Can Neural Networks Learn Implicit Logic from Physical Reasoning?
Authors: Aaron Traylor
Roman Feiman
Ellie Pavlick
Venue: ICLR 2023 poster (2023)
Keywords: logic
logical operators
logical reasoning
intuitive physics
physical reasoning
representation learning
developmental psychology
cognitive science

Abstract: Despite the success of neural network models in a range of domains, it remains an open question whether they can learn to represent abstract logical operators such as negation and disjunction. We test the hypothesis that neural networks without inherent inductive biases for logical reasoning can acquire an implicit representation of negation and disjunction. Here, implicit refers to limited, domain-specific forms of these operators, and work in psychology suggests these operators may be a precursor (developmentally and evolutionarily) to the type of abstract, domain-general logic that is characteristic of adult humans. To test neural networks, we adapt a test designed to diagnose the presence of negation and disjunction in animals and pre-verbal children, which requires inferring the location of a hidden object using constraints of the physical environment as well as implicit logic: if a ball is hidden in A or B, and shown not to be in A, can the subject infer that it is in B? Our results show that, despite the neural networks learning to track objects behind occlusion, they are unable to generalize to a task that requires implicit logic. We further show that models are unable to generalize to the test task even when they are trained directly on a logically identical (though visually dissimilar) task. However, experiments using transfer learning reveal that the models do recognize structural similarity between tasks which invoke the same logical reasoning pattern, suggesting that some desirable abstractions are learned, even if they are not yet sufficient to pass established tests of logical reasoning.

Published as a conference paper at ICLR 2023
CAN NEURAL NETWORKS LEARN IMPLICIT LOGIC FROM PHYSICAL REASONING?
Aaron Traylor,' Roman Feiman, & Ellie Pavlick'
1 Department of Computer Science
2 Department of Cognitive, Linguistic Psychological Sciences
Brown University, Providence, Rhode Island, USA
laaron_traylor, roman_feimar. ellie_pavlick taaeeppawwcckkerro......o @brown edu
ABSTRACT
Despite the success of neural network models range of domains, it remains open question whether they can learn represent abstract logical operators such as negation and disjunction. We test the hypothesis that neural networks without inherent inductive biases for logical reasoning can acquire an implicit representation of negation and disjunction. Here, implicit refers to limited, domain- specific forms of these operators, which work psychology suggests may be a precursor (developmentally and evolutionarily) to the type of abstract, domain- general logic that is characteristic of adult humans. To test neural networks, we adapt a test designed to diagnose the presence of negation and disjunction in animals and pre-verbal children, which requires inferring the location of hidden object using constraints of the physical environment well as implicit logic: if a ball is hidden in A or B, and shown not to be in A, can the subject infer that it is in B? Our results show that, despite the neural networks learning to track objects behind occlusion, they are unable to generalize to a task that requires implicit logic. We further show that models are unable generalize to the test task even when they are trained directly on a logically identical (though visually dissimilar) task. However, experiments using transfer learning reveal that the models do recognize structural similarity between tasks which invoke the same logical reasoning pattern, suggesting that some desirable abstractions are learned, even they are not yet sufficient to pass established tests of logical reasoning.
INTRODUCTION
People have the capacity for flexible logical reasoning. For example, given two alternatives (A or B), and subsequent information that allows ruling out one of them (not A), people conclude that the other is true with certainty (therefore B), termed reasoning by exclusion. is an open question whether achieving similar reasoning with neural models will require explicit logical components to be built into the network architecture or if the capacity for such reasoning can be learned from data.
Prior work logical reasoning in neural networks (Marcus) 2001 Evans al. 2018 among others) has focused on whether models are able to acquire abstract, domain- -gnneral logical operators, such as the and found in first order logic. However, recent psychological studies of logic in non-human animals and human infants have suggested that this powerful reasoning machinery does not appear in adults fully formed, ex nihilo. Rather, this work has argued that both over the human lifespan and across species, Nomain-generte logical operators may develop and evolve from scaffolding provided by precursors that are themselves more limited. These precursors are implicit logical operators that can differ from the explicit,
forms in two ways: they might only be able to operate on content specific domains, and they might perform only some of the functional role of their
full-fiedged counterparts (Völter & Call 2017 Bermudez 2003 Cesana-Arlotti et al. 2018, (see
Feiman et al. 2022 for discussion).
In this work, ask whether neural network models, which lack explicit representations of the logical operators for negation and disjunction, can nonetheless acquire implicit representations of such operators via sepf-supervised training. In particular, we focus implicit logic within the domain

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of intuitive physics, as this is one of the earliest domains in which such reasoning emerges in young children Clesama-Arlott et al., 2018 2020; Feiman et al., (022). We design a set of experiments in which models are trained to track objects they move throughout visual scene, and then evaluated on a task from developmental psychology that requires reasoning about the location of a hidden object and is considered to be face-valid test for the representation of (implicit) negation and disjunction. We find that, by most measures, object-tracking neural networks are unable to generalize zero-shot to the logical reasoning test, even when given training data which directly illustrates the requisite reasoning pattem. However, in transfer learning experiments, we find evidence that neural networks encode some degree of structural similarity between visually distinct but logically equivalent tasks, suggesting that they may yet be capable of representing the desired operators. Future work will need to determine the exact training conditions under which they would do so.
In summary, our primary contributions are: (1) We introduce the notion of implicit logic, taken from developmental and comparative psychology, into the repertoire of neural network evaluation; (2) We adapt standard test of logical inference in humans and use it to evaluate neural network models; (3) We present a series of studies which present primarily negative results regarding neural networks' ability to learn implicit logical reasoning in the physical domain, but which offer some suggestive evidence regarding the models' ability to transfer representations between logically equivalent tasks.
2
BACKGROUND
2.1 TWo TESTS OF REASONING BY EXCLUSION
To test whether computational models can reason using implicit negation and disjunction, we adapt two tasks previously used with infants (Feiman et al., [022] Piaget 1954) and many species of non-human animals (Call 20004] Völter & Call. 2017 for review). In the "Two-Cup" task (see Figure D. participants first see two cups, which are then hidden behind a screen. An object (e.g., a toy or Tood) is then lowered behind the screen into one cup (setting up A or B). The screen is then removed, showing that one cup is empty (not A), licensing the inference that the object must be in the other cup (therefore B). Finally, participants are invited to search. Success requires representing (explicitly or implicitly) that the ball is not in the empty cup in order to avoid searching there. Infants and many animal species succeed on this task in zero-shot setting. In Piaget's (1954) "Invisible Displacement" paradigm, participants see a hand holding an object. The hand closes to hide the object, moves behind an occluder, and then emerges again, empty palm facing the participant (A B; not A). This licenses the inference that the object must have been deposited behind the occluder (therefore B). In this work, we use the Two-Cup task as our target test task. In Sections $4.2 and $4.3] we train on Invisible Displacement in order to assess whether neural model trained to solve one reasoning-by- by-exclusion task can transfer its representations to another task that is formally similar but visually distinct.
2.2 EXPLICIT Vs. IMPLICIT LOGICAL REASONING
One way to solve both tasks is with explicit symbolic logical reasoning: represent the initial pos- sibilities for the object's location as AVB, and represent evidence ruling out one of them -A, thus licensing the conclusion B. However, more minimal solutions are also possible. [eeman et al.] (2022) propose that logical representations (negation, disjunction), can be implicit in two senses. First, while explicit logic is characteristically domain-general (OR and NOT can compose with any concepts, regardless of their content), implicit logical operations can be domain-specific, operating only over certain kinds of content (e.g. representations of objects' locations). Second, implicit logical representations might perform only part of the function of their explicit counterparts. For example, a function that compares two arguments (e.g. blue and red) for incompatibility is an implicit negation in this sense. It plays part of the functional role of representing blue as not red even as it would (correctly) not represent the negation of red as equivalent to blue in other computational contexts. In the Two-Cup task, participants could use an implicit representation of negation to represent that the cup being empty is incompatible with it containing the object (see Feiman et al. 2022 for discussion).
After ruling out the empty cup from consideration, further deriving the certain conclusion that the object must then be in the other cup is a signature of disjunction. This conclusion could be licensed by an explicit logical operator (AVB), but it could also be the consequence of an implicit representation with only part of the functional role of V. For instance, the two options could be linked
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probabilistically. such that learning that the object is not in one cup increases the probability that it is in the other (see Feiman et al., 2022 Mody & Carey. 2016; Rescorla 2009).
2.3 THIS WORK
(Feiman et al. 2022) propose that such implicit logical representations both with partial function and limited to a specific domain - could be evolutionary and developmental precursors to their explicit counterparts. On this account, implicit logical representations could emerge from specific content knowledge that is not logically structured, such as the intuitive physical understanding that predicts how objects might move space based on visual input. In this paper, we test whether models trained to represent object-tracking and occlusion will possess emergent representations of negation and disjunction that are implicit both senses: representations limited to the content domain of intuitive physics, and to the function of detecting incompatibility between two input states.
3 EXPERIMENTAL DESIGN
3.1 EVALUATION TASK
To test whether a model has an implicit representation of negation and disjunction, we evaluate its performance on the Two-Cup task. Figure shows our implementation of this task. We convert the task into a 2D video format using pygame and Box2D. Our environment consists of wedges and cups (which are static), a ball (which obeys gravity), and occluders (which move up and down from the bottom of the screen). The task is to predict the location the ball at each frame of the video. In each sequence, the ball falls from the top of the screen, and can either roll off the wedge into the left or the right cup, each of which are occluded. Because the ball's path off the wedge also occluded, it is ambiguous which cup the ball falls into until the occluders are removed. The occluder in front of the cup that does not contain the ball is the first to fall, thus licensing the negation inference.
We designate the frame which the first cup is revealed be empty (frame in Figure I be the critical frame-i.e., the frame at which a model with implicit logic should be able to determine with certainty the location of the ball. We thus evaluate models by comparing before and after the critical frame whether the model predicts the ball to be in the correct cup, the incorrect cup, or elsewhere on the screen. After our initial tests showed that variance in performance across examples was low, we constructed a set of 100 test examples over which to compute this metric.
Figure I: Frames from the Two-Cup task test video. Frames cl create ambiguity between the two possible hiding locations for the ball, and frames e-h are the part of the task on which we evaluate the model. The goal is to determine the location of the small yellow ball, which drops at frame d. At frame e, the subject should know that the ball is either the left cup or the right cup, but its exact location is unknown. When the left occluder drops at frame f, the subject should know that the ball not the left cup, and must be in the right cup, despite not seeing it. This is the critical frame.
3.1.1 MODEL
To test whether the capacity for implicit logical reasoning emerges in systems designed to represent an intuitive understanding of Newtonian physics, we use a neural network model that has a built-in notion of discrete objects, but which must learn the physical dynamics (and their generalization to logical reasoning tasks) from data. In addition to being consistent with developmental evidence on the emergence of logic, this architectural choice simplifies the learning problem and thus allows to study the phenomena we aim to study without needing to train extremely large models, as would be the case if we took tabula rasa approach.
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We use the Ubject-Permaneed Network (OPNet) model described by (Shamsian et al. 2020). OPNet is an LSTM trained on video data that tracks objects as they move and are occluded by other objects. It thus learns to track and predict object locations without a built-in representation of object physics. Specifically, OPNet consists of a) an object detection module that segments a frame into visible elements (rather than use this module, we feed in ground truth bounding boxes), b) an LSTM that attends to the scene and produces a distribution over current objects to identify which the target object (in our case, the ball) is currently behind, if any, and finally c) a "where is it" LSTM that predicts a bounding box for the target object based on a weighted average of components a) and b).
3.1.2 TRAINING
In our experiments ($4.142...3 we consider variety of training conditions in order to determine which, if any, allow the model to encode an implicit negation and disjunction to succeed on the Two-Cup task. In all experiments, we require at minimum that the model has been exposed to the basic elements of the Two-Cup task, so that the visual appearance of this task is in-distribution. We also require that the evaluation task itself (namely, the sub-sequence of frames (e)-(h) in Figure I remains entirely unseen in training, to ensure that the model cannot exploit specific heuristics of that sequence in order to solve the task. With these constraints, we design three sets of training data
schemas, described below in Section 4 Each training set contains 5,000 videos of 57 frames each.
Physical Reasoning Schema We generate simple scenes which show the basic physical phenomena of the environment. Each example has randomly selected template, each of which enumerates different interactions the ball may have within the environment; e.g. it falls into the cup. it falls onto a wedge and then into a cup, it falls onto wedge and then rolls along the ground, etc. In each template, the ball falls from a randomly chosen point on the x-axis (though the height from which it falls is kept constant) random time within the first 40 frames of the video. Randomly generated occluders appear throughout the scene and may or may not block the path of the ball. Attributes of the cups and wedges (e.g. x-location, size, height) are also chosen uniformly at random from pre-set ranges. When the ball rolls along the ground of the scene, it will stop at randomly selected x location
Two-Cup Ablations Training Schema We construct a set of training examples which are designed to expose the model to the general concepts necessary to solve the Two-Cup task, without giving it access to heuristics it could use to succeed on evaluation without representing implicit logic. Specifically, we considered all variations and perturbations of the Two-Cup task's s sequence of events, e.g., varying the number of cups, number of occluders, and the order in which the occluders rise and fall. We then filter out any sequence of events which either (1) were logically equivalent to the
Two-Cup task and thus would prevent the Two-Cup tasks from being held out (2) had direct overlap with the true Two-Cup task's 's frames at and after the critical frame, even if they did not require the same logical reasoning. For example, if in Figure [ we changed the order of the events in frames b-d from "small occluder rise", "large occluder rise". "M "ball fall"' to "ball fall", "small occluder rise", "large occluder rise" (d-b-c) b- bc), it would not be permissible in this training set because frames h remain the same as the Two-Cup task. We found that 38 perturbations of the Two-Cup Scene were permissible, and full list is available in the Appendix. For each video made using this procedure, we randomly select a permissible perturbation, and vary elements such as cup size, wedge size, and x-axis of the midpoint of the scene, but keep the order of events and location of the ball constant.
Invisible Displacement Training Schema Finally, we generate a training set which exposes the model to the same logical reasoning pattern that occurs in the Two-Cup task, but which is visually distinct. We use this training data in subset of our experiments ($4.2) in which we seek to provide the model with better chance at passing the Two-Cup task without traminn on the Two-Cup task itself. To generate such a training set, we use a variation on Piaget's 's Invisible Displacement experiments (1..). In our Invisible Displacement data, as shown in Fig. 2 the ball rolls off of wedge and then behind two occluders that are positioned directly next to each other. The ball stops at a random point
'The loss in the original OPNet model consists of MAE compared to the ground truth location of the ball, and a "consistency error" that penalizes the model for moving its prediction from one frame to the next. In order to ensure that the model can update its predictions during the Two-Cup task, we remove the consistency loss. "hhis constraint ensures compatibility with the Invisible Displacement training schema. In the examples derived from the Two-Cup task, the hall does not roll along the ground.
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behind the occluders (similar the procedure in the Physical Reasoning schema), and its location is ambiguous until one occluder falls, revealing that the location behind it is empty.
Figure 2: Frames from the Invisible Displacement task within experimental framework. At frame b, because of the random stopping, it is ambiguous whether the ball has landed behind the yellow or the red occluder. At the critical frame c, it becomes possible infer the ball's location.
3.2 PROOF-OF-CONCEPT
Our primary studies 4 ask whether neural network models can learn implicit negation and disjunc- tion in the context of physical reasoning tasks. In this section, proof-of-coneepp that such implicit reasoning is possible. Using a model that has a built-in (rather than learned) physics engine, we illustrate that model with explicit representation of physical dynamics is able to reason using implicit negation and disjunction, and can succeed on the Two-Cup task.
demonstrate
3.2.1 MODEL
We use pared-down version of ADEPT (Smith et al. 2019), model of humans' object tracking as constrained by their intuitive physics. This model not trained and works out-of-the-box ADEPT uses Bayesian filtering algorithm to represent beliefs about the locations of occluded objects, and probabilistically represents potential future trajectories those objects using a built- in physics simulator. This model is not trained and works nut-of-the-boo- For video sequence Ii, I2,.... ..., It.... the model receives ground truth object segmentations of bounding boxes around the visible objects in the scene at each frame 2;. Objects that occluded not included.
An important feature of ADEPT is its ability to maintain beliefs about multiple possible worlds, which is done explicitly using particle filter. ADEPT maintains set of "particles", each of which is a representation of the complete scene at time f. The next step of each particle is generated using noisy internal physics simulator. After several steps, the particles likelihood, which is calculated based on the overlap between the particle's 's representation of the world and the observations. Additional details explaining the ADEPT model are included in the Appendix.
resampled based their
We evaluate the accuracy of the ADEPT model on the Two-Cup task data using 100 particles F We calculate the likelihood of each particle at the critical frame, and then group particles based by where they represent the ball in the scene. If particle represents the ball as being in the same cup that the ground truth ball in, that particle is coded as "correct cup". if it's in the other cup is coded as "incorrect cup", and anywhere else on the screen is "elsewhere". We then sum the likelihood of the particles in each of the three groups to arrive at a final score.
3.2.2 RESULTS AND DISCUSSION
Our results are shown in Figure Before the critical frame, the ADEPT model is uncertain about the location of the ball (frame f), and its belief is distributed roughly evenly over the cups. After the critical frame, its belief shifts entirely to the correct cup (frame g). This pattern is consistent with the negation and disjunction inferences, and the ADEPT model thus succeeds the Two-Cup task.
We experimented with many values of particle count, and found that the choice did not affect the results as long there reasonable chance that least one particle would end up in each cup.
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Figure 3: Key frames of the Two-Cup task, visualizing the particles of the ADEPT model. There are 100 particles, and each circle one particle's representation of its beliefs about the ball's location.
These results illustrate how implicit representations of negation and disjunction can work. The model succeeds the Two-Cup task, but it does using a representational mechanism specific to the physical reasoning domain (here, the particle filter). The disjunction is implicit by virtue of all the particles being simulated in either cup at the same time, prior to the reveal of the empty cup. The negation is then implicit in how ADEPT responds to the empty cup. The probability of resampling any particle which the ball had been in the empty cup is reduced to zero. Clearly, this mechanism could not readily transfer to other logical reasoning tasks (e.g., linguistic reasoning) in the way formal logical operator could. These results thus illustrate a plausible way in which neural network models might learn to solve the same task by modeling the physical world. Namely, if the neural network learns to represent the physics objects' motion, as well as a representation of uncertainty and resampling in the face of unexpected observations, it should be able to pass the Two-Cup task.
EXPERIMENTS
We present three experiments, which get progressively casier, each requiring less generalization from the model than the previous. This experimental structure is due to the fact that we observe negative results in the earlier experiments, and thus progressively relax requirements in order to understand the conditions under which the model can succeed (if at all). First, we train OPNet only on basic object tracking task, and evaluate whether such training is sufficient for the model to encode an implicit negation and disjunction, measured by the Two-Cup task ($4.1) Second, we train on the Invisible Displacement task ($2.I) in addition to basic object tracking ($4.2). D. Finally, we consider a transfer learning paradigm, which the model trained first on the Invisible Displacement task and then fine-tuned on the Two-Cup task ( (4.3)
4.1 EXPERIMENT 1: ZERO-SHOT TRANSFER FROM OBJECT TRACKING
We first test whether model trained only on object tracking will acquire capacity for implicit logical reasoning that is sufficient to generalize directly to the Two-Cup task. We train an OPNet model on Physical Reasoning Two-Cup Ablations data. To compare this model's performance to a plausible ceiling benchmark, we also train a model on a separate dataset of 5,000 Two-Cup task videos, which are instead drawn from the same distribution the held-out Two-Cup test set. We compare the accuracy of the two models to "hypothetical success" on the Two-Cup task - before the critical frame, the ball could be in either cup. but after the critical frame which one cup is revealed to be empty, an ideal model will always predict that the ball is in the other cup. We select the model that minimizes loss on the dev set (100 examples for Physical Reasoning + Two-Cup Ablations data, 50 examples for Two-Cup data). Model training details are in the Appendix.
Control Experiments In order to ensure that the experimental model has learned to track objects in this environment, we also test on several control datasets. These control datasets are permutations of the Two-Cup task and are intended to ensure that the model has succeeded in encoding the basic environmental knowledge (other than the logical reasoning patterns) on which the Two-Cup task depends. First, Two-Cup Freebie is designed to rule out failure based on the task setup. This test set contains the same setup as Two-Cup: but the first revealed cup shows the ball, thus removing the need reason by exclusion. Next, to ensure that the model can track the ball's location, occluded, we create the Known Specifie Location and Known Cup Location test sets. In the former, reorder the frames in Fig. such that the ball falls, then the occluders rise, before proceeding like
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Train on Two-Cup task, test on Two-Cup task
Dataset
Correct
Incorrect
Elsewhere
Two-cup task
0.81
0.19
0.00
Train on Physical Reasoning Two-Cup Ablations, test on Two-Cup task
Dataset
Correct
Incorrect
Elsewhere
Two-cup task
0.48
0.50
0.02
Freebie
1.00
0.00
0.00
Known Specific Location
1.00
0.00
0.00
Known Cup Location
0.94
0.03
0.03
Outside (visible)
n/a
0.00
1.00
Outside (occluded)
n/a
0.12
0.88
Table 1: Results on the Two-Cup task and the control datasets. The models' predictions before the critical frame are always split roughly evenly between the two cups, when relevant. In the Outside experiments, "elsewhere" is the correct answer, because the ball is outside of both cups.
normal. This should give away the ball's location before any inference is necessary. Similarly, in the latter, to ensure that the model can track an occluded ball with only general knowledge of its location (i.e. it identifies that the ball is in cup, but not exactly where), we reorder the frames such that the small occluders rise, then the ball falls, then the scene proceeds. Finally, to ensure that the model is tracking the ball and not just guessing a cup, we create the Outside control set. In this set use the Two-Cup setup, but the ball falls entirely outside of the cup-and-wedge structure. There are two settings: occluded, where falls behind a third occluder, and visible. where it is never obscured.
The experimental model succeeds with high accuracy (88%-100% on each of the control sets, as shown in Table More detailed explanations for the results are in the Appendix.
Two-Cup Task Experiment As shown in Table I the predictions of the experimental model (Physical Reasoning + Two-Cup Ablations) do not change after the critical frame. In each test video, the occluder falling to reveal the empty space does not cause the experimental model to update its prediction. Comparatively, when the model is trained directly on the Two-Cup task, predicts the correct cup after the critical frame roughly 81% of the time. These results show that the neural network model trained only on object tracking within the physical constraints of the Two-Cup setup does not learn implicit representation of the logical operators required to pass the Two-Cup task.
4.2 EXPERIMENT 2: ZERO-SHOT TRANSFER FROM DEASONING-B--EXCLUSS TASK
One explanation for the failure observed in the above experiment is that the models never encountered a situation in which the ball could be in either of two, non-contiguous locations at training time, and thus never learned to represent and reason about this form of uncertainty, or to update its beliefs about the location of the ball once the uncertainty resolved (as the ADEPT model from $3.2 was able to do). To test this possibility, we provide the model with much richer training data, training it on the logical structure of the task without giving away the visual details of the solution. We train an OPNet model not only our original Physical Reasoning Two-Cup Cup Ablations data, but also on Invisible Displacement data, which requires the same inferences as the Two-Cup task but uses a visually different setup. We then observe that model's performance the Two-Cup task.
Control Experiments Similarly to the Physical Reasoning + Two-Cup Ablations experiments, we also introduce control experiments in order rule out the possibility that the model fails learn the necessary object tracking. We test the Physical Reasoning + Two-Cup Ablations + Invisible Displacement model on all of the earlier control sets, plus three designed to test the model's ability to learn from the Invisible Displacement training task- Invisible Displacement Test, Invisible Displacement Freebie and Roll-then-occlude Invisible Displacement Test is held-out test data. In Invisible Displacement Freebie, to rule out failure in the object tracking required for the Invisible Displacement task itself, when the first occluder drops in the Invisible Displacement task, the ball is found. Finally in we test to see that the model can track an observed ball behind occlusion. The ball rolls and comes to stop before the occluders rise, and then the scene progresses like normal.
similarly to the "Known Specific/Cup Location" experiments,
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The model succeeds the control experiments, (including the Invisible Displacement test), scoring between 95-100% accuracy on all datasets. Detailed results can found the Appendix.
Two-Cup Task Experiment Again, as in the prior experiment, the model performs at chance on the Two-Cup test (details in Appendix). The neural model makes the same emrors in the other tests: when the occluder falls, does not update its prediction. Even though the model trained on examples of the exact reasoning pattern which it is tested, it is still unable generalize the Two-Cup task. There are at least two possible explanations. First, the failure might suggest that the model did not learn solve the Invisible Displacement task the "right way", and thus despite learning to solve that task at training time, the learning does not result in representations that are reusable on the Two-Cup task. A second explanation is that the representations learned do capture the logical structure of the task, but the model is not able to recognize the similarity between the tasks in the zero-shot transfer setting. This latter fallure would suggest that the neural network could succeed with additional training focused on recognizing visually novel instantiations of the same logic.
4.3 EXPERIMENT 3: TRANSFER LEARNING ACROSS REASONING- BEEINNG------CCE BY-EXCLUSION TASKS
In our final experiment, test whether the neural models that failed to reason by exclusion might nevertheless be learning some representation relevant to the logical structure of both tasks. If they do, pretraining Invisible Displacement and then finetuning to succeed more quickly at the held-out Two-Cup test than training on the Two-Cup task alone. To examine this, compare how quickly OPNet models begin succeed on the Two-Cup task when first trained on Invisible Displacement or Physical Reasoning to models initialized from scratch.
the Two-Cup task might allow it
Figure shows the results. We find that the model that is first trained on Invisible Displacement and then trained on the Two-Cup training data succeeds at the held-out Two-Cup test set before both model that is trained on the Two-Cup task from scratch and model trained only on object tracking.
0.8
Accurscy
0.6
0.4-
Pretroining
0.2
From Physical Reasoning invisible Displacement
From Random
60
Epochs
Figure 4: Accuracy (% of examples that place bounding box for the ball in the "correct cup") " on the Two-Cur task over time when finetuned on the Two-Cup task and pretrained using various methods. Each is averaged across random seeds. There are 5,000 data points in one epoch.
DISCUSSION
This work asks whether neural network models are capable of learning implicit representations of logic from self-supervised training in the domain of physical reasoning. Overall, the results in 4 are primarily negative. We see in $ that the neural networks trained on a basic physical reasoning task fail to generalize to the Two-Cup task. More importantly, in $4.2 we see the same models failed even when trained on the Invisible Displacement task, task which should in principle rely exactly the same conceptual representations as does the target Two-Cup task. Thus, the evidence strongly suggests that the neural networks are learning to solve the training tasks using representations other than those which the tasks designed to require. However, in Section 4.3 see suggestive evidence that the neural network might learn some desirable representations related to logical reasoning, demonstrated by the fact that training
Section
logical reasoning tasks speeds
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learning on another logically identical task. While this falls short of our test for possession of an (implicit) logical representation, it does indicate that the network may be capable of developing the desired representation, e.g., under different training conditions.
As a prooffof-concept, the ADEPT model we analyzed in $3.2 was able to succeed on the Two-Cup task. This indicates that, at minimum, a good model of the physical dynamics of the environment combined with a good model of possible worlds is sufficient to deploy implicit logical operators for reasoning. Thus, when we observe that the object tracking neural network models fail on our evaluations, it implies that they are failing to learn at least one of the relevant components of ADEPT"s model of intuitive physics. Our control conditions presented in Sections 4.1 and 4.2 suggest the model learns to track objects throughout the environment reasonably well. Thus, we are ielineed to conclude that the neural model fails because does not learn to represent uncertainty over multiple possibilities and/or lacks mechanisms for updating beliefs about possibilities in response to observations. Future work considering alternative architectures and loss functions may well reveal more positive results.
6 RELATED WORK
Intuitive physics is thought to be one of the domains of "core knowledge" in human cognition, which are the foundations of higher-level mental processes (Spelke & Kinzler 2007 Carey 2009). In recent years, computational approaches to intuitive physics problems have gained popularity- Duan et al. (2022) have conducted a comprehensive survey. We focus on models with object-centric representations (Smith al., 2019 Shamsian et al. 2020).
There are several datasets of intuitive physics tasks for computational models to train and test on. IntPhys 2019 is benchmark dataset, on which models are trained only on positive examples; the test task is then to distinguish examples that do and do not conform to the physics of the environment (Riochet et al. 2018). Published concurrently is (Piloto et al. 2018), which takes a similar approach. Rather than distinguishing consistent/inconsisten image sequences, the PHYRE task is dataset of physical reasoning tasks where the objective is to take one action to manipulate the scene and reach a goal state (Bakhtin et al.) 2019). Within the realm of object tracking in video, the CATER dataset contains videos of a target object as it is occluded and shuffled behind and within other objects in a dine-dimmnsional scene (Girdhar& & Ramanan 2020). Although it is not intuitive physies task per se, similarly to this work, the ACRE dataset borrows the "blicket detector" task from developmental psychology in order to measure the ability of neural network-based and neurosymbolic reasoning models at the task of causal induction, or inferring causality from limited data (Zhang et al. 2021).
be able to learn representations of explicit logical operators that generalize flexibly (Marcus) 200I). Some work pursues that question empirically, and seeks determine whether, given a fixed set of symbols, the functions of explicit logical operators can be learned or distinguished from one another (Evans et al.] 2018 Traylor et al. 2021 T). Other work seeks to determine whether these models can generalize negation to novel symbols (Hill et al., 2020). In the field of natural language processing, large neural language models are often trained on large corpora of text, and then tested on natural language inference tasks, or those requiring negation (sentences containing words such as and not, which is an analogous framework to the implicit logic testing presented in this work. The representation of negation within these models tends to be dependent on the sentential context (Kassner & Schütze 2020 Talmor et al. 2020).
Neural network models are commonly thought
7 CONCLUSION
In this work, we measured neural models' ability to learn implicit representations of negation and disjunction from data. We found that, despite tracking objects as they move and are occluded throughout the environment, the neural models were not able to generalize to a diagnostic task requiring implicit negation and disjunction without observing examples from that diagnostic task itself. Furthermore, when trained on visually dissimilar data that requires the same logical capabilities, transferring the representations to the target task did not improve performance. However, when training on the diagnostic task, pretraining target task faster than other initialization methods. These results show a potential weakness of models that attempt to learn and generalize logical capability from data.
similar logical task caused the models to learn the

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Published as a conference paper at ICLR 2023
8 ACKNOWLEDGEMENTS
This research is supported in part by DARPA via the GAILA program (HRO01 1990064), The views and conclusions contained herein are those of the authors and should not be interpreted necessarily representing the official policies, either expressed or implied, of DARPA or the U.S. Government. We would also like to thank James Tompkin, George Konidaris, Tomer Ullman, Kevin Smith, Chen Sun, Jack Merullo, Nihal Nayak, and the participants of the McDonnell Workshop for their helpful comments.
REFERENCES
Anton Bakhtin, Laurens der Maaten, Justin Johnson, Laura Gustafson, and Ross Girshick. Phyre: A new benchmark for physical reasoning. Advances in Neural Information Processing Systems, 32, 2019.
Jose Luis Bermudez. Thinking Without Words. Oxford University Press USA, 2003.
Josep Call. Inferences about the location of food in the great apes (pan paniscus, pan troglodytes, gorilla gorilla, and pongo pygmacus). Journal of Comparative Psychology, 118(2):232, 2004.
Susan. Carey.
The origin of concepts. Oxford series in cognitive development. Oxford University Press, Oxford ;, 2009. ISBN 9780195367638.
Nicoló Cesana-Arlott Ana Martín, Ernö Téglás, Liza Vorobyova, Ryszard Cetnarski, and Luca Bonatti. Precursors of logical reasoning in preverbal human infants. Science, (59(6381):1223-1 2018.
Nicolò Cesana-Arlotti, Ágnes Melinda Kovács, and Emn Téglás. Infants recruit logic to learn about the social world. Nature communications, 11(1):1-9, 2020.
Jiafei Duan, Arijit Dasgupta, Jason Fischer, and Cheston Tan. A survey machine learning approaches for modelling intuitive physics. arXiv preprint arXiv:2202.0648// 2022.
Richard Evans, David Saxton, David Amos, Pushmeet Kohli, and Edward Grefenstette. Can neural
networks understand logical entailment? In International Conference Learning Representations, 2018.
Roman Feiman, Shilpa Mody, and Susan Carey. The development of reasoning by exclusion in infancy. Cognitive Psychology, 135:101473, 2022.
Rohit Girdhar and Deva Ramanan. CATER: A diagnostic dataset for Compositional Actions and TEmporal Reasoning. In ICLR, 2020.
Felix Hill, Andrew Lampinen, Rosalia Schneider, Stephen Clark, Matthew Botvinick, James McClelland, and Adam Santoro. Environmental drivers of systematicity and generalization in situated agent. In International Conference on Learning Representations, 2020.
Nora Kassner and Hinrich Schütze. Negated and misprimed probes for pretrained language models: Birds can talk, but cannot fly. In Proceedings of the 58th Annual Meeting of the Association for Com- putattional Linguistics, pp. 7811 1-7818. Association for Computational Linguisties, July 2020. doi: 10.18653//1/2020.ac.// www.:/20...mmmm..66606
URL https: wwwp://wwww..cc wtwp://wwwwb.og//ttoolloo...
acl main. 698
Gary Mareus. The algebraic mind: Integrating connectionism and cognitive science. MIT press, 2001.
Shilpa Mody and Susan Carey. The emergence of reasoning by the disjunctive syllogism in early childhood. Cognition, 154:40 48, 2016.
Jean Piaget. The construction of reality in the child. Routledge, 1954.
Luis Piloto, Ari Weinstein, Dhruva TB, Arun Ahuja, Mehdi Mirza, Greg Wayne, David Amos, Chia-chun Hung, and Matt Botvinick. Probing physics knowledge using tools from developmental psychology. arXiv preprint arXiv: 1804. 0/ 128, 2018.
10

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Published as a conference paper at ICLR 2023
Michael Rescorla. Chrysippus' dog study in non-linguistic cognition. The philosophy of animal minds, pp. 52-71, 2009.
Ronan Riochet, Mario Ynocente Castro, Mathieu Bernard, Adam Lerer, Rob Fergus, Véronique Izard, and Emmanuel Dupoux. Intphys: A framework and benchmark for visual intuitive physics reasoning. arXiv preprint arXiv: 2018.
Aviv Shamsian, Ofri Kleinfeld, Amir Globerson, and Gal Chechik. Learning object permanence from video. In European Conference on Computer Vision, pp. 35-50. Springer, 2020.
Kevin Smith, Lingjie Mei, Shunyu Yao, Jiajun Wu, Elizabeth Spelke, Josh Tenenbaum, and Tomer Ullman. Modeling expectation violation in intuitive physics with coarse probabilistic object representations. Advances neural information processing systems, 32, 2019.
Elizabeth S Spelke and Katherine D Kinzler. Core knowledge. Developmemaal science, 10(1):89-96 2007.
Alon Talmor, Yanai Elazar, Yoav Goldberg, and Jonathan Berant, oLMMics-on what language model pre-training captures. Transactions of the Association for Compulational Linguistics, 8:743-758, 2020. doi: 10. 10.1162/tac__s a_peol____0422_ tacl 1.
Aaron Traylor, Roman Feiman, and Ellie Pavlick. And does not mean Using formal languages to study language models' representations. In Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the I Ith International Joint Conference Natural Language Processing (Volume 2: Short Papers), pp. 158-167, 2021.
Christoph Völter and Josep Call. Causal and inferential reasoning in animals. 2017.
Chi Zhang, Baoxiong Jia, Mark Edmonds, Song-Chun Zhu, and Yixin Zhu. Acre: Abstract causal reasoning beyond covariation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattemn Recognition, pp. 10653,10653, 2021.


Reviews:
[{"review_id": "xDB0TQcnCaB", "reviewer": "Reviewer_7YcZ", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "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": "This paper presents an in-depth study on the ability of neural networks (NN) to learn implicit logic of negation and disjunction. Specifically implicit negation and disjunction here refers to the ability to tell that if a ball fall in one of two recipients, the NN doesn't know which one, but then one is shown empty (the ball is not there) then the agent should know that the ball is in the other recipient. \n\nAuthors do not train the agent directly on the task above, which is used as test task but train in related tasks with the same objects and background. Results in control experiments show that the NN learns to track the ball but it is not able to solve the task.", "summary_of_the_review": "Careful and detail experiment in a novel setting for a key ingredient of intelligence. However, authors missed key pieces of literature exploring the very same questions that are the main focus of this work. This leaves this paper incomplete since authors haven't checked if a key ingredient in those earlier studies is what they were missing here.\n\n\n----------------UPDATE---------------------\n\nAfter discussing with the authors, I agree with them that from the point of view of demonstrating that physical reasoning has arisen, but it does not mean that (implicit) logical reasoning has arisen too, this work is novel. \n\nI still believe that the last experiments suggest that if the agent had been trained in at least 6 different contexts implicit logic reasoning might have arisen. Since Hill et al., demonstrated that agents struggled to learn logic without enough examples  and León et al.  pointed that with object-based architectures -as the one in this paper- 6 examples is enough for compositional logic reasoning to arise. I think this should be pointed in the future directions as a possible solution to tackle why the agents are failing in the experiments of this paper.\n\nI believe that the points above need still to be better clarified/incorporated in the discussion conclusion section, but given author's response so far, I am confident that they will and updating my score accordingly.", "strength_and_weaknesses": "The paper follows a recurrent and very important topic on the ability of NNs to do compositional generalisation of logic reasoning in a novel set up. One of the main strengths of the paper is the careful detail of the experiments and control tests -which rule out plausible concerns about if the model is really failing to solve the task due to the inability of generalisation of logic reasoning or something else-.\n\nMy main concern about the paper is that, while authors cover a good amount of related literature, they missed several key papers about compositional generalisation in reinforcement learning. I strongly encourage authors to check those earlier studies because they would explain why the NNs fails to generalise in this work, and what should have been done (or at least tried) for the model to past this test:\n\n* Hill et all, 2020 did an experiment on the ability of DRL agents to generalise negation to unseen instructions. In that work the agent is trained with positive instructions such as \"find a plane\" or \"find a ball\" and the agent should find those object in a room and stare at them for a few second to succeed. For some of those objects the agent was trained with negation with instructions such as \"find something that is not a plane\", and then evaluated to do  find something that is not X, where x was a training object that had been used for positive instructions only. Hill et al. found that for the agents to succeed, they required to had been trained with at least 100 negated instructions to pass this test.\n\n* Also in that line, León et all. did a similar experiment in 2D scenarios to test the ability of DRL agent to achieve compositional generalisation with negation and disjunction and found that with object-based encoders - that this paper under review is using already-  and early stopping, 6 objects are enough to generalise negation and disjunction.\n\nI believe that those two works study a form of implicit logic in a similar fashion that this paper does, but even in the latest they required 6 examples of that form of reasoning before achieving successful results. Thus, when this work shows in Section 4.1 that the agent is not doing that form of generalisation after just one example, it actually aligns with those existing works. Also the result from section 4.2 showing that the agent that has learnt to solve this kind of generalisation once is able to learn to solve the experiment faster also reinforces the hypothesis from those previous works that I cited.\n\nThus, I believe that it would be key for this paper to be complete to do one further test where they train the NNs with 6 different variants of implicit reasoning and then evaluate the NNs with the two cups test again. Since the setup of this work and context is so different (this is not an RL work for instance) it would be a great contribution to see if the hypothesis from those previous works are confirmed here as well.\n\nI believe then that authors should include those two previous works in their RW section and carry an additional experiment to see if that helps the NNs to pass the test.\n\nHill, Felix, et al. \"Environmental drivers of systematicity and generalization in a situated agent.\" International Conference on Learning Representations. 2020.\n\nLeón, Borja G., Murray Shanahan, and Francesco Belardinelli. \"Agent, do you see it now? systematic generalisation in deep reinforcement learning.\" ICLR Workshop on Agent Learning in Open-Endedness. 2022.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "ujw-y8JNkO", "reviewer": "Reviewer_1KAw", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "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: The paper mainly explores whether the neural network can learn the implicit representations of negation and disjunction. The results of experiment shows that the neural network lack the ability to generalize to task that requires implicit logic. \nContributions: \n1)The authors introduce the notion of implicit logic into the repertoire of neural network evaluation. \n2)The authors use a test of logical inference in humans to evaluate the neural network. \n3)The experiments offer some suggestive evidence about the models’ ability to transfer representations between logically equivalent tasks.\n", "summary_of_the_review": "The research work of this paper mainly focus on neural network’s ability of learning implicit representations. Overall this paper is a comprehensive and complete work.\nIf the above problems are well-addressed, this reviewer believes that the essential contribution of this paper are important for research of neural models’ ability to learn implicit representations.\n", "strength_and_weaknesses": "Strengths: \nA number of training modes were designed and detailed experiments were conducted to comprehensively evaluate the ability of neural network to learn implicit representations of negation and disjunction from data. It has a strong reference significance for works in logical reasoning in neural networks.\n\nWeaknesses: \nThere are too few experimental charts, thus the experimental process is not clear and intuitive enough. Another obvious problem with this paper is lack of sufficient explanation of the results. You need to explain your simulation results in detail and why you got such results. In page 9, DISCUSSION, “Thus, we are inclined to conclude that the neural model fails because it does not learn to represent uncertainty over multiple possibilities and/or lacks mechanisms for updating beliefs about possibilities in response to observations. ”, this explanation is ambiguous and not convincing.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "nYmw579EaAs", "reviewer": "Reviewer_ggkT", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "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": "The paper proposes an experiment for evaluating whether neural models can learn to represent logical reasoning operators purely from observations. The experiments are taken out of literature in developmental and comparative psychology, in which a neural network is trained to represent negation and disjunction operators. The focus is on learning implicit representation, which are domain-specific and may not necessarily generalize to other domains but nonetheless measure the ability of neural models to implicitly perform logical reasoning in some limited fashion.\n\nThe experiments reveal that neural networks are indeed not able to learn to represent logical operators without being trained directly on test data. However, the transfer experiments show that neural networks do learn some useful representations from one domain with similar logical task but different features, that enable them to quickly learn to perform well on a test task.", "summary_of_the_review": "More research work highlighting the failures of neural networks and drawing insights on how to improve them, is needed. This work adds to the list of benchmarks of highlighting the limitations of neural networks on logical reasoning tasks. While more experimentation on other types of reasoning tasks and for a wide range of neural architectures is still needed, this work will open up more opportunities for other works to follow in the same vein.", "strength_and_weaknesses": "Strength\n\nAnalyzing the limitations of neural networks is an important contribution to the field, which enables researchers to further enhance the capabilities of neural networks. \nThe paper proposes the first set of experiments to characterize the failures of neural networks in tasks that require reasoning. It's well known in the literature that neural network in general lack reasoning capabilities but it's rarely explicitly demonstrated in a set of experiments. This work pushes that boundary.\nThe proposed work is grounded in theory that aims to understand how logical reasoning \"emerges\" from human and non-human animals alike.\n\nWeaknesses\n\nFine-tuning experiments, although in a logical reasoning context, are not really revealing anything new that we don't already know about neural networks.\nThe experiments are only limited to one type of logical reasoning task and neural network architecture.\nIt's not clear what it means for a neural network to succeed in solving the Two-Cup task. The ADEPT baseline seems to predict the correct cup 100% of the time but the neural network is considered successful by predicting the correct cup 81% of the time.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "gU4xT5BGToI", "reviewer": "Reviewer_mWJf", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "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": "The paper studies the problem of whether a neural network model can learn an implicit representation of negation and disjunction in the domain of intuitive physical understanding that predicts how objects might move in space based on visual input. Three experiments are carefully designed to draw two conclusions: on one hand, neural models cannot generalize to a diagnostic task requiring implicit negation and disjunction without observing examples from that diagnostic task; on the other hand, when training on the diagnostic task, pretraining on a similar logical task can enable the models to learn the target task faster than other initialization methods.", "summary_of_the_review": "The paper studies an interesting and important problem on whether a neural model can do perform implicit logical reasoning in the domain of intuitive physical understanding. Some findings are made through carefully designed experiments. However, the findings do not tell whether neural models have logical reasoning ability when computer vision processing is not needed.", "strength_and_weaknesses": "Strengths:\n\n(1) A new study on the logical reasoning ability of neural models in the domain of intuitive physical understanding.\n\n(2) Carefully designed experiments conducted to prove or refute some interesting hypotheses.\n\nWeaknesses:\nThe study is restricted on a relatively small domain where the results are entangled with computer vision processing. The findings are hard to adapt to general domains about the reasoning ability for classical logics. In particular, the findings do not tell whether neural models have logical reasoning ability when computer vision processing is not needed.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "NVoSEGVnzH", "reviewer": "Reviewer_9VQw", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "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": "This paper tries to study if deep neural networks (with a built-in representation of object physics) can learn logical relations such as negation and disjunction. Inspired by cognitive science, the authors propose a task called Two-Cup which requires the agent to have the ability of reason by exclusion. This work has designed extensive experiments and ablation studies, the results show that the tested neural network failed to learn the target concepts.", "summary_of_the_review": "This paper trys to answer an important problem in AI research, the authors have provided an interesting task and extensive emprical study to answer this question. The experimental methodology could be improved and the result is not strong enough.", "strength_and_weaknesses": "### Strengths:\n- The authors has designed many experiments and ablation datasets, which have covered different aspects in cognition for learning logic reasoning.\n- The paper is generally well writen, all the details are covered either in the main text or in the appendix. The authors also provide enough discussion content to explain the observations.\n- The paper targets answering an important problem in AI.\n\n### Weaknesses:\n- Although the motivation of this paper is intriguing, the methodology adopted by this paper might be weak, because it is difficult to evaluate neural networks' logical reasoning ability by just an empirical study on one type of task. Results on one or two tasks could not prove that they can represent or learn logical calculus theoretically.\n- The comparing approach has a built-in Bayesian modelling module, which is too strong in my opinion. The conclusion could be more convincing if the authors can choose a learning system enhanced with explicit symbolic representation, e.g., Neuro-Symbolic Systems.\n- It would be more interesting if the authors could provide a set of experiments with preverbal children or animals using the same set of training data. I think the number of training examples could be drastically reduced compared to deep learning models.\n- I appreciate that this paper provides many datasets and experiments to make sure the empirical study covers every possible aspect of this problem, the naming of datasets and organisation of experiments are a bit messy. Maybe the reading experience could be improved by adding a graph of the datasets/tasks illustrating their relations, instead of hiding them in the main text.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster