DO-AutoEncoder: Learning and Intervening Bivariate Causal Mechanisms in Images
Authors: Tianshuo Cong
Dan Peng
Furui Liu
Zhitang Chen
Venue:  (2020)
Keywords: Causality discovery
AutoEncoder
Deep representation learning
Do-calculus

Abstract: Some fundamental limitations of deep learning have been exposed such as lacking generalizability and being vunerable to adversarial attack. Instead, researchers realize that causation is much more stable than association relationship in data. In this paper, we propose a new framework called do-calculus AutoEncoder(DO-AE) for deep representation learning that fully capture bivariate causal relationship in the images which allows us to intervene in images generation process. DO-AE consists of two key ingredients: causal relationship mining in images and intervention-enabling deep causal structured representation learning. The goal here is to learn deep representations that correspond to the concepts in the physical world as well as their causal structure. To verify the proposed method, we create a dataset named PHY2D, which contains abstract graphic description in accordance with the laws of physics. Our experiments demonstrate our method is able to correctly identify the bivariate causal relationship between concepts in images and the representation learned enables a do-calculus manipulation to images, which generates artificial images that might possibly break the physical law depending on where we intervene the causal system.

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DO-AUTOENCODER: LEARNING AND INTERVENING BIVARIATE CAUSAL MECHANISMS IN IMAGES
Anonymous authors Paper under double-blind review
ABSTRACT
Some fundamental limitations of deep learning have been exposed such as lacking generalizability and being vunerable to adversarial attack. Instead, researchers realize that causation is much more stable than association relationship in data. this paper, we propose a new framework called do-calculus AutoEncoder(DO-AA for deep representation learning that fully capture bivariate causal relationship in the images which allows us to intervene in images generation process. DO- AE consists of two key ingredients: causal relationship mining in images and inlervention-enallin
deep causal structured representation learning. The goal here is to learn deep representations that correspond to the concepts the physical world well their causal structure. To verify the proposed method, create dataset named PHY2D, which contains abstract graphic description in accordance with the laws of physics. Our experiments demonstrate our method is able correctly identify the bivariate causal relationship between concepts in images and the representation learned enables do-calculus manipulation images, which generates artificial images that might possibly break the physical law depending on where we intervene the causal system.
INTRODUCTION
Recent breakthrough of deep learning (LeCun et al. advanced the development of Artificial Intelligence (AI). However, statistical prediction and infer- ence models, no matter traditional machine learning models such random forest, support vector machines or deep models have their limitations such as lacking generalizability. being vulnerable to adversarial attacks as well as lacking interpretability (Zhang et al., 2016 Papernot et al. 2016). All these limitations prevent AI from wide applications to high stake scenarios including healthcare, au- tonomous driving (Chen al.) 2015) etc. Tremendous amount of efforts from the Al community has been devoted to understanding and improving the robustness of deep models and researchers come to consensus that after training with huge amount data, deep models exploit "superficial" associ- ation in data to make prediction. However, such kind of subtle association relationship is unstable across domains. For example, the association relationship between pixels related to "grassland" and the label "elephant" is real but it is rather weak. Deep models, trained with hundreds of thousands of natural images where elephants reside on grassland, exploit too much pixel level association of the image the label. Unfortunately, such models fail to detect an elephant if the background of the im- age is changed to living room. More and more evidences show that deep models exploit association instead of causation when making the prediction, rendering weak in term of domain generalization and robustness against adversarial attacks. As a consequence, researchers are advocating bringing causality into the life-cycle of deep neural networks.
2015 Goodfellow et al. (0166) has significantly
In Judea Pearl book "The book of why" (Pearl & Mackenzie 2018). he gives ladder of causation: The lowest level is concerned with patterns of association observed data. The next level focuses on intervention and the highest one is counterfactual inference. In order to realize real Machine Intelligence, we must replace reasoning by association with reasoning by causality. However, how to incorporate causality into current machine learning framework is very challenging and little work has been found yet until the most recently, researchers start to look at disentangled representation learning. In the deep learning community, researchers realized that good representation enables better generalizability and might possibly enjoy better interpretability. Disentangled representation is believed to be good representation and become research focus in past few years (Hsu al.

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2017 Narayanaswamy al. 2017 Locatello et al. 2018). The idea behind disentangled repre- sentation learning is that we prefer the learned representations as independent as possible such that they correspond the independent generative factors of the image, e.g. the illumination. azimuth, elevation etc for 3D graphics. The advantage of disentangled representation is that it offers het- ter explainablity and it is claimed that deep models with disentangled representations enjoy better generalization performance for downstream tasks.
Although significant progress has been achieved in the area of deep representation learning in the past few years, most of existing work assume that the representations or the latent codes are sta- tistically independent and they are trained by adding regularization term of mutual information between latent codes to the loss function (Chen et al. (016)). It is of great interest and has shown advantage over entangled representation, but forcing the latent codes to be independent might limit itself both in term of theoretical understanding and practical applications. In various scenarios, we are rather interested in learning latent representations that correspond to the causally related con- cepts. For example, given an image consisting concepts like tree, sunshine and shadow, idea representation learning algorithm is expected to yield latent codes that could each corresponds to the above three concepts. Obviously, these three concepts are by means independent, i.e. the concept of tree and that of sunshine together causes the concept of shadow. If we are able to extract latent codes with their causal structure, we able intervene the whole system, e.g. intervene the latent code of shadow such that we can generate images with the shadow removed. This could be potentially great value many applications such as autonomous driving.
In this paper, we propose a framework called DO-AutoEncoder (DO-AE) to learn causally related concepts in images, which is achieved by firstly discovering the causal relationship of concepts in the images by comparing complexities of generative models (C(cuus)) G(effect (cause)) in either hypothetic directions and the generative models are realized by AutoEncoder structures. The latent codes are then used to reconstruct the original input images and the whole AutoEncoder structure is trained by minimizing the reconstruction error. The framework mimics the whole data generating mechanism, i.e. the joint distribution P(cause, effect) is factorized as P(cause) P(effect, cause) ac- cording to the causal direction. As Figure shows, the light is projected from the vertical direction upside down, yielding the time-varying shadow of a swinging pendulum. So the causal direction is from angle (of pendulum) to length (of shadow). We aim at developing deep representation learning model and algorithm discover such causally related concepts from series of images describing the law of physics. In addition to the pendulum data, in this paper we create a series of dataset named PHY2D, the collection of images of abstract graphic description of physics laws.
Longth
Figure 1: The laws of physics can be expressed by functions, and the independent variables and de- pendent variables in the function can be abstracted the pixels the image. These pixels therefore have a causal direction. Finally, the real physical world can be abstracted into a causal diagram.
RELATED WORK
People have studied causality for a long time and related work can be found in philosophical pub- lications, religious scriptures and science publications. Ancient Greek famous thinker Aristotle proposed "Four causes" which includes the final cause, the material cause, the formal cause and the efficient cause. He believes that all natural phenomena follow the causal law. Scottish philosopher David Hume recognizes cause-effect relation both a philosophical relation and natural relation, and he argued that this relation is pivotal in reasoning (Hume 2003). (Harari) 2014) provide that human ancestor's causal imagination is the basis for mutual communication. The instinct of human
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beings to explore the cause and effect of things makes human beings more intelligent, and causal thinking is the foundation of the development of science and technology. Causality is a bridge between science and philosophy.
In science, causality can be found in several fields such as economics (Moneta et al. 2013). neuro- science (Ramsey al. 2014), environment science (Sugihara et al. 2012) and especially machine learning. Pearl shows that machine learning without causal inference will encounter sule-Simpsons Paradox, which means the model can get two completely contradicting conclusions with the same dataset. Recent efforts from machine learning community try to link causality and ML methods. To name a few, (Schölkopf et al. 2012) argues that suni--upereieed learning only works in anti- anti-casual direction. (Bengio et al. 2019) propose meta-learning framework to determine the causal rela- tionship between two observed variables. The correct modeling according the causal direction usually leads to faster adaptation to shifted data distribution due to interventions to the system.
Using machine learning for analyzing physics is hot topic (Watters et al., 2017; Fragkiadaki al. [2015] Janner et al. (0188. (Bakhtin al.] 2019) provide a 2D physical classical mechanical puzzle dataset to encourage more useful models for physics. interdisciplinary field of computer vision and causality, (Lebeda et al.) 2015) provide statistical tools based on transfer entropy to explore the causality relationship between the camera motion and the object motion to predict object location. The prediction accuracy is increased over non-causal predictor. (Lopez-Paz et al., 2017) focus on establishing the existence of causality based on observable statistical signal carried in image datasets, by using causal discovery technique Neural Causation CoefficientNNCCC. These recent advances show that causal inference in images is gaining increasing amount of attention from the AI community.
METHOD
As mentioned in Sec D we aim at representation learning that correspond to the concepts as well as their causal structure in images. To achieve this target, the first step is to discover the causal relationship between the concepts in images, i.e. we need to identify which one is the cause or effect. In this paper, we follow the Independent Mechanism principle proposed by (Janzing & Scholkopf 2010). Secondly, we need to learn the generating mechanisms the cause and the generating mechanism mapping the cause the effect. We propose to use AutoEncoder as the generative model.
Given observations of two variables X and Y. distinguishing the cause from effect is challenging problem. There is postulate named Independent Mechanism principle (Janzing & Scholkopf] (2110) stating that the joint distribution factorization has asymmetric statistical behaviors in causal versus anticausal directions. Specifically, decomposition of the joint distribution according to the causal direction is natural and simpler than the anti-causal direction. This principle can also be explained
by the famous Occam's Razor principle. If there are multiple models that can explain the data equally well, we prefer the simplest one.
The definition of simplicity varies in different methods. For example, (Janzing & Scholkopi 2010) argues that the Kolmogorov complexity of conditional and marginal distributions smaller causal direction than that in anticausal direction. It can be written as the following inequation:
KC(Px) KC(PPi)) S K(PP) K(Px(y))
where KC(-) is the Kolmogorov complexity. However, the Kolmogorov complexity is not com- putable, and thus researchers proposed other statistical methods including Mimimal Discription Length (MDL) or Reproducing Kernel Hilbert Space (RKHS) norms (Sun al., 2007] as approxi- mation. Recently, (Bengio et al. (211)) showed that the joint distribution decomposed according to the causal direction is much easier learn and is able to adapt much faster to the distributional shift in data than the anti-causal direction. Inspired by this work, in this paper propose to learn the causal direction of concepts in images according to model complexities.
Firstly, we introduce how identify the causal direction according to the loss after model training. Denote by A, B the ground truth hypothetic cause and effect concepts in the images, e.g. in the pendulum case, if assume that the pendulum causes the shadow, then A corresponds to the
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concept of pendulum and B corresponds the concept of shadow. We further denote by À and B the corresponding generated concepts by generative models f (enc; 0) and g gA;; n), where the original input image and and 7) are model parameters. this paper, we use AutoErcoder the generative functions.
The likelihood the generative concepts defined as follows:
Ps B) exp(-114 All2) exp( -B12)
(2)
Two generative models, i.e. the model generating the cause and the model mapping the cause to the effect then trained by minimizing the negative logeliiklihood follows:
0* n arg min B|||A (enc, 0)1|2| Bi| 9(A:n)
Note that B n)2=m = = 9 - B g(A; n)]l2] +
Elllg( A; m) g( A; m)) [2] S EEI AA; n) LE[]A- Al]2]. if we assume that is Lipschitz
continuous and we denote by L the Lipschitz constant.
We then can get the lower bound of the log-likelihooo i.c.
C. (1 L) -frAA--(nnnc f(enc, 1)11
E[| g(A: m))
(3)
However, this still requires choosing L which might be unknown. We further relax the loss function be
CA-B - L) 0f flncc 0)11 (1 + L) g(A;m)
To identify the causal direction, we only need to compare which direction gives lower loss, given the same model complexity. i.c.
A - B, if LA-B LB-AA B - A, if LB-A < LA-Bi NO conclusion, otherwise.
(5)
Our whole pipeline is in 2igure The whole DO-AE inputs an image and then tries to reconstruct the output. Instead of using single AutoEncoder, we propose a modularized one by decomposing the whole system into two sub-modules, and each is an AutoEncoder. The first module aims at generating the hypothetic cause, followed by second one to generate the hypothetic effect from the hypothetic cause. By controlling the model capacity, the likelihood are then used to decide which direction is more plausible to be the causal direction. prefer the direction with higher likelihood according to the Independent Mechanism principle. One should be noted that cannot with too rich flexibility otherwise the aforementioned method might not work as it could be the case that with very expressive models, the likelihoods of both hypothetic direction are almost equally good and thus not distinguishable. We verify this conjecture in the experiment section. Note that in experiments simply set I. 0 since its value would not have impact the inference rule.
model
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MSE
DO-AE
ISSE
Figure 2: DO-AE model structure. The original images and its segmented parts are outlined in teal and the generated images are outlined orange. This figure illustrates the true direction pendulum um - shadow, and the same architecture applies to the opposite direction. We extract the latent code to intervene the whole system. Doing cause latent code does not affect the generation and doing effect code can generate images which break the physical law.
PHY2D: UNDERSTANDING PHYSICAL LAWS IN IMAGES
We create dataset named PHY2D verify the effectivness of proposed approach. The dataset contains seven category of abstract graphic descriptions accordance with the laws of physics. The detailed descriptions are shown in Table Each category contains 5000 figures.
In data BEVEL, the height of the ball generates the gravity potential energy, and gravity potential energy converts kinetic energy based energy conversion. For the elements in the figure, the red circles height and the wooden board shape cause the blue circles' track and the leftmost blue circle's s position. In data PENDULUM, the light projected upside down, because light propagates straightly, the swinging pendulum blocks light, creating shadow with varying length. Other dataset can be explained as follows: (1) BUOYANCY: The volume of ball causes the water level; (2) SPRING: The mass of ball causes the spring's 's length; (3) BOWL: The initial position of the red ball causes the rolling track; (4) CONVEX: The width of incident light causes refracted light direction. (5) FLOW: Water column height causes the trajectory of water flow. The example pictures of the whole dataset showed in Figure B and it contains 7 5000 * 3 figures.
Table 1:
The PHY2D dataset detailed descriptions. Description
Order
Name
Physical law Energy conversion
REVEL
A small ball rolls off from frictional bevel. The red ball stands for the initial state and the motion track is shown as blue balls.
2
PENDULUM
Rectilinear propagation
A rotating red and yellow colored pendu- lum and its shadow.
3
BUOYANCY
Buoyancy force
Balls with different sizes are placed in measuring cylinder filled with water.
4
SPRING
Elastic force
Balls of different weights hung from the lower end of the spring.
BOWL
Energy conservation
A ball released from the smooth inner wall of the bowl. The blue circles stand for the rolling track.
6
CONVEX
Refraction law
Parallel light rays converge the focus of the convex lens.
7
FLOW
Pressure
Water flowing out from the hole on the cylinder filled with water.
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A
input
imputz
cause
effect
PINDULDM
BOWL
CONVEX
Figure 3: PHY2D dataset.
EXPERIMENTS
In this section, we present experimental results. We firstly give detailed description of the net- work architectures used in our paper. Then, we analyze the results the experiments on different datasets. In encoder and decoder framework, We design two kinds network structures: simple structure and flexible structure. The network architectures are shown in Table A| The whole experiments are conducted with the following set- tings:
traditional convolution neural netNork(CNN).
Operating system: Ubuntu 16.04.
Software version: Python 3.5.2; Pytorch 1.0.1; Numpy 1.17.0.
GPU: NVIDIA TESLA V100.
Table 2: Network architectures for causality discovery.
Simple structure
Flexible structure
Input 96 96 3-channel Color image
4 X 4 conv. 64 IRELU. stride 2.
4 x conv. 64 IRELU, stride 2.
4 X conv. 100 IRELU. stride 2. batchnorm
4 x conv. 128 IRELU. stride batchnorm
X upconv. 64 IRELU. stride 2. batchnorm
4 conv. 256 IRELU. stride batchnorm
4 X 4 upconv. 3 IRELU. stride 2.
4 conv. 512 IRELU, stride 2. batchnorm
x conv. 1024 IRELU. stride 2. batchnorm
4 conv. 100 IRELU. stride batchnorm
4 x upconv. 1024 IRELU. stride 2. batchnorm
4 X upconv. 512 IRELU. stride 2. batchnorm
4 X upconv. 256 IRELU. stride batchnorm
4 X upconv. 128 IRELU. stride 2. batchnorm
4 x upconv. 64 IRELU. stride 2. batchnorm
4 upconv. 3 IRELU. stride
Output 96 x 96 3-channel Color image
Foor the dataset P PENDULUM, we use specific network (different from simple or flexible ones). The network architecture used PENDULUM is in Table 3 in appendix A

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Figure 4 shows the likelihood curves data FLOW using two architectures. Due to the powerful fitting capability of neural networks, if the causal mechanism of the image is relatively simple, the curves of two hypothetic directions are not distinguishable. On the contrary, simple neural network architecture with capacity control is able to make the asymmetry. One can notice that even with a simple neural network architecture, generative model according to the causal direction yields larger likelihood than the anti-causal direction. This shows that generating the image according to the true causal direction may be much simpler and more straightorwward.
0.10
0.10
0.00
000
-0.05
-0.05
-0.00
0.20
3000
0.20
Serations
(a) Likelihood curves simple network structure.
(b) Likelihood curves of flexible network structure.
Figure 4: Likelihood curves on FLOW.
We plot two kinds of experimental results on different datasets: the images generated by the AEs in first 5 training epochs (as illustrated in F) and curves of model likelihood during training process (as illustrated in Fig
From Fig 5 we find that the images generated in the causal direction is in general of better quality than those the anti-causal direction, which aligns with our initial conjecture and justifies the effectiveness of our proposed method.
LI
LL
1
$
F
F
LI
LI
>
(a) PENDULUM
(b) CONVEX
(c) BUOYANCY
(d) BOWL
(e) FLOW
(I) BEVEL
Figure 5: The cause and effect images generated by AEs during the first 5 training epochs in two hypothetic directions. Figures on the first row illustrate the generated hypothetic cause images in the causal direction A + B. The second row shows the generated hypothetic cause images in anti- causal direction B A. The third and fourth rows show the corresponding hypothetic effect images respectively.
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(a) PENDULUM
(b) CONVEX
(c) BUOYANCY
(d) BOWL.
(c) FLOW
(f) BEVEL
Figure 6: Likelihood curves of DO-AE models on datasets with simple network architecture.
5.1 RESULT ANALYSIS ON PENDULUM
We here specifically analyze 2 datasets. First, we show experimental results when AE is designed using the flexible network structure on dataset PENDULUM in Figure Figure shows the images generated by the AEs during first 5 training epochs. Figure (b) shows likelihood curves of models in CA-B and LB-A pathways. In A + pathway, we find that cause-to-effect generation is simpler. The quality of effect image is acceptable. However, in B A pathway, the cause images generated from the effect image include two pendulums in one picture. This is because the function corresponding to the causal mechanism is not invertible. Under this scenario, using the cause image to generate the effect image is better than using the effect image to generate the cause image. Another observation that the likelihood curves in Figure ( A + B way converges to zero faster. In B + A way, as the number of iterations increases, the curve begins to fluctuate, indicating that the effect images can not stably reason about the cause image.
0.00
LA-B
002
L8-A
-005
LA-18
LB-AA
-020
1000
.0120
4300
2000
1900
(a) Generation process.
(b) Likelihood curves.
Figure 7: Causal discovery results with flexible network architecture on PENDULUM.
5.2 RESULT ANALYSIS ON SPRING
We then analyze the dataset SPRING. We observe that both simple and flexible networks don't work on this dataset. We show the results (AE being the flexible network) in Figure The generated figures in + B pathway and B + A pathway are not very different. The likelihood curves show certain degree of entanglement. This indicates that DO-AE model cannot find the causal direction
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between spring length and ball weights. However, this doesn't 't mean that model lacks the ability of causality discovery. We try to explain this phenomenon by rethinking the dataset. Newton third law of motion said for every action has equal and opposite reaction. So the gravity generated by small ball causes the spring to undergo an elongated deformation. Meanwhile, the spring in the stretched state generates elastic force, pulling the ball up. So, the spring length also cause the position of ball. It is possible the case that DO-AE model could not conclude when it encounters bidirectional causal scenario.
LA-B
Lg-AA
Liddtood
LA-B
-0.15
LB-A
-0.2
1200
1302
2000
2320
2000
2000
Barabona
(a) Generation process.
(b) Likelihood curves.
Figure 8: Causal discovery results with flexible network architecture on SPRING.
5.3 INTERVENING THE IMAGE GENERATION PROCESS
After the model training process for causal discovery, we can choose the causal pathway our generative model and intervene the image generation process to achieve do-calculus. DO-AE model outputs two latent codes. The second latent code contains the information of the causal mechanisms. By fixing the first or second latent code in the whole generating process, we intervene the whole model and the system outputs some counterfactual images. We show some images generated by DO-AEs trained on PENDULUM in Figure
Figure 9: Do-calculus result. In the first row, we do the cause image to show the result image of P((cause, effect) do(cause Ag)) (first pictures) and P((cause, (dofet)) A1)) (last 4 pictures), and the second row shows P((cause, dofecct)do(efffcct Bo)).
6 CONCLUSION
In this paper, propose a deep learning framework DO-AE to discover bivariate causal relation- ships in images. Experiments suggest that DO-AE can learn the causal relationship between objects. We perform interventions on the generative model to produce counterfactual images that break the physical law. the future, we hope to provide an approach for mining multivariate causal relation- ships, and provide causal way to solve the combinatorial explosion problem.

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A
APPENDIX
The network structure used in Sec. 5 curve is shown below.
When our simple network structure, the likelihood
Table 3: Network architectures on Data PENDULUM
Network structure
Input 96 x 96 3-channel Color image
4 conv. 64 IRELU. stride 2.
4 X conv. 128 IRELU. stride 2. batchnorm
4 X conv. TOO IRELU. stride batchnorm
4 upeonv. 128 IRELU. stride batchnorm
4 X upconv. 64 IRELU. stride 2. batchnorm
4 x upconv. 3 IRELU, stride 2. Output 96 x 96 3-channel Color image
010
005
0.00
0000
-0.20
Figure 10: Likelihood curves PENDULUM
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Reviews:
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The paper contains some potentially interesting ideas, but the presentation quality is not sufficient for publication. The paper should be substantially improved before re-submission.\n\nStrengths:\n- Causality is an important and established research area, and papers on this topic would be timely.\n- Paper contains some interesting ideas to integrate causality into an auto-encoder (but see weaknesses below)\n- Paper proposes a new dataset for evaluating causal mechanisms (but the approach is not evaluated)\n\nWeaknesses:\n- The quality of the writing is inappropriate for a scientific venue. Language throughout the paper is loose, eg \"physics is a hot topic\" or \"People have studied causality for a long time\" or \"Causality is a bridge between science and philosophy\" The paper should be re-written so that it is precise and clear.\n- The technical approach has several typos and lacks discussion of the approach. Instead, several high-level statements are made, with long equations. This makes appreciating the contribution of the paper difficult. \n- The dataset is potentially interesting, but it is artificial. A much more exciting dataset would be realistic data.\n- The experiments only evaluate the likelihood, but it is not clear whether this is on a training or testing set. \n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "SkgN4O6TFB", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Thank you for your submission.\n\n- What is the specific question/problem tackled by the paper?\n\nThe paper proposes a VAE architecture to learn causal relations and allow for interventions. The architecture requires knowledge of the causal graph, and the direction of the causal arrows are inferred by comparing the log-likelihoods of generated images. The architecture may also require knowledge that an arrow exists between two vertices. This relies on the principle that \"low-capacity\" neural networks can predict better along the causal arrows (with the cause as input and the effect as the output) than in the opposite direction (with the effect as input and the cause as the output).\n\nThe paper focuses on the graph (A, B) where one wants to understand whether A causes B, or B causes A. The paper also discusses intervening in this graph.\n\nThe paper uses a new dataset for evaluating the approach, based on simple Newtonian systems. \n\n- Is the approach well motivated, including being well-placed in the literature?\n\nI think the motivation is adequate, but the review of the literature glosses over related work (or the absence thereof) in predicting the direction of arrows in causal graphs. The comparison of the proposed dataset against existing ones is missing.\n\n- Does the paper support the claims? This includes determining if results, whether theoretical or empirical, are correct and if they are scientifically rigorous.\n\nThe procedure for determining whether A causes B (or B causes A) is qualitative. The paper demonstrates that the performance gap between the correct and incorrect explanations is consistently distinguishable across multiple experiments.\n\nVisual inspection of the generated images is also used for assessing the quality of the models.\n\nBecause the results are qualitative, the support for the claims is not as strong as it could be (with quantitative results).\n\n- Summarize what the paper claims to do/contribute. Be positive and generous.\n\nThe paper has two main contributions:\n* Evidence to the Independent Mechanism principle (in a setting different from Bengio et al.'s transfer setup).\n* A new dataset for evaluating learning causal arrows (with accessible ground-truths).\n\nI think these are interesting contributions.\n\n- Is the paper clearly written?\n\nThe paper has a number of grammatical errors that should be fixed.\n\nThe explanation of how the latent interventions are made is important and should be included.\n\n- Clearly state your decision (accept or reject) with one or two key reasons for this choice.\n\nI vote for a weak accept.\n\n- Provide supporting arguments for the reasons for the decision.\n\nI trust that the writing issues will be addressed in due course, but I am also concerned about the fact that evaluations are qualitative. The qualitative results provide support for the contributions that could be strengthened. \n\nThe dataset is also an interesting contribution and it is a good idea to give it visibility. For this, though, it is important that the paper assess its strengths and limitations in comparison to alternative datasets.\n\n- Provide additional feedback with the aim to improve the paper. Make it clear that these points are here to help, and not necessarily part of your decision assessment.\n\nI am not convinced that mentioning Kolmogorov complexity is an efficient use of the space. I think the content could be improved by making the motivation section more concise and adding a few more experimental results or discussion.\n\nWhich discussions would be good to have? I think it should be noted that the intervention on effect should behave as demonstrated (creating implausible scenarios). Also some more development on the spring example: What is the right causal graph for it, and can the arrows in that graph be learned?\n\nQuantitative results would also improve the paper. Maybe decide between A->B or A<-B based on a statistical test?\n\nYou give an example about elephant-grassland association. Please cite a source for that.\n\nSuppose that both likelihoods for A->B and B<-A are about the same. How do you decide if your model is too rich, or if there's no relationship? (This is an important question to understand if the method requires knowledge that an (A,B) arrow exists or not.)\n\nThe panels in Figure 5 do not support the claim. The simple net gets better at the cause, but in some cases the rich representation does a better job at the effect.\n\nI think the physics dataset is also a contribution, so its originality & impact should be discussed in comparison to related work. Why is this an adequate benchmark? How does it address limitations of other benchmarks that could be used to evaluate proposed solutions for the problem in question?\n\nIn summary, my suggestions for improving the paper are:\n1) Make sure & demonstrate (by adequate discussion of related work) the originality of the contributions:\n1.1) The method for detecting the direction of causal arrows.\n1.2) The dataset as a benchmark for the problem being studied.\n2) Report quantitative results across the dataset and maybe across multiple setups for each name/physical law, with good coverage. You may consider a test set where the parameters are within the sampling range of your training set, and also outside the sampling range (where success of the method would be even more interesting). ", "extra_scores": {"experience_assessment": "I do not know much about this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "HyeKwG52tH", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This paper presented an image data that are generated from two variables using some physics law. It also proposed a model to identify the causal relationship between the two variables using the image dataset. The method, in general, utilize the general idea that the causal direction is easier for the model to describe than the anti-causal direction. So the image is fad into a VAE based model in two different ways. The one with lower loses represents the correct causal direction. \n\nPros:\n1. Causal discovery is, in general, an interesting problem and causal discovery based on representation learning are of great importance.  \n2. The dataset presented can be used for generic causal discovery evaluation which can be useful for the community.\n\nCons and other details:\n1. The method assumes that A and B are known and given which is very unrealistic in natural images. Also with this assumption, the problem is not much different from causal discovery from measurement data rather than image data. \n2. Based on the previous point, the method, in general, does not match the motivation in the introduction where a causal representation needs to be learned as the images are already separated into different components. \n3. The method cannot be scaled to more than two variables even with all components given as it requires exponentially many trials of the method. This setting is not so interesting anymore with image input. \n4. There is much-related work with causality and representation learning also causality with NN or VAE. None of these related work has been discussed.  for example Leon Bottou https://arxiv.org/pdf/1907.02893.pdf; Many works from Mingming Gong etc\n5. The math is not very rigorous in general. For example, Eq(2) s a valid-loss but not likelihood. Also, the work did not say what likelihood under what distribution. This is propositional to Gaussian likelihood which may work fine in practice but the math presentation is not rigorous.  \n6. For the method (see figure 2), I did not see why the first part needs to be there as the second part takes the ground truth A as input. Using only the second part of the model which tries to see whether A->B is easier or B->A is easier is sufficient for the aim of identifying the relationship between given A and B. \n7. The dataset may be more useful to the causality community if it is released as a simulator rather than the images. \n", "extra_scores": {"experience_assessment": "I have published one or two papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The idea of integrating causality into an auto-encoder is interesting and very timely. While the reviewers find this paper to contain some interesting ideas, the technical contributions and mathematical rigor, scope of the method, and the presentation of results would need to be significantly improved in order for this work to reach the quality bar of ICLR.
Decision: Reject