For hand actions we skip the judge: the two verbs just have to map to the same Ego4D verb class. Then we count time from both sides. Every second of the model's timeline that sits inside an agreeing human segment is credited, and so is every second of the human timeline covered by an agreeing model segment. The score is the credited time over the total time on both timelines. If the model splits a step into finer pieces, or merges a few into one, every second still agrees and it still scores 1. Wrong labels and bad boundaries both cost time.
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  #### Worked example: the stairs
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- The human labels one segment, "sweeping the stairs", from 0 to 5 s.
 
 
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  | Model output | Permissible subsegment Jaccard | WGO-Bench semantic F1 |
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  |---|---|---|
@@ -202,11 +197,25 @@ The human labels one segment, "sweeping the stairs", from 0 to 5 s.
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  | C. "sweeping the stairs" 0–3 s, "putting the broom away" 3–5 s | first piece agrees: (3 + 3) / (5 + 5) = **0.6** | IoU 0.6, below 0.75 → **0.0** |
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  | D. "carrying the broom" 0–5 s | judge says it's a different action → **0.0** | timing matches but the label doesn't → **0.0** |
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- Case B is the one we ran into calibrating annotators: a valid, more detailed breakdown gets zero under one-to-one matching and full credit under our metric. Case C shows we still give partial credit for the part the model got right, where a fixed IoU cutoff gives nothing. (WGO-Bench's semantic F1 pairs segments one-to-one, counts a pair only when its temporal IoU is at least 0.75 and the judge accepts the labels, and scores 2 · matches / (predicted + gold segments).)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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  #### Degenerate baselines
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- To check the metric can't be gamed, we scored answers that ignore the video entirely, with the same metric and judge. Generic labels are "doing chores" for subtasks, "using the hands" for captions and "hold", the most frequent verb, for hand actions.
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  | Answer (no video used) | Subtask | Hand action | Hand caption |
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  |---|---:|---:|---:|
@@ -222,7 +231,7 @@ Label judge: gemini-3.5-flash, temperature 0, thinking off; prompt in the reposi
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  ### Annotation methodology
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- We begin by synthetically labeling videos, and then having humans edit the initial annotations. A member of our research team then reviewed every clip by hand. Across all four annotation types, the average time to re-annotate a video was 116 minutes per minute of video.
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  | Annotation type | Active minutes per minute of video | Agreement of the synthetic seed with the final human labels |
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  |---|---:|---|
@@ -232,11 +241,15 @@ We begin by synthetically labeling videos, and then having humans edit the initi
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  | Hand captions | 32.6 | 0.688 (permissible subsegment Jaccard) |
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  | All four | 115.9 | |
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- Every annotator goes through a calibration with 3 attempts to reach high agreement with a clip labeled by a member of our research staff. Crowdsourced annotators then go through a 10-clip calibration against each other, graded by how high their interannotator agreement is compared to their agreement with the original labels. Through this process we chose 5 annotators for the evaluation set.
 
 
 
 
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  ### Subtasks
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- Open-vocabulary descriptions of what's happening during the video. The average video has 14.0 segments.
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  | Subtask segments | |
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  |---|---:|
@@ -258,7 +271,7 @@ Open-vocabulary descriptions of what's happening during the video. The average v
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  ### Hand boxes
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- Annotated by humans at 10 fps, then smoothed up to 30 fps. The corpus has 417,912 boxes on 216,225 frames.
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  | Hand on screen | % of frames |
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  |---|---:|
@@ -267,10 +280,11 @@ Annotated by humans at 10 fps, then smoothed up to 30 fps. The corpus has 417,91
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  | Both | 94.3% |
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  | Either | 99.0% |
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  | Neither | 1.0% |
 
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  ### Hand actions
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- Annotators choose a label from the closed-vocabulary [Ego4D action schema](https://ego4d-data.org/docs/benchmarks/hands-and-objects/): 118 actions to choose from, 47 of which occur in the release.
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  | Hand actions | Left | Right |
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  |---|---:|---:|
@@ -279,13 +293,14 @@ Annotators choose a label from the closed-vocabulary [Ego4D action schema](https
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  | Mean duration | 2.49 s | 2.39 s |
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  | < 0.5 s | 171 | 248 |
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  | < 1 s | 731 | 939 |
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- | Same action on both hands | 42.7% of video time | 55.8% of time both hands are labeled |
 
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  Most frequent verbs: hold (802), take (615), put (595), fold (427), move (310), arrange (257), adjust (227), smooth (214), lift (207), wash (163).
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  ### Hand captions
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- Annotators write free-form captions describing what the hands are doing. There are 3,948 distinct labels across both hands.
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  | Hand captions | Left | Right |
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  |---|---:|---:|
@@ -294,7 +309,8 @@ Annotators write free-form captions describing what the hands are doing. There a
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  | Mean duration | 2.50 s | 2.38 s |
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  | < 0.5 s | 145 | 179 |
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  | < 1 s | 707 | 844 |
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- | Same caption on both hands | 29.3% of video time | 35.3% of time both hands are labeled |
 
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  ## Citation
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  ### Hand box metric: centroid hit fraction
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+ To measure hand box prediction accuracy, we simply ask each model to produce timestamped bounding boxes for the hand locations throughout the video. For each frame we check whether the centroid of the predicted box falls inside of the ground truth box, we then divide by the total number of frames for which there's an annotation.
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+ We evaluate each model only on the subset of the ground truth corresponding to its configured FPS. For instance Gemini 1FPS would measure the centroid hit fraction only on the 60 frames sampled. Technically this metric is slightly more lenient to lower FPS configurations since higher frame rates give more opportunities to be incorrect, but in practice we see most models perform better at higher frame rate.
 
 
 
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+ Mathematically this can be expressed as
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+ $$
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+ \frac{\displaystyle\sum_{i \in F_p \cup F_t} \mathbb{1}\left[\operatorname{Centroid}(p_i) \in t_i\right]}{\left| F_p \cup F_t \right|}
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+ $$
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+ Where $F_p$ is the set of frames for which there is a predicted hand, $F_t$ is the set of frames for which there's a ground truth hand, and $\operatorname{Centroid}(p_i)$ is an indicator variable indicating if the predicted box has its centroid inside the target box.
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  ![Centroid hit on one 2 s span: 107 of 120 frame-hands hit, a score of 0.89](assets/hand_box_metric_3d.gif)
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  ### Subtask, action, and hand caption metric: permissible subsegment Jaccard
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+ We developed our subtask correctness metric while attempting to find a fair way to calibrate our annotators. We initially used a metric similar to WGO-Bench's semantic F1, which performs bipartite matching between the target and prediction and then calculating F1 between the predicted and target sets.
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+ Bipartite matching, which is common in object segmentation benchmarks, allows each ground truth segment to be paired with exactly one predicted segment. In other words, during scoring, the mapping between predicted and ground truth is one-to-one.
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+ We've found, however, that there are many valid ways to break down the subtasks in a video. Even if you show the same annotator the same video, in one sitting they may break down washing the dishes into a single task or they may break it down into many smaller segments.
 
 
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+ Rather than encouraging models to overfit to one particular choice of temporal granularity, we opted to allow the ground truth and predicted segments to match to each other in a many-to-many mapping, and we've tailored our LLM as judge prompt to permit predicted tasks to be subtasks of the ground truth or vice versa.
 
 
 
 
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+ We call our metric **permissible subsegment jaccard.**
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  #### Worked example: the stairs
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+ Let's say the ground truth labeled the time span 0 to 5s as one segment, "sweeping the stairs".
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+
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+ The table below demonstrates how various predictions would be graded under our many-to-many permissible subsegment jaccard, vs the one-to-one WGO-Bench semantic F1.
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  | Model output | Permissible subsegment Jaccard | WGO-Bench semantic F1 |
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  |---|---|---|
 
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  | C. "sweeping the stairs" 0–3 s, "putting the broom away" 3–5 s | first piece agrees: (3 + 3) / (5 + 5) = **0.6** | IoU 0.6, below 0.75 → **0.0** |
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  | D. "carrying the broom" 0–5 s | judge says it's a different action → **0.0** | timing matches but the label doesn't → **0.0** |
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+ While calibrating annotators, we frequently ran into Case B: a valid, more detailed breakdown gets a score of zero under one-to-one matching and full credit under ours. Case C shows we still give partial credit for the part the model got right, where a fixed IoU cutoff gives nothing. (WGO-Bench's semantic F1 pairs segments one-to-one, counts a pair only when its temporal IoU is at least 0.75 and the judge accepts the labels).
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+
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+ We found that this metric adhered much more closely to subjective measures of fairness when evaluating human annotators' performance during calibration, thus we opted to release it as our official metric for the benchmark.
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+
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+ It can be expressed mathematically as follows:
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+
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+ $$
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+ \operatorname{PSJ}(P, T) = \frac{\displaystyle\sum_{p \in P} m(p, T) + \sum_{t \in T} m(t, P)}{\displaystyle\sum_{p \in P} |I(p)| + \sum_{t \in T} |I(t)|}
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+ $$
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+
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+ $$
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+ m(s, S) = \Bigl|\, I(s) \cap \bigcup_{\substack{s' \in S \\ J(s, s') = 1}} I(s') \,\Bigr|
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+ $$
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+
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+ Let $P$ and $T$ be the predicted and ground-truth segments. Each segment $s$ has a time interval $I(s)$ and a label, and $|\cdot|$ is duration. $J(s,s') \in \{0,1\}$ is the LLM judge's verdict on whether two labels are permissible matches: the same action, or one a subtask of the other. $m(s,S)$ is the portion of $s$'s duration that overlaps some segment in $S$ that the judge accepts.
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  #### Degenerate baselines
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+ In order to ensure the metric isn't trivially gameable check the metric can't be gamed, we scored answers that ignore the video entirely, with the same metric and judge. Generic labels are "doing chores" for subtasks, "using the hands" for captions and "hold", the most frequent verb, for hand actions.
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  | Answer (no video used) | Subtask | Hand action | Hand caption |
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  |---|---:|---:|---:|
 
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  ### Annotation methodology
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+ We begin by synthetically labeling videos, and then having humans edit the initial annotations. We then had a member of our research team review every clip by hand. Due to the quality of our initial annotations and our proprietary review pipeline, we were able to get the overall average time to re-annotate a video down to 116 minutes per minute of video across all four annotation types.
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  | Annotation type | Active minutes per minute of video | Agreement of the synthetic seed with the final human labels |
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  |---|---:|---|
 
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  | Hand captions | 32.6 | 0.688 (permissible subsegment Jaccard) |
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  | All four | 115.9 | |
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+ #### Ensuring annotator quality
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+
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+ Every annotator undergoes a calibration where they have 3 attempts to get high agreement with a clip labeled by a member of our research staff (the minimum performance criteria was determine by having multiple members of our research staff attempt the same clip and then choosing fair guidelines by which to include or exclude participants). After each attempt they are allowed to see what parts of their answer were marked as incorrect (but not able to see the ground truth), they are then allowed to re-attempt the calibration clip after seeing feedback.
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+
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+ After their initial calibration, crowdsourced annotators then go through a 10-clip calibration against each other, where they are graded by how high their interannotator agreement is compared to their agreement with the original labels. Via this process we chose 5 annotators to serve as the annotators on our evaluation set, keeping lower performing members of our annotation pool to work on other tasks.
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  ### Subtasks
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+ Similar to WGO-Bench, we have open vocab descriptions of the high level goal of what task the subject is performing e.g. "scrubbing the stovetop". The average video has 14.0 segments. The distribution of durations is below:
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  | Subtask segments | |
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  |---|---:|
 
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  ### Hand boxes
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+ We annotate every hand box with human annotators at 10FPS then apply proprietary smoothing algorithms to extrapolate up to 30FPS. Here is the percentage of time the right and left hand are on screen in the corpus:
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  | Hand on screen | % of frames |
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  |---|---:|
 
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  | Both | 94.3% |
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  | Either | 99.0% |
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  | Neither | 1.0% |
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+ | Boxes | 417,912 on 216,225 frames |
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  ### Hand actions
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+ We have annotators choose an accurate hand action label from the closed vocabulary [Ego4D action schema](https://ego4d-data.org/docs/benchmarks/hands-and-objects/); there are 118 total actions to choose from (47 occur in the release).
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  | Hand actions | Left | Right |
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  |---|---:|---:|
 
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  | Mean duration | 2.49 s | 2.39 s |
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  | < 0.5 s | 171 | 248 |
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  | < 1 s | 731 | 939 |
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+ | Distinct labels (both hands) | 47 | |
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+ | Time both hands have the exact same action | 42.7% of video time | 55.8% of time both hands are labeled |
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  Most frequent verbs: hold (802), take (615), put (595), fold (427), move (310), arrange (257), adjust (227), smooth (214), lift (207), wash (163).
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  ### Hand captions
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+ We have annotators write free-form hand captions describing what the hands are doing during the video.
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  | Hand captions | Left | Right |
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  |---|---:|---:|
 
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  | Mean duration | 2.50 s | 2.38 s |
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  | < 0.5 s | 145 | 179 |
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  | < 1 s | 707 | 844 |
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+ | Distinct labels (both hands) | 3,948 | |
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+ | Time both hands have the exact same caption | 29.3% of video time | 35.3% of time both hands are labeled |
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  ## Citation
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