Original: Motion Forecasting with Unlikelihood Training in Continuous Space
Revised: Motion Forecasting with Unlikelihood Training in Continuous Space

Original: Anonymous Author(s)

Original: AfﬁliationAddress email

Original: Abstract: Motion forecasting is essential for making safe and intelligent decisionsin robotic applications such as autonomous driving.
Revised: Abstract: Motion forecasting is essential for making safe and intelligent decisions in robotic applications such as autonomous driving.

Original: Existing methods often formulate it as a sequence-to-sequence prediction problem, solved in an encoder-decoderframework with a maximum likelihood estimation objective.
Revised: Existing methods often formulate it as a sequence-to-sequence prediction problem, solved in an encoder-decoder framework with a maximum likelihood estimation objective.

Original: State-of-the-art models leverage contextual information, including the map and states of surroundingagents.
Revised: State-of-the-art models leverage contextual information, including the map and states of surrounding agents.

Original: However, we observe that they still assign a high probability to unlikelytrajectories resulting in unsafe behaviors, including road boundary violations.
Revised: However, we observe that they still assign a high probability to unlikely trajectories resulting in unsafe behaviors, including road boundary violations.

Original: Orthogonally, we propose a new objective, unlikelihood training, which forcespredicted trajectories that conﬂict with contextual information to be assigned alower probability.
Revised: Orthogonally, we propose a new objective, unlikelihood training, which forces predicted trajectories that conﬂict with contextual information to be assigned a lower probability.

Original: We demonstrate that our method can improve state-of-art models’performance on the challenging nuScenes and Argoverse real-world trajectory forecasting datasets by avoiding up to 56% context-violated prediction and improvingup to 9% prediction accuracy.
Revised: We demonstrate that our method can improve state-of-art models’ performance on the challenging nuScenes and Argoverse real-world trajectory forecasting datasets by avoiding up to 56% context-violated prediction and improving up to 9% prediction accuracy.

Original: Code will be made publically available.
Revised: Code is avaliable at https://github.com/Vision-CAIR/UnlikelihoodMotionForecasting

Original:  Introduction
Revised:  Introduction

Original: For robotic applications deployed in the real world, the ability to foresee the future motions ofagents in the surrounding environment plays an essential role in safe and intelligent decision-making,which is a very challenging task.
Revised: For robotic applications deployed in the real world, the ability to foresee the future motions of agents in the surrounding environment plays an essential role in safe and intelligent decision-making, which is a very challenging task.

Original: For example, in the autonomous driving domain, to predict nearbyagents’ future trajectories accurately, an agent must consider contextual information such as their pasttrajectories, potential interactions and map information.
Revised: For example, in the autonomous driving domain, to predict nearby agents’ future trajectories accurately, an agent must consider contextual information such as their past trajectories, potential interactions and map information.

Original: State of the art prediction models [1, 2, 3]directly take contextual information as part of their input and use techniques such as graph neuralnetworks to extract high-level features for prediction.
Revised: State of the art prediction models [1, 2, 3] directly take contextual information as part of their input and use techniques such as graph neural networks to extract high-level features for prediction.

Original: They are typically trained with a maximumlikelihood estimation (MLE) objective of ground truth trajectories in the predicted distribution.
Revised: They are typically trained with a maximum likelihood estimation (MLE) objective of ground truth trajectories in the predicted distribution.

Original: Although MLE loss encourages the prediction to be geometrically close to the ground truth, there isno explicit motivation to learn a distribution that leverages contextual information.
Revised: Although MLE loss encourages the prediction to be geometrically close to the ground truth, there is no explicit motivation to learn a distribution that leverages contextual information.

Original: These modelsmay predict trajectories that violate the contextual information (e g., go to opposite driving directionor out of the driving area) but still closes to ground truth.
Revised: These models may predict trajectories that violate the contextual information (e.g., go to opposite driving direction or out of the driving area) but still closes to ground truth.

Original: In contrast, humans can quickly notice thatthese trajectories are unlikely in a speciﬁc context.
Revised: In contrast, humans can quickly notice that these trajectories are unlikely in a speciﬁc context.

Original: This observation suggests that using MLE losscannot fully leverage contextual information, and hence may predict unsafe trajectories more likely.
Revised: This observation suggests that using MLE loss cannot fully leverage contextual information, and hence may predict unsafe trajectories more likely.

Original: To address the problem, existing methods (e.g., Casas et al.
Revised: To address the problem, existing methods (e.g., Casas et al.

Original: [4], Park et al.
Revised: [4], Park et al.

Original: [5]), using contextualinformation, either introduce new learning parameters or apply reinforcement learning methodsrequiring further reward engineering.
Revised: [5]), using contextual information, either introduce new learning parameters or apply reinforcement learning methods requiring further reward engineering.

Original: We propose a novel and simple method, unlikelihood training,that injects contextual information as a learning signal.
Revised: We propose a novel and simple method, unlikelihood training, that injects contextual information as a learning signal.

Original: Our loss penalizes the trajectories that violatethe contextual information, dubbed as negative trajectories, by minimizing their likelihood in thepredicted distribution.
Revised: Our loss penalizes the trajectories that violate the contextual information, dubbed as negative trajectories, by minimizing their likelihood in the predicted distribution.

Original: To generate negative or unlikely trajectories, we ﬁrst draw many candidatetrajectories from our model’s predicted distribution.
Revised: To generate negative or unlikely trajectories, we ﬁrst draw many candidate trajectories from our model’s predicted distribution.

Original: Then, we introduce a context checker to identifythe trajectories that violate contextual information as negative trajectories 1 .
Revised: Then, we introduce a context checker to identify the trajectories that violate contextual information as negative trajectories 1 .

Original: The model is thenencouraged to use contextual information to avoid predictions that violate context by minimizing thelikelihood of negative trajectories.
Revised: The model is then encouraged to use contextual information to avoid predictions that violate context by minimizing the likelihood of negative trajectories.

Original: Hence, the predicted trajectories can be more accurate and, moreimportantly, safer.
Revised: Hence, the predicted trajectories can be more accurate and, more importantly, safer.

Original: Unlikelihood training [6] has been applied to neural language generation in discrete space.
Revised: Unlikelihood training [6] has been applied to neural language generation in discrete space.

Original: To thebest of our knowledge, we are the ﬁrst to propose unlikelihood training for continuous space oftrajectories.
Revised: To the best of our knowledge, we are the ﬁrst to propose unlikelihood training for continuous space of trajectories.

Original: For the discrete space of token sequences, repeating tokens or n-grams in the generatedsequence are chosen as negative tokens.
Revised: For the discrete space of token sequences, repeating tokens or n-grams in the generated sequence are chosen as negative tokens.

Original: In contrast, we design a context checker to select negativetrajectories sampled from the continuous distribution of model predictions to build an unlikelihoodloss.
Revised: In contrast, we design a context checker to select negative trajectories sampled from the continuous distribution of model predictions to build an unlikelihood loss.

Original: In this case, our learning signals contain not only the information of the ground truth trajectoriesfrom the MLE, but also the the context information from our proposed loss.
Revised: In this case, our learning signals contain not only the information of the ground truth trajectories from the MLE, but also the the context information from our proposed loss.

Original: Our method can beviewed as a simple add-on to models that estimate the distribution of future trajectories.
Revised: Our method can be viewed as a simple add-on to models that estimate the distribution of future trajectories.

Original: It improvestheir performance by encouraging models to focus more on contextual information without increasingthe number of model parameters.
Revised: It improves their performance by encouraging models to focus more on contextual information without increasing the number of model parameters.

Original: Our contributions are summarized as follows:
Revised: Our contributions are summarized as follows:

Original: • We propose a novel and simple method, continuous unlikelihood training for motion fore- casting in autonomous driving that encourages models to use contextual information by minimizing the likelihood of trajectories that violate contextual information.
Revised: • We propose a novel and simple method, continuous unlikelihood training for motion forecasting in autonomous driving that encourages models to use contextual information by minimizing the likelihood of trajectories that violate contextual information.

Original: Our method can be incorporated into state-of-the-art models that predict the future as distributions.•
Revised: Our method can be incorporated into state-of-the-art models that predict the future as distributions.

Original:  Our large-scale experimental results on two challenging real-world trajectory forecasting datasets, nuScenes, and Argoverse, show that continuous unlikelihood training can im- prove the quality of the predicted distribution by avoiding maximally 56% context-violated prediction and improving 9% prediction performance.
Revised: • Our large-scale experimental results on two challenging real-world trajectory forecasting datasets, nuScenes, and Argoverse, show that continuous unlikelihood training can improve the quality of the predicted distribution by avoiding maximally 56% context-violated prediction and improving 9% prediction performance.

Original:  Related Work
Revised:  Related Work

Original: Trajectory Forecasting Trajectory forecasting of dynamic agents, a core problem for roboticapplications such as autonomous driving and social robots, has been well studied in the literature.
Revised: Trajectory Forecasting Trajectory forecasting of dynamic agents, a core problem for robotic applications such as autonomous driving and social robots, has been well studied in the literature.

Original: State-of-the-art models solve it as a sequence-to-sequence multi-modal prediction problem [7, 8, 9, 3,10 , 2, 11, 1, 12].
Revised: State-of-the-art models solve it as a sequence-to-sequence multi-modal prediction problem [7, 8, 9, 3, 10, 2, 11, 1, 12].

Original: Cui et al.
Revised: Cui et al.

Original: [8], Chai et al.
Revised: [8], Chai et al.

Original: [9], Ridel et al.
Revised: [9], Ridel et al.

Original: [11] predict multiple future trajectorieswithout learning low dimensional latent agent behaviors.
Revised: [11] predict multiple future trajectories without learning low dimensional latent agent behaviors.

Original: Recent works including [7, 10, 3, 12]encode agent behaviors in continuous low dimensional latent space while Tang and Salakhutdinov[2], Salzmann et al.
Revised: Recent works including [7, 10, 3, 12] encode agent behaviors in continuous low dimensional latent space while Tang and Salakhutdinov [2], Salzmann et al.

Original: [1] use discrete latent variables.
Revised: [1] use discrete latent variables.

Original: Discrete latent variables succinctly capturesemantically meaningful modes such as turn left, turn right.
Revised: Discrete latent variables succinctly capture semantically meaningful modes such as turn left, turn right.

Original: Tang and Salakhutdinov [2], Salzmannet al.
Revised: Tang and Salakhutdinov [2], Salzmann et al.

Original: [1] learn discrete latent variables without explicit labels.
Revised: [1] learn discrete latent variables without explicit labels.

Original: They adopt a maximum likelihoodestimation (MLE) objective or its approximations (e.g., VAE).
Revised: They adopt a maximum likelihood estimation (MLE) objective or its approximations (e.g., VAE).

Original: In this paper, we show that MLE losscan ignore contextual information such as maps and states of surrounding agents.
Revised: In this paper, we show that MLE loss can ignore contextual information such as maps and states of surrounding agents.

Original: As a result, modelswith MLE loss only may assign a very high probability to unlikely trajectories.
Revised: As a result, models with MLE loss only may assign a very high probability to unlikely trajectories.

Original: To alleviate this issue,
Revised: To alleviate this issue,

Original: R2P2 [13] trains a surrogate ground truth distribution ﬁrst and use it to regularize the training ofthe predictor.
Revised: R2P2 [13] trains a surrogate ground truth distribution ﬁrst and use it to regularize the training of the predictor.

Original: However, the surrogate is still trained by MLE loss only.
Revised: However, the surrogate is still trained by MLE loss only.

Original: In contrast, we propose anunlikelihood training objective that is based directly on the context information to reduce unlikelyprediction, and we show that models with the maximum likelihood estimation objective can beneﬁtfrom it.
Revised: In contrast, we propose an unlikelihood training objective that is based directly on the context information to reduce unlikely prediction, and we show that models with the maximum likelihood estimation objective can beneﬁt from it.

Original: Unlikelihood Training.
Revised: Unlikelihood Training.

Original: In the context of language generation, Welleck et al.
Revised: In the context of language generation, Welleck et al.

Original: [6], Li et al.
Revised: [6], Li et al.

Original: [14]proposes unlikelihood training as a new method to utilize negative language data, which includescommon degenerate cases like token repetition and distribution mismatch.
Revised: [14] proposes unlikelihood training as a new method to utilize negative language data, which includes common degenerate cases like token repetition and distribution mismatch.

Original: The distribution mismatches occur as an artifact of beam search, which is biased to high-frequency tokens compared tolow-frequency tokens which appear rarely.
Revised: The distribution mismatches occur as an artifact of beam search, which is biased to high-frequency tokens compared to low-frequency tokens which appear rarely.

Original: The method minimizes the likelihood of negative tokensto improve text generation quality in addition to maximizing the likelihood of the ground truth tokens.
Revised: The method minimizes the likelihood of negative tokens to improve text generation quality in addition to maximizing the likelihood of the ground truth tokens.

Original: However, their approach operates in the discrete space.
Revised: However, their approach operates in the discrete space.

Original: In contrast, our proposed method works in thecontinuous space of trajectories.
Revised: In contrast, our proposed method works in the continuous space of trajectories.

Original: We model negative data by a context checker that we propose, whichoperates on predictions to populate unlikely trajectories.
Revised: We model negative data by a context checker that we propose, which operates on predictions to populate unlikely trajectories.

Original: Predicted trajectories that violate the checkerare selected to leverage contextual information by minimizing their likelihood objective.
Revised: Predicted trajectories that violate the checker are selected to leverage contextual information by minimizing their likelihood objective

Original: We showthe generality of our approach on two state-of-the-art distribution-based approaches: Trajectron++[1] and a distribution-based variant of LaneGCN [15].
Revised: We show the generality of our approach on two state-of-the-art distribution-based approaches: Trajectron++ [1] and a distribution-based variant of LaneGCN [15].

Original:  Method 
Revised:  Method 3.1 Problem Deﬁnition

Original: 3.1 Problem Deﬁnition

Original: We aim at predicting the future trajectory Y i more accurately of a vehicle i given input X i .
Revised: We aim at predicting the future trajectory Y i more accurately of a vehicle i given input X i .

Original: X i caninclude related information like rasterized maps or past positions of vehicle i and surrounding agents.
Revised: X i can include related information like rasterized maps or past positions of vehicle i and surrounding agents.

Original: Because of the generality of our training mechanism, we skip the speciﬁc choice of this additionalinformation and denote it as X i for conciseness.
Revised: Because of the generality of our training mechanism, we skip the speciﬁc choice of this additional information and denote it as X i for conciseness.

Original: Due to different driving strategies, driving intents,and the complex trafﬁc environment, there are usually multiple possible future trajectories given aninput X i ; despite that there is only one ground truth future trajectory Y i,gt in a dataset recorded inthe real world.
Revised: Due to different driving strategies, driving intents, and the complex trafﬁc environment, there are usually multiple possible future trajectories given an input X i ; despite that there is only one ground truth future trajectory Y i,gt in a dataset recorded in the real world.

Original: To facilitate predicting multiple modalities, most state of the art methods [1, 2] modela distribution of possible future trajectories p θ
Revised: To facilitate predicting multiple modalities, most state of the art methods [1, 2] model a distribution of possible future trajectories p θ

Original: ( Y i | X i ) to cover all the possibilities given the input
Revised: ( Y i | X i ) to cover all the possibilities given the input

Original: X i instead of predicting one trajectory.
Revised: X i instead of predicting one trajectory.

Original: θ denotes the learning parameters of the model.
Revised: θ denotes the learning parameters of the model.

Original: Trainingsuch models can be done by Maximum Likelihood Estimation (MLE) that directly maximizes thelikelihood of ground truth trajectory Y i,gt or its lower bound in the predicted distribution.
Revised: Training such models can be done by Maximum Likelihood Estimation (MLE) that directly maximizes the likelihood of ground truth trajectory Y i,gt or its lower bound in the predicted distribution.

Original: Limitation of MLE on Motion Forecasting MLEencourages the model to predict a distribution thatallocates reasonable probability mass to the region where Y i,gt is located by minimizing the KLdivergence between the ground truth distributionand the predicted distribution.
Revised: Limitation of MLE on Motion Forecasting MLE encourages the model to predict a distribution that allocates reasonable probability mass to the region where Y i,gt is located by minimizing the KLdivergence between the ground truth distribution and the predicted distribution.

Original: Because the trajectory distribution domain is over the geometric locations, MLE makes these two distributions “close”to each other geometrically.
Revised: Because the trajectory distribution domain is over the geometric locations, MLE makes these two distributions “close” to each other geometrically.

Original: However, we arguethat maintaining the geometrical nearness only isnot good enough for motion forecasting tasks in autonomous driving.
Revised: However, we argue that maintaining the geometrical nearness only is not good enough for motion forecasting tasks in autonomous driving.

Original: In complex trafﬁc scenarios, therecan be many potential trajectories close enough tothe ground truth geometrically but are very unlikelyto happen.
Revised: In complex trafﬁc scenarios, there can be many potential trajectories close enough to the ground truth geometrically but are very unlikely to happen.

Original: For example, if the ground truth trajectory Y i,gt is on the outermost lane, a trajectory thatis close to Y i,gt but outside the drivable region is unlikely to happen in the real world.
Revised: For example, if the ground truth trajectory Y i,gt is on the outermost lane, a trajectory that is close to Y i,gt but outside the drivable region is unlikely to happen in the real world.

Original: MLE loss willnot impose a signiﬁcant enough penalty to avoid such a prediction.
Revised: MLE loss will not impose a signiﬁcant enough penalty to avoid such a prediction.

Original: Fig.1 demonstrates a predictionexample from an MLE-based method Trajectron++ [1].
Revised: Fig.1 demonstrates a prediction example from an MLE-based method Trajectron++ [1].

Original: Part of the distribution in this example isoutside of the derivable region or on the lane in the wrong direction.
Revised: Part of the distribution in this example is outside of the derivable region or on the lane in the wrong direction.

Original: The MLE-based loss only offerslearning signals that contain the geometric location information of the ground truth trajectories.
Revised: The MLE-based loss only offers learning signals that contain the geometric location information of the ground truth trajectories.

Original: Allthe other contextual information like the drivable region is missing in this learning signal.
Revised: All the other contextual information like the drivable region is missing in this learning signal.

Original: Therefore,the model is not encouraged during training to utilize the rich contextual information in the input toavoid predictions that are geometrically close to ground truth but violates the context.
Revised: Therefore, the model is not encouraged during training to utilize the rich contextual information in the input to avoid predictions that are geometrically close to ground truth but violates the context.

Original: In contrast,this is quite a simple task for humans.
Revised: In contrast, this is quite a simple task for humans.

Original: 3.2 Unlikelihood Loss
Revised: 3.2 Unlikelihood Loss

Original: To mitigate this problem, we design a new loss term that encourages the model to consider contextualinformation more.
Revised: To mitigate this problem, we design a new loss term that encourages the model to consider contextual information more.

Original: Inspired by the positive and negative data pairs in contrastive learning andunlikelihood training, we additionally train our model to minimize the likelihood of trajectories thatviolate the contextual information given input X i .
Revised: Inspired by the positive and negative data pairs in contrastive learning and unlikelihood training, we additionally train our model to minimize the likelihood of trajectories that violate the contextual information given input X i .

Original: We denote them as negative trajectories Y i,neg .
Revised: We denote them as negative trajectories Y i,neg .

Original: Let’s ﬁrst assume that we already have a distribution of negative trajectories
Revised: Let’s ﬁrst assume that we already have a distribution of negative trajectories

Original: p neg ( Y i |
Revised: p neg ( Y i |

Original: X i ) .
Revised: X i ) .

Original: Oneintuitive way is to directly minimize the log likelihood of Y i,neg in our predicted distribution, similarto MLE but in an opposite manner, as shown in Eq.1.
Revised: One intuitive way is to directly minimize the log likelihood of Y i,neg in our predicted distribution, similar to MLE but in an opposite manner, as shown in Eq.1.

Original: We call it unlikelihood loss.
Revised: We call it unlikelihood loss.

Original: We use a coefﬁcientγ to balance L unlike .
Revised: We use a coefﬁcient γ to balance L unlike .

Original: Our loss can be combined with models that predict trajectory distribution asoutput.
Revised: Our loss can be combined with models that predict trajectory distribution as output.

Original: Eq.2 shows the ﬁnal training objective.
Revised: Eq.2 shows the ﬁnal training objective.

Original: [Equation]
Revised: [Equation]

Original: L orig indicates the original training objective of the method we combine with.
Revised: L orig indicates the original training objective of the method we combine with.

Original: L unlike helps leveragethe context into the learning objective, force the model to better extract and use contextual informationin X i , and generate a more reasonable distribution to avoid high L unlike .
Revised: L unlike helps leverage the context into the learning objective, force the model to better extract and use contextual information in X i , and generate a more reasonable distribution to avoid high L unlike .

Original: 3.3 Negative Trajectories
Revised: 3.3 Negative Trajectories

Original: Our proposed loss term is highly dependent on the negative samples
Revised: Our proposed loss term is highly dependent on the negative samples

Original: Y i,neg from the distributionp neg ( Y i | X i ) .
Revised: Y i,neg from the distribution p neg ( Y i | X i ) .

Original: However, these are not given in the dataset.
Revised: However, these are not given in the dataset.

Original: To solve this issue, we approximatethe samples by directly drawing a set of trajectories from the predicted distribution and select the trajectories that violate the contextual information out by a context checker.
Revised: To solve this issue, we approximate the samples by directly drawing a set of trajectories from the predicted distribution and select the trajectories that violate the contextual information out by a context checker.

Original: Note that this checkerdoes not need to be differentiable and it can be as complex and advanced as necessary.
Revised: Note that this checker does not need to be differentiable and it can be as complex and advanced as necessary.

Original: The typeof unlikely predictions the model learns to avoid by our method depends on the type of unlikelytrajectories the checker can identify.
Revised: The type of unlikely predictions the model learns to avoid by our method depends on the type of unlikely trajectories the checker can identify.

Original: Context Checker Design.
Revised: Context Checker Design.

Original: We provide and implement a map-based checker design here to judgewhether a given trajectory is compliant with context and road rules.
Revised: We provide and implement a map-based checker design here to judge whether a given trajectory is compliant with context and road rules.

Original: In detail, the checker examineswhether the trajectory goes into the lane in the opposite direction or out of the road.
Revised: In detail, the checker examines whether the trajectory goes into the lane in the opposite direction or out of the road.

Original: We create amap that stores the lane direction at every location of lanes and the drivable region.
Revised: We create a map that stores the lane direction at every location of lanes and the drivable region.

Original: Two examplesare shown in Fig.2.
Revised: Two examples are shown in Fig.2.

Original: We ﬁrst check whether all the locations of a given trajectory are in the drivableregion.
Revised: We ﬁrst check whether all the locations of a given trajectory are in the drivable region.

Original: If so, we further calculate angles between velocity and the lane direction at each time stepto see whether they are all within 90 degree.
Revised: If so, we further calculate angles between velocity and the lane direction at each time step to see whether they are all within 90 degree.

Original: The velocities are approximated by differentiating thetrajectory.
Revised: The velocities are approximated by differentiating the trajectory.

Original: The trajectories that fail to pass the test are identiﬁed as negative trajectories
Revised: The trajectories that fail to pass the test are identiﬁed as negative trajectories

Original: Y i,neg .
Revised: Y i,neg .

Original: Notethat the lane direction information might be incomplete in some examples in the dataset, and in thecase, we only use the drivable region information.
Revised: Note that the lane direction information might be incomplete in some examples in the dataset, and in the case, we only use the drivable region information.

Original: In addition, human drivers also go against thecontext occasionally.
Revised: In addition, human drivers also go against the context occasionally.

Original: We disable L unlike if the ground truth trajectory violates the context to allow asimilar prediction.
Revised: We disable L unlike if the ground truth trajectory violates the context to allow a similar prediction.

Original: Although this checker is not perfect, it is able to select out meaningful negativetrajectories to support the training.
Revised: Although this checker is not perfect, it is able to select out meaningful negative trajectories to support the training.

Original: Note that recent works like Beelines [16] provide other methodsto detect the unlikely trajectories and it is possible to adopt them as additional rules in our checker.
Revised: Note that recent works like Beelines [16] provide other methods to detect the unlikely trajectories and it is possible to adopt them as additional rules in our checker.

Original: We leave it for future research.
Revised: We leave it for future research.

Original: [Figure]
Revised: [Figure]

Original: 3.4 Algorithm
Revised: 3.4 Algorithm

Original: The ﬁnal algorithm is shown in Alg.1.
Revised: The ﬁnal algorithm is shown in Alg.1.

Original: At each iteration, we ﬁrst run the forward pass of the model toget the output distribution p θ ( Y i | X i ) given the input X i .
Revised: At each iteration, we ﬁrst run the forward pass of the model to get the output distribution p θ ( Y i | X i ) given the input X i .

Original: Then, K negative candidate trajectoriesare drawn from this distribution and we select the negative trajectories out Y i,neg via our checker.
Revised: Then, K negative candidate trajectories are drawn from this distribution and we select the negative trajectories out Y i,neg via our checker.

Original: After that, ground truth trajectory and negative trajectories are used to calculate the loss function,update the model, and go to the next iteration.
Revised: After that, ground truth trajectory and negative trajectories are used to calculate the loss function, update the model, and go to the next iteration.

Original: Note that if there are no Y i,neg in the K negativecandidates judged by our checker for data i , we don’t apply L unlike on i .
Revised: Note that if there are no Y i,neg in the K negative candidates judged by our checker for data i , we don’t apply L unlike on i .

Original: 3.5 Gradient Analysis
Revised: 3.5 Gradient Analysis

Original: Assume a single-mode prediction case that the future position y i,gt,t at time step t of agenti is modeled by a simple Gaussian distribution N ( y i,t ; ˆ µ i,t , ˆ σ i,t I ) .
Revised: Assume a single-mode prediction case that the future position y i,gt,t at time step t of agent i is modeled by a simple Gaussian distribution N ( y i,t ; ˆ µ i,t , ˆ σ i,t I ) .

Original: ˆ µ and ˆ σ i,t are calculatedby the model.
Revised: ˆ µ and ˆ σ i,t are calculated by the model.

Original: With a single negative position y i,neg,t we deﬁne a simple loss for step t
Revised: With a single negative position y i,neg,t we deﬁne a simple loss for step t

Original: L t = − log N ( y gt,t ; ˆ µ t , ˆ σ t I )
Revised: L t = − log N ( y gt,t ; ˆ µ t , ˆ σ t I )

Original: + log N ( y neg,t ; ˆ µ t , ˆ σ t I ) and omit the subscript i for brevity.
Revised: + log N ( y neg,t ; ˆ µ t , ˆ σ t I ) and omit the subscript i for brevity.

Original: Thegradient of L t with respect to ˆ µ t and ˆ σ t in this case is (Derivation in supplementary):
Revised: The gradient of L t with respect to ˆ µ t and ˆ σ t in this case is (Derivation in supplementary):

Original: [Equation]
Revised: [Figure]

Original: [Equation]
Revised: [Equation]

Original: Eq.3 shows that the center of the predicted distribution ˆ µ t is pushed towards y gt,t and pushed awayfrom y neg,t by this learning objective.
Revised: Eq.3 shows that the center of the predicted distribution ˆ µ t is pushed towards y gt,t and pushed away from y neg,t by this learning objective.

Original: In Eq.4, when y gt,t is closer to the center than y neg,t , ∂L∂ ˆ σ t [Figure]
Revised: In Eq.4, when y gt,t is closer to the center than y neg,t , ∂L∂ ˆ σ t is positive and ˆ σ t is decreased.

Original: Algorithm
Revised: Note that y neg,t is selected out from samples of N (ˆ µ t , ˆ σ t I )) , this means when N (ˆ µ t , ˆ σ t I )) covers context-violated region and this region is farther than ground truth region, N (ˆ µ t , ˆ σ t I )) will shrink to exclude the negative region and become a better estimation to the true data distribution.

Original: Initialize the model parameters θ , learning rate α and coefﬁcient γ while not converge do
Revised: Initialize the model parameters θ , learning rate α and coefﬁcient γ while not converge do

Original: X i , Y i,gt ∼ D
Revised: X i [Equation] Y i

Revised: [Equation]

Revised: gt ∼ D

Original: Predict distribution p θ ( Y i |
Revised: Predict distribution p θ ( Y i |

Original: X i )
Revised: X i )

Original: Draw K trajectories
Revised: Draw K trajectories

Original: Y i,k ∼ p θ ( Y i | X i )
Revised: Y i,k ∼ p θ ( Y i | X i )

Original: Select Y i,neg from Y i,k via checkerCompute original loss L orig
Revised: Select Y i,neg from Y i,k via checkerCompute original loss L orig

Original: Compute L unlike using Eq.
Revised: Compute L unlike using Eq.

Original: L = L orig + γL unlike θ = θ − α ∇ θ ( L ) end
Revised: L = L orig + γL unlike θ = θ − α ∇ θ ( L ) end

Original: Soft γ .
Revised: Soft γ .

Original: At the beginning of training, the model performs poorly and may generate bad predictions faraway from the ground truth y gt,t .
Revised: At the beginning of training, the model performs poorly and may generate bad predictions far away from the ground truth y gt,t .

Original: In this case, thestandard deviation ˆ σ t will increase according to Eq.4and make the prediction more uncertain.
Revised: In this case, the standard deviation ˆ σ t will increase according to Eq. and make the prediction more uncertain.

Original: To alleviatethis issue, we turn on L unlike smoothly after the ﬁrstfew training epochs by making γ in Eq.2 as a Sigmoidfunction of the training epoch centered at a speciﬁedepoch as a warm-up.
Revised: To alleviate this issue, we turn on L unlike smoothly after the ﬁrst few training epochs by making γ in Eq.2 as a Sigmoid function of the training epoch centered at a speciﬁed epoch as a warm-up.

Original:  Experimental Results
Revised:  Experimental Results

Original: In this section, we present the experimental resultsof our method.
Revised: In this section, we present the experimental results of our method.

Original: Our method can be applied to thestate of the art models that generate a future trajectorydistribution and further improve the predicted distribution quality.
Revised: Our method can be applied to the state of the art models that generate a future trajectory distribution and further improve the predicted distribution quality.

Original: We evaluated our method onnuScenes dataset [18] applied on Trajectron++ [1] and Argoverse dataset [19] applied on a distributionbased variant of LaneGCN [15].
Revised: We evaluated our method on nuScenes dataset [18] applied on Trajectron++ [1] and Argoverse dataset [19] applied on a distributionbased variant of LaneGCN [15].

Original: Evaluation Metrics We use average l 2 displacement error (ADE) and ﬁnal l 2 displacement error(FDE) to evaluate the prediction.
Revised: Evaluation Metrics We use average l 2 displacement error (ADE) and ﬁnal l 2 displacement error (FDE) to evaluate the prediction.

Original: We target improving the quality of the predicted distribution.
Revised: We target improving the quality of the predicted distribution.

Original: Toquantify the distribution quality, we randomly sample 200 trajectories from the predicted distributionand average ADE and FDE over these samples as the metric ADE-Full and FDE-Full.
Revised: To quantify the distribution quality, we randomly sample 200 trajectories from the predicted distribution and average ADE and FDE over these samples as the metric ADE-Full and FDE-Full.

Original: In addition,we report the context-violation rate of these 200 trajectories as measured by the context checker.
Revised: In addition, we report the context-violation rate of these 200 trajectories as measured by the context checker.

Original: 4.1 Experiments on nuScenes Dataset
Revised: 4.1 Experiments on nuScenes Dataset

Original: nuScenes dataset [18] contains 1000 city driving scenes from both left-hand (Singapore) and righthand (Boston) trafﬁc regions.
Revised: nuScenes dataset [18] contains 1000 city driving scenes from both left-hand (Singapore) and righthand (Boston) trafﬁc regions.

Original: Each scene is 20s long and recorded at 2Hz.
Revised: Each scene is 20s long and recorded at 2Hz.

Original: nuScenes is one of themost prominent open-source motion forecasting datasets with detailed semantic maps.
Revised: nuScenes is one of the most prominent open-source motion forecasting datasets with detailed semantic maps.

Original:  Test Model Trajectron++ [1] is a CVAE-based [20] model.
Revised: [Table] [Table] Test Model Trajectron++ [1] is a CVAE-based [20] model.

Original: Its input X i contains positions, velocities, headings of the predicted and surrounding vehicles, and a map patch.
Revised: Its input X i contains positions, velocities, headings of the predicted and surrounding vehicles, and a map patch.

Original: The output distributionp θ ( Y i | X i ) =
Revised: The output distribution p θ ( Y i | X i ) =

Original: (cid:80) z p θ 1 ( z | X i ) p θ 2 ( Y i |
Revised: (cid:80) z p θ 1 ( z | X i ) p θ 2 ( Y i |

Original: X i , z ) is a Gaussian mixture model with 25 componentsand modeled by an encoder net p θ 1 ( z | X i ) and a decoder net p θ 1 ( Y i |
Revised: X i , z ) is a Gaussian mixture model with 25 components and modeled by an encoder net p θ 1 ( z | X i ) and a decoder net p θ 1 ( Y i |

Original: X i , z ) .
Revised: X i , z ) .

Original: In addition, it hasanother encoder net q θ 3 ( z | X i , Y i,gt ) used only in training.
Revised: In addition, it has another encoder net q θ 3 ( z | X i , Y i,gt ) used only in training.

Original: The original learning objective is shownin supplementary materials.
Revised: The original learning objective is shown in supplementary materials.

Original: I q denotes the mutual information.
Revised: I q denotes the mutual information.

Original: [Table]

Original: [Table]

Original: Experiments The batch size is set to 1024.
Revised: Experiments The batch size is set to 1024.

Original: Models are trained for 35 epochs and we test theweights from the best epoch measured by average ADE on the validation set.
Revised: Models are trained for 35 epochs and we test the weights from the best epoch measured by average ADE on the validation set.

Original: The coefﬁcient γ in
Revised: The coefﬁcient γ in

Original: Alg.1 increases gradually from 0 to 1 as a sigmoid function centered at the 24th epoch.
Revised: Alg.1 increases gradually from 0 to 1 as a sigmoid function centered at the 24th epoch.

Original: The initiallearning rate is 3e-3 and it decays exponentially by 0.9995 per iteration.
Revised: The initial learning rate is 3e-3 and it decays exponentially by 0.9995 per iteration.

Original: These hyperparametersexcept γ are optimized for Trajectron++ and lead to better performance than that in the original paper.
Revised: These hyperparameters except γ are optimized for Trajectron++ and lead to better performance than that in the original paper.

Original: To increase the numerical stability of the training, we add a small constant (cid:15) = 1 e − 9 in Eq.1 toavoid the inﬁnity gradient region of log function.
Revised: To increase the numerical stability of the training, we add a small constant (cid:15) = 1 e − 9 in Eq.1 to avoid the inﬁnity gradient region of log function.

Original: In this case, Eq.1 becomes:
Revised: In this case, Eq.1 becomes:

Original: [Equation]
Revised: [Equation]

Original: Mathematically, (cid:15) term scales the original gradient by p θ ( Y i,neg | X i)
Revised: Mathematically, (cid:15) term scales the original gradient by p θ ( Y i,neg [Equation] X i

Original: p
Revised: [Equation]

Original: θ ( Y i,neg | X i )+ (cid:15) .
Revised: Y i,neg | X [Equation] )+ (cid:15) .

Original: Proof is shown in supplementary materials.
Revised: Proof is shown in supplementary materials.

Original: In addition, we rotate the scenes randomly from 15 ◦ to 345 ◦ in the training set fordata augmentation following the setting of the original Trajectron++.
Revised: In addition, we rotate the scenes randomly from 15 ◦ to 345 ◦ in the training set for data augmentation following the setting of the original Trajectron++.

Original: For each model, we run ﬁveexperiments and report the mean and standard deviation of the measured metrics.
Revised: For each model, we run ﬁve experiments and report the mean and standard deviation of the measured metrics.

Original: The models aretrained to predict 3 seconds into the future.
Revised: The models are trained to predict 3 seconds into the future.

Original: To evaluate generalization beyond the training horizon,we test on both 3 second and 4-second prediction horizons.
Revised: To evaluate generalization beyond the training horizon, we test on both 3 second and 4-second prediction horizons.

Original: Tab.1 shows the quantitative results of the 4s prediction measured by the FDE/ADE-Full metricsand the context-violation rate.
Revised: Tab.1 shows the quantitative results of the 4s prediction measured by the FDE/ADE-Full metrics and the context-violation rate.

Original: Our unlikelihood loss encourages the prediction to respect contextinformation more measured by the reduction of the context violation rate from 10.59% to 8.85%.
Revised: Our unlikelihood loss encourages the prediction to respect context information more measured by the reduction of the context violation rate from 10.59% to 8.85%.

Original: Besides, our method increases the prediction accuracy as both FDE and ADE are reduced by about8%.
Revised: Besides, our method increases the prediction accuracy as both FDE and ADE are reduced by about 8%.

Original: Results indicate that our method helps improve the quality of the predicted distribution from bothcontext-compliant and accuracy perspectives.
Revised: Results indicate that our method helps improve the quality of the predicted distribution from both context-compliant and accuracy perspectives.

Original: This is also demonstrated in the qualitative comparisonin Fig.3.
Revised: This is also demonstrated in the qualitative comparison in Fig.3.

Original: The predicted distribution from our methods covers the not-drivable and wrong directionregion less.
Revised: The predicted distribution from our methods covers the not-drivable and wrong direction region less.

Original: In contrast, original Trajectron++ tends to violate the contextual information when theprediction horizon is long.
Revised: In contrast, original Trajectron++ tends to violate the contextual information when the prediction horizon is long.

Original: This shows that our method encourages the model to be more sensitive tothe road boundary and the lane direction.
Revised: This shows that our method encourages the model to be more sensitive to the road boundary and the lane direction.

Original: Comparison with other methods is shown in Tab.2.
Revised: Comparison with other methods is shown in Tab.2.

Original: The
Revised: The

Original: FDE for the single predicted trajectory is also improved by our method.
Revised: FDE for the single predicted trajectory is also improved by our method.

Revised: Gaussian LaneGCN, our proposed method reduces the context violation by a large margin and avoid 56% of prediction that violates context.

Revised: ADE-Full and FDE-Full are reduced by 8% and 6%, respectively.

Revised: Results indicate a better-predicted distribution with our unlikelihood loss L unlike

Revised: [Table]

Original: 4.2 Experiments on Argoverse Dataset
Revised: 4.2 Experiments on Argoverse Dataset

Original: Argoverse dataset [19] contains 300,000 5-second tracked scenarios in 2 American cities Miami and
Revised: Argoverse dataset [19] contains 300,000 5-second tracked scenarios in 2 American cities Miami and

Original: Pittsburgh with semantic maps.
Revised: Pittsburgh with semantic maps.

Original: The data is recorded at 10 Hz.
Revised: The data is recorded at 10 Hz.

Original: The ﬁrst 2 seconds are used as inputto predict the next 3 seconds’ future.
Revised: The ﬁrst 2 seconds are used as input to predict the next 3 seconds’ future.

Original: Test Model LaneGCN [15] is one of the state of the art models on Argoverse dataset.
Revised: Test Model LaneGCN [15] is one of the state of the art models on Argoverse dataset.

Original: [-It takesthe historical trajectories and a graph representation of lanes as input and directly generates 
-]
Revised: [-It takesthe historical trajectories and a graph representation of lanes as input and directly generates 
-]

Original: Gaussian LaneGCN, our proposed method reduces the context violation by a large margin and avoid 56% of prediction that violates context.

Original: ADE-Full and FDE-Full are reduced by 8% and6% respectively. Results indicate a better predicted [Table] deterministic trajectories as the prediction of each vehicle.
Revised: It takes the historical trajectories and a graph representation of lanes as input and directly generatesdeterministic trajectories as the prediction of each vehicle.

Original: The predicted trajectories are trained byregression using smooth L1 loss.
Revised: The predicted trajectories are trained by regression using smooth L1 loss.

Original: To investigate the effectiveness of our method on distribution-basedmodels, we applied our method on a distribution-based variant of LaneGCN that predicts 6 trajectorydistributions instead.
Revised: To investigate the effectiveness of our method on distribution-based models, we applied our method on a distribution-based variant of LaneGCN that predicts 6 trajectory distributions instead.

Original: The predicted position at each timestep is modeled by a simple isotropic
Revised: The predicted position at each timestep is modeled by a simple isotropic

Original: Gaussian distribution with predicted variance.
Revised: Gaussian distribution with predicted variance.

Original: This is done by extending the dimension of the ﬁnaloutput layer to include a log variance prediction additionally for each timestep.
Revised: This is done by extending the dimension of the ﬁnal output layer to include a log variance prediction additionally for each timestep.

Original: In addition, the modelis modiﬁed to predict velocity distribution.
Revised: In addition, the model is modiﬁed to predict velocity distribution.

Original: The trajectory distribution is calculated by the integrationover the velocity distribution.
Revised: The trajectory distribution is calculated by the integration over the velocity distribution.

Original: The smooth L1 regression loss is replaced by the minus log likelihoodof the ground truth future (MLE training).
Revised: The smooth L1 regression loss is replaced by the minus log likelihood of the ground truth future (MLE training).

Original: The original training objective is shown in supplementarymaterials.
Revised: The original training objective is shown in supplementary materials.

Original: This variant is denoted as Gaussian LaneGCN.
Revised: This variant is denoted as Gaussian LaneGCN.

Original: Experiments Argoverse does not release the ground truth future trajectories for the test dataset.
Revised: Experiments Argoverse does not release the ground truth future trajectories for the test dataset.

Original: Therefore, we use the original validation set as our test set in this experiment.
Revised: Therefore, we use the original validation set as our test set in this experiment.

Original: For both Gaussian
Revised: For both Gaussian

Original: LaneGCN and our method, we set the batch size to 128.
Revised: LaneGCN and our method, we set the batch size to 128.

Original: The initial learning rate is 1e-3 and it decaysto 1e-4 after 32 epochs.
Revised: The initial learning rate is 1e-3 and it decays to 1e-4 after 32 epochs.

Original: The model is trained for 36 epochs.
Revised: The model is trained for 36 epochs.

Original: The coefﬁcient γ of the unlikelihoodloss in Alg.1 increases gradually from 0 to 1 as a sigmoid function centered at the 12th epoch.
Revised: The coefﬁcient γ of the unlikelihood loss in Alg.1 increases gradually from 0 to 1 as a sigmoid function centered at the 12th epoch.

Original: Theresults are listed in Tab.3.
Revised: The results are listed in Tab.3.

Original: With our unlikelihood training loss, we signiﬁcantly reduce the contextviolation rate from 9.0% to 4.0% compared to the original Gaussian LaneGCN.
Revised: With our unlikelihood training loss, we signiﬁcantly reduce the context violation rate from 9.0% to 4.0% compared to the original Gaussian LaneGCN.

Original: 56% of predictionsthat violate the context are avoided with our method.
Revised: 56% of predictions that violate the context are avoided with our method.

Original: In addition, ADE-Full and FDE-Full are alsoreduced by 8% and 6%, respectively.
Revised: In addition, ADE-Full and FDE-Full are also reduced by 8% and 6%, respectively.

Original: Results indicate that our method successfully improves thepredicted distribution quality by encouraging the model to focus on context information more.
Revised: Results indicate that our method successfully improves the predicted distribution quality by encouraging the model to focus on context information more.

Original: 4.3 Ablation Study
Revised: 4.3 Ablation Study

Original: The Inﬂuence of Our Loss Without Map Input
Revised: The Inﬂuence of Our Loss Without Map Input

Original: In this experiment, we remove the map inputfrom the model and demonstrate the inﬂuence of our unlikelihood loss in nuScenes. Results areshown in Tab.4.
Revised: Here we remove the map input from the model and demonstrate the inﬂuence of our unlikelihood loss in nuScenes in Tab.4.

Original: Interestingly, our loss helps improve the performance from 2.89 to 2.67 measuredby the FDE-Full although the model does not see the context during inference.
Revised: Interestingly, our loss helps improve the performance from 2.89 to 2.67 measured by the FDE-Full although the model does not see the context during inference.

Original: We think the reasonis that compared to the Trajectron++ without map input, our unlikelihood loss still offers contextinformation to support the training since this loss is calculated using the context.
Revised: We think the reason is that compared to the Trajectron++ without map input, our unlikelihood loss still offers context information to support the training since this loss is calculated using the context.

Original: Therefore, our modelreceives more information during training and performs better.
Revised: Therefore, our model receives more information during training and performs better.

Original: Besides, our method without mapinput even achieves a comparable result (FDE-Full 2.67) compared to Trajectron++ with map input(FDE-Full 2.74).
Revised: Besides, our method without map input even achieves a comparable result (FDE-Full 2.67) compared to Trajectron++ with map input (FDE-Full 2.74).

Original: This experiment shows that our loss can inject context information into learningsignals.
Revised: This experiment shows that our loss can inject context information into learning signals.

Original: In addition, using map input only as the context information source improves FDE-Full of Trajectron++ by 0.15 (from 2.89 to 2.74).
Revised: In addition, using map input only as the context information source improves FDE-Full of Trajectron++ by 0.15 (from 2.89 to 2.74).

Original: In contrast, if we use both map input and our unlikelihoodloss , the performance is improved by 0.38 (from 2.89 to 2.51).
Revised: In contrast, if we use both map input and our unlikelihood loss , the performance is improved by 0.38 (from 2.89 to 2.51).

Original: Our loss doubles the contribution ofcontext information.
Revised: Our loss doubles the contribution of context information.

Original: Remove Context-Violated Prediction Directly
Revised: Remove Context-Violated Prediction Directly

Original: An intuitive way to avoid context-violated predictions is simply removing these predictions as a post-processing step.
Revised: An intuitive way to avoid context-violated predictions is simply removing these predictions as a post-processing step.

Original: Even though this is straightforward, the predictor model in this case isn’t trained to obtain the context violation knowledge.
Revised: Even though this is straightforward, the predictor model in this case isn’t trained to obtain the context violation knowledge.

Original: Ourmethod encourages the model to understand the context better and to avoid the context violationby itself.
Revised: Our method encourages the model to understand the context better and to avoid the context violation [Table] [Table] [Table]

Original:  Therefore, our model is more ‘intelligent’ compared to the method directly removing thecontext-violated prediction and leads to a better prediction.
Revised: by itself. Therefore, our model is more ‘intelligent’ compared to the method directly removing the context-violated prediction and leads to a better prediction.

Original: In addition, context violation is sometimesneeded.
Revised: In addition, context violation is sometimes needed.

Original: A small part of the ground truth trajectories also violates the context.
Revised: A small part of the ground truth trajectories also violates the context.

Original: The model trained byour method can still give us context-violated prediction as our context violation rate is not zero in Tab1.
Revised: The model trained by our method can still give us context-violated prediction as our context violation rate is not zero in Tab1.

Original: We list the ADE/FDE-Full of Trajectron++, Trajectron++ removing the context-violated prediction [Table] [Table] [Table]
Revised: We list the ADE/FDE-Full of Trajectron++, Trajectron++ removing the context-violated prediction directly, and our method in Tab.5.

Original: [Table]

Original: directly, and our method in Tab.5.

Original: Although simply removing the context-violated prediction helpsimprove the distribution accuracy, our method still performs better.
Revised: Although simply removing the context-violated prediction helps improve the distribution accuracy, our method still performs better.

Original: Hyperparameter γ
Revised: Hyperparameter γ

Original: In our previous experiments, γ is simply set to 1 and turned on smoothlyduring training.
Revised: In our previous experiments, γ is simply set to 1 and turned on smoothly during training.

Original: We further performed ablations on γ with values including 0.1, 0.3, 3, 10.
Revised: We further performed ablations on γ with values including 0.1, 0.3, 3, 10.

Original: Weobserved performance degradation for smaller γ , and similar performance to γ = 1 for bigger γ is;see the detailed ablations in the Section ’Hyperparameter γ ’ of the Appendix.
Revised: We observed performance degradation for smaller γ , and similar performance to γ = 1 for bigger γ is; see the detailed ablations in the Section ’Hyperparameter γ ’ of the Appendix.

Original: Check-horizon for negative candidates Assume we have a 3-second predicted trajectory thatobeys our checker but tends to violate it in the near future (e.g., in 1 second).
Revised: Check-horizon for negative candidates Assume we have a 3-second predicted trajectory that obeys our checker but tends to violate it in the near future (e.g., in 1 second).

Original: Such a trajectory isable to pass our checker’s examination, butit is still unlikely to happen in the real world.
Revised: Such a trajectory is able to pass our checker’s examination but still unlikely to happen in the real world.

Original: To classifyit as a negative trajectory, we check the future of this prediction. This can be done by extendingthe prediction horizon of the candidate trajectories and checking this extended version.
Revised: To classify it as a negative trajectory, we check the future of this prediction by extending the prediction horizon of the candidate trajectories and checking this extended version.

Original: In Tab.6,we show ablation studies with extended check-horizon from 3 seconds to 4, 5, 6 seconds to verifywhether this mechanism improves our method.
Revised: Tab.6 shows ablation studies with extended check-horizon from 3 seconds to 4, 5, 6 seconds to verify whether this mechanism improves our method.

Original: Note that the extended horizon is only used forselecting out the negative trajectories.
Revised: Note that the extended horizon is only used for selecting out the negative trajectories.

Original: Trajectories are truncated back to 3 seconds when computingthe unlikelihood loss L unlike .
Revised: Trajectories are truncated back to 3 seconds when computing the unlikelihood loss L unlike .

Original: Our method beneﬁts from an adequately extended check-horizon asextending the negative trajectories to 4 seconds improves the FDE Full by about 0.08.
Revised: Our method beneﬁts from an adequately extended check-horizon as extending the negative trajectories to 4 seconds improves the FDE Full by about 0.08.

Original: Note thatwhen we further extend the check-horizon to 5 seconds and 6 seconds, we do not observe a betterperformance.
Revised: Note that when we further extend the check-horizon to 5 seconds and 6 seconds, we do not observe a better performance.

Original: This might be because the future of the prediction itself is too inaccurate when weextend the horizon too much and make the judgment of the original prediction unreliable.
Revised: This might be because the future of the prediction itself is too inaccurate when we extend the horizon too much and make the judgment of the original prediction unreliable.

Original: Numbersare averaged over two training instances.
Revised: Numbers are averaged over two training instances.

Original:  Conclusion
Revised:  Conclusion

Original: We present an unlikelihood guided trajectory prediction method that leverages context informationinto learning signals by minimizing the probability of unlikely trajectories.
Revised: We present an unlikelihood guided trajectory prediction method that leverages context information into learning signals by minimizing the probability of unlikely trajectories.

Original: During training, ourcontext checker detects predicted unlikely trajectories and their probabilities are minimized using an unlikelihood loss.
Revised: During training, our context checker detects predicted unlikely trajectories and their probabilities are minimized using an unlikelihood loss.

Original: Our method can be seamlessly incorporated into state-of-the-art distribution-based models with a maximum likelihood estimation objective.
Revised: Our method can be seamlessly incorporated into state-of-the-art distribution-based models with a maximum likelihood estimation objective.

Original: Our experimental results demonstrate that our method signiﬁcantly improves the predicted distribution quality of state-of-the-art trajectoryprediction models.
Revised: Our experimental results demonstrate that our method signiﬁcantly improves the predicted distribution quality of state-of-the-art trajectory prediction models.

Original: We hope that our work may encourage future work on exploring better unlikelihood methods for trajectory prediction and improved context checker models.  
Revised: We hope that our work may encourage future work on exploring better unlikelihood methods for trajectory prediction and improved context checker models.  Acknowledgement

Revised: This work is funded by a KAUST BAS/1/1685-01-0.