Original: C AUSAL A GENTS : A R OBUSTNESS B ENCHMARK FOR M OTION F ORECASTING
Revised: C AUSAL A GENTS : A R OBUSTNESS B ENCHMARK FOR M OTION F ORECASTING

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: As machine learning models become increasingly prevalent in motion forecasting for autonomous vehicles (AVs), it is critical to ensure that model predictions are safe and reliable.
Revised: As machine learning models become increasingly prevalent in motion forecasting for autonomous vehicles (AVs), it is critical to ensure that model predictions are safe and reliable.

Original: However, exhaustively collecting and labeling the data necessary to fully test the long tail of rare and challenging scenarios is difﬁcult and expensive.
Revised: However, exhaustively collecting and labeling the data necessary to fully test the long tail of rare and challenging scenarios is difﬁcult and expensive.

Original: In this work, we construct a new benchmark for evaluating and improving model robustness by applying perturbations to existing data.
Revised: In this work, we construct a new benchmark for evaluating and improving model robustness by applying perturbations to existing data.

Original: Speciﬁcally, we conduct an extensive labeling effort to identify causal agents, or agents whose presence inﬂuences human drivers’ behavior in any format, in the Waymo Open Motion
Revised: Speciﬁcally, we conduct an extensive labeling effort to identify causal agents, or agents whose presence inﬂuences human drivers’ behavior in any format, in the Waymo Open Motion

Original: Dataset (WOMD), and we use these labels to perturb the data by deleting non-causal agents from the scene.
Revised: Dataset (WOMD), and we use these labels to perturb the data by deleting non-causal agents from the scene.

Original: We evaluate a diverse set of state-of-the-art deep-learning model architectures on our proposed benchmark and ﬁnd that all models exhibit large shifts under even non-causal perturbation: we observe a 25 - 38% relative change in minADE as compared to the original.
Revised: We evaluate a diverse set of state-of-the-art deep-learning model architectures on our proposed benchmark and ﬁnd that all models exhibit large shifts under even non-causal perturbation: we observe a 25 - 38% relative change in minADE as compared to the original.

Original: We also investigate techniques to improve model robustness, including increasing the training dataset size and using targeted data augmentations that randomly drop non-causal agents throughout training.
Revised: We also investigate techniques to improve model robustness, including increasing the training dataset size and using targeted data augmentations that randomly drop non-causal agents throughout training.

Original: Finally, we release the causal agent labels as an additional attribute to
Revised: Finally, we release the causal agent labels as an additional attribute to

Original: WOMD and the robustness benchmarks to aid the community in building more reliable and safe deep-learning models for motion forecasting.
Revised: WOMD and the robustness benchmarks to aid the community in building more reliable and safe deep-learning models for motion forecasting (see supplementary).

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Machine learning models are increasingly prevalent in trajectory prediction and motion planning tasks for autonomous vehicles (AVs)
Revised: Machine learning models are increasingly prevalent in trajectory prediction and motion planning tasks for autonomous vehicles (AVs)

Original: (Casas et al., 2020; Chai et al., 2019; Cui et al., 2019; Ettinger et al., 2021; Varadarajan et al., 2021;
Revised: (Casas et al., 2020; Chai et al., 2019; Cui et al., 2019; Ettinger et al., 2021; Varadarajan et al., 2021;

Original: Rhinehart et al., 2019; Lee et al., 2017; Hong et al., 2019;
Revised: Rhinehart et al., 2019; Lee et al., 2017; Hong et al., 2019;

Original: Salzmann et al., 2020; Zhao et al., 2019; Mercat et al., 2020; Khandelwal et al., 2020; Liang et al., 2020).
Revised: Salzmann et al., 2020; Zhao et al., 2019; Mercat et al., 2020; Khandelwal et al., 2020; Liang et al., 2020).

Original: To safely deploy such models, they must have reliable, robust predictions across a diverse range of scenarios and they must be insensitive to spurious features , or patterns in the data that fail to generalize to new environments.
Revised: To safely deploy such models, they must have reliable, robust predictions across a diverse range of scenarios and they must be insensitive to spurious features , or patterns in the data that fail to generalize to new environments.

Original: However, collecting and labeling the required data to both evaluate and improve model robustness is often expensive and difﬁcult, in part due to the long tail of rare and difﬁcult scenarios (Makansi et al., 2021).
Revised: However, collecting and labeling the required data to both evaluate and improve model robustness is often expensive and difﬁcult, in part due to the long tail of rare and difﬁcult scenarios (Makansi et al., 2021).

Original: In this work, we propose perturbing existing data via agent deletions to evaluate and improve model robustness to spurious features.
Revised: In this work, we propose perturbing existing data via agent deletions to evaluate and improve model robustness to spurious features.

Original: To be useful in our setting, the perturbations must preserve the correct labels and not change the ground truth trajectory of the AV.
Revised: To be useful in our setting, the perturbations must preserve the correct labels and not change the ground truth trajectory of the AV.

Original: Since generating such perturbations requires high-level scene understanding as well as causal reasoning, we propose using human labelers to identify irrelevant agents.
Revised: Since generating such perturbations requires high-level scene understanding as well as causal reasoning, we propose using human labelers to identify irrelevant agents.

Original: Speciﬁcally, we deﬁne a non-causal agent as an agent whose deletion does not cause the ground truth trajectory of a given target agent to change.
Revised: Speciﬁcally, we deﬁne a non-causal agent as an agent whose deletion does not cause the ground truth trajectory of a given target agent to change.

Original: We then construct a robustness evaluation dataset that consists of perturbed examples where we remove all non-causal agents from each scene, and we study model behavior under alternate perturbations, such as removing causal agents, removing a subset of non-causal agents, or removing stationary agents.
Revised: We then construct a robustness evaluation dataset that consists of perturbed examples where we remove all non-causal agents from each scene, and we study model behavior under alternate perturbations, such as removing causal agents, removing a subset of non-causal agents, or removing stationary agents.

Original: Using our perturbed datasets, we then conduct an extensive experimental study exploring how factors such as model architecture, dataset size, and data augmentation effect model sensitivity.
Revised: Using our perturbed datasets, we then conduct an extensive experimental study exploring how factors such as model architecture, dataset size, and data augmentation affect model sensitivity.

Original: We also propose novel metrics to quantify model sensitivity, including one that captures per-example absolute changes between predicted and ground truth trajectories and another that directly reﬂects how the model outputs change under perturbation via IoU (intersection-over-union) without referring to the ground truth trajectory.
Revised: We also propose novel metrics to quantify model sensitivity, including one that captures per-example absolute changes between predicted and ground truth trajectories and another that directly reﬂects how the model outputs change under perturbation via IoU (intersection-over-union) without referring to the ground truth trajectory.

Original: The second metric helps to address the issue that the ground truth trajectory is one sample from a distribution of many possibly correct trajectories.
Revised: The second metric helps to address the issue that the ground truth trajectory is one sample from a distribution of many possibly correct trajectories.

Original: Additionally, we visualize scenes with large model sensitivity to understand why performance degrades under perturbations.
Revised: Additionally, we visualize scenes with large model sensitivity to understand why performance degrades under perturbations.

Original: [Figure]
Revised: [Figure]

Original: Our results show that existing motion forecasting models are sensitive to deleting non-causal agents and can have pathological behavior dependencies on faraway or distant agents.
Revised: Our results show that existing motion forecasting models are sensitive to deleting non-causal agents and can have pathological behavior dependencies on faraway or distant agents.

Original: For example, Figure 1 illustrates an original (left) and perturbed (right) scenes with non-causal agents removed.
Revised: For example, Figure 1 illustrates an original (left) and perturbed (right) scenes with non-causal agents removed.

Original: In the perturbed example, the model’s prediction misses the right-turn mode, which corresponds to the ground-truth trajectory.
Revised: In the perturbed example, the model’s prediction misses the right-turn mode, which corresponds to the ground-truth trajectory.

Original: Such brittleness could lead to serious consequences in autonomous driving systems if we rely on deep-learning models without further safety assurance from other techniques such as optimization and robotics algorithms.
Revised: Such brittleness could lead to serious consequences in autonomous driving systems if we rely on deep-learning models without further safety assurance from other techniques such as optimization and robotics algorithms.

Original: The main contributions of our work are as follows:
Revised: The main contributions of our work are as follows:

Original: We contribute a new robustness benchmark for the WOMD for evaluating trajectory prediction models’ sensitivity to spurious correlations.
Revised: We contribute a new robustness benchmark for the WOMD for evaluating trajectory prediction models’ sensitivity to spurious correlations.

Original: We release the causal agent labels from human labelers as additional attributes to WOMD so that researchers can utilize the causal relationships between the agents for robustness evaluation and for other tasks such as agents relevance or ranking (Refaat et al., 2019; Tolstaya et al., 2021).
Revised: We release the causal agent labels from human labelers as additional attributes to WOMD so that researchers can utilize the causal relationships between the agents for robustness evaluation and for other tasks such as agents relevance or ranking (Refaat et al., 2019; Tolstaya et al., 2021).

Original: We introduce two metrics to quantify the robustness of motion forecasting models to perturbations, including absolute per-example change in minADE and a trajectory set metric that measures sensitivity without using the ground truth as a reference.
Revised: We introduce two metrics to quantify the robustness of motion forecasting models to perturbations, including absolute per-example change in minADE and a trajectory set metric that measures sensitivity without using the ground truth as a reference.

Original: We evaluate the robustness of several state-of-the-art motion forecasting models, including Multipath++
Revised: We evaluate the robustness of several state-of-the-art motion forecasting models, including Multipath++

Original: (Varadarajan et al., 2021), Wayformer (Nayakanti et al., 2022) , and
Revised: (Varadarajan et al., 2021), Wayformer (Nayakanti et al., 2022) , and

Original: SceneTransformer (Ngiam et al., 2021).
Revised: SceneTransformer (Ngiam et al., 2021).

Original: We show that the absolute per-example change in minADE can range from 0.07-0.23 m (a signiﬁcant 25 − 38% change relative to the original minADE).
Revised: We show that the absolute per-example change in minADE can range from 0.07-0.23 m (a signiﬁcant 25 − 38% change relative to the original minADE).

Original: We ﬁnd that all models are sensitive to deleting non causal agents
Revised: We ﬁnd that all models are sensitive to deleting non causal agents

Original: , and the model with the best overall performance (in terms of regular metrics used to quantify the trajectory prediction performance such as minADE) is not necessarily the most robust.
Revised: , and the model with the best overall performance (in terms of regular metrics used to quantify the trajectory prediction performance such as minADE) is not necessarily the most robust.

Original: We show that increasing training dataset size and targeted data augmentations that remove non-causal agents can help improve model robustness.
Revised: We show that increasing training dataset size and targeted data augmentations that remove non-causal agents can help improve model robustness.

Original: Overall, this is the ﬁrst work focusing on the robustness of trajectory prediction models to perturbations based on human labels.
Revised: Overall, this is the ﬁrst work focusing on the robustness of trajectory prediction models to perturbations based on human labels.

Original: Such robustness is critical for models deployed in a self-driving car where the reliability and safety requirements are of utmost importance.
Revised: Such robustness is critical for models deployed in a self-driving car where the reliability and safety requirements are of utmost importance.

Original: Ultimately, our goal is to provide a robustness benchmark which can aid the community to better evaluate model reliability, detect possible spurious correlations in deep-learning-based trajectory prediction models, and facilitate the development of more robust models or other mitigation techniques such as optimization and traditional robotic algorithms as complementary solutions to minimize safety risks.
Revised: Ultimately, our goal is to provide a robustness benchmark which can aid the community to better evaluate model reliability, detect possible spurious correlations in deep-learning-based trajectory prediction models, and facilitate the development of more robust models or other mitigation techniques such as optimization and traditional robotic algorithms as complementary solutions to minimize safety risks.

Original:  R ELATED WORK
Revised:  R ELATED WORK

Original: Robustness evaluation on perturbations.
Revised: Robustness evaluation on perturbations.

Original: Machine learning models are known to have brittle predictions under distribution shift.
Revised: Machine learning models are known to have brittle predictions under distribution shift.

Original: Across multiple domains, researchers have proposed robustness evaluation protocols that move beyond a ﬁxed test set (Recht et al., 2019; Biggio & Roli, 2018;
Revised: Across multiple domains, researchers have proposed robustness evaluation protocols that move beyond a ﬁxed test set (Recht et al., 2019; Biggio & Roli, 2018;

Original: Szegedy et al., 2013; Hendrycks & Dietterich, 2019;
Revised: Szegedy et al., 2013; Hendrycks & Dietterich, 2019;

Original: Gu et al., 2019; Shankar et al., 2019; Taori et al., 2020).
Revised: Gu et al., 2019; Shankar et al., 2019; Taori et al., 2020).

Original: Evaluation can be broadly categorized into three types: (i) slicing, i.e. existing test data is sliced over multiple dimensions, (ii) perturbations, i.e. existing test data is modiﬁed via transformations, or (iii) dataset shift, i.e. new test data is drawn from a different distribution.
Revised: Evaluation can be broadly categorized into three types: (i) slicing, i.e. existing test data is sliced over multiple dimensions, (ii) perturbations, i.e. existing test data is modiﬁed via transformations, or (iii) dataset shift, i.e. new test data is drawn from a different distribution.

Original: Our work focuses on perturbations, which have previously been explored in both computer vision and NLP.
Revised: Our work focuses on perturbations, which have previously been explored in both computer vision and NLP.

Original: In computer vision, researchers perturb images via pixel level noise corruptions (Geirhos et al., 2018;
Revised: In computer vision, researchers perturb images via pixel level noise corruptions (Geirhos et al., 2018;

Original: Hendrycks & Dietterich, 2019), spatial transformations (Engstrom et al., 2019; Fawzi & Frossard, 2015), and adversarial modiﬁcations (Biggio et al., 2013; Szegedy et al., 2013).
Revised: Hendrycks & Dietterich, 2019), spatial transformations (Engstrom et al., 2019; Fawzi & Frossard, 2015), and adversarial modiﬁcations (Biggio et al., 2013; Szegedy et al., 2013).

Original: Such synthetic shifts are easy to apply to arbitrary images, but limited in that they do not test model invariance to more complex modiﬁcations such as deleting or modifying irrelevant parts of the image.
Revised: Such synthetic shifts are easy to apply to arbitrary images, but limited in that they do not test model invariance to more complex modiﬁcations such as deleting or modifying irrelevant parts of the image.

Original: In trajectory prediction, perturbations are potentially more valuable, since the models train on discrete inputs, namely, the agents and the roadgraph.
Revised: In trajectory prediction, perturbations are potentially more valuable, since the models train on discrete inputs, namely, the agents and the roadgraph.

Original: Because of the structure of the problem, it is easier to reliably construct perturbations that do not modify the ground truth labels.
Revised: Because of the structure of the problem, it is easier to reliably construct perturbations that do not modify the ground truth labels.

Original: This situation mirrors that of
Revised: This situation mirrors that of

Original: NLP, where sentences composed of discrete words can be modiﬁed in ways that do not change the prediction task, and indeed, such transformations have proven valuable for testing the robustness of models and identifying possible biases (Dhole et al., 2021).
Revised: NLP, where sentences composed of discrete words can be modiﬁed in ways that do not change the prediction task, and indeed, such transformations have proven valuable for testing the robustness of models and identifying possible biases (Dhole et al., 2021).

Original: Robustness evaluation for trajectory prediction.
Revised: Robustness evaluation for trajectory prediction.

Original: The three types of robustness evaluation (slicing, perturbations, and dataset shift) described above also characterize the trajectory prediction literature.
Revised: The three types of robustness evaluation (slicing, perturbations, and dataset shift) described above also characterize the trajectory prediction literature.

Original: Slicing.
Revised: Slicing.

Original: The most common approach is to slice model performance along different hyperparameters and buckets, such as duration of the historical trajectories (Radwan et al., 2020), size of the training data (Huynh & Alaghband, 2019;
Revised: The most common approach is to slice model performance along different hyperparameters and buckets, such as duration of the historical trajectories (Radwan et al., 2020), size of the training data (Huynh & Alaghband, 2019;

Original: Ngiam et al., 2021), sampling frequency (Bera et al., 2016), number of agents in the scene (Rhinehart et al., 2019; Ngiam et al., 2021), criticality / interactivity of the scenarios (Kooij et al., 2019; Ettinger et al., 2021), and speed of the AV (Ngiam et al., 2021).
Revised: Ngiam et al., 2021), sampling frequency (Bera et al., 2016), number of agents in the scene (Rhinehart et al., 2019; Ngiam et al., 2021), criticality / interactivity of the scenarios (Kooij et al., 2019; Ettinger et al., 2021), and speed of the AV (Ngiam et al., 2021).

Original: Perturbations.
Revised: Perturbations.

Original: Another thread of related work focuses on the robustness of the algorithms to perturbations in both training and test data.
Revised: Another thread of related work focuses on the robustness of the algorithms to perturbations in both training and test data.

Original: For example, (Bera et al., 2016) introduced synthetic sensor noises into both the training and test process to evaluate the model’s accuracy against sensor noises.
Revised: For example, (Bera et al., 2016) introduced synthetic sensor noises into both the training and test process to evaluate the model’s accuracy against sensor noises.

Original: (Han et al., 2019) introduced 30% anomalies into the training data (with extra labels), and evaluated the robustness of the algorithm to anomalies in the training process.
Revised: (Han et al., 2019) introduced 30% anomalies into the training data (with extra labels), and evaluated the robustness of the algorithm to anomalies in the training process.

Original: Dataset shift.
Revised: Dataset shift.

Original: Less work has focused on dataset shift due to the difﬁculty of collecting, annotating, and releasing entirely new data.
Revised: Less work has focused on dataset shift due to the difﬁculty of collecting, annotating, and releasing entirely new data.

Original: Examples include training and testing in different locations or routes (Sch ¨ oller et al., 2019;
Revised: Examples include training and testing in different locations or routes (Sch ¨ oller et al., 2019;

Original: Sun et al., 2021), weather, time of day, and sensor noise (Sun et al., 2021).
Revised: Sun et al., 2021), weather, time of day, and sensor noise (Sun et al., 2021).

Original: Unlike prior work, we evaluate trajectory prediction models trained on the original dataset on “noncausal” domain shifts instead of hard domain shifts (such as weather or locations) since we manually transform our test set by leveraging the causal relationships among agents in the scene.
Revised: A related body of work has studied adversarial robustness for trajectory prediction. In particular, Cao et al. (2022b) propose an adversarial training framework for trajectory predictions as well as domain-speciﬁc data augmentations and show that both empirically improve robustness to adversarial attacks.

Original: Because these non-causal perturbations are closer to the original validation dataset than the hard domain shifts, the discrepancies we observe are in some ways a more immediate priority for improving model robustness.
Revised: Additionally, researchers have generated more realistic adversarial attack models and benchmarked models against them: Cao et al. (2022a) generates adversarial realistic trajectories using a differentiable dynamic model, Zhang et al. (2022) perturbs existing trajectories to maximize prediction error, Saadatnejad et al.

Original: We focus on evaluating models’ sensitivity to  agent interactions because that is a complicated component of trajectory prediction and is crucially important for safety.
Revised: (2022) perturbs trajectories to result in agent collisions, and Wang et al. (2021) simulates directly from sensor data to modify trajectories in a physically plausible manner. Unlike prior work, we evaluate model robustness to “non-causal” domain shifts instead of hard (e.g. weather, location) or adversarial domain shifts. Because these non-causal perturbations are closer to the original validation dataset than the hard domain shifts and do not assume worst-case behavior or presence of an adversary, the discrepancies we observe are in some ways a more immediate priority for improving model robustness.

Original: Agent relevance for autonomous driving.
Revised: Agent relevance.

Original: Since trajectory prediction in autonomous driving systems must reason about other agents in the scene, researchers have attempted to efﬁciently rank agents according to their impact on the AV.
Revised: Since trajectory prediction in AV systems must reason about other agents in the scene, researchers have attempted to efﬁciently rank agents according to their impact on the AV.

Original: The main motivationof this line of work is to determine which agents to allocate  computational resources to for processing in real time.
Revised: The main motivation is to determine which agents to allocate real-time computational resources to.

Original: In particular, Aksoy et al.
Revised: In particular, Aksoy et al.

Original: (2020) proposed a driver’s saliency prediction model which incorporates an attention mechanism to understand salient features for driving context.
Revised: (2020) proposed a driver’s saliency prediction model which incorporates an attention mechanism to understand salient features for driving context.

Original: Refaat et al.
Revised: Refaat et al.

Original: (2019) approximated an agent’s inﬂuence by looking at the difference between two plans(a planner is running in simulation) when a given agent is accounted for versus not.
Revised: (2019) approximated an agent’s inﬂuence by looking at the difference between two plans when a given agent is accounted for versus not.

Original: However, removing one agent at a time does not account for certain situations where multiple agents may be inﬂuencing the car in the same way i.e. two pedestrians are blocking the path of the car and removing one of the pedestrians has no inﬂuence on the car.
Revised: However, removing one agent at a time does not account for certain situations where multiple agents may be inﬂuencing the car in the same way e.g. two pedestrians are blocking the path of the car and removing one of the pedestrians has no inﬂuence on the car.

Original: In similar work, Tolstaya et al.
Revised: In similar work, Tolstaya et al.

Original: (2021) quantiﬁes interactivity using a deep learning model which can suffer from the same robustness issues.
Revised: (2021) quantiﬁes interactivity using a deep learning model which can suffer from the same robustness issues.

Original: More generally, algorithmically deﬁned importance/relevance or interaction scores can be unreliable, especially in scenes with complex interactions between the AV and surrounding agents.
Revised: More generally, algorithmically deﬁned importance/relevance or interaction scores can be unreliable, especially in scenes with complex interactions between the AV and surrounding agents.

Original: In this work, we use human labeling to decide which agents are important, and our motivation is to use these labels to test model robustness.
Revised: In this work, we use human labeling to decide which agents are important, and our motivation is to use these labels to test model robustness.

Original: In the future, our causal agent labels can be used to verify algorithmic deﬁnitions of agent importance or relevance.
Revised: In the future, our causal agent labels can be used to verify algorithmic deﬁnitions of agent importance or relevance.

Original: Causal reasoning in autonomous driving.
Revised: Causal reasoning in autonomous driving.

Original: In a similar line of work, Ramanishka et al.
Revised: In a similar line of work, Ramanishka et al.

Original: (2018) collect causal annotations using human labelers for the Honda Research Institute Driving Dataset and they slice performance of an object detector over scenes with varying causal attributes.
Revised: (2018) collect causal annotations using human labelers for the Honda Research Institute Driving Dataset and they slice performance of an object detector over scenes with varying causal attributes.

Original: Our work instead uses causal labels to evaluate model robustness for trajectory prediction on WOMD, and we provide more ﬁne-grained per-agent measurements of causality.
Revised: Our work instead uses causal labels to evaluate model robustness for trajectory prediction on WOMD, and we provide more ﬁne-grained per-agent measurements of causality.

Original:  M ETHODS 3. L ABELING CAUSAL AGENTS IN WOMD
Revised:  M ETHODS 3. L ABELING CAUSAL AGENTS IN WOMD

Original: The objective of the labeling task is to identify all agents — cars, cyclists, or pedestrians — that are causal to the AV at any time during a driving segment.
Revised: The objective of the labeling task is to identify all agents — cars, cyclists, or pedestrians — that are causal to the AV at any time during a driving segment.

Original: Although we are more interested in removing non-causal agents from each scene, we ask labelers to identify causal agents since there are typically fewer of them and they tend to be closer to the AV, making them easier for labelers to identify.
Revised: Although we are more interested in removing non-causal agents from each scene, we ask labelers to identify causal agents since there are typically fewer of them and they tend to be closer to the AV, making them easier for labelers to identify.

Original: Data.
Revised: Data.

Original: We focus on labeling the WOMD validation data because our primary goal is to evaluate the robustness of models trained on the original dataset.
Revised: We focus on labeling the WOMD validation data because our primary goal is to evaluate the robustness of models trained on the original dataset.

Original: Each example in WOMD is 9.1 seconds in length (91 steps at 10Hz) and is generated in overlapping windows from a 20-second video segment.
Revised: Each example in WOMD is 9.1 seconds in length (91 steps at 10Hz) and is generated in overlapping windows from a 20-second video segment.

Original: We label the 20-second segments to give labelers access to a longer time horizon and to not waste resources on labeling overlapping scenes.
Revised: We label the 20-second segments to give labelers access to a longer time horizon and to not waste resources on labeling overlapping scenes.

Original: Moreover, both the regular and interactive WOMD validation sets are generated from the same 20-second segments of data, hence, our causal labels can be used for both.
Revised: Moreover, both the regular and interactive WOMD validation sets are generated from the same 20-second segments of data, hence, our causal labels can be used for both.

Original: Labeling policy and UI.
Revised: Labeling policy and UI.

Original: Causality is an inherently subjective label since human drivers may vary in their judgements of which agents in the scene affect their decisions.
Revised: Causality is an inherently subjective label since human drivers may vary in their judgements of which agents in the scene affect their decisions.

Original: Therefore, we want to be overly conservative and identify as many causal agents as possible to maximize the likelihood that removed agents are actually non-causal.
Revised: Therefore, we want to be overly conservative and identify as many causal agents as possible to maximize the likelihood that removed agents are actually non-causal.

Original: If human labelers are unsure if an agent is causal or not, we instruct them to include it as causal.
Revised: If human labelers are unsure if an agent is causal or not, we instruct them to include it as causal.

Original: We emphasize that false positives (identifying an agent as causal when it is truly non-causal) are acceptable to a certain extent, but we should avoid false negatives (failing to identify a truly causal agent).
Revised: We emphasize that false positives (identifying an agent as causal when it is truly non-causal) are acceptable to a certain extent, but we should avoid false negatives (failing to identify a truly causal agent).

Original: (Appendix A includes the exact instructions given to labelers.)
Revised: (Appendix A includes the exact instructions given to labelers.)

Original: That said, in ambiguous situations, we did not expect labelers to reason about chained causality relationships.
Revised: That said, in ambiguous situations, we did not expect labelers to reason about chained causality relationships.

Original: For example, if the AV is driving behind a queue of 5 cars and the ﬁrst car were to brake, it could eventually cause the car in front of the AV to brake.
Revised: For example, if the AV is driving behind a queue of 5 cars and the ﬁrst car were to brake, it could eventually cause the car in front of the AV to brake.

Original: In this situation we would only expect the labeler to identify the car directly in front as causal.
Revised: In this situation we would only expect the labeler to identify the car directly in front as causal.

Original: The labeling UI is a web-based 3D view of the AV and its surroundings in the 20-second segmented videos.
Revised: The labeling UI is a web-based 3D view of the AV and its surroundings in the 20-second segmented videos.

Original: An example is shown in Fig.
Revised: An example is shown in Fig.

Original: 2 where the camera images from a randomly selected scene overlaid with the causal annotations provided by the human labelers.
Revised: 2 where the camera images from a randomly selected scene overlaid with the causal annotations provided by the human labelers.

Original: Human annotations.
Revised: Human annotations.

Original: To maximize coverage and avoid false negatives, each scene is annotated by 5 human labelers and we designate causal agents as all agents that any labeler identiﬁed as causal.
Revised: To maximize coverage and avoid false negatives, each scene is annotated by 5 human labelers and we designate causal agents as all agents that any labeler identiﬁed as causal.

Original: Appendix B shows the distribution over causal agents for the number of human labelers who selected the agent as causal.
Revised: Appendix B shows the distribution over causal agents for the number of human labelers who selected the agent as causal.

Original: The majority of causal agents are selected by all 5 labelers, but a signiﬁcant portion (24%) are selected by only 1 labeler.
Revised: The majority of causal agents are selected by all 5 labelers, but a signiﬁcant portion (24%) are selected by only 1 labeler.

Original: 3. C AUSAL AGENT STATISTICS
Revised: 3. C AUSAL AGENT STATISTICS

Original: To understand the properties of causal agents, we compute several statistics of causal agents in the
Revised: To understand the properties of causal agents, we compute several statistics of causal agents in the

Original: WOMD validation dataset, including the percentage of causal agents (Figure 3a), the distribution of the relative distance between the AV and the causal agents versus all surrounding agents (Figure 3b), and the breakdown of causal versus all surrounding agents by agent type (vehicle, pedestrian, or cyclist) (Figure 3c).
Revised: WOMD validation dataset, including the percentage of causal agents (Figure 3a), the distribution of the relative distance between the AV and the causal agents versus all surrounding agents (Figure 3b), and the breakdown of causal versus all surrounding agents by agent type (vehicle, pedestrian, or cyclist) (Figure 3c).

Original: Figure 3a shows that the majority of agents are actually non-causal: on average, only 13% of the total agents in the scene are labeled as causal, and 93% of scenes have less than 30%  of the agents labeled as causal.
Revised: Figure 3a shows that the majority of agents are actually non-causal: on average, only 13% of the total agents in the scene are labeled as causal, and 93% of scenes have less than 30% [Figure] of the agents labeled as causal.

Original: Figure 3b shows that causal agents are typically closer to the AV than non-causal agents; causal agents are an average distance of 28.4m from the AV, compared to an average of 49.4m over all agents.
Revised: Figure 3b shows that causal agents are typically closer to the AV than non-causal agents; causal agents are an average distance of 28.4m from the AV, compared to an average of 49.4m over all agents.

Original: Figure 3c shows the likelihood that an agent of a given type (Vehicle, Ped, or Cyclist) is causal.
Revised: Figure 3c shows the likelihood that an agent of a given type (Vehicle, Ped, or Cyclist) is causal.

Original: Surprisingly, cyclists are more likely to be causal agents than any other agents, and vehicles are more likely to be causal than pedestrians.
Revised: Surprisingly, cyclists are more likely to be causal agents than any other agents, and vehicles are more likely to be causal than pedestrians.

Original: We hypothesize that this is because cyclists usually share the road with the AV and have a strong prior of not respecting road[Figure] boundaries like a car, whereas there are many parked cars that are not necessarily interacting with the
Revised: We hypothesize that this is because cyclists usually share the road with the AV and have a strong prior of not respecting road boundaries like a car, whereas there are many parked cars that are not necessarily interacting with the

Original: AV and similarly pedestrians can be off the road on sidewalks.
Revised: AV and similarly pedestrians can be off the road on sidewalks.

Original: 3. P ERTURBED DATASETS
Revised: 3. P ERTURBED DATASETS

Original: In this work, we consider perturbations that modify the scene by deleting agents.
Revised: In this work, we consider perturbations that modify the scene by deleting agents.

Original: While it is possible to create more complex perturbations, such as adding noise to the xyz position of the agents, we start with deletion since it directly reﬂects the models’ robustness regarding the causal relationships of agents in the scene.
Revised: While it is possible to create more complex perturbations, such as adding noise to the xyz position of the agents, we start with deletion since it directly reﬂects the models’ robustness regarding the causal relationships of agents in the scene.

Original: Object track states in the WOMD consist of the object’s states (e.g., 3D center point, velocity vector, heading), as well as a valid ﬂag to indicate which time steps have valid measurements.
Revised: Object track states in the WOMD consist of the object’s states (e.g., 3D center point, velocity vector, heading), as well as a valid ﬂag to indicate which time steps have valid measurements.

Original: To delete an agent from the scene, we set its valid mask to false throughout all time steps (and we double check for each model implementation that all agent state is ignored if the valid bit is false).
Revised: To delete an agent from the scene, we set its valid mask to false throughout all time steps (and we double check for each model implementation that all agent state is ignored if the valid bit is false).

Original: We consider four different perturbations:
Revised: We consider four different perturbations:

Original: RemoveNoncausal : Removes all non-causal agents in the dataset. 2.
Revised: RemoveNoncausal : Removes all non-causal agents in the dataset. 2.

Original: RemoveNoncausalEqual :
Revised: RemoveNoncausalEqual :

Original: Removes an equal number of randomly selected non-causal agents as there are causal agents in the scene For example, if a scene has 5 causal agents, we randomly remove 5 non-causal agents.
Revised: Removes an equal number of randomly selected non-causal agents as there are causal agents in the scene. For example, if a scene has 5 causal agents, we randomly remove 5 non-causal agents.

Original: RemoveNoncausalEqual is meant to be a less aggressive form of RemoveNoncausal since it deletes fewer agents and it allows us to compare to RemoveCausal when controlling for the number of agents deleted.
Revised: RemoveNoncausalEqual is meant to be a less aggressive form of RemoveNoncausal since it deletes fewer agents and it allows us to compare to RemoveCausal when controlling for the number of agents deleted.

Original: RemoveStatic :
Revised: RemoveStatic :

Original: Removes agents whose xyz positions do not change above a certain threshold (e.g. parked cars).
Revised: Removes agents whose xyz positions do not change above a certain threshold (e g. parked cars).

Original: We use a threshold of .1 m on the L2 distance of the agent’s xyz state to account for sensor noise.
Revised: We use a threshold of .1 m on the L2 distance of the agent’s xyz state to account for sensor noise.

Original: Not all static agents are non-causal.
Revised: Not all static agents are non-causal.

Original: RemoveCausal : Removes all causal agents; the complement of RemoveNoncausal.
Revised: RemoveCausal : Removes all causal agents; the complement of RemoveNoncausal.

Original: Among them, we categorize both RemoveNoncausal and RemoveNoncausalEqual as “non-causal” perturbations.
Revised: Among them, we categorize both RemoveNoncausal and RemoveNoncausalEqual as “non-causal” perturbations.

Original: Speciﬁcally, to deﬁne non-causal perturbations, let us assume X is a scenario representation, Y is the ground truth trajectory of the AV, and f is the ground-truth model that gives the relationship between X and Y .
Revised: Speciﬁcally, to deﬁne non-causal perturbations, let us assume X is a scenario representation, Y is the ground truth trajectory of the AV, and f is the ground-truth model that gives the relationship between X and Y .

Original: If a perturbation ∆ X satisﬁes f ( X +∆ X ) = f
Revised: If a perturbation ∆ X satisﬁes f ( X +∆ X ) = f

Original: ( X ) =
Revised: ( X ) =

Original: Y , we deﬁne it as noncausal perturbation since it does not impact the relationship between X and Y .
Revised: Y , we deﬁne it as noncausal perturbation since it does not impact the relationship between X and Y .

Original: We deﬁne a deep learning model ˆ f to be robust to non-causal perturbations if ˆ f ( X +∆ X )
Revised: We deﬁne a deep learning model ˆ f to be robust to non-causal perturbations if ˆ f ( X +∆ X )

Original: =
Revised: =

Original: ˆ f ( X ) =
Revised: ˆ f ( X ) =

Original: ˆ Y ∀ non-causal ∆ X , where ˆ Y is the predicted trajectory from the model.
Revised: ˆ Y ∀ non-causal ∆ X , where ˆ Y is the predicted trajectory from the model.

Original: Additionally, we consider RemoveStatic as an important baseline that does not require the human labels.
Revised: Additionally, we consider RemoveStatic as an important baseline that does not require the human labels.

Original: We can thus apply it to the training dataset, which we explore in Section 4.3.
Revised: We can thus apply it to the training dataset, which we explore in Section 4.3.

Original: Finally, we include the RemoveCausal perturbation as a sanity to ensure models are sensitive to deleting causal agents.
Revised: Finally, we include the RemoveCausal perturbation as a sanity to ensure models are sensitive to deleting causal agents.

Original: 3. E VALUATION
Revised: 3. E VALUATION

Original: Since we only have camera and LiDAR data from the AV perspective, we only collect causal labels and evaluate model predictions for the AV trajectory.
Revised: Since we only have camera and LiDAR data from the AV perspective, we only collect causal labels and evaluate model predictions for the AV trajectory.

Original: We report the average minADE (following the deﬁnition from Ettinger et al. over 3, 5 and 8 seconds on both the original and perturbed datasets. 
Revised: We report the average minADE (Ettinger et al., 2021), or minimum Average Displacement Error, which computes the L2 norm between the ground truth trajectory and the model’s closest prediction, over 3, 5 and 8 seconds on both the original and perturbed datasets. We measure minADE in units of meters.

Original: In all instances, we use the top 6 trajectories for each model (K=6).
Revised: In all instances, we use the toptrajectories for each model (K=6).

Original: Robustness Metrics.
Revised: Robustness Metrics.

Original: Since we found in our results that the perturbed minADE often improves for a large fraction of the examples, averaging over examples cancels out some of the effects we would like to measure.
Revised: Since we found in our results that the perturbed minADE often improves for a large fraction of the examples, averaging over examples cancels out some of the effects we would like to measure.

Original: Thus, we introduce a metric to measure the per-example absolute change in minADE:
Revised: Thus, we introduce a metric to measure the per-example absolute change in minADE:

Original: [Equation]
Revised: Abs (∆) = 1 n n (cid:88) i = | perturbed minADE ( i ) − original minADE ( i ) | (1)

Original: We report Abs( ∆ ), the standard deviation of Abs( ∆ ), and the the relative percentage change in
Revised: We report Abs( ∆ ), the standard deviation of Abs( ∆ ), and the the relative percentage change in

Original: Abs( ∆ ) with respect to the original minADE.
Revised: Abs( ∆ ) with respect to the original minADE.

Original: Finally, since the ground truth may represent only one of several correct ways to drive, in Section 4.2 we also consider pairwise differences between the original and perturbed predictions to measure model sensitivity. 
Revised: Finally, since the ground truth may represent only one of several correct ways to drive, in Section 4.2 we also consider pairwise differences between the original and perturbed predictions to measure model sensitivity. [Table]

Original: Model
Revised: The IoU-based metric. The IoU-based trajectory metric is computed as follows: given two predicted trajectory sets (with and without perturabtion), we ﬁrst upsample all predicted trajectories (6 of them in each set) to 100Hz, and then voxelize them into a 2D top down grid with resolution of 0.5 meters. We then count the number of voxels both sets occupy, divided by the total number of voxels either output set occupies.

Original: [Table]
Revised: To simplify computation, we explicitly ignore the probabilities and speeds of trajectories. This measure quantiﬁes ”how geometrically different the trajectories look”. An IoU ofmeans the trajectories did not meaningfully change, and an IoU of 0 means the trajectories do not overlap at all. While more complicated versions of this metric could be computed (e.g. earth movers distance), we found this metric intuitive and useful for ﬁnding interesting shifts due to perturbation.

Original: Models.
Revised: Models.

Original: We select three representative deep learning models for evaluation: MultiPath++ (Varadarajan et al., 2021), Scene Transformer (Ngiam et al., 2021), and Wayformer (Nayakanti et al., 2022).
Revised: We select three representative deep learning models for evaluation: MultiPath++ (Varadarajan et al., 2021), Scene Transformer (Ngiam et al., 2021), and Wayformer (Nayakanti et al., 2022).

Original: Importantly, we only consider non-ensembled models (Multipath++ reports ensemble results in their paper and on the WOMD leaderboard).
Revised: Importantly, we only consider non-ensembled models (Multipath++ reports ensemble results in their paper and on the WOMD leaderboard).

Original: Table 1 reviews the architectural differences and parameter counts of the models.
Revised: Table 1 reviews the architectural differences and parameter counts of the models.

Original: Since we only evaluate on the AV, we typically only train the models to predict the AV, but for MultiPath++ and SceneTransformer we also train models on all agents (which we indicate by appending –All to the model name).
Revised: Since we only evaluate on the AV, we typically only train the models to predict the AV, but for MultiPath++ and SceneTransformer we also train models on all agents (which we indicate by appending –All to the model name).

Original: Additionally, for SceneTransformer–All, we include both the marginal and joint models (these models are the same when training on only the AV.)
Revised: Additionally, for SceneTransformer–All, we include both the marginal and joint models (these models are the same when training on only the AV

Original:  R ESULTS 4. 
Revised:  R ESULTS 4. M ODEL SENSITIVITY TO NON - CAUSAL PERTURBATIONS

Original: [Figure]

Original: In order to understand model sensitivity on a per-example level, Figure 4 plots the perturbed versus original minADE across each perturbation for MultiPath++ (see Appendix H for other models).
Revised: In order to understand model sensitivity on a per-example level, Figure 4 plots the perturbed versus original minADE across each perturbation for MultiPath++ (see Appendix H for other models).

Original: For each perturbation type, we observe that the majority of examples show minimal change (i.e. are clustered around the y = x axis), but a long tail of outlier examples experience a large change ( > 1 m ).
Revised: For each perturbation type, we observe that the majority of examples show minimal change (i.e. are clustered around the y = x axis), but a long tail of outlier examples experience a large change ( > 1 m in minADE).

Original: Among perturbation types, the model is most sensitive to RemoveCausal, which is expected since removing causal agents can change the correct ground-truth trajectory.
Revised: Among perturbation types, the model is most sensitive to RemoveCausal, which is expected since removing causal agents can change the correct ground-truth trajectory.

Original: Interestingly, models are signiﬁcantly more robust to RemoveNoncausalEqual than RemoveNoncausal, which means removing more agents increases model sensitivity.
Revised: Interestingly, models are signiﬁcantly more robust to RemoveNoncausalEqual than RemoveNoncausal, which means removing more agents increases model sensitivity.

Original: When comparing RemoveCausal and RemoveNoncausalEqual, which controls for the number of agents removed, we see that the model is signiﬁcantly more sensitive to removing causal agents than removing non-causal agents.
Revised: When comparing RemoveCausal and RemoveNoncausalEqual, which controls for the number of agents removed, we see that the model is signiﬁcantly more sensitive to removing causal agents than removing non-causal agents.

Original: Surprisingly, across all perturbation types, including RemoveCausal, the model sees a large portion of examples where minADE improves  : 42.7% of examples show an improvement under the RemoveCausal perturbation, 43.0% for RemoveNoncausal, 49.6% for RemoveNoncausalEqual and 51.0% for RemoveStatic.
Revised: Surprisingly, across all perturbation types, including RemoveCausal, the model sees a large portion of examples where minADE improves (i.e. the minADE itself becomes smaller under the perturbation) : 42.7% of examples show an improvement under the RemoveCausal perturbation, 43.0% for RemoveNoncausal, 49.6% for RemoveNoncausalEqual and 51.0% for RemoveStatic.

Original: This ﬁnding is counter-intuitive and motivated us to measure model sensitivity in terms of Abs( ∆ ), deﬁned in Equation 1.
Revised: This ﬁnding is counter-intuitive and motivated us to measure model sensitivity in terms of Abs( ∆ ), deﬁned in Equation 1.

Original: Across all models, the average Abs( ∆ ) is 0.1450 for 
Revised: Across all models, the average Abs( ∆ ) is 0.1450 for RemoveCausal, 0.131 for

Original: RemoveCausal, 0.131 for RemoveNoncausal, 0.051 for RemoveNoncausalEqual, and 0.089 for RemoveStatic.
Revised: RemoveNoncausal, 0.051 for RemoveNoncausalEqual, and 0.089 for RemoveStatic.

Original: Appendix C reports Abs( ∆ ) for each individual model and perturbation type.
Revised: Appendix C reports Abs( ∆ ) for each individual model and perturbation type.

Original: Comparing models.
Revised: Comparing models.

Original: Focusing on the RemoveNoncausal perturbation, in Table 2, we evaluate each modelarchitectures and report the original minADE, perturbed minADE, Abs( ∆ ), the standard deviation of Abs( ∆ ), and Abs (∆)
Revised: Focusing on RemoveNoncausal, in Table 2, we evaluate each model and report the original minADE, perturbed minADE, Abs( ∆ ), the standard deviation of Abs( ∆ ), and Abs (∆)

Original: minADE Ori (see Appendix C for other perturbations.)
Revised: minADE Ori (see Appendix C for other perturbations.)

Original: The SceneTransformer Marginalmodel shows the lowest average absolute sensitivity to the perturbation, whilethe MultiPath++–Allmodel shows the lowest sensitivity relative to original minADE.
Revised: SceneTransformer Marginal shows the lowest average absolute sensitivity, while MultiPath++–All shows the lowest sensitivity relative to original minADE.

Original: In general, Abs( ∆ ) decreases with the original minADE, but there is no clear relationship between relative Abs( ∆ ) and minADE.
Revised: In general, Abs( ∆ ) decreases with the original minADE, but there is no clear relationship between relative Abs( ∆ ) and minADE.

Original: Unexpectedly, the marginal SceneTransformer is more robust than the joint (we hypothesize that jointly modeling agents in the scene causes the model to pay more attention to non-causal agents and thus lead to relatively bad robustness).
Revised: Unexpectedly, the marginal SceneTransformer is more robust than the joint (we hypothesize that jointly modeling agents in the scene causes the model to pay more attention to non-causal agents).

Original: In Appendix G, we reportaggregate results for minFDE, overlap rate, miss rate [Table] and mAP
Revised: In Appendix G, we report minFDE, overlap rate, miss rate, and mAP.

Original: [Table]
Revised: [Table]

Original: Slicing the robustness metric.
Revised: Slicing the robustness metric.

Original: We further slice the robustness of the models (Abs( ∆ )) along several dimensions: AV’s current speed, the percentage of removed non-causal agents (the number of removed non-causal agents divided by the number of all context agents), and the minimum distance from the AV to removed non-causal agents.
Revised: We further slice the robustness of the models (Abs( ∆ )) along several dimensions: AV’s current speed, the percentage of removed non-causal agents (the number of removed non-causal agents divided by the number of all context agents) [Table] and the minimum distance from the AV to removed non-causal agents.

Original: The full results are given in Figure 12 in Appendix E.
Revised: The full results are given in Figure 12 in Appendix E.

Original: We see that, across all models, model sensitivity increases when we drop a larger fraction of non-causal agents and when the speed of the AV is greater.
Revised: We see that, across all models, model sensitivity increases when we drop a larger fraction of non-causal agents and when the speed of the AV is greater.

Original: We also see that model sensitivity typically decreases when we drop agents that are farther away from the AV, though the SceneTransformer models have much noisy robustness measurements when dropping far away agents.
Revised: We also see that model sensitivity typically decreases when we drop agents that are farther away from the AV, though the SceneTransformer models have much noisy robustness measurements when dropping far away agents.

Original: Visualizing examples.
Revised: Visualizing examples.

Original: We also visualize some examples with the largest output changes under the
Revised: We also visualize some examples with the largest output changes under the

Original: RemoveNoncausal perturbation in Appendix E.
Revised: RemoveNoncausal perturbation in Appendix E.

Original: The ﬁndings are discussed in Section 5.
Revised: The ﬁndings are discussed in Section 5.

Original: 4. S ENSITIVITY VIA AN I O U- BASED TRAJECTORY SET METRIC
Revised: 4. S ENSITIVITY VIA AN I O U- BASED TRAJECTORY SET METRIC

Original: To directly measure the magnitude of model output changes with and without perturbation,in this section we introduce a simple IoU (intersection-over-union) based metric  to compare the sensitivityacross models to different perturbations.The IoU-based metric.
Revised: To directly measure the magnitude of model output changes with and without perturbation, we use an IoU (intersection-over-union) based metric (deﬁned in Section 3.4) to compare model sensitivity to different perturbations.

Original: The IoU-based trajectory metric is computed as follows: given two predicted trajectory sets (with and without perturabtion), we ﬁrst upsample all predicted trajectories (6 of them in each set) to 100Hz, and then voxelize them into a 2D top down grid with resolution of 0.5 meters. We then count the number of voxels both sets occupy, divided by the total number of voxels either output set occupies. To simplify computation, we explicitly ignore the probabilities and speeds of trajectories.
Revised: The results of three AV-only models under perturbations RemoveCausal,

Original: This measure quantiﬁes ”how geometrically different the trajectories look”.

Original: An IoU ofmeans the trajectories did not meaningfully change, and an IoU of 0 means the trajectories do not overlap at all. While more complicated versions of this metric could be computed (e.g. earth movers distance), we found this metric intuitive and useful for ﬁnding interesting shifts due to perturbation. Results. The results of three AV-only models under perturbations RemoveCausal, RemoveNoncausal and RemoveNoncausalEqual are shown in Figure 5.
Revised: RemoveNoncausal and RemoveNoncausalEqual are shown in Figure 5.

Original: We ﬁnd that models are least sensitive to RemoveNoncausalEqual, and much more sensitive to RemoveCausal and RemoveNoncausal.
Revised: We ﬁnd that models are least sensitive to RemoveNoncausalEqual, and much more sensitive to RemoveCausal and RemoveNoncausal.

Original: This is consistent with our ﬁnding in Section 4.1, indicating the model is more sensitive to large perturbations since there are more non-causal agents than causal ones in most examples. 
Revised: This is consistent with our ﬁnding in Section 4.1, indicating the model is more sensitive to large perturbations since there are more non-causal agents than causal ones in most examples. [Figure]

Original: 4. T RAINING WITH DATA AUGMENTATIONS IMPROVES MODEL ROBUSTNESS
Revised: 4. T RAINING WITH DATA AUGMENTATIONS IMPROVES MODEL ROBUSTNESS

Original: We experiment with two types of data augmentation: 1) data augmentations that use a heuristic deﬁnition of non-causal agents, such as randomly dropping any static context agent 1 , and 2)[Figure] robustness-targeted data augmentations that directly drop only non-causal agents using a labeled portion of the val set.
Revised: We experiment with two types of data augmentation: 1) data augmentations that use a heuristic deﬁnition of non-causal agents, such as randomly dropping any static context agent 1 , and 2) robustness-targeted data augmentations that directly drop only non-causal agents using a labeled portion of the val set.

Original: Heuristic data augmentation.
Revised: Heuristic data augmentation.

Original: The beneﬁt of using a heuristic deﬁnition of non-causal agents for data augmentations is that it can be applied without collecting causal labels.
Revised: The beneﬁt of using a heuristic deﬁnition of non-causal agents for data augmentations is that it can be applied without collecting causal labels.

Original: We implement 2 types of heuristic-based data augmentation in the training set of WOMD:
Revised: We implement 2 types of heuristic-based data augmentation in the training set of WOMD:

Original: Drop Context (randomly dropping context agents) as a baseline, and Drop Static Context (randomly dropping static context agents).
Revised: Drop Context (randomly dropping context agents) as a baseline, and Drop Static Context (randomly dropping static context agents).

Original: We use the MultiPath++–All model and we set the probability of dropping an agent to 0 .
Revised: We use the MultiPath++–All model and we set the probability of dropping an agent to 0 .

Original: 1 (the best one among 0 .
Revised: 1 (the best one among 0 .

Original: 5 , and 0 . 8 ).
Revised: 5 , and 0 . 8 ).

Original: Table 3 summarizes the results for the RemoveNoncausal perturbation (for the per-scene distribution of model sensitivity, see Appendix K).
Revised: Table 3 summarizes the results for the RemoveNoncausal perturbation (for the per-scene distribution of model sensitivity, see Appendix K).

Original: Models with data augmentation show less sensitivity to the perturbations, and, in particular, Drop Static Context shows a signiﬁcant improvement in minADE and Abs( ∆ ) over Drop Context.
Revised: Models with data augmentation show less sensitivity to the perturbations, and, in particular, Drop Static Context shows a signiﬁcant improvement in minADE and Abs( ∆ ) over Drop Context.

Original: We hypothesize that Drop Static Context does better because the static context agents are less likely to be causal.
Revised: We hypothesize that Drop Static Context does better because the static context agents are less likely to be causal.

Original: Overall, the results for Drop
Revised: Overall, the results for Drop

Original: Static Context imply that dropping non-causal agents via data augmentation in training can improve model robustness to such perturbations at test time
Revised: Static Context imply that dropping non-causal agents via data augmentation in training can improve model robustness to such perturbations at test time.

Revised: Heuristic Data Augs, RemoveNoncausal, minADE , ∆ =

Revised: Perturbed - Original

Original: [Table]
Revised: [Table]

Original: Non-causal data augmentations.
Revised: Non-causal data augmentations.

Original: Motivated by our results that dropping static context agents improves model robustness, we further explore using non-causal perturbations as a data augmentation strategy during training.
Revised: Motivated by our results that dropping static context agents improves model robustness, we further explore using non-causal perturbations as a data augmentation strategy during training.

Original: We randomly sample approximately 70% of the original validation dataset (i
Revised: We randomly sample approximately 70% of the original validation dataset (i

Original: [Table]
Revised: [Table]

Original: e. 30k scenes), perturb multiple copies of them via the causal labels
Revised: e. 30k scenes), perturb multiple copies of them via the causal labels

Original: [Table]
Revised: [Table]

Original: and add the perturbed versions into the training dataset.
Revised: and add the perturbed versions into the training dataset.

Original: We leave the remaining 30% of the validation set as a holdout for evaluation.
Revised: We leave the remaining 30% of the validation set as a holdout for evaluation.

Original: We then train a baseline model on the new training dataset as well as a model that randomly drops non-causal agents (when possible) with probability 0.1.
Revised: We then train a baseline model on the new training dataset as well as a model that randomly drops non-causal agents (when possible) with probability 0.1.

Original: In Table 4, we see that similarly dropping non-causal agents helps improve minADE as well as model robustness.
Revised: In Table [Table] we see that similarly dropping non-causal agents helps improve minADE as well as model robustness

Original: [Table]
Revised: [Table]

Original: 4. L ARGER DATASET SIZE IMPROVES MODEL ROBUSTNESS
Revised: 4. L ARGER DATASET SIZE IMPROVES MODEL ROBUSTNESS

Original: We also evaluate model robustness with increasing training data.
Revised: We also evaluate model robustness with increasing training data.

Original: We randomly select 10%, 20%, 50%, 80% of the training dataset and train separate models on each split.
Revised: We randomly select 10%, 20%, 50%, 80% of the training dataset and train separate models on each split.

Original: We sample three datasets for each split and average the performance and robustness of each model.
Revised: We sample three datasets for each split and average the performance and robustness of each model.

Original: Appendix D summarizes the results.
Revised: Appendix D summarizes the results.

Original: As we increase the training data size, the model performance improves (minADE decreases) and both the absolute and relative robustness improves.
Revised: As we increase the training data size, the model performance improves (minADE decreases) and both the absolute and relative robustness improves.

Original: Interestingly, previously when varying model architectures, we found that the model with the lowest minADE did not always have the best relative robustness.
Revised: Interestingly, previously when varying model architectures, we found that the model with the lowest minADE did not always have the best relative robustness.

Original: Here, we see a strong trend: for a ﬁxed model architecture, lowering the minADE by increasing the training data results in lower relative sensitivity.
Revised: Here, we see a strong trend: for a ﬁxed model architecture, lowering the minADE by increasing the training data results in lower relative sensitivity.

Original:  D ISCUSSION
Revised:  D ISCUSSION

Original: We now discuss a few hypotheses and initial supporting evidence for why models are not robust to the non-causal perturbations.
Revised: We now discuss a few hypotheses and initial supporting evidence for why models are not robust to the non-causal perturbations.

Original: There may be other reasons we have yet to ﬁnd strong evidence for, but we hope future work can utilize the labels to explore these ideas further.

Original: Overﬁtting.
Revised: Overﬁtting.

Original: One reason models may fail to generalize to the non-causal perturbations is that they overﬁt to spurious correlations in the training data (i.e. features that correlate with certain ground truth trajectories but fail to generalize).
Revised: One reason models may fail to generalize to the non-causal perturbations is that they overﬁt to spurious correlations in the training data (i.e. features that correlate with certain ground truth trajectories but fail to generalize).

Original: In our experiments, we observe that models that overﬁt on the original training dataset (as measured by increasing minADE on the original validation dataset) are more sensitive to the non-causal perturbations (see Fig.
Revised: In our experiments, we observe that models that overﬁt on the original training dataset (as measured by increasing minADE on the original validation dataset) are more sensitive to the non-causal perturbations (see Fig.

Original: 11 in Appendix E).
Revised: 11 in Appendix E).

Original: Thus, the more the model overﬁts to spurious features like the number of parked cars in a faraway parking lot, the less well it generalizes to examples where these features are absent.
Revised: Thus, the more the model overﬁts to spurious features like the number of parked cars in a faraway parking lot, the less well it generalizes to examples where these features are absent.

Original: Data augmentation and increasing dataset size may improve robustness by protecting against overﬁtting.
Revised: Data augmentation and increasing dataset size may improve robustness by protecting against overﬁtting.

Original: Distribution shift.
Revised: Distribution shift.

Original: Models may fail to generalize to perturbations that are signiﬁcantly different from any data seen during training.
Revised: Models may fail to generalize to perturbations that are signiﬁcantly different from any data seen during training.

Original: In our results, we observe that the more non-causal agents we remove, the less robust models are.
Revised: In our results, we observe that the more non-causal agents we remove, the less robust models are.

Original: Perhaps certain types of scenes with few agents are relatively rare in the training dataset and the model does not generalize well to the distribution shift.
Revised: Perhaps certain types of scenes with few agents are relatively rare in the training dataset and the model does not generalize well to the distribution shift.

Original: By evaluating on the perturbations, we essentially expose the model to rare scenarios not seen in training.
Revised: By evaluating on the perturbations, we essentially expose the model to rare scenarios not seen in training.

Original: One reason that training with data augmentations via dropping (static) context agents or non-causal agents improves robustness could be that it exposes the model to similar scenes during training.
Revised: One reason that training with data augmentations via dropping (static) context agents or non-causal agents improves robustness could be that it exposes the model to similar scenes during training.

Original: Over-reliance on agents instead of roadmap.
Revised: Over-reliance on agents instead of roadmap.

Original: A third possible reason that models fail to generalize is that they utilize the non-causal agents to infer the drivable areas instead of using the mapping information in the input (we serve high-deﬁnition maps and trafﬁc control signals as input features for all models).
Revised: A third possible reason that models fail to generalize is that they utilize the non-causal agents to infer the drivable areas instead of using the mapping information in the input (we serve high-deﬁnition maps and trafﬁc control signals as input features for all models).

Original: Our evidence comes from visualizing examples where dropping non-causal agents creates predictions that disobey the roadgraph rules (see Fig.
Revised: Our evidence comes from visualizing examples where dropping non-causal agents creates predictions that disobey the roadgraph rules (see Fig.

Original: 10 in Appendix E).
Revised: 10 in Appendix E).

Original: Data-dependent modes.
Revised: Data-dependent modes.

Original: Finally, many of the state of the art models (e.g. (Ngiam et al., 2021;
Revised: Finally, many of the state of the art models (e.g. (Ngiam et al., 2021;

Original: Varadarajan et al., 2021)) utilize modes (e.g. straight, left, u-turn, etc.)
Revised: Varadarajan et al., 2021)) utilize modes (e.g. straight, left, u-turn, etc.)

Original: learned from the data distribution, where the input data inﬂuences how the model will utilize its K predictions to minimize its loss function.
Revised: learned from the data distribution, where the input data inﬂuences how the model will utilize its K predictions to minimize its loss function.

Original: While effective at minimizing minADE-like metrics, these methods provide no coverage guarantees, and can encourage the model to predict multiple speed proﬁles for the same mode instead of diverse modes.
Revised: While effective at minimizing minADE-like metrics, these methods provide no coverage guarantees, and can encourage the model to predict multiple speed proﬁles for the same mode instead of diverse modes.

Original: When we triage examples (see Fig.
Revised: When we triage examples (see Fig.

Original: 9 in Appendix E), we ﬁnd some of the largest failures come from agent deletions that inﬂuence which modes the model predicts, demonstrating a weakness of this approach and the metrics they perform well on.
Revised: 9 in Appendix E), we ﬁnd some of the largest failures come from agent deletions that inﬂuence which modes the model predicts, demonstrating a weakness of this approach and the metrics they perform well on.

Original:  C ONCLUSIONS
Revised:  C ONCLUSIONS

Original: We establish a benchmark and metrics for evaluating the robustness of several state-of-the-art models for trajectory prediction for autonomous driving.
Revised: We establish a benchmark and metrics for evaluating the robustness of several state-of-the-art models for trajectory prediction for autonomous driving.

Original: We ﬁnd that most state-of-the-art models (with different model architectures and coordination systems) show signiﬁcant levels of sensitivity to perturbations that remove non-causal agents, with higher sensitivity when removing a greater number of them.
Revised: We ﬁnd that most state-of-the-art models (with different model architectures and coordination systems) show signiﬁcant levels of sensitivity to perturbations that remove non-causal agents, with higher sensitivity when removing a greater number of them.

Original: While most examples show minimal change in minADE ( ≤ 0 .
Revised: While most examples show minimal change in minADE ( ≤ 0 .

Original: 1 m), there is a long tail of examples that can have large changes ( ≥ 1 m and sometimes up to 8m).
Revised: 1 m), there is a long tail of examples that can have large changes ( ≥ 1 m and sometimes up to 8m).

Original: Surprisingly, removing either causal or non-causal agents can cause a signiﬁcant fraction of examples to improve their minADE.
Revised: Surprisingly, removing either causal or non-causal agents can cause a signiﬁcant fraction of examples to improve their minADE.

Original: We also ﬁnd that increasing dataset size and data augmentation can help improve the model robustness.
Revised: We also ﬁnd that increasing dataset size and data augmentation can help improve the model robustness.

Original: Overall, our results indicate that current machine learning models for trajectory prediction may not be reliable enough on their own, and careful thought needs to be given to how to integrate such models with non-learning components to make a safe system.
Revised: Overall, our results indicate that current machine learning models for trajectory prediction may not be reliable enough on their own, and careful thought needs to be given to how to integrate such models with non-learning components to make a safe system.

Original: Finally, we will publish the causal agent labels as complementary attributes to the WOMD to aid future researchers in building more robust models.
Revised: Finally, we will publish the causal agent labels as complementary attributes to the WOMD to aid future researchers in building more robust models.

Original: A L ABELING P OLICY
Revised: A L ABELING P OLICY

Original: Below is the exact text given to labelers to deﬁne causal agents:
Revised: Below is the exact text given to labelers to deﬁne causal agents:

Original: The objective is to identify all agents - cars, cyclists, or pedestrians - that are causal to the AV at any time.
Revised: The objective is to identify all agents - cars, cyclists, or pedestrians - that are causal to the AV at any time.

Original: A causal agent is one whose presence would modify or inﬂuence human driver behavior in any way.
Revised: A causal agent is one whose presence would modify or inﬂuence human driver behavior in any way.

Original: Causality is an inherently subjective label.
Revised: Causality is an inherently subjective label.

Original: If you are unsure if an agent is causal or not, please err on the side of including it.
Revised: If you are unsure if an agent is causal or not, please err on the side of including it.

Original: In other words, false positives (identifying an agent as causal when it is truly non-causal) are okay, but we should avoid false negatives (failing to identify a truly causal agent).
Revised: In other words, false positives (identifying an agent as causal when it is truly non-causal) are okay, but we should avoid false negatives (failing to identify a truly causal agent).

Original: If the behavior of a human driver would be modiﬁed because of a potential action that an agent is likely to take, then that agent should be causal.
Revised: If the behavior of a human driver would be modiﬁed because of a potential action that an agent is likely to take, then that agent should be causal.

Original: On the other hand, if the human driver would drive the same regardless of whether the agent is there or not, the agent is non-causal.
Revised: On the other hand, if the human driver would drive the same regardless of whether the agent is there or not, the agent is non-causal.

Original: The labeling policy also included several examples scenarios with causal agents identiﬁed such as
Revised: The labeling policy also included several examples scenarios with causal agents identiﬁed such as

Original: Figure 6.
Revised: Figure 6.

Original: [Figure]
Revised: [Figure]

Original: C M ODEL SENSITIVITY TO VARIOUS PERTURBATION TYPES
Revised: C M ODEL SENSITIVITY TO VARIOUS PERTURBATION TYPES

Original: In this section, we summarize the robustness metrics across different model architectures for each of the perturbation types (RemoveCausal, RemoveNoncausal, RemoveNoncausalEqual, RemoveStatic).
Revised: In this section, we summarize the robustness metrics across different model architectures for each of the perturbation types (RemoveCausal, RemoveNoncausal, RemoveNoncausalEqual, RemoveStatic).

Original: We report the model’s original minADE, perturbed minADE, average absolute difference between perturbed and original minADE computed per-example (Abs( ∆ )), standard deviation of Abs( ∆ ), and the relative % change (Abs( ∆ ) divided by the original minADE).
Revised: We report the model’s original minADE, perturbed minADE, average absolute difference between perturbed and original minADE computed per-example (Abs( ∆ )), standard deviation of Abs( ∆ ), and the relative % change (Abs( ∆ ) divided by the original minADE).

Original: Each table below shows the results for a different perturbation dataset.
Revised: Each table below shows the results for a different perturbation dataset.

Original: RemoveCausal minADE , ∆ =
Revised: RemoveCausal minADE , ∆ =

Original: Perturbed - Original
Revised: Perturbed - Original

Original: [Table]
Revised: [Table]

Original: MP
Revised: MP

Original: [Table] [Table]
Revised: [Table] [Table]

Original: ±
Revised: ±

Original: [Table]
Revised: [Table]

Original: ST
Revised: ST

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: ±
Revised: ±

Original: [Table]
Revised: [Table]

Original: Wayformer
Revised: Wayformer

Original: [Table] [Table]
Revised: [Table] [Table]

Original: ±
Revised: ±

Original: [Table]
Revised: [Table]

Original: MP
Revised: MP

Original: [Table]
Revised: [Table]

Original: ±
Revised: ±

Original: [Table] [Table]
Revised: [Table] [Table]

Original: ST
Revised: ST

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: ±
Revised: ±

Original: [Table] [Table]
Revised: [Table] [Table]

Original: ST-
Revised: ST-

Original: [Table]
Revised: [Table]

Original: ± 0.
Revised: ± 0.

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table]
Revised: [Table]

Original: To make it easier to compare across perturbation types
Revised: To make it easier to compare across perturbation types

Original: [Table]
Revised: [Table]

Original: we also report the average Abs(PerturbedOriginal) minADE for each model and perturbation type in Table 9.
Revised: we also report the average Abs(PerturbedOriginal) minADE for each model and perturbation type in Table 9.

Original: [Table]
Revised: [Table]

Original: D I NCREASING DATASET SIZE
Revised: D I NCREASING DATASET SIZE

Original: [Table]
Revised: [Table]

Original: E E XAMPLE VISUALIZATION E. F AILURE ( NON - ROBUST ) CASES UNDER NON - CAUSAL PERTURBATION
Revised: E E XAMPLE VISUALIZATION E. F AILURE ( NON - ROBUST ) CASES UNDER NON - CAUSAL PERTURBATION

Original: We have triaged several top sensitive examples under the RemoveNoncausal perturbation.
Revised: We have triaged several top sensitive examples under the RemoveNoncausal perturbation.

Original: Among these examples, we have found three failure patterns: 1) predictions under the perturbation violate trafﬁc rules, as shown in Figure 8; 2) predictions under the perturbation missed to capture the groundtruth mode, as shown in Figure 9; and 3) predictions under the perturbation violates the causality, for instance, unnecessary slows down when the road becomes more empty due to the removal of non-causal agents, such as the bottom example in Figure 11.
Revised: Among these examples, we have found three failure patterns: 1) predictions under the perturbation violate trafﬁc rules, as shown in Figure 8; 2) predictions under the perturbation missed to capture the groundtruth mode, as shown in Figure 9; and 3) predictions under the perturbation violates the causality, for instance, unnecessary slows down when the road becomes more empty due to the removal of non-causal agents, such as the bottom example in Figure 11.

Original: Meanwhile, we also have identiﬁed examples where the predictions under the non-causal perturbation becomes better, as shown in Figure
Revised: Meanwhile, we also have identiﬁed examples where the predictions under the non-causal perturbation becomes better, as shown in Figure

Original: [Figure]
Revised: [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: E. A N EVIDENCE EXAMPLE FOR NON - ROBUSTNESS DUE TO OVERFITTING
Revised: E. A N EVIDENCE EXAMPLE FOR NON - ROBUSTNESS DUE TO OVERFITTING

Original: In this section, we show an example scenario that showcases overﬁtting is one potential reason for poor robustness.
Revised: In this section, we show an example scenario that showcases overﬁtting is one potential reason for poor robustness.

Original: We have trained the MP++ with 1M iterations, which overﬁtted at 210k iterations.
Revised: We have trained the MP++ with 1M iterations, which overﬁtted at 210k iterations.

Original: We then visualize the predictions of a same example with two different checkpoints, one at 210k iteration and another at 1M.
Revised: We then visualize the predictions of a same example with two different checkpoints, one at 210k iteration and another at 1M.

Original: The results are shown in Figure 11.
Revised: The results are shown in Figure 11.

Original: We can see that the robustness of the model under non-causal perturbation becomes bad when the model over-ﬁts.
Revised: We can see that the robustness of the model under non-causal perturbation becomes bad when the model over-ﬁts.

Original: [Equation]
Revised: [Equation]

Original: F S LICING RESULTS
Revised: F S LICING RESULTS

Original: We further slice the robustness of the models along several dimensions, including the AV’s current speed, the percentage of removed non-causal agents (the number of removed non-noncausal agents divided by the number of all context agents) in the scenarios, and the minimum distance from the AV to removed non-causal agents.
Revised: We further slice the robustness of the models along several dimensions, including the AV’s current speed, the percentage of removed non-causal agents (the number of removed non-noncausal agents divided by the number of all context agents) in the scenarios, and the minimum distance from the AV to removed non-causal agents.

Original: Results are given in Figure 12.
Revised: Results are given in Figure 12.

Original: We found that:
Revised: We found that:

Original: • Along the percentage of removed non-causal agents, we found all models are more sensitive if a larger fraction of agents are removed.
Revised: • Along the percentage of removed non-causal agents, we found all models are more sensitive if a larger fraction of agents are removed.

Original: Across them, ST Marginal and Wayformer are the most robust models.
Revised: Across them, ST Marginal and Wayformer are the most robust models.

Original: Compared to Wayformer, ST marginal is less sensitive when more than 40% of the context agents are non-causal and removed from the data (Figure 12 left).
Revised: Compared to Wayformer, ST marginal is less sensitive when more than 40% of the context agents are non-causal and removed from the data (Figure 12 left).

Original: • Along the AV’s speed, ST Marginal is more robust when the AV’s speed is slower than 45mph (Figure 12 top-left).
Revised: • Along the AV’s speed, ST Marginal is more robust when the AV’s speed is slower than 45mph (Figure 12 top-left).

Original: Note that the high ﬂuctuations at high speed ( > 45 mph) is because we have fewer examples there (the count of examples in each bin is provided in Appendix).
Revised: Note that the high ﬂuctuations at high speed ( > 45 mph) is because we have fewer examples there (the count of examples in each bin is provided in Appendix).

Original: • Along the minimum distance between the removed non-causal agents to the AV, Wayformer is the most robust one, particularly when the minimum distance is larger (i
Revised: • Along the minimum distance between the removed non-causal agents to the AV, Wayformer is the most robust one, particularly when the minimum distance is larger (i

Original: e., all removed non-causal agent are relatively far away from the AV, Figure 12 right).
Revised: e., all removed non-causal agent are relatively far away from the AV, Figure 12 right).

Original: Such results indicate that Wayformer learns to not pay too much attention to far-away non-causal agents.
Revised: Such results indicate that Wayformer learns to not pay too much attention to far-away non-causal agents.

Original: On the contrary, we noticed that ST models tend to be more sensitive to far-away non-causal agents.
Revised: On the contrary, we noticed that ST models tend to be more sensitive to far-away non-causal agents.

Original: We hypothesize that this might be because the global coordination that ST models are used makes it more sensitive to large coordinate values.
Revised: We hypothesize that this might be because the global coordination that ST models are used makes it more sensitive to large coordinate values.

Original: G A GGREGATE RESULTS FOR ALTERNATE METRICS
Revised: G A GGREGATE RESULTS FOR ALTERNATE METRICS

Original: In this section
Revised: In this section

Original: [Table]
Revised: [Table]

Original: we report aggregate results for minFDE, overlap rate, miss rate
Revised: we report aggregate results for minFDE, overlap rate, miss rate

Original: [Table]
Revised: [Table]

Original: and mAP on the
Revised: and mAP on the

Original: RemoveNoncausal perturbation.
Revised: RemoveNoncausal perturbation.

Original: [Table]
Revised: [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: H P ER - EXAMPLE SCATTER PLOTS
Revised: H P ER - EXAMPLE SCATTER PLOTS

Original: I C OMPARISON ACROSS MODELS
Revised: I C OMPARISON ACROSS MODELS

Original: J C OMPARISON ACROSS PERTURBATION TYPES
Revised: J C OMPARISON ACROSS PERTURBATION TYPES

Original: Figure 20 shows the sensitivity of the Wayformer AV Only, ST Marginal AV
Revised: Figure 20 shows the sensitivity of the Wayformer AV Only, ST Marginal AV

Original: Only, and MultiPath++
Revised: Only, and MultiPath++

Original: All Agents models to each of the perturbation types.
Revised: All Agents models to each of the perturbation types.

Original: The perturbation can either increase or decrease the minADE.
Revised: The perturbation can either increase or decrease the minADE.

Original: On average, it increase the minADE but this depends on the pertubation type (RemoveCausalAgents causes the strongest increase; see Appendix C).
Revised: On average, it increase the minADE but this depends on the pertubation type (RemoveCausalAgents causes the strongest increase; see Appendix C).

Original: The models are most sensitive to both the RemoveCausalAgents and RemoveNoncausalAgents perturbations.
Revised: The models are most sensitive to both the RemoveCausalAgents and RemoveNoncausalAgents perturbations.

Original: The RemoveCausalAgents has the largest effect on the model, producing the most outliers that increase the difference between the perturbed and original minADE, followed closely by RemoveNoncausalAgents, then RemoveStaticAgents, and then RemoveNoncausalAgentsEqual.
Revised: The RemoveCausalAgents has the largest effect on the model, producing the most outliers that increase the difference between the perturbed and original minADE, followed closely by RemoveNoncausalAgents, then RemoveStaticAgents, and then RemoveNoncausalAgentsEqual.

Original: Surprisingly, the sensitivity of RemoveNoncausalAgents is close to that of RemoveCausalAgents (exact numbers TODO).
Revised: Surprisingly, the sensitivity of RemoveNoncausalAgents is close to that of RemoveCausalAgents (exact numbers TODO).

Original: However, when we change the number of non-causal agents removed (in RemoveNoncausalAgentsEqual) to be the same as the number of causal agents removed (in RemoveCausalAgents), the sensitivity is much less.
Revised: However, when we change the number of non-causal agents removed (in RemoveNoncausalAgentsEqual) to be the same as the number of causal agents removed (in RemoveCausalAgents), the sensitivity is much less.

Original: K D ATA AUGMENTATIONS
Revised: K D ATA AUGMENTATIONS

Original: L T RAJECTORY S ET M ETRICS ( CONTINUED )
Revised: L T RAJECTORY S ET M ETRICS ( CONTINUED )

Original: Since ∆ (Ptb-Ori) on minADE only quantiﬁes how the perturbations impact the models’ robustness in terms of the distance between ground-truth and the closest predicted trajectories, it does not directly reﬂect the difference between the two predicted trajectory sets (w/ and w/o perturbations).
Revised: Since ∆ (Ptb-Ori) on minADE only quantiﬁes how the perturbations impact the models’ robustness in terms of the distance between ground-truth and the closest predicted trajectories, it does not directly reﬂect the difference between the two predicted trajectory sets (w/ and w/o perturbations).

Original: We thus introduce two trajectory set metrics to capture such difference: an IoU based metric as given in
Revised: We thus introduce two trajectory set metrics to capture such difference: an IoU based metric as given in

Original: Section 3.4 in the main context and a trajectory set minADE deﬁned below.
Revised: Section 3.4 in the main context and a trajectory set minADE deﬁned below.

Original: Ideally, a model’s predicted trajectory sets would not be sensitive to dropping non-causal agents, meaning we expect a low difference on the trajectory set metrics.
Revised: Ideally, a model’s predicted trajectory sets would not be sensitive to dropping non-causal agents, meaning we expect a low difference on the trajectory set metrics.

Original: minADE between trajectory sets (TS minADE) .
Revised: minADE between trajectory sets (TS minADE) .

Original: Let ˆ p ipert,orig represent the i -th predicted trajectory in the predicted trajectory sets w/ and w/o perturbation, respectively.
Revised: Let ˆ p ipert,orig represent the i -th predicted trajectory in the predicted trajectory sets w/ and w/o perturbation, respectively.

Original: We deﬁne TS minADE
Revised: We deﬁne TS minADE

Original: = min
Revised: = min

Original: L 2 (ˆ p iorig , ˆ p jpert ) , i, j = 1 , 2 , · · · , N where N is the number of the predicted trajectories of the model.
Revised: L 2 (ˆ p iorig , ˆ p jpert ) , i, j = 1 , 2 , · · · , N where N is the number of the predicted trajectories of the model.

Original: Hence, a smaller TS minADE means that two predicted trajectory sets are more similar.
Revised: Hence, a smaller TS minADE means that two predicted trajectory sets are more similar.

Original: The results for all the models are given in Table 15.
Revised: The results for all the models are given in Table 15.

Original: We can see that most of the models are sensitive to the RemoveNoncausal perturbation.
Revised: We can see that most of the models are sensitive to the RemoveNoncausal perturbation.

Original: The Wayformer is least sensitive, which is good.
Revised: The Wayformer is least sensitive, which is good.

Original: However, it is also least sensitive to RemoveCausal, which indicate that the model is less sensitive to agent removal in general.
Revised: However, it is also least sensitive to RemoveCausal, which indicate that the model is less sensitive to agent removal in general.

Original: [Table]
Revised: [Table]