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saier

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unarXive_citrec

like 7

9e00ef99-96fb-43c3-8f89-51bd2a0f07e0

Causality plays a central role in understanding distribution changes, which can be modelled as causal interventions [1]}. The Sparse Mechanism Shift hypothesis [1]}, [3]} (SMS) states that naturally occurring shifts in the data distribution can be attributed to sparse and local changes in the causal generative process. This implies that many causal mechanisms remain invariant across domains [4]}, [5]}, [6]}. In this light, learning a causal model of the environment enables agents to reason about distribution shifts and to exploit the invariance of learnt causal mechanisms across different environments. Hence, we posit that world models with a causal structure can facilitate modular transfer of knowledge. To date, however, methods for causal discovery [7]}, [8]}, [9]}, [10]}, [11]} require access to abstract causal variables to learn causal models from data. These are not typically available in the context of world model learning, where we wish to operate directly on high-dimensional observations.

[10]

https://openalex.org/W3103069071

0ceb8202-d9f6-4419-bc1d-5b7b206b46ff

Causality plays a central role in understanding distribution changes, which can be modelled as causal interventions [1]}. The Sparse Mechanism Shift hypothesis [1]}, [3]} (SMS) states that naturally occurring shifts in the data distribution can be attributed to sparse and local changes in the causal generative process. This implies that many causal mechanisms remain invariant across domains [4]}, [5]}, [6]}. In this light, learning a causal model of the environment enables agents to reason about distribution shifts and to exploit the invariance of learnt causal mechanisms across different environments. Hence, we posit that world models with a causal structure can facilitate modular transfer of knowledge. To date, however, methods for causal discovery [7]}, [8]}, [9]}, [10]}, [11]} require access to abstract causal variables to learn causal models from data. These are not typically available in the context of world model learning, where we wish to operate directly on high-dimensional observations.

[11]

https://openalex.org/W2979174981

ec875b0b-8f99-4ec6-84cb-b9a0a5f81a76

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[1]

https://openalex.org/W3025660841

2e41c1ed-9f8a-4fdf-a658-16c6f3f01fb3

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[2]

https://openalex.org/W2890208753

a2e00aed-1a27-4347-8434-e985e69cbd14

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[3]

https://openalex.org/W2995298643

0335f128-30d0-43d2-9040-516ae52f58f9

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[4]

https://openalex.org/W2900152462

2b06f66c-7b8f-4711-8cb9-2f00448a580f

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[7]

https://openalex.org/W2889347284

069516e6-4483-48f1-b290-24ee70deb6d5

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[8]

https://openalex.org/W2963430173

15ee302f-152a-41c3-9426-6e923e728372

Predictive models of the environment can be used to derive exploration- [1]} or reward-driven [2]}, [3]}, [4]} behaviours. In this paper, we focus on the learning of latent dynamics models. World models [2]} train a representation encoder and a RNN-based transition model in a two-stage process. Other approaches [4]}, [7]}, [8]} learn a generative model by jointly training the representation and the transition via variational inference. PlaNet [4]} parameterises the transition model with RNNs. E2C [8]}, [11]} and SOLAR [7]} use locally-linear transition models, arguing that including constraints in the dynamics model yields structured latent spaces that are suitable for control problems. Our proposed approach shares the general principle that latent representations can be shaped by structured transition mechanisms [13]}. However, to the best of our knowledge, VCD is the first approach that implements a causal transition model given high-dimensional inputs.

[13]

https://openalex.org/W3210352550

136a6982-290a-47bb-a083-207910a853d5

Causal discovery methods enable the learning of causal structure from data. Approaches can be categorised as constraint-based (e.g. [1]}) and score-based (e.g. [2]}). The reader is referred to [3]} for a detailed review of causal discovery methods. Motivated by the fact that these methods require access to abstract causal variables, recent efforts have been made to reconcile machine learning, which has the ability to operate on low-level data, and causality [4]}. Our current work situates within this broader context of causal representation learning, and aims to identify causally meaningful representations via the discovery of causal transition dynamics. To this end, [5]} proposes a similar framework to ours and provide a theoretical discussion around the identifiability of causal variables. Our approach differs in that we focus on the adaptation capabilities of causal models and show that the method is applicable to image observations.

[1]

https://openalex.org/W1524326598

abce2049-f3a9-41ff-b975-f599274af60e

Causal discovery methods enable the learning of causal structure from data. Approaches can be categorised as constraint-based (e.g. [1]}) and score-based (e.g. [2]}). The reader is referred to [3]} for a detailed review of causal discovery methods. Motivated by the fact that these methods require access to abstract causal variables, recent efforts have been made to reconcile machine learning, which has the ability to operate on low-level data, and causality [4]}. Our current work situates within this broader context of causal representation learning, and aims to identify causally meaningful representations via the discovery of causal transition dynamics. To this end, [5]} proposes a similar framework to ours and provide a theoretical discussion around the identifiability of causal variables. Our approach differs in that we focus on the adaptation capabilities of causal models and show that the method is applicable to image observations.

[2]

https://openalex.org/W2103659055

16748e03-1c07-4577-8c81-da64b818a0a5

Causal discovery methods enable the learning of causal structure from data. Approaches can be categorised as constraint-based (e.g. [1]}) and score-based (e.g. [2]}). The reader is referred to [3]} for a detailed review of causal discovery methods. Motivated by the fact that these methods require access to abstract causal variables, recent efforts have been made to reconcile machine learning, which has the ability to operate on low-level data, and causality [4]}. Our current work situates within this broader context of causal representation learning, and aims to identify causally meaningful representations via the discovery of causal transition dynamics. To this end, [5]} proposes a similar framework to ours and provide a theoretical discussion around the identifiability of causal variables. Our approach differs in that we focus on the adaptation capabilities of causal models and show that the method is applicable to image observations.

[3]

https://openalex.org/W2801890059

37f25f52-8bbc-4cfc-8644-a3542d8bccc0

Causal discovery methods enable the learning of causal structure from data. Approaches can be categorised as constraint-based (e.g. [1]}) and score-based (e.g. [2]}). The reader is referred to [3]} for a detailed review of causal discovery methods. Motivated by the fact that these methods require access to abstract causal variables, recent efforts have been made to reconcile machine learning, which has the ability to operate on low-level data, and causality [4]}. Our current work situates within this broader context of causal representation learning, and aims to identify causally meaningful representations via the discovery of causal transition dynamics. To this end, [5]} proposes a similar framework to ours and provide a theoretical discussion around the identifiability of causal variables. Our approach differs in that we focus on the adaptation capabilities of causal models and show that the method is applicable to image observations.

[4]

https://openalex.org/W3135588948

68c25c9f-9647-4770-8c63-b30b6d59ce2a

Another branch of related work leverages the invariance of causal mechanisms by learning invariant predictors across environments [1]}, [2]}, [3]}, [4]}, [5]}. This invariance has been studied in the context of state abstractions in MDPs [6]}, and invariant policies can be learnt via imitation learning from different environments [7]}. In contrast, our approach models the full generative process of the data across different environments rather than learning discriminative predictors.

[1]

https://openalex.org/W1515756431

c14fb118-0a2a-4431-917a-0b343b3b524d

Another branch of related work leverages the invariance of causal mechanisms by learning invariant predictors across environments [1]}, [2]}, [3]}, [4]}, [5]}. This invariance has been studied in the context of state abstractions in MDPs [6]}, and invariant policies can be learnt via imitation learning from different environments [7]}. In contrast, our approach models the full generative process of the data across different environments rather than learning discriminative predictors.

[2]

https://openalex.org/W2144020560

19f9cd20-a61b-440d-a324-45757eb6feb4

Another branch of related work leverages the invariance of causal mechanisms by learning invariant predictors across environments [1]}, [2]}, [3]}, [4]}, [5]}. This invariance has been studied in the context of state abstractions in MDPs [6]}, and invariant policies can be learnt via imitation learning from different environments [7]}. In contrast, our approach models the full generative process of the data across different environments rather than learning discriminative predictors.

[3]

https://openalex.org/W1905064697

536060cc-289f-48f7-a181-e835a1b408f8

Another branch of related work leverages the invariance of causal mechanisms by learning invariant predictors across environments [1]}, [2]}, [3]}, [4]}, [5]}. This invariance has been studied in the context of state abstractions in MDPs [6]}, and invariant policies can be learnt via imitation learning from different environments [7]}. In contrast, our approach models the full generative process of the data across different environments rather than learning discriminative predictors.

[5]

https://openalex.org/W2953494151

2c4212b5-9056-4a97-823f-6a5180b1947d

Another branch of related work leverages the invariance of causal mechanisms by learning invariant predictors across environments [1]}, [2]}, [3]}, [4]}, [5]}. This invariance has been studied in the context of state abstractions in MDPs [6]}, and invariant policies can be learnt via imitation learning from different environments [7]}. In contrast, our approach models the full generative process of the data across different environments rather than learning discriminative predictors.

[6]

https://openalex.org/W3034932139

4a0a9dfc-8cf4-465c-afc3-a50c3dbb1236

In a complex environment with high-dimensional observations, such as images, learning a compact latent state space that captures the dynamics of the environment has been shown to be more computationally efficient than learning predictions directly in the observation space [1]}, [2]}. Given a dataset of sequences \(\lbrace (o^{0:T}, a^{0:T}_i)\rbrace _{i=0}^N\)In the current work, we focus on environments without rewards. However, the proposed method can be readily extended to include reward prediction., with observations \(o^t\) and actions \(a^t\) at discrete timesteps \(t\) , a generative model of the observations can be defined using latent states \(z^{0:T}\) as \(p(o^{0:T}, a^{0:T}) = \int \prod _{t=0}^T p_\theta (o^t|z^t)p(a^t|z^t)p_\theta (z^t|z^{t-1}, a^{t-1}) dz^{0:T},\)

[1]

https://openalex.org/W2900152462

48797bc7-5a2b-4e40-b2e7-bdb91121df75

In a complex environment with high-dimensional observations, such as images, learning a compact latent state space that captures the dynamics of the environment has been shown to be more computationally efficient than learning predictions directly in the observation space [1]}, [2]}. Given a dataset of sequences \(\lbrace (o^{0:T}, a^{0:T}_i)\rbrace _{i=0}^N\)In the current work, we focus on environments without rewards. However, the proposed method can be readily extended to include reward prediction., with observations \(o^t\) and actions \(a^t\) at discrete timesteps \(t\) , a generative model of the observations can be defined using latent states \(z^{0:T}\) as \(p(o^{0:T}, a^{0:T}) = \int \prod _{t=0}^T p_\theta (o^t|z^t)p(a^t|z^t)p_\theta (z^t|z^{t-1}, a^{t-1}) dz^{0:T},\)

[2]

https://openalex.org/W2786019934

a9de60eb-5061-4376-a95c-f29492b5d8fd

where \(q_\phi (z^t|o^t)\) is a learnable approximate posterior of the observations. See Appendix for the derivation. RSSM [1]} employs a flexible transition model parameterised as a fully connected recurrent neural network, where the transition probability is split into a stochastic part and a deterministic recurrent part, \(z^t \sim p_\theta (z^t|h^t), \quad h^t = f_\theta (h^{t-1}, z^{t-1}, a^{t-1}),\)

[1]

https://openalex.org/W2900152462

19a7d4f7-b48c-45e0-9ce8-156e2f4ea622

where \(f(\cdot )\) is instantiated as a GRU [1]} and \(h^t\) is the associated hidden state. Intuitively, this provides a path through which information can be passed on over multiple timesteps.

[1]

https://openalex.org/W2157331557

eff8f2ab-1f29-4341-b9ea-c10006450a27

A causal graphical model (CGM) [1]} is defined as a set of random variables \(\lbrace X_1, ..., X_d\rbrace \) , their joint distribution \(P_X\) , and a directed acyclic graph (DAG), \(\mathcal {G}=(X,E)\) , where each edge \((i,j)\in E\) implies that \(X_i\) is a direct cause of \(X_j\) . The joint distribution admits a causal factorisation such that \(p(x_1,...,x_d) = \prod _{i=0}^d p(x_i| PA_i),\)

[1]

https://openalex.org/W2801890059

2ab2bfba-dd92-475c-bb50-7d98c9216d18

where \(p^{\prime }(\cdot |\cdot )\) is the new conditional distribution corresponding to the intervention. The SMS hypothesis [1]} posits that naturally occurring distribution shifts tend to correspond to sparse changes in a causal model when factorized as (REF ), i.e., changes of a few mechanisms only. Causal mechanisms thus tend to be invariant across environments [2]}, [3]}, [4]}. In this light, we argue that a causal world model can structurally leverage the invariance within distribution shifts as an inductive prior. In order to learn a causal model in the context of world models, we draw inspiration from recent advances in causal discovery which aim to learn causal structures from data.

[1]

https://openalex.org/W3135588948

6b4b7e5c-05e5-4369-b322-7b3174841779

where \(p^{\prime }(\cdot |\cdot )\) is the new conditional distribution corresponding to the intervention. The SMS hypothesis [1]} posits that naturally occurring distribution shifts tend to correspond to sparse changes in a causal model when factorized as (REF ), i.e., changes of a few mechanisms only. Causal mechanisms thus tend to be invariant across environments [2]}, [3]}, [4]}. In this light, we argue that a causal world model can structurally leverage the invariance within distribution shifts as an inductive prior. In order to learn a causal model in the context of world models, we draw inspiration from recent advances in causal discovery which aim to learn causal structures from data.

[2]

https://openalex.org/W2144020560

6decda73-a5c0-4a72-9423-f9354f9a44b6

where \(p^{\prime }(\cdot |\cdot )\) is the new conditional distribution corresponding to the intervention. The SMS hypothesis [1]} posits that naturally occurring distribution shifts tend to correspond to sparse changes in a causal model when factorized as (REF ), i.e., changes of a few mechanisms only. Causal mechanisms thus tend to be invariant across environments [2]}, [3]}, [4]}. In this light, we argue that a causal world model can structurally leverage the invariance within distribution shifts as an inductive prior. In order to learn a causal model in the context of world models, we draw inspiration from recent advances in causal discovery which aim to learn causal structures from data.

[3]

https://openalex.org/W1905064697

8dc974a1-e167-488e-9ee7-47dcf5614eec

where \(p^{\prime }(\cdot |\cdot )\) is the new conditional distribution corresponding to the intervention. The SMS hypothesis [1]} posits that naturally occurring distribution shifts tend to correspond to sparse changes in a causal model when factorized as (REF ), i.e., changes of a few mechanisms only. Causal mechanisms thus tend to be invariant across environments [2]}, [3]}, [4]}. In this light, we argue that a causal world model can structurally leverage the invariance within distribution shifts as an inductive prior. In order to learn a causal model in the context of world models, we draw inspiration from recent advances in causal discovery which aim to learn causal structures from data.

[4]

https://openalex.org/W2740437707

5b32b80f-cf5d-488e-ab37-fbb479a6fd5d

We focus on methods that formulate causal discovery as a continuous optimisation problem [1]}, [2]}, [3]} as these can be naturally incorporated into the variational inference framework. Furthermore, since the causal variables are learnt in our model, the causal discovery module is required to learn causal graphs from unknown intervention targets. In this work, we follow the formulation in Differentiable Causal Discovery with Interventional data [1]} (DCDI), which optimises a continuously parameterised probabilistic belief over graph structures and intervention targets. See Appendix for further detail.

[1]

https://openalex.org/W3103069071

6779bf16-6b5f-4cc2-ba7f-244045b86719

We focus on methods that formulate causal discovery as a continuous optimisation problem [1]}, [2]}, [3]} as these can be naturally incorporated into the variational inference framework. Furthermore, since the causal variables are learnt in our model, the causal discovery module is required to learn causal graphs from unknown intervention targets. In this work, we follow the formulation in Differentiable Causal Discovery with Interventional data [1]} (DCDI), which optimises a continuously parameterised probabilistic belief over graph structures and intervention targets. See Appendix for further detail.

[2]

https://openalex.org/W2979174981

4d6b52d2-9bf8-4e4c-a8df-7fb4a38d70fb

We focus on methods that formulate causal discovery as a continuous optimisation problem [1]}, [2]}, [3]} as these can be naturally incorporated into the variational inference framework. Furthermore, since the causal variables are learnt in our model, the causal discovery module is required to learn causal graphs from unknown intervention targets. In this work, we follow the formulation in Differentiable Causal Discovery with Interventional data [1]} (DCDI), which optimises a continuously parameterised probabilistic belief over graph structures and intervention targets. See Appendix for further detail.

[3]

https://openalex.org/W2914607694

9f4eab91-c983-46fb-ba24-bb9352f200d1

where \(d\) is the dimension of the latent space, to be set as a hyperparameter. \(z_i\) denotes the \(i\) th dimension of the latent state, and each conditional distribution \(p_i\) is a one-dimensional normal distribution with mean and variance given by separate neural networks. This factorisation and separation of parameters is motivated by the Independent Causal Mechanism principle, which states that the causal generative process of a system’s variables is composed of autonomous modules that do not inform or influence each other [1]}. This explicit modularity of the model structure enables the notion of interventions, where individual conditional distributions are locally changed without affecting the other mechanisms.

[1]

https://openalex.org/W3135588948

f159127b-af7c-4992-9527-41e50b2e8836

Following the structure of a CGM, we condition each variable only on its causal parents according to the learnable causal graph \(\mathcal {G}\) , rather than the full state. Given a graph \(\mathcal {G}\) , we define the binary adjacency mask \(M^\mathcal {G}\) where the entry \(M^\mathcal {G}_{ij}\) is 1 if and only if \([z^{t-1}, a^{t-1}]_i\) is a causal parent of \(z_j^t\) . This is consistent with the intuition that, in physical systems, states interact with each other in a sparse manner [1]}, and actions tend to have a direct effect on only a subset of the states. Under this parameterisation, the causal transition probability can be written as \(p(z^t | z^{t-1}, a^{t-1}) = \prod _i^d p_i(z_i^t | M^\mathcal {G}_i \odot [z^{t-1}, a^{t-1}]),\)

[1]

https://openalex.org/W2976023236

6ce0e2b2-64c2-4349-ad47-8577a14e15d4

Following the SMS hypothesis [1]}, we assume that changes in distributions across the \(K\) intervened environments are due to sparse interventions in the ground truth causal generative process. In order to incorporate sparse interventions in VCD, given the set of learnt intervention targets \(\mathcal {I}_k\) for each environment, we define the binary intervention mask \(R^\mathcal {I}\) where the entry \(R^\mathcal {I}_{ki}\) is 1 if and only if the variable \(z_i\) is in the set of intervention targets in environment \(k\) . For each variable \(z_i\) , \(R^\mathcal {I}_{ki}\) acts as a switch between reusing a shared observational model and an environment-specific interventional model. The full interventional causal model of the transition probability in the environment \(k\) can be written as \(p^k(z^t|z^{t-1}, a^{t-1}) = \prod _i^d p^{(0)}_i(z_i^t | M^\mathcal {G}_i \odot [z^{t-1}, a^{t-1}])^{1-R^\mathcal {I}_{ki}} p^{(k)}_i(z_i^t | M^\mathcal {G}_i \odot [z^{t-1}, a^{t-1}])^{R^\mathcal {I}_{ki}},\)

[1]

https://openalex.org/W3135588948

4b68fcef-4421-47b7-84db-2a9e1bb94933

Similar to RSSM [1]}, we augment the model with a deterministic recurrent path to enable long-term predictions. To ensure that each conditional distribution only has access to the causal parents, in the same way that each conditional distribution is modelled by a separate network, each conditional distribution keeps a separate recurrent unit and a corresponding hidden activation: \(z^t_i \sim p_i(z^t_i|h^{t}_i), \quad h^t_i = f_i(h^{t-1}_i, M^\mathcal {G}_i \odot [z^{t-1}_i, a^{t-1}_i]),\)

[1]

https://openalex.org/W2900152462

41db38d5-ca51-4166-9d8e-46c51ef5f029

where \(f_i\) is a recurrent module specific to the variable \(z_i\) , instantiated as a GRU [1]}.

[1]

https://openalex.org/W2157331557

e3d7caf7-9ce9-4219-a093-0eba0f16f135

\(p^{(k)}_\theta (z^t|z^{t-1}, a^{t-1})\) is further factorised as in Equation (REF ). The gradients through the outer expectation and the expectation term in ELBO are estimated using the straight-through Gumbel-max trick [1]} and the reparameterisation trick [2]} respectively. For further implementation details, derivation of the lower bound, and model architectures, see Appendices and .

[1]

https://openalex.org/W2547875792

3324bba4-94d9-4499-a284-cbda4908a4bc

\(p^{(k)}_\theta (z^t|z^{t-1}, a^{t-1})\) is further factorised as in Equation (REF ). The gradients through the outer expectation and the expectation term in ELBO are estimated using the straight-through Gumbel-max trick [1]} and the reparameterisation trick [2]} respectively. For further implementation details, derivation of the lower bound, and model architectures, see Appendices and .

[2]

https://openalex.org/W1959608418

fbd168cd-bec3-498a-a885-80549d539e35

We compare the performance of VCD against RSSM [1]}, a state-of-the-art latent world model that served as inspiration for VCD. As RSSM does not support learning from multiple environments, we consider two adaptations of RSSM with different levels of knowledge transfer between environments: (1) RSSM, where one transition model is trained over all environments, i.e., maximum parameter sharing across environments; and (2) MultiRSSM, where individual transition models are trained on each environment, with shared encoders and decoders. This corresponds to the case where no knowledge about dynamics is transferred, i.e., each model is a local expert. We hypothesise that, compared to these two extremes of knowledge sharing, VCD is able to capture environment-specific behaviours whilst reusing invariant mechanisms via modular transfer.

[1]

https://openalex.org/W2900152462

480d9d46-7a4a-4a7f-acec-19b15a02ad55

In this paper, we propose VCD, a predictive world model with a causal structure that is able to consume high-dimensional observations. This is achieved by jointly training a representation and a causally structured transition model using a modified causal discovery objective. In doing so, VCD is able to identify causally meaningful representations of the observations and discover sparse relationships in the dynamics of the system. By leveraging the invariance of causal mechanisms, VCD is able to adapt to new environments efficiently by identifying relevant mechanism changes and updating in a modular way, resulting in significantly improved data efficiency. One exciting avenue of future research is to explore the synergy between causal world models and object-centric generative models [1]}, [2]}, [3]}.

[1]

https://openalex.org/W3167771209

45df6581-b954-4e45-a55b-8ec9d92c78ed

In this paper, we propose VCD, a predictive world model with a causal structure that is able to consume high-dimensional observations. This is achieved by jointly training a representation and a causally structured transition model using a modified causal discovery objective. In doing so, VCD is able to identify causally meaningful representations of the observations and discover sparse relationships in the dynamics of the system. By leveraging the invariance of causal mechanisms, VCD is able to adapt to new environments efficiently by identifying relevant mechanism changes and updating in a modular way, resulting in significantly improved data efficiency. One exciting avenue of future research is to explore the synergy between causal world models and object-centric generative models [1]}, [2]}, [3]}.

[2]

https://openalex.org/W3154552141

5b4f2131-3e43-40bd-bd51-631d81bb7638

The KL terms can be computed analytically since the conditional distributions in the last expression are univariate Gaussian distributions. In training time, the gradients through the expectation terms in the ELBO is estimated by drawing a sample from the posterior distribution using the reparameterisation trick [1]}.

[1]

https://openalex.org/W1959608418

1fbb8a04-2f78-4d12-8672-0bed0b10640d

This section covers the formulation of DCDI [1]} and the graph learning method. These are subsequently used in the learning of VCD.

[1]

https://openalex.org/W3103069071

94e4ff6a-4f64-4293-a4e6-8d6c044a967f

The gradients through the outer expectation can be estimated using the Gumbel-Softmax trick [1]}. To implement this, the ELBO term is evaluated with a sample of the causal graph using the following expression for each entry, \(M^\mathcal {G}_{ij} = \mathbb {I}(\sigma (\alpha _{ij}+L_{ij}) > 0.5) + \sigma (\alpha _{ij}+L_{ij}) - stop\_gradient(\sigma (\alpha _{ij}+L_{ij}) ),\)

[1]

https://openalex.org/W2547875792

8a0b195f-35ee-40bc-b0de-f52e0d8543ee

In the mixed-state experiment, all conditional distributions (including encoders, decoders and transition models) are parameterised by feedforward MLPs with two hidden layers of 64 hidden units each. The recurrent modules are implemented as GRUs [1]} with 64 hidden units. Distributions in the latent space are 16-dimensional diagonal Gaussian distributions with predicted mean and log variance.

[1]

https://openalex.org/W2157331557

718aec46-7f41-4e19-b667-e901f587afe4

In the image experiment, the encoders and decoders are parameterised as convolutional and deconvolutional networks from [1]}. In the RSSM models, the transition models are parameterised as feedforward MLPs with two hidden layers of 300 hidden units. The recurrent module is a GRU with 300 hidden units. In VCD, to compensate for the fact each dimension in the latent space has a separate model, the number of hidden units in the GRU and MLP are reduced to 32 to avoid over-parameterisation. We found that initialising the encoders and decoders by pretraining them as a variational autoencoder helped with training stability for both RSSM and VCD.

[1]

https://openalex.org/W2890208753

41f79478-da84-4910-a3dc-ac0de562c3d0

In both experiments, the training objective is maximised using the ADAM optimiser [1]} with learning rate \(10^{-3}\) for mixed-state, and \(10^{-4}\) for images. In both environments, we clip the log variance to \(-3\) , with a batch size of two trajectories from each of six environments with \(T=50\) . In VCD, the hyperparameters \(\lambda _{\mathcal {G}}, \lambda _{\mathcal {I}}\) are both set to 0.01. All models are trained on a single Nvidia Tesla V100 GPU.

[1]

https://openalex.org/W2964121744

fb5a92b2-2ac5-4131-9b37-214ca51a94a8

Conditional generative adversarial networks (GANs) [1]}, widely used in other generative tasks, have been the primary choice for this line of tasks. Conditional GANs used in the facial de-occlusion and reconstruction are classified into two categories with regard to their architecture for the generator part; U-net-based generator and modulated-generator-based approach. U-net-based generator focuses on completing only the masked region, and conventionally the rest part of an image is directly copy-and-pasted from the conditioned image. However, the fact that it does not train to construct the whole image is postulated to have a negative effect on its generative capability, as when U-net-based generators are confronted with novel masks in shape and size not seen during training, they tend to significantly underperform. Figure REF shows the failure cases of the U-net-based generator when tested on the different mask types unseen during the training.

[1]

https://openalex.org/W2125389028

b48206fb-4fc9-44fd-bd0e-1e35d38df479

Modulated generative approach is one of the recent advances among the conditional GANs, which regards an input as a random constant and each convolution layer adjusts the intermediate latent vectors with denormalization factors (e.g. scale and bias) [1]}. Modulated approach has further advanced the generative capability and edit-ability. However, in the case of conditional generation, there is information loss when a conditioned image is compressed to a low-dimensional latent vector. [2]} The lost information is mostly high-frequency details or the infrequent information such as background, as GAN tends to sustain common information of a domain. This leads to the model's under-performance at pixel preservation of the unmasked region as well, resulting in the prediction being largely different from the conditioned input.

[1]

https://openalex.org/W2962770929

fcad6486-b708-46d8-8bce-75fa17d6d5ad

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[1]

https://openalex.org/W2295936755

31235ab1-4597-457d-a265-862128c08248

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[2]

https://openalex.org/W2012875423

6913ae5d-bc58-4f9f-997c-aea0fa01ddfe

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[3]

https://openalex.org/W2116013899

8748b646-c462-4cf9-b41d-77d96c11bc4d

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[4]

https://openalex.org/W1999360130

dac40063-6e45-4ea1-bb41-3c2d9f2c7296

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[5]

https://openalex.org/W2125873654

ff0a5446-cbf3-4185-8ab4-5375f78f3f6d

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[6]

https://openalex.org/W2105038642

dbb8ef52-c224-41fb-a338-1ef4de4f1d40

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[8]

https://openalex.org/W2963420272

6f43c3fe-a399-477c-a8a6-61c8263b19b0

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[10]

https://openalex.org/W2738588019

4f820834-45de-4350-834f-95b91408333b

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[11]

https://openalex.org/W2611104282

38380364-6cc6-4c49-b340-7c60568d949a

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[12]

https://openalex.org/W2963270367

0afa9ab0-f94d-474e-bc62-7e4e0609e3dd

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[13]

https://openalex.org/W2963231084

86c8e274-f941-4810-8ca3-c74a22326368

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[14]

https://openalex.org/W3176913662

b62e22d9-3e77-4595-9991-a6e7ef696e40

Image Inpainting is defined as a task of reconstructing missing regions in an image as well as removing objects that occlude an image. Early non-learning-based approaches used to fill the masked regions with the information retrieved directly from their surrounds [1]}, [2]}, or replace the missing regions with the best matching patch [3]}, [4]}, [5]}, [6]}, [7]}. With the advent of deep learning, various learning-based methods for image inpainting have been studied. [8]} was the first to use GANs [9]} for image inpainting, using an encoder-decoder architecture. Until now, numerous studies using the U-Net architecture have been conducted [10]}, [11]}, [12]}, [13]} and more recently, the modulated generator approaches started to generate photo-realistic images, while some studies utilized them as generators and trained encoders correspond to them [14]}, [15]}.

[15]

https://openalex.org/W3178406257

2cbd405b-b277-4eae-a796-8fc8162917c1

Semantic Image Inpainting refers to the problem of filling in large holes that require semantic information. Even with the advances in GANs, image inpainting is still an ill-posed problem, especially when most of the semantic knowledge is lost. There have been a number of novel approaches to the problem [1]}, [2]}. [3]} pointed out that existing studies have focused only on rectangular-shaped holes, and proposed PConv to address irregular masks by constructing the U-Net architecture with partial convolution layers. [4]} proposed a contextual attention layer to explicitly utilize surrounding image features, overcoming the ineffectiveness of convolutional neural networks in explicitly utilizing distant surrounding information.

[1]

https://openalex.org/W2963917315

a9999a6e-77c5-40e7-adbe-da56d32186a7

Semantic Image Inpainting refers to the problem of filling in large holes that require semantic information. Even with the advances in GANs, image inpainting is still an ill-posed problem, especially when most of the semantic knowledge is lost. There have been a number of novel approaches to the problem [1]}, [2]}. [3]} pointed out that existing studies have focused only on rectangular-shaped holes, and proposed PConv to address irregular masks by constructing the U-Net architecture with partial convolution layers. [4]} proposed a contextual attention layer to explicitly utilize surrounding image features, overcoming the ineffectiveness of convolutional neural networks in explicitly utilizing distant surrounding information.

[2]

https://openalex.org/W2611104282

713641f4-1ab7-42f0-89ae-9614eee2b3d9

Semantic Image Inpainting refers to the problem of filling in large holes that require semantic information. Even with the advances in GANs, image inpainting is still an ill-posed problem, especially when most of the semantic knowledge is lost. There have been a number of novel approaches to the problem [1]}, [2]}. [3]} pointed out that existing studies have focused only on rectangular-shaped holes, and proposed PConv to address irregular masks by constructing the U-Net architecture with partial convolution layers. [4]} proposed a contextual attention layer to explicitly utilize surrounding image features, overcoming the ineffectiveness of convolutional neural networks in explicitly utilizing distant surrounding information.

[3]

https://openalex.org/W2798365772

2a8bc640-1fe7-424d-9275-52471afc7715

Semantic Image Inpainting refers to the problem of filling in large holes that require semantic information. Even with the advances in GANs, image inpainting is still an ill-posed problem, especially when most of the semantic knowledge is lost. There have been a number of novel approaches to the problem [1]}, [2]}. [3]} pointed out that existing studies have focused only on rectangular-shaped holes, and proposed PConv to address irregular masks by constructing the U-Net architecture with partial convolution layers. [4]} proposed a contextual attention layer to explicitly utilize surrounding image features, overcoming the ineffectiveness of convolutional neural networks in explicitly utilizing distant surrounding information.

[4]

https://openalex.org/W3043547428

5515c165-7bae-48c8-9e18-16cfb7e1b1b6

As semantic image inpainting is an ill-posed problem, several attempts have been made to utilize additional information. EdgeConnect [1]} is a two-stage adversarial network where an edge generator generates surrounding edges in an image and an image completion module is provided with this additional information about the edges. There has also been an attempt to integrate landmark information of the face [2]} or utilize the semantic maps for facial reconstruction. [3]}, [4]}

[1]

https://openalex.org/W2907097116

022940ed-dbcc-4a17-acd4-88929d2cf6db

As semantic image inpainting is an ill-posed problem, several attempts have been made to utilize additional information. EdgeConnect [1]} is a two-stage adversarial network where an edge generator generates surrounding edges in an image and an image completion module is provided with this additional information about the edges. There has also been an attempt to integrate landmark information of the face [2]} or utilize the semantic maps for facial reconstruction. [3]}, [4]}

[4]

https://openalex.org/W2888039002

58501e91-0971-40e4-8b22-017ab8c2af75

The usage of semantic map allows us to grasp both the purpose and performance of the model. Although requiring the semantic labeling can accompany much efforts, we overcome this by using a semantic map predictor which enables obtaining the semantic label in an on-the-fly manner so that we can neglect the need of human labeling. It is important to note that the semantic map predictor is a pre-trained network trained with a separate non-overlapping dataset with the SGIN's training data, and fortunately it generalizes well to the SGIN's training data. Given the masked image \(X_{masked}\) , the semantic map predictor predicts the semantic label map \(L = \lbrace l_{1}, \cdots , l_{C} \rbrace \) . Each \(l_c , c \in [C]\) , indicates the binary class label map for eleven regions (i.e, \(C=11\) ). We trained BiseNet [1]} for our generalized semantic map predictor.

[1]

https://openalex.org/W2886934227

d04453ab-33ea-4ae9-b8e2-ab718836f8df

We chose Feature Pyramid Network (FPN) [1]} as our encoder, which generates latent codes through multi-scaled hierarchical features. Style representations from the latent code are fully determined by the masked image \(X_{masked}\) and the semantic label map \(L_{n}, n \in [N]\) , where \(N\) indicates the number of layers in the FPN's feature map. As we use the semantic map \(L_{n}\) for additional semantic knowledge, the output latent code needs to disentangle styles (e.g, color, patterns ...) for each semantic region. In order to achieve this, we first concatenate the semantic label \(L_{n}\) and the masked image \(X_{masked}\) channel-wise. Then each pyramid network produces \(F_{n}\) , where \(H_{n}\) and \(W_{n}\) indicate the spatial dimension of height and width for each layer. We expand \(F_{n}\in \mathbb {R}^{H_{n} \times W_{n} \times 512}\) to \(F_{exp_{n}} \in \mathbb {R}^{H_{n} \times W_{n} \times 512 \times C}\) by broadcasting along the dimension of binary class map. Also, the semantic label map \(L_{n} \in \mathbb {R}^{H_{n} \times W_{n} \times C}\) is broadcasted along the dimension of feature map channels, producing \(L_{exp_{n}} \in \mathbb {R}^{H_{n} \times W_{n} \times 512 \times C}\) . Additionally, it is difficult to construct faithful style embeddings in the missing holes, because there are no features extracted from the masked region. In the light of this, we harness the well-known contextual attention module [2]} in between the feature pyramids, which can provide additional attention-wise information in the masked region as well. Ablation study shows that the attention module helps increasing the prediction quality.

[1]

https://openalex.org/W3176913662

e369375d-c350-45cd-a38b-284eaa4ebd44

We chose Feature Pyramid Network (FPN) [1]} as our encoder, which generates latent codes through multi-scaled hierarchical features. Style representations from the latent code are fully determined by the masked image \(X_{masked}\) and the semantic label map \(L_{n}, n \in [N]\) , where \(N\) indicates the number of layers in the FPN's feature map. As we use the semantic map \(L_{n}\) for additional semantic knowledge, the output latent code needs to disentangle styles (e.g, color, patterns ...) for each semantic region. In order to achieve this, we first concatenate the semantic label \(L_{n}\) and the masked image \(X_{masked}\) channel-wise. Then each pyramid network produces \(F_{n}\) , where \(H_{n}\) and \(W_{n}\) indicate the spatial dimension of height and width for each layer. We expand \(F_{n}\in \mathbb {R}^{H_{n} \times W_{n} \times 512}\) to \(F_{exp_{n}} \in \mathbb {R}^{H_{n} \times W_{n} \times 512 \times C}\) by broadcasting along the dimension of binary class map. Also, the semantic label map \(L_{n} \in \mathbb {R}^{H_{n} \times W_{n} \times C}\) is broadcasted along the dimension of feature map channels, producing \(L_{exp_{n}} \in \mathbb {R}^{H_{n} \times W_{n} \times 512 \times C}\) . Additionally, it is difficult to construct faithful style embeddings in the missing holes, because there are no features extracted from the masked region. In the light of this, we harness the well-known contextual attention module [2]} in between the feature pyramids, which can provide additional attention-wise information in the masked region as well. Ablation study shows that the attention module helps increasing the prediction quality.

[2]

https://openalex.org/W3043547428

c1ed1104-a196-40f3-bb1d-c1eb42fd2974

The semantics-guided inpainting network (SGIN) is comprised of a number of serially connected SGI blocks (SGIB), the exact number of which is determined by the resolution of training images. As shown in Fig. REF , each convolution block has two convolution layers, which is composed of a normalization layer and a convolution layer. The input in the normalization layer is firstly instance-normalized, and then denormalized by the semantic region adapative block (SEAN) [1]} in an attempt to reflect the previously extracted semantic features on the reconstructed image. While the spatially adaptive (SPADE) normalization block [2]}, which can separately process spatial parameters of each image, we chose SEAN, a variant of SPADE, as our denormalizer as it is able to process not only the spatial parameters but also style modulation parameters. Overall, the generator of our framework is expressed as follows; \(G(X_{masked},L) = \text{SGIN}(\text{RAP}(\text{FPN}(X;L));L)\)

[1]

https://openalex.org/W3106333289

bf553850-fdcd-4b0f-9424-1aa3d629e8e2

The semantics-guided inpainting network (SGIN) is comprised of a number of serially connected SGI blocks (SGIB), the exact number of which is determined by the resolution of training images. As shown in Fig. REF , each convolution block has two convolution layers, which is composed of a normalization layer and a convolution layer. The input in the normalization layer is firstly instance-normalized, and then denormalized by the semantic region adapative block (SEAN) [1]} in an attempt to reflect the previously extracted semantic features on the reconstructed image. While the spatially adaptive (SPADE) normalization block [2]}, which can separately process spatial parameters of each image, we chose SEAN, a variant of SPADE, as our denormalizer as it is able to process not only the spatial parameters but also style modulation parameters. Overall, the generator of our framework is expressed as follows; \(G(X_{masked},L) = \text{SGIN}(\text{RAP}(\text{FPN}(X;L));L)\)

[2]

https://openalex.org/W2962974533

3a3050f1-231c-4d8c-8561-e239fb08461c

Feeding back the lost features directly to the generation module has been one of the best solutions to this problem [1]}. Yet, such a model requires heavy memory with large computational units such as consultation fusion mapping networks, adaptive distortion mapping networks and various data augmentation techniques.

[1]

https://openalex.org/W3200670538

1916313a-cfe9-4e5c-a07e-41ca6fca4e44

We introduce the concept of self-distillation loss, which provides the feature-level supervision directly to the generator for preserving high-fidelity details of the input. Inspired by the `privileged information' in the work of PISR [1]}, where a teacher network is forwarded with a ground truth image to produce further detailed features and a student network learns the feature map of the teacher network through distillation, we devised an information flow that the generator is fed with its own first coarse image along with the loss calculated from the comparison between the feature map of the ground truth and the predicted output. Thus, we call this as the self-distillation loss. The details of the calculation are as follows: The generator is forwarded with the ground truth image \(X_{gt}\) with no masked region, and produce compact feature maps \(f_{i}(X_{gt})\) in the \(i^{th}\) SGI block. Then, the \(L_2\) difference between the feature map of the initially forwarded masked input \(X_m\) and the groundtruth, \(X_{gt}\) , is calculated. Finally, the self distillation loss is defined as \(\mathcal {L}_{sd} = \sum _{i=1}^{K} ||f_{i}(X_{gt}) - f_{i}(X_m)||_2\) , where \(K\) denotes the number of SGI blocks. The advantageous effect of using self-distillation loss can be found in the ablation study section.

[1]

https://openalex.org/W3107716502

b3a92120-af4b-43ab-8d61-b20e128a4b2f

In addition, we applied several conventionally used loss functions in the literature of image inpainting. The discriminator computes the \(\mathcal {L}_{feat}\) , which is the \(L_1\) loss between the discriminator features for the \(X_{gt}\) and the predicted image, as well as an adversarial loss \(\mathcal {L}_{adv}\) . Also, we used the \(\mathcal {L}_{per}\) , which is the perceptual loss between the features of \(X_{gt}\) and \(X_{masked}\) extracted from a VGG-19 network [1]}. \(\mathcal {L}_{adv}\) and \(\mathcal {L}_{per}\) are defined as follows: \(\mathcal {L}_{adv} = \mathbb {E}_X[\log D(X))] + \mathbb {E}_X[\log (1-D(G(X_{masked} |L))],\) \(\mathcal {L}_{per} = ||\text{Vgg}(G(X_{masked} |L)) - \text{Vgg}(X)||_2.\)

[1]

https://openalex.org/W1686810756

3dee760a-e25b-4127-9f73-ead8c0289089

To generate diverse occluded facial images, we used Naturalistic Occlusion Generation (NatOcc) [1]} to overlay human facial images from HELEN [2]} and CelebA-HQ [3]} with occluding objects and create naturalistic synthetic images (See Fig. REF for some examples). As for the occluding objects, we used 128 objects across 20 categories from Microsoft Common Objects in Context (COCO) and 200 hands from EgoHands [4]}. Note that for the training of our semantic map predictor, HELEN-derived occlusion images are used and its evaluation is done using CelebA-HQ images. Different from this, for the SGIN, we only used CelebA-HQ. We split CelebAMask-HQ-derived images into 22,300 training images and 2,800 validation images. For more implementation details, please refer to the supplementary information. <FIGURE><TABLE><TABLE>

[2]

https://openalex.org/W1796263212

3e0d045a-0c4e-432b-bb46-9e4f882f0a01

To generate diverse occluded facial images, we used Naturalistic Occlusion Generation (NatOcc) [1]} to overlay human facial images from HELEN [2]} and CelebA-HQ [3]} with occluding objects and create naturalistic synthetic images (See Fig. REF for some examples). As for the occluding objects, we used 128 objects across 20 categories from Microsoft Common Objects in Context (COCO) and 200 hands from EgoHands [4]}. Note that for the training of our semantic map predictor, HELEN-derived occlusion images are used and its evaluation is done using CelebA-HQ images. Different from this, for the SGIN, we only used CelebA-HQ. We split CelebAMask-HQ-derived images into 22,300 training images and 2,800 validation images. For more implementation details, please refer to the supplementary information. <FIGURE><TABLE><TABLE>

[3]

https://openalex.org/W3034521057

eec2a7ee-6e00-4711-9f4e-ee9123621e11

To generate diverse occluded facial images, we used Naturalistic Occlusion Generation (NatOcc) [1]} to overlay human facial images from HELEN [2]} and CelebA-HQ [3]} with occluding objects and create naturalistic synthetic images (See Fig. REF for some examples). As for the occluding objects, we used 128 objects across 20 categories from Microsoft Common Objects in Context (COCO) and 200 hands from EgoHands [4]}. Note that for the training of our semantic map predictor, HELEN-derived occlusion images are used and its evaluation is done using CelebA-HQ images. Different from this, for the SGIN, we only used CelebA-HQ. We split CelebAMask-HQ-derived images into 22,300 training images and 2,800 validation images. For more implementation details, please refer to the supplementary information. <FIGURE><TABLE><TABLE>

[4]

https://openalex.org/W2204609240

a96db6a7-38ad-42bb-bdca-e22055775db1

We compared our SGIN with various image-inpainting models different in their types and schemes. For the U-net architecture, we chose Deepfill-v2 [1]} and Crfill [2]}, and for the modulated generator architecture, we chose PsP [3]} and E4E [4]}. We also included SEAN [5]} in that it also uses semantic maps. and MAT [6]}, the current state-of-art (SOTA) inpainting module which is based on a transformer model. For a fair comparison, all of these baseline models are trained with the same NatOcc datasets with the same masks obtained from our Occlusion Detector, and SEAN is trained with the same semantic maps obtained from our semantic map predictor, except for MAT whose large computational cost is unaffordable in our devices. Alternatively, we made our comparison based on the pretrained CelebA-HQ MAT model uploaded at the author's GitHub repository and used the same masks as ours.

[1]

https://openalex.org/W2982763192

faff17f0-2579-438c-a436-061c504f028a

We compared our SGIN with various image-inpainting models different in their types and schemes. For the U-net architecture, we chose Deepfill-v2 [1]} and Crfill [2]}, and for the modulated generator architecture, we chose PsP [3]} and E4E [4]}. We also included SEAN [5]} in that it also uses semantic maps. and MAT [6]}, the current state-of-art (SOTA) inpainting module which is based on a transformer model. For a fair comparison, all of these baseline models are trained with the same NatOcc datasets with the same masks obtained from our Occlusion Detector, and SEAN is trained with the same semantic maps obtained from our semantic map predictor, except for MAT whose large computational cost is unaffordable in our devices. Alternatively, we made our comparison based on the pretrained CelebA-HQ MAT model uploaded at the author's GitHub repository and used the same masks as ours.

[3]

https://openalex.org/W3176913662

f766850e-fd4a-4722-b338-229277fc3fe1

We compared our SGIN with various image-inpainting models different in their types and schemes. For the U-net architecture, we chose Deepfill-v2 [1]} and Crfill [2]}, and for the modulated generator architecture, we chose PsP [3]} and E4E [4]}. We also included SEAN [5]} in that it also uses semantic maps. and MAT [6]}, the current state-of-art (SOTA) inpainting module which is based on a transformer model. For a fair comparison, all of these baseline models are trained with the same NatOcc datasets with the same masks obtained from our Occlusion Detector, and SEAN is trained with the same semantic maps obtained from our semantic map predictor, except for MAT whose large computational cost is unaffordable in our devices. Alternatively, we made our comparison based on the pretrained CelebA-HQ MAT model uploaded at the author's GitHub repository and used the same masks as ours.

[4]

https://openalex.org/W3178406257

ae28912e-406a-4c4b-9e05-e236bc8e4f83

We compared our SGIN with various image-inpainting models different in their types and schemes. For the U-net architecture, we chose Deepfill-v2 [1]} and Crfill [2]}, and for the modulated generator architecture, we chose PsP [3]} and E4E [4]}. We also included SEAN [5]} in that it also uses semantic maps. and MAT [6]}, the current state-of-art (SOTA) inpainting module which is based on a transformer model. For a fair comparison, all of these baseline models are trained with the same NatOcc datasets with the same masks obtained from our Occlusion Detector, and SEAN is trained with the same semantic maps obtained from our semantic map predictor, except for MAT whose large computational cost is unaffordable in our devices. Alternatively, we made our comparison based on the pretrained CelebA-HQ MAT model uploaded at the author's GitHub repository and used the same masks as ours.

[5]

https://openalex.org/W3106333289

984915e2-ea22-492a-adca-b67d704213c0

As some previous papers [1]}, [2]} have pointed out, image generation tasks lack a good quantitative metric for quantitative evaluation. For example, it is possible to have a different but highly plausible reconstructed image from the ground truth but the scores from SSIM or RMSE may fluctuate simply because of its difference from the ground truth. In the light of this, we employed six metrics that can shed light on the different aspects of the quality of reconstruction; PSNR, SSIM [3]}, MS-SSIM [4]}, RMSE, LPIPS [5]}, and FID [6]}. We evaluated the average scores for all of the validation samples.

[1]

https://openalex.org/W2887695188

94e6ad8b-6e23-4aef-b3f5-2e52c3cede68

As some previous papers [1]}, [2]} have pointed out, image generation tasks lack a good quantitative metric for quantitative evaluation. For example, it is possible to have a different but highly plausible reconstructed image from the ground truth but the scores from SSIM or RMSE may fluctuate simply because of its difference from the ground truth. In the light of this, we employed six metrics that can shed light on the different aspects of the quality of reconstruction; PSNR, SSIM [3]}, MS-SSIM [4]}, RMSE, LPIPS [5]}, and FID [6]}. We evaluated the average scores for all of the validation samples.

[2]

https://openalex.org/W2963185411

649a91d5-1885-4171-b901-bf428a9f08ce

As some previous papers [1]}, [2]} have pointed out, image generation tasks lack a good quantitative metric for quantitative evaluation. For example, it is possible to have a different but highly plausible reconstructed image from the ground truth but the scores from SSIM or RMSE may fluctuate simply because of its difference from the ground truth. In the light of this, we employed six metrics that can shed light on the different aspects of the quality of reconstruction; PSNR, SSIM [3]}, MS-SSIM [4]}, RMSE, LPIPS [5]}, and FID [6]}. We evaluated the average scores for all of the validation samples.

[3]

https://openalex.org/W2133665775

dbad9c78-3b61-4e5a-8a56-f48820dcb876

As some previous papers [1]}, [2]} have pointed out, image generation tasks lack a good quantitative metric for quantitative evaluation. For example, it is possible to have a different but highly plausible reconstructed image from the ground truth but the scores from SSIM or RMSE may fluctuate simply because of its difference from the ground truth. In the light of this, we employed six metrics that can shed light on the different aspects of the quality of reconstruction; PSNR, SSIM [3]}, MS-SSIM [4]}, RMSE, LPIPS [5]}, and FID [6]}. We evaluated the average scores for all of the validation samples.

[4]

https://openalex.org/W1580389772

8ec07b05-9660-4b66-8541-42462aa1dad3

As some previous papers [1]}, [2]} have pointed out, image generation tasks lack a good quantitative metric for quantitative evaluation. For example, it is possible to have a different but highly plausible reconstructed image from the ground truth but the scores from SSIM or RMSE may fluctuate simply because of its difference from the ground truth. In the light of this, we employed six metrics that can shed light on the different aspects of the quality of reconstruction; PSNR, SSIM [3]}, MS-SSIM [4]}, RMSE, LPIPS [5]}, and FID [6]}. We evaluated the average scores for all of the validation samples.

[5]

https://openalex.org/W2962785568

8d595403-eeb0-4dd3-ba68-1feadf6a2633

As some previous papers [1]}, [2]} have pointed out, image generation tasks lack a good quantitative metric for quantitative evaluation. For example, it is possible to have a different but highly plausible reconstructed image from the ground truth but the scores from SSIM or RMSE may fluctuate simply because of its difference from the ground truth. In the light of this, we employed six metrics that can shed light on the different aspects of the quality of reconstruction; PSNR, SSIM [3]}, MS-SSIM [4]}, RMSE, LPIPS [5]}, and FID [6]}. We evaluated the average scores for all of the validation samples.

[6]

https://openalex.org/W2963981733

2a26a261-5e76-484e-9fa9-7dcc0c4cf507

There are many works dedicated to interactive data visualization or real-time data visualization in the CFD domain. ViSTA FlowLib[1]} uses haptic rendering techniques to give a better understanding of the unsteady fluid flows data. Another work [2]} provides and evaluates multimodal feedback such as sonification during interaction with fluid simulation, especially to address visual overload. Stam J. has pioneered the development of the interactive simulation using an unconditionally stable model[3]}. Until today, most applications based on interactive simulation approach use particle-based methods such as Translating Eulerian Grids[4]} or Smoothed Particle Hydrodynamics (SPH)[5]}. These methods target extreme performance, high level rendering, and stability, but at the expense of the physical relevance, which is required by decision-making, physics education or research. Using more relevant methods requires computing centers that are often isolated from the visualization resources which are usually undersized. Even if a lot of technical results were published to support the interactive fluid simulation approach, this methodology remains rarely used. Moreover, there are only a few studies that deal with the problem of the usefulness of interactive simulations in terms of performance and user experience. We propose in this paper a work-in-progress to address this issue by designing an interactive fluid simulation platform based on Unity 3D and evaluating the benefit of the interactive simulation approach on decision making from fluid simulation on a simple but realistic use case.

[3]

https://openalex.org/W2295821368

6174f1ab-f37e-4fc8-97f1-bbe9b281cc04

There are many works dedicated to interactive data visualization or real-time data visualization in the CFD domain. ViSTA FlowLib[1]} uses haptic rendering techniques to give a better understanding of the unsteady fluid flows data. Another work [2]} provides and evaluates multimodal feedback such as sonification during interaction with fluid simulation, especially to address visual overload. Stam J. has pioneered the development of the interactive simulation using an unconditionally stable model[3]}. Until today, most applications based on interactive simulation approach use particle-based methods such as Translating Eulerian Grids[4]} or Smoothed Particle Hydrodynamics (SPH)[5]}. These methods target extreme performance, high level rendering, and stability, but at the expense of the physical relevance, which is required by decision-making, physics education or research. Using more relevant methods requires computing centers that are often isolated from the visualization resources which are usually undersized. Even if a lot of technical results were published to support the interactive fluid simulation approach, this methodology remains rarely used. Moreover, there are only a few studies that deal with the problem of the usefulness of interactive simulations in terms of performance and user experience. We propose in this paper a work-in-progress to address this issue by designing an interactive fluid simulation platform based on Unity 3D and evaluating the benefit of the interactive simulation approach on decision making from fluid simulation on a simple but realistic use case.

[5]

https://openalex.org/W2141435354

4da3a341-2988-4e4a-a249-ab7991b514cc

Because of the Covid-19 sanitary condition, an experiment in the lab was not permitted. Therefore, before the experiment, an email containing an information notice and a consent form was sent to the subjects. Once they signed the document, they were contacted by phone and invited to connect to our computer remotely via Teamviewer. Then, they had to perform a 5-minute familiarisation task with a training scene to familiarize themselves with interactive features and goals. After this training stage, the first session of the experiment started with each mode of simulation (interactive mode or non-interactive condition). After 3 scenes with the same mode of simulation, they were invited to fill the NASA TLX questionnaire[1]}. Then the subject entered the second session: another training part with the other mode of simulation started followed by 3 other scenes of the experiment. After the second part, the experiment ended with the same questionnaire for the second session.

[1]

https://openalex.org/W2151905266

e5a248e4-d5e6-4342-bbf8-4dd18e710e0d

Autonomous driving promises to revolutionize how we transport goods, travel, and interact with our environment. To safely plan a route, a self-driving vehicle must first perceive and localize mobile traffic participants such as other vehicles and pedestrians in 3D. Current state-of-the-art 3D object detectors are all based on deep neural networks [1]}, [2]}, [3]}, [4]} and can yield up to 80 average precision on benchmark datasets[5]}, [6]}.

[1]

https://openalex.org/W2964062501

6b3a4370-cda4-4f47-8b76-166086c34671

Autonomous driving promises to revolutionize how we transport goods, travel, and interact with our environment. To safely plan a route, a self-driving vehicle must first perceive and localize mobile traffic participants such as other vehicles and pedestrians in 3D. Current state-of-the-art 3D object detectors are all based on deep neural networks [1]}, [2]}, [3]}, [4]} and can yield up to 80 average precision on benchmark datasets[5]}, [6]}.

[2]

https://openalex.org/W2949708697

13e753bf-6efd-490e-bd83-44a8ee17cea2

Autonomous driving promises to revolutionize how we transport goods, travel, and interact with our environment. To safely plan a route, a self-driving vehicle must first perceive and localize mobile traffic participants such as other vehicles and pedestrians in 3D. Current state-of-the-art 3D object detectors are all based on deep neural networks [1]}, [2]}, [3]}, [4]} and can yield up to 80 average precision on benchmark datasets[5]}, [6]}.

[3]

https://openalex.org/W2798965597

1cb61609-b009-471a-9cb7-dbc4e17a263a

Autonomous driving promises to revolutionize how we transport goods, travel, and interact with our environment. To safely plan a route, a self-driving vehicle must first perceive and localize mobile traffic participants such as other vehicles and pedestrians in 3D. Current state-of-the-art 3D object detectors are all based on deep neural networks [1]}, [2]}, [3]}, [4]} and can yield up to 80 average precision on benchmark datasets[5]}, [6]}.

[4]

https://openalex.org/W3034314779

c9dbd71c-3e35-4b8a-914c-38fa3b1d9f0e

Autonomous driving promises to revolutionize how we transport goods, travel, and interact with our environment. To safely plan a route, a self-driving vehicle must first perceive and localize mobile traffic participants such as other vehicles and pedestrians in 3D. Current state-of-the-art 3D object detectors are all based on deep neural networks [1]}, [2]}, [3]}, [4]} and can yield up to 80 average precision on benchmark datasets[5]}, [6]}.

[5]

https://openalex.org/W2150066425

54af1c44-21ef-49c9-b6a0-7d3d40c14b85

Autonomous driving promises to revolutionize how we transport goods, travel, and interact with our environment. To safely plan a route, a self-driving vehicle must first perceive and localize mobile traffic participants such as other vehicles and pedestrians in 3D. Current state-of-the-art 3D object detectors are all based on deep neural networks [1]}, [2]}, [3]}, [4]} and can yield up to 80 average precision on benchmark datasets[5]}, [6]}.

[6]

https://openalex.org/W2115579991

685c12d1-6697-4c1b-b56e-7e804f3bdf76

However, as with all deep learning approaches, these techniques have an insatiable need for labeled-data. Specifically, to train a 3D object detector that takes LiDAR scans as input, one typically needs to first come up with a list of objects of interest and annotate each of them with tight bounding boxes in the 3D point cloud space. Such a data annotation process is laborious and costly, but worst of all, the resulting detectors only achieve high accuracy when the training and test data distributions match [1]}. In other words, their accuracy deteriorates over time and space, as looks and shapes of cars, vegetation, and background objects change. To guarantee good performance, one has to collect labeled training data for specific geo-fenced areas and re-label data constantly, greatly limiting the applicability and development of self-driving vehicles.

[1]

https://openalex.org/W3034975685

503ae5c1-4aae-4695-a00d-abd5aa0f7e36

Concretely, whenever we discover multiple traversals of one route, we calculate a simple ephemerality statistic [1]} for each LiDAR point, which characterizes the change of its local neighborhood across traversals. We cluster LiDAR points according to their coordinates and ephemerality statistics. Resulting clusters with high ephemerality statistics, and located on the ground, are considered as mobile objects and are further fitted with upright bounding boxes.

[1]

https://openalex.org/W2963170338

cdc45969-6528-4173-9c5b-71770ce22c1f

Self-training (ST). While this initial seed set of mobile objects is not exhaustive (e.g., parked cars may be missed) and somewhat noisy in shape, we demonstrate that an object detector trained upon them can already learn the underlying object patterns and is able to output more and higher-quality bounding boxes than the seed set. This intriguing observation further opens up the possibility of using the detected object boxes as “better” pseudo-ground truths to train a new object detector. We show that such a self-training cycle [1]}, [2]} enables the detector to improve itself over time; notably, it can even benefit from additional, unlabeled data that do not have multiple past traversals associated to them.

[2]

https://openalex.org/W3035160371