On Incorporating Semantic Prior Knowlegde in Deep Learning Through Embedding-Space Constraints
Authors: Damien Teney
Ehsan Abbasnejad
Anton van den Hengel
Venue:  (2020)
Keywords: regularizers
vision
language
vqa
visual question answering

Abstract: The knowledge that humans hold about a problem often extends far beyond a set of training data and output labels. While the success of deep learning mostly relies on supervised training, important properties cannot be inferred efficiently from end-to-end annotations alone, for example causal relations or domain-specific invariances. We present a general technique to supplement supervised training with prior knowledge expressed as relations between training instances. We illustrate the method on the task of visual question answering to exploit various auxiliary annotations, including relations of equivalence and of logical entailment between questions. Existing methods to use these annotations, including auxiliary losses and data augmentation, cannot guarantee the strict inclusion of these relations into the model since they require a careful balancing against the end-to-end objective. Our method uses these relations to shape the embedding space of the model, and treats them as strict constraints on its learned representations. %The resulting model encodes relations that better generalize across instances. In the context of VQA, this approach brings significant improvements in accuracy and robustness, in particular over the common practice of incorporating the constraints as a soft regularizer. We also show that incorporating this type of prior knowledge with our method brings consistent improvements, independently from the amount of supervised data used. It demonstrates the value of an additional training signal that is otherwise difficult to extract from end-to-end annotations alone.

Under review as a conference paper at ICLR 2020
ON INCORPORATING SEMANTIC PRIOR KNOWLEDGE IN DEEP LEARNING THROUGH EMBEDDING-SPACE CONSTRAINTS
Anonymous authors Paper under double-blind review
ABSTRACT
The knowledge that humans hold about problem often extends far beyond set of training data and output labels. While the success of deep learning mostly relies on supervised training, important properties cannot be inferred efficiently from end-to-end annotations alone, for example causal relations domain- -speaiiii-siiiiieeeee in- variances. We present a general technique to supplement supervised training with prior knowledge expressed relations between training instances. We illustrate the method on the task of visual question answering (VQA) to exploit various auxiliary annotations, including relations of equivalence and of logical entailment between questions. Existing methods to use these annotations, including auxiliary losses and data augmentation, cannot guarantee the strict inclusion of these rela- tions into the model since they require careful balancing against the end-to-en objective. Our method uses these relations to shape the embedding space of the model, and treats them as strict constraints on its learned representations. In the context of VQA, this approach brings significant improvements robustness, in particular over the common practice of incorporating the constraints as a soft regularizer. We also show that incorporating this type of prior knowledge with our method brings consistent improvements, independently from the amount supervised data used. It demonstrates the value an additional training signal that is otherwise difficult to extract from end-to-ent annotations alone.
accuracy and
INTRODUCTION
The capacity to generalize beyond the training data is one of the central challenges to the practical applicability of deep learning, and grows as the task considered grows more and more complex. End- to-end training provides a weak supervisory signal when the task requires a long chain of reasoning between its input and output (Glasmachers) (0177] Marcus 2018 Zador 2019). A prime example is found in the task of visual question answering (VQA), where a model must predict the answer to given text question and related image (see Fig- D). Typical VQA models trained with supervision (questions/images and ground truth answers) tend to capture superficial statistical correlations, rather than the underlying reasoning steps required for strong generalization (Goyal al. 2016 Agrawal et al. 2018: Teney & van den Hengel 2016). Prior knowledge that reflects a deeper understanding of the data than the ground truth answers offers an invaluable although currently ignored source of information to train models more effectively.
We propose method to incorporate, deep learning models, prior knowledge that is specified as relations between training examples. Incorporating knowledge beyond end-to-end supervision is an opportunity to improve generalization by providing high-level guidance complementary to ground truth labels. The fact that two data elements are equivalent, e.g. two questions being rephrasings of task, provides more information than merely illustrating that they share the same answer. Such a constraint of equivalence exemplifies high-level, general concept that is much more powerful than a set of examples sharing a label.
each other a question-answe
Prior knowledge has previously been incorporated into network architectures in multiple ways, e.g. by sharing weights spatially in a CNN (Nowlan & Hinton] 1992). Existing approaches are however often task-specifie, and more importantly, usually operate in parameter space (Cohen & Welling

---

Under review as a conference paper at ICLR 2020
Equivalent questions
Are the sneakers white, or black? Black.
What material is the box made of? Plastic.
Are the sneakers black, or white? Black.
What is the rectangular container made of? Plastic.
Entailed questions
Are there any hats here that not orange? Yes. + Is there hat in the picture? Yes.
Are there chairs plates here? No.
Are there any chairs here? No.
Annotations functional programs
Is the backpack the same color the house ? No.
Is the tie brown No. selectitis veri fo:colooobbboooo
sele seleettoo backpack, se select:o house, same:co color
We demonstrate our method on the task of visual question answering (VQA), where we exploit three types of auxiliary annotations expressed relations between training questions. This task-spec knowledge (for example the equivalence of synonymous questions) provides a training signal complementary to the end-to-end annotations of ground truth answers.
Figure I:
2016
Guttenberg et al. 2016 Laptev Buhmann) 2015 Teney Hebert 2016). In contrast,
our approach uses knowledge expressed in embedding space, which we find far more intuitive for expressing higher-level knowledge. Indeed, in embedding space, one can specify how the network represents data. parameter space, one can guide how the network processes these representations. While both can be useful, the former can map more directly task- or domain expert's s knowledge of the data used. The additional knowledge that we use comes as annotations of relations between specific training instances. We do not require all of the training data be annotated with this addi- tional knowledge.
Technically, propose novel training method that operates in phases (see Fig. 2). First, employ the constraints derived from the annotations soft regularizers. They guide the optimiza- tion of the target task to loosely satisfy the constraints. Second, we retrain the earlier layers of the network by distillation (Hinton et al. 2015) using, as targets, embeddings projected on the manifold where the constraints are met perfectly. This second phase is the crux to enforce hard constraints on the learned embeddings. A major finding in our experiments is that these hard constraints are more effective the soft regularizers, in all of our test cases.
We present extensive suite of experiments on synthetic and large-scale datasets (Section In the context of VQA, we apply the method on top of the popular model of Anderson et al. (2018) leverage three types of annotations illustrated Fig. I relations of equivalence between ques- tions (i.e. being rephrasings of one another), of entailment (the answer to general question being deducible from that of more specific one), and relations of set membership, where questions are known to share some reasoning steps (e.g. questions referring to similar objects or requiring similar reasoning operations). These annotations are provided with the GQA dataset (Hudson & Manning 2019), but have largely been overlooked due to the difficulty of combining this type of knowledge with end-to-end training. hIWe show that imposing hard constraints on linguistic embeddings in this context is superior to the corresponding soft regularizers. We also demonstrate consistent improve- ments in robustness and accuracy independent from the amount of supervised data, which supports the benefits of such training signals in complement to end-to-end annotations.
2

---

Under review as a conference paper at ICLR 2020
The contributions of this paper are summarized follows.
1. We propose a method to exploit prior knowledge expressed as relations between training in- stances when training a deep learning model. The method enforces hard constraints the inter- nal representations learned by the model while allowing end-to-end supervised training, which alleviates issues with soft regularizers.
2. We show that the method is applicable to a range of tasks and types of prior knowledge. We de- scribe its application to three generic types of relations (symmetriccequivallnees asymmetric, and set membership) and show that it does not require domain-specific expert knowledge. In many cases, the specification of constraints in embedding space is more intuitive than the alternative practice of designing regularizers in parameter space.
We demonstrate the benefits of the method on the task of VQA. We show how to exploit three types of auxiliary annotations about the training questions (equivalence, entailment, and common reasoning steps). This is the first published VQA model to make use of these annotations, which our method allows us to leverage to bring clear improvements in robustness and accuracy. Our results suggest that they provide a training signal complementary to end-to-end annotations.
RELATED WORK
Rules and prior knowledge in neural networks Approaches for including rules in machine learning either rely on priors following from Bayes rule, or on regularizers that induce constraints in the parameter space of the model. Hu et al. (016)) used posterior regularization to embed first- order rules. Their objective is to improve the predictions of a learned model to better comply with hand-designed rules describing the task of interest. In comparison, we are interested in embedding instance-level auxiliary annotations, which can be seen as rules applied only to some of the training examples. The objectives of the two methods are distinct and complementary. The major innovation of our method is to enforce hard constraints on the learned embeddings, whereas general rules in Hu et al. 2016 are softly balanced with the learned predictions.
Works on differentiable theorem proving (Rocktäschel & Riedel 2017) and neural reasoning (Peng ett al. 2015) Marra et al.) 2019) learn vector representations of symbols under constraints such as mutual proximity of similar symbols. General techniques for imposing hierarchical structure on an embedding space include order embeddings (Vendrov et al., 2016) and non-Euclidean representa- tions (Ganea et al. 2018 Nickel & Kiela 2017). In this paper, we use similar ideas to constrain the embeddings learned for a complex mulumodal task (VQA), with the objective of enforcing spe- cific (grounded) constraints, rather than imposing a prior on the overall structure of the embedding space. We propose novel training procedure to enforce these hard constraints, whereas the above works use soft objectives and regularizers. Many existing works have also described models that en- force known invariances and equivariances (e.g. Cohen & Welling (2016); Guttenberg et al. (2016); Laptev& & Buhmann (0155: Teney& & Hebert (2016)) although they each use an ad ad-hoc, task sssccsscccffcc design rather than a general technique.
In one of our use cases for VQA, we turn annotations of set membership (program annotations) into linear constraints on the learned embeddings. This bears similaritics with (Pathak et al. 2015), where the authors turned image-level tags into linear constraints to train a model for semantic image seg- mentation. They derive, from the constrained optimization problem, an objective amenable to SGD and competing constraints. Our contribution, on the opposite, shows
that is robust to how to enforce constraints strictly, which, in our applications, proved superior soft-regularized objective.
Visual question answering (VQA) The task of VQA requires model to answer a previously unseen question expressed natural language about a previously unseen image (Antol et al. 2015] Goyal et al. 2016 Teney et al., 2017): Wu et al., 2017). The mainstream approach poses VQA as a classification task over a large set of typical short answers, and it uses supervised training with a large training set of questions/answers We use VQA as testbed in this paper, because the task exposes flaws of a purely end-to-end. supervised approach (Agrawal et al. 20188] Goyal et al.) 2016 training question makes it difficult for models to capture reasoning procedures that generalize across examples and
Teney & van den Hengel 2016). The weak signal provided by the answer
domains (Chao et al.
2018 Teney & van den Hengel 2017 2019). The method proposed in this
3

---

Under review as a conference paper at ICLR 2020
paper allows using additional annotations during training. A line of works have used the CLEVR synthetic dataset (Johnson et al. 2016) and its annotations of questions as programs (sequence of reasoning steps to be carried out to find the answer) annotations are typically used to learn modular network architectures (Andreas et al., 2016a bb. but these annotations were only possible due to the closed-world synthetic nature of the dataset. The method we propose is much more flexible than these approaches. It can exploit partial annotations on subset of the data (i.e. some questions have some operations in common). It does not associate a particular meaning to operations in the programs, allowing program-like annotations that are not actually executable.
additional source of supervision. These
Shah et al. (2019) proposed generative model of questions conditioned on the answer for VQA. They used it for data augmentation while ensuring that all generated versions lead to the same an- swer, i.e. enforcing cycle consistency. One of our use cases also involves multiple forms of a same question, but these are given in our dataset, whereas Shah et al. (2019) focuses on learning them from the data.
Mao et al. 2019 combined symbolic Al with neural networks for VQA. The system learns a vocab- ulary of visual concepts, but its operation depends on a pre-specified nomain-speciffe language and designed modules. These contributions are orthogonal to ours. For example, our method could apply the representations of questions learned their semantic parser.
Distillation of neural networks The original purpose of distillation is to transfer knowledge from a "teacher" model to a "student" that uses smaller computational resources (Bucilua et al. 2006 Hinton al. 2013 Furlanello et al. 2018). In this paper of a network to produce desired embeddings. The outputs of the teacher are first projected to fit desired constraints, and the projections are then used as targets by the student. The student thereby learns the teacher's knowledge in addition to the prior knowledge represented by the constraints. The method of Hu et al. (2016) mentioned above uses teacher/student distillation procedure during training. Their best results are however obtained with the teacher network at test time, rather than the student. In our case, the distillation phase is critical to enforee hard constraints.
distillation retrain some layers
3 PROPOSED APPROACH
3.1 OVERVIEW
The intuition behind our approach is that the knowledge we wish to incorporate can serve to shape the space of the learned representations. First, we translate this task-specific knowledge into con- straints to be placed on representations learned by the model. This translation does not necessarily require domain knowledge. Our experiments on VQA demonstrate three generic types of constraints (vector equality, norm inequality, and linear programs). As one specific example, the knowledge of equivalence between pairs of questions as in Fig. | translates to constraint of equality of their corresponding embeddings Φ and 222 We then train network that strictly respects these con- straints thanks to two-phase procedure (see Fig. 2). In the first phase, we optimize the network end-to-end for the target task objective, with a regularizer that encourages a soft version of the con- straints (the distance ||z x; 2| in the above example). We also insert a special operation in the network that projects x; onto xi, that lies on the manifold where the constraints are strictly met, The subsequent layers only receive this version æy of the embeddings, such that they are optimized to deal with embeddings that satisfy the constraints. The first phase ends once overfitting is detected (early stopping). At this point, the soft regularizer only helped to loosely fit the constraints since the optimization is interrupted before the loss reaches its minimum. The second phase then serves to improve the fit to the constraints, without further overfitting the task objective. the second phase, the output layers are thus frozen, and we retrain the earlier layers with a distillation objective, using ar as targets (which do respect the constraints). Since the output layers are frozen, this second phase can proceed convergence, i.e. until these earlier layers produce embeddings that perfectly fit of the desired constraints.
The following describes each phase formally. Additional details provided in the appendix.
4

---

Under review as a conference paper at ICLR 2020
Input imguqq
Question embedding
Fusion classirier
embedding
9d
54
Mup
projection
answers
30
2
Loqu
Regularizer(s)
CvQu
Ldst
Distillation loss
(a) Training phase I
(b) Training phase
(c) Test time
We propose two-phase training procedure to combine task supervision with hard con- straints on learned embeddings. the first phase, the model is trained with the end-to-end supervi- sion (task loss), regularizers that represent soft versions of the constraints, and internal projection of the embeddings (see text for details). In the second phase, the embedding layers are retrained with distillation objective, using the projected embeddings targets. The trained layers are highlighted.
Figure 2:
3.2 PHASE I: TASK LOSS AND SOFT REGULARIZERS
We first train all layers of the network end-to-end. In the model depicted in Fig. these layers make up the functions f-(-). (o(-), and h(-). We use the supervised task loss together with soft regularizers. The task loss for VQA the binary cross-entropy LvQA (a, à) where hot encoding of the ground truth answer. The soft regularizers encourage embeddings to respect the constraints defined the previous section. For the equivalent questions, we use the squared L2 distance: Lequ (2), 22) = ||22- 111... For the entailed questions, we the difference of p-norms: Lent (I), cross-entropy on top of logistic regression that uses the boundary of the half-space associated with Ho,((o + 6y); [(ok E Q:)). See Table for
the one-
max (0, | | For the annotations of operations, we use the binary
Oş as its decision boundary: (x,) summary.
The model is optimized with objective that combines the task loss with the three regularizers:
min 8 (wx)).)
E, Lvqa(a,;ee
+ Aoqu Lequ (Ii, Fequ(i))
Aent Lene (x,, Fent(())
Aaps (a.)(
where the functions equ(i) and ent(i) sample training instances respectively equivalent to, and entailed by the ith one. The factors Angus Aent, and Aops non-negative scalar hyperparameters (see Section D). This objective encourages the embeddings to follow the desired constraints in a soft manner, balanced with the end-to-end task objective. However, some constraints are known to be exact. Taking the case of equivalent questions as an example, the network must learn identical representations for synonymous questions. We therefore project the learned embeddings {æ,) onto { in such way that they collectively respect the desired constraints. The projected embeddings are then used by the remaining of the network, i.e. hy y). In this way, the remaining layers are optimized use embeddings that perfectly respect the constraints, which supports the second training phase described below.
The projection functions are given in Table bottom row. For equivalent questions, we replace their embeddings by their arithmetic mean to make them identical. For entailed questions, we normalize them to the mean of their norms make the incquality constraint just satisfied. For the program operations, we perform descent on the gradient of Lxp)(x;) for a fixed number of steps (see appendix for details). This identifies local projection x that best respects the constraints resulting from the constituent operations of the question, even when the conjunction of these constraints is not strictly feasible.
3.3 PHASE 2: ENFORCING HARD CONSTRAINTS BY DISTILLATION
The second step of our training procedure aims improving the layers (fa) that produce the embed- dings such that the constraints are more closely respected. In principle, this could be achieved with the soft regularizers, but in practice, the task loss often converges at different rate than the regu- larizers regardless of the weights assigned to each term in the objective. Indeed, carly stopping is usually employed prevent overfitting before the convergence of the regularizers. A naive, fur-
5

---

Under review as a conference paper at ICLR 2020
Table I: Summary of the constraints, soft regularizers, and projection functions for the three types of annotations we use for VQA. The figures are conceptual representations in a 2D embedding space.
Equivalent questions
Entailed questions
Functional programs (operations)
Q Q2
Q1
Q2
Q, (2,,0,,.. O2, ok,}
Constraints on question embeddings
3 20
| 1be 2 ||2 lp
Moozeq (WLR: by 2 0) NBoLEO1Q: (WERs + by < 0)
(using p = 1)
Soft regularizers
Cequ (21, x2)
(e1 222) max (0, 1|222le - 111))
(xps EQ, loglo(wsaa;
|| x1 2
Exro, log( 1-o lo (wxg
Projections to enforce hard constraints
(z)
+
ar
|
o = m. then, for steps:
2
1 1pp
2
(2) + m2)
222
+ |malle
of + x V Cops((r))
1
wa
11
2/2
ther training using the regularizers alone will cause the learned embeddings to diverge from the task objective and performance will decrease. Our solution is to retrain the layers = [e(() by distilla- tion, using the projected embeddings x' as targets (Fig. 2). Practically, the other parts of the network are frozen (go() (-) and (-)) and we optimize the following objective: ming. E. ||ar x 2|2 with = for(f() (Q). This objective uses an L2 loss with x' as the targets. The key here is to hold these targets fixed during the distillation (i.e., they remain the projection of the embeddings obtained the end of first phase of training). There is now no risk of overfitting on the target task (not any further than at the time the distillation is started) and the only factor driving an evolution of the network is the objective of closely following the constraints resulting from the projection.
3.4 APPLICATION TO VISUAL QUESTION ANSWERING
Baseline VQA model The proposed method is generally applicable to a variety of tasks and ar- chitectures. We now describe its application to the context of VQA used in main experiments. We abstract a VQA model as depicted in Fig. 2. The input question Q and image are passed through the embedding functions fo(-) and g-( respectively. The first is typically word embed- ding followed by an LSTM or GRU, while the second is typically a CNN or R-CNN feature extractor followed by non-linear transformation. These embedding layers produce the vector represen- tations x = (Q() and g ()), with x E R-M E R These vectors are passed to a fusion and output stage that produces the vector a hyg(x, (x, y) containing scores over a large set of candidate answers. Attention mechanisms are contained within /1()) with the given notations, leaving æ and y purely unimodal. This general notation encompasses all "joint embedding" approaches typically used for VQA (Wu et al. (017) and the contributions of this paper are agnostic to the underlying implementation.
Embedding-space constraints for VQA We consider three exemplar forms of prior knowledge for VQA that can be used independently or in conjunction. We first describe how to translate this task-specific knowledge to constraints that we will enforce on the question embeddings æ, learned within the model. Refer to Table for summary.
1. First, we consider relations of equivalence between questions, denoted by Q1 = Q2 Such questions are rephrasings of one another, using synonyms or linguistic patterns that do not affect their overall meaning (see example in Fig. [ We naturally translate this to a constraint of equality of the embeddings, that is æ 222

---

Under review as a conference paper at ICLR 2020
2. Second, we consider relations of entailment between questions, denoted by Q1 Q2- This generally corresponds to a specific question being informative to answer a more general one, e.g. Is there blue car in the picture Yes. = Is this a car ? Yes. The major distinction with equivalence relations is that entailment is generally not symmetric. Motivated by works on order
emheddings (Vendrov al. 2016) and hyperbolic networks (Ganea et al.) 2018 Nickel & Kiela 2017), we impose an order on the p-norm of the learned embeddings, such that [1 The L1 norm proved the most effective in practice.
22
3. Third, we consider annotations of functional programs, i.e. the reasoning operations involved in each question. A question can be translated to a set of operations Q; {01,02, Ok, with OF E O, a large vocabulary of possible operations (see Section D). In order to deal with the variable size of such definition (the number of operations often depends on the length and complexity of the question), we translate such a definition of question to the membership of its embedding to the intersection of subspaces associated with its operations (see Table lower- right). The subspaces are learned: for each possible operation Ok O, we define its associated subspace as {æ w + by 2 0} with learned vector wa E IR and scalar bg Since a question usually involves multiple operations, its embedding is subject to conjunction of constraints as defined in [able
A practical benefit of our overall approach is its ability to use partial annotations. In other words, not all of the above true relations need to be specified. This is particularly relevant for the functional programs, where only some of the operations of some questions may be annotated.
EXPERIMENTS
4.1 EXPERIMENTS ON A TOY TASK: SEQUENTIAL ARITHMETIC
We first evaluate the method controlled conditions. We designed a simple arithmetic task which the model receives integer digit 2 E 1-9. +9] input, together with variable-length sequence of operations {or .... each one being an addition or multiplication with an integer digit. The desired output is the result of the application of these operations in sequence (i.e. without taking into account precedence, see Fig. 3). We build a simple baseline model to learn this task from a supervised dataset (see details in appendix [B). This model first maps every token input (digit and operations) to a vector embedding. The operation vectors are passed through GRU. The final state of the GRU (corresponding to æ in Section is concatenated with the embedding of the input digit (w) and passed through an MLP with a linear output layer. The model is optimized by SGD for regression loss (squared L2). Note that the input digit and operations are embedded separately so that we can apply constraints on the embedding of the operations alone.
The proposed method is used on this task as follows. We generated, with our training set, ad- ditional annotations of sequences of operations that are known be equivalent. For example, the training instances {3, +1, +2, = 8) and f4,+2, 22 = 10} are marked as such, since (.r * 2 ((x * 2) 2) + 4 for all z. These experiments test whether annotations of equiva- lent sequences are complementary to training examples, where the operations are demonstrated on specific s's. These annotations are naturally translated into constraints of equivalence of the embed- dings of operations æ as described in Table D. column 1. We compare in Fig. 3 the effect of our method with baseline that uses a standard soft regularizer (squared L2 distance) to minimize the distance between the embeddings of equivalent sets of operations (the weight of this regularizer is tuned by cross-validation). Our method proves more effective with all tested amounts of training data and amounts of additional annotations. The data augmentation baseline consists in replacing the set of operations of a training example by another equivalent one, sampled at random from other training examples. This is a particularly strong baseline as seen in Fig. 3 but importantly, it is only relevant for relations of equivalence, while the proposed method has much wider applicabil- ity. Finally, the use of these additional annotations shows significant benefits over a model trained solely from end-to-end supervision across range of number of training examples. This further sup- ports the overall benefit of leveraging complementary training signals in additional to supervised, end-to-end training.
7

---

Under review as a conference paper at ICLR 2020
Inout digit operetions
ourput
Regression objective
100
3
Embedding
MLP
15
Embedding
GRU
+
80
Squared L2 loss
3
Accurory (56)
70-
60
50
40
Propoond mithoel
Baseline with data aupoentation
30
Baseline togulatiarr
Baseline, end-toomt tinining only
Number of training examples
Boseline
Proposed
Figure 3: Experiment on a toy task for sequential arithmetic (see Section 4.1p. The baseline model (top left) takes in a digit and sequence of operations, and is trained with supervision to predict the result. We use the proposed method to exploit auxiliary annotations of equivalence between sequerey
sequences of operations from multiple training examples. This brings significant improvements in accuracy (right plot) over the baseline and over classical techniques that use the same additional annotations. We visualize T-SNE projections (bottom right) of the learned representations (x:) of sequences of operations from the test set with the baseline (left) and the proposed model (right; 1000 points in both cases). We draw gray lines between the representations of equivalent sets operations: with the proposed method, equivalent representations are virtually identical (only one gray line is visible).
4.2 EXPERIMENTS ON VISUAL QUESTION ANSWERING
We conducted an extensive set of experiments to evaluate the proposed method on top of a popular VQA model (the Bottom- Sae--UUUTTppp Siip-TTp-Dooo -own Attention, BUTD of Anderson et al. (2018); Teney et al. (018 ) We use the GQA dataset (Hudson & Manning 2019). which contains all three types of annotations discussed in Section 3.4 Details on the implementation and on the data are provided in the supplementary material.
Ablative evaluation We first evaluate the three types of annotations in isolation (see Table Op- timal loss weights were determined empirically as =0 A2=0.1, and A3=0, for best performance on the validation set. In the following experiments, we set the weights of the losses not used to 0,
Equivalent questions. We first evaluate a simple baseline to use equivalent questions by data augmentation. We simply replace questions at random during training by any of their equivalent forms (including themselves). The resulting model (row 2) is actually slightly worse than the original one. Training with the proposed soft regularizer, in contrast, provides significant im- provement accuracy. Adding the projection to further constrain the embeddings has minimal effect on its own, but it allows to retrain the embedding layers by distillation, which provides another clear boost in performance (see also Fig. 3). We compare two variants: a distillation "stu- dent" initialized from scratch, or initialized with the weights of the teacher. The former option follows more closely the intent of the original works on distillation (Bucilua et al.) [2006] Hin- ton et al., 2015 Furlanello al. 2018). Intuitively, a re-optimization from scratch might better exploit the gradients of the distillation loss and lead the SGD through less circuitous path than the loss used when training the teacher. In practice, both options performed well with slight advantage for fine-tuning.
Entailed questions. We compare two types of soft regularizers. The first, as a baseline, is the same 1.2 distance as used for the equivalent questions (row 7). The second, our proposed order on L11 norms proves clearly superior (row 8). Entailment relations are asymmetric and this can- not be captured with the L2 distance. We experimented with the reverse order in the proposed formulation (swapping the premise and consequence) and results were similar (not in the table). This further confirms that the key to model the asymmetry in the relations. We also exper- imented with alternative options, including order embeddings (Vendrov et al.) 2016) and order on L2 norms, neither which matched the performance of the order on LI norms. Adding the projection and the distillation has again positive effect.
8

---

Under review as a conference paper at ICLR 2020
GQA test-dex accuracy (96)
55
Proposed method, with
equisalent quastioons
Baseline
40
0
0.2 0.4
0.6
0.8
Praction training used
Figure 4: We compare the proposed method with the baseline trained with reduced amounts of data. The absolute improvement over the baseline is consistent and maintained regardless of the amount of training data used. This suggests that the additional information brought in truly complementary to end-to-end supervision. Model used: row (6) in Table 2 we plot the mean accuracy of four single models trained with different random seeds; error bars represent +/- one standard deviation.
Table 2: Ablative evaluation on GQA (answer accuracy in percents). Every experiment was repeated with four different random seeds. We report the mean and standard deviation of single models, the performance of the ensemble of these four models as in Teney et al. (2018).
Method
GQA validation
GQA test-dev
CNN+LSTM (Hudson & Manning 2019)
49.2
BUTD, implementation of Hudson Manning 2019
52.2
MAC (Hudson Manning 2018)
57.5
Our BUTD baseline
58.9 + 0.2
61.5
51.3 + 0.6
54.2
Equivalent questions
( Data augmentation
58.4 + 0.2
61.5
51.0 0.4
53.8
(3) Soft regularizer
59.1 + 1.1
61.5
52.4
54.7
(4) Soft reg. + projection
59.9 0.1
62.0
52.3
1
55.0
(5) Soft reg. + proj. + distillation
59.9 1 0.3
62.4
52.2
0.3
54.5
Soft reg. + proj. distillation (fine-tuned)
60.3 0.1
62.5
52.9
1 0.4
55.2
Entailed questions
Soft regularizer (symmetric L2 dist.)
58.6 4.4 0.4
61.3
51.5
54.3
(8) Soft regularizer (proposed)
59.2 1 0.2
61.4
52.0
544
(9) Soft reg. + projection
59.0 + 0.3
60.8
0.5
54.5
(10) Soft reg. proj. + distillation
59.7 + 0.2
61.7
5.3
54.3
Soft reg. proj. distillation (fine-tuned)
59.8 0.2
61.7
5.4
54.7
Functional programs
Soft regularizer
59.0 + 0.4
61.4
5.3
53.9
(13) Soft reg. projection
58.4 0.3
61.2
5..9
53.5
(14) Soft reg. proj. distillation
59.1 0.3
61.4
5..7
54.0
(15) Soft reg. + proj. + distillation (fine-tuned)
59.4 = 0.2
61.6
5..
54.4
(16) Combination (6) + (11)
59.9 0.2
61.9
5..
54.9
(17) Combination (6) +15)
59.6 + 0.2
61.8
51.9
54.3
Combination (11) + (15)
59.8 + 0.2
62.1
52.7
54.8
(19) Combination (6) (1 (15)
60.7 0.1
62.7
53.4 1
0.3
55.7
Annotations of functional programs. The use of these annotations with our method shows small but positive improvement over the baseline. Again, the soft regularizer is effective its own, and the additional projection combined with the distillation bring an additional improve- ment. Remember that different from existing methods that rely on complete program annotations to train modular archi- tectures. Our method can partial annotations and should more easily extend other datasets and human-produced annotations.
using here only limited vocabulary of operations, which is very
Combinations. Finally, we combine the best version of each the three constraints (last rows). The results show that they complimentary to each other, since the best results obtained with the full combination. Note however that the relations of equivalence and entailment could, in principle, be deduced from the functional programs. This shows that our handling of program

---

Under review as a conference paper at ICLR 2020
annotations is still suboptimal. An ideal method should get the full benefits from using program annotations alone.
Comparison to existing methods Finally, we compare our method to existing models using the extended set of metrics proposed in Hudson & Manning (2019) (see Table 3 in the appendix for the full results). Our method performs better than the complex MAC model. More interestingly, vastly improve on the metric of consistency, which measures the accuracy over sets of related questions about a same image. This is precisely the type of benefit that was expected from our approach.
Finally, in Fig. 3, we plot the accuracy of the model trained on varying amounts of training data, with a baseline and with the proposed method and annotations of equivalence (although similar trend was observed for the other types of annotations). Very interestingly. the absolute improvement the baseline is consistent and maintained regardless of the amount of training data used. This strong result suggests that the training signal provided through these additional annotations is truly complementary to the answer annotations, and that this knowledge is otherwise difficult for the model to learn from end-to-end supervision alone. This reinforces the overall motivation for bringing in prior knowledge to the training of deep models.
CONCLUSIONS
We presented an approach to incorporate prior knowledge in deep learning models in the form of constraints on its internal representations. We then applied the method the task of VQA to lever- age multiple types of relations between training questions. This application is of particular interest because VQA is prime example of a task where the end-to-end supervised paradigm shows its lim- its. due to the long chains of reasoning that connect the inputs and outputs. The proposed approach served to shape the space of the internal representations learned by the model. Our experiments with the GQA dataset showed clear benefits in improving the accuracy and robustness of an exist- ing VQA model. Interestingly, these benefits hold regardless of the amount of training data used for end-to-end supervision, suggesting that the type of prior knowledge used cannot otherwise be effectively captured in the model through end-to-end annotations alone. Technically, the proposed method treats the additional knowledge hard constraints the model's 's internal representations. This proved more clearly effective than existing methods to exploit this type of annotations, includ- ing soft regularizers and data augmentation.
The proposed method can apply to a variety tasks and domains that we hope to explore in future work. Concrete applications overlap with those considered for topological embeddings such as learning representations for knowledge bases, and other tree- or graph-structured data (Ganea al. 2018 Nickel & Kiela, 2017] Vendrov et al. 2016). Enforcing hard constraints on a learned model also allows one provide guarantees that otherwise impractical meet with purely data- driven approach. In particular, the method could be used to integrate known causal relations in a model. known outcomes of interventions on specific training examples. This holds the promise of making further steps toward generalizable and trustworthy machine learning models.
REFERENCES
Aishwarya Agrawal, Dhruv Batra, Devi Parikh, and Aniruddha Kembhavi. Don't just assume; look and answer: Overcoming priors for visual question answering. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn,, 2018
Peter Anderson. Xiaodong He, Chris Buehler, Damien Teney, Mark Johnson, Stephen Gould, and Lei Zhang. Bottom-up and top-down attention for image captioning and vqa. CVPR, 2018.
Jacob Andreas, Marcus Rohrbach, Trevor Darrell, and Dan Klein. Neural Module Networks. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., 2016a.
Jacob Andreas, Marcus Rohrbach, Trevor Darrell, and Dan Klein. Learning to compose neural networks for question answering. 2016b.
Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zit- nick, and Devi Parikh. VQA: Visual Question Answering. In Proc. IEEE Int. Conf. Comp. Vis., 2015.
10

---

Under review as a conference paper at ICLR 2020
Cristian Bucilua, Rich Caruana, and Alexandru Niculescu-Mine Model compression. In Pro- ceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 535-541. ACM, 2006.
Wei-Lun Chao, Hexiang Hu, and Fei Sha. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), June 2018.
adaptation for visual question answering.
Taco Cohen and Max Welling. Group equivariant convolutional networks. In International confer- ence on machine learning, pp. 2990-2999, 2016.
Tommaso Furlanello, Zachary C Lipton, Michael Tschannen, Laurent Itti, and Anima Anandkumar. Born again neural networks. arXiv preprint arXiv:1805.04770 2018.
Octavian Ganea, Gary Bécigneul, and Thomas Hofmann. Hyperbolic neural networks. In Proc. Advances in Neural Inf. Process. Syst. pp. 5345-5355, 2018.
Tobias Glasmachers. Limits of end-to-end learning. arXiv preprint arXiv:1704.08500 2017.
Yash Goyal, Tejas Khot, Douglas Summers-Stay Dhruv Batra, and Devi Parikh. Making the V in VQA matter: Elevating the role of image understanding in Visual Question Answering. arXiv preprint arXiv: 2016
Nicholas Guttenberg, Nathaniel Virgo, Olaf Witkowski, Hidetoshi Aoki, and Ryota Kanai. Permutation-equiivrraat neural networks applied to dynamics prediction. arXiv preprint 1w 2016.
Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge neural network. arXiv 2015.
preprint arXiv:1503.00
Zhiting Hu, Xuezhe Ma. Zhengzhong Liu, Eduard Hovy, and Eric Xing. Harnessing deep neural networks with logic rules. Proc. Conf. Association for Computational Linguistics, pp. 2410- 2420, 2016.
Drew A Hudson and Christopher D Manning. Compositional attention networks for machine rea- soning. arXiv preprint 1rX3v:1803.0030 180..03067 2018.
Drew A Hudson and Christopher D Manning. Gqa: A new dataset for real-world visual reasoning and compositional question answering. In Proc. IEEE Conf. Comp. Vis. Patt. Recogn., 2019.
Justin Johnson, Bharath Hariharan, Laurens van der Maaten, Li Fei-Fei, C. Lawrence Zitnick, and Ross B. Girshick. CLEVR: A diagnostic dataset for compositional language and elementary visual reasoning. arXiv preprint 112.v:661. 2016.
Dmitry Laptev and Joachim M Buhmann. leanforratiioninvaaraaa convolutional jungles. In Pro- ceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3043-3051, 2015.
Jiayuan Mao, Chuang Gan, Pushmeet Kohli, Joshua B Tenenbaum, and Jiajun Wu. The neuro- symbolic concept learner: Interpreting scenes, words, and sentences from natural supervision. arXiv preprint arXiv: 1904. 12584, 2019.
Gary Mareus. Deep learning: critical appraisal. arXiv preprint arXiv:1801.0063 2018.
Giuseppe Marra, Francesco Giamnini, Michelangelo Diligenti, and Marco Gori. Integrating learning and reasoning with deep logic models. CoRR, abs/1901 abss/1901.0419.. 2019.
Maximillian Nickel and Douwe Kiela. Poincaré embeddings for learning hierarchical representa- tions. In Proc. Advances Neural Inf. Process. Syst., pp. 6338-6347, 2017.
Steven J Nowlan and Geoffrey E Hinton. Simplifying neural networks by soft weight-sharing. Neural computation, 4(4):473-493) 1992.
Deepak Pathak, Philipp Krahenbuhl, and Trevor Darrell. Constrained convolutional neural networks for weakly supervised segmentation. Proceedings of the IEEE international conference on computer vision, pp. 1796-1804 2015.
11

---

Under review as a conference paper at ICLR 2020
Baolin Peng, Zhengdong Lu, Hang Li, and Kam-Fai Wong. Towards neural network-based reason- ing. arXiv preprint arXiv:1508. 05508, 2015.
Tim Rocktäschel and Sebastian Riedel. End-to-end differentiable proving. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (eds.), Proc. Ad- vances in Neural Inf. Process. Syst., pp. 3788-3800. Curran Associates, Inc., 2017.
Meet Shah, Xinlei Chen, Marcus Rohrbach, and Devi Parikh. Cycle-consistency for robust visual question answering. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 6649-6658, 2019.
D. Teney, Q- Wu, and A. den Hengel. Visual question answering: A tutorial. IEEE Signal Processing Magazine, 34:63-75, 2017.
Damien Teney and Martial Hebert. Learning to extract motion from videos in convolutional neural networks. In Asian Conference on Computer Vision, pp. 412-428. Springer, 2016.
Damien Teney and Anton van den Hengel. Zero-shot visual question answering. CoRR, abs/1611.0555 1.005466,, 2016.
Damien Teney and Anton van den Hengel. Visual question answering meta learning task. 2017.
Damien Teney and Anton den Hengel. Actively seeking and learning from live data. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019.
Damien Teney, Peter Anderson, Xiaodong He, and Anton van den Hengel. Tips and tricks for visual question answering: Learnings from the 2017 challenge. CVPR, 2018.
Ivan Vendrov, Ryan Kiros, Sanja Fidler, and Raquel Urtasun. Order-Embeeddings of Images and Language. In Proc. Int. Conf. Learn. Representations. 2016.
Qi Wu, Damien Teney, Peng Wang, Chunhua Shen, Anthony Dick, and Anton van den Hengel.
Visual question answering: A survey of methods and datasets. Computer Vision and Image Un- derstanding, 2017. ISSN 1077-3142.
Anthony M Zador A critique of pure learning and what artificial neural networks can learn from animal brains. Nature communications, 10(1):1-7, 2019.
12

---

Under review as a conference paper at ICLR 2020
A
APPENDIX
B IMPLEMENTATION OF THE BASELINE MODEL FOR THE TOY TASK
The hyperparameters and implementation details of the model used for our toy task were set manu- ally for reasonable performance of the baseline model. Most importantly, they were not particularly tuned for optimal performance of the proposed contributions. The size of learned embeddings and all other layers (GRU state, MLP hidden layers) is fixed to 64. We train the model with AdaDelta with mini-batch of size 64. The MLP uses a single layer of gated tanh units (Teney et al. 2018) followed by linear layer for the regression output. The task loss is the square L2 distance between the model's output and the ground truth value. The ground truth output is always an integer, so we define, as the evaluation metrie, the accuracy as the ratio of test instances for which the output rounded to the nearest integer is correct (i.e. the predicted output is within less than 0.5 from the ground truth).
To produce the dataset, we generate every possible instance of the task with a sequence of one to three operations. We reserve 20k of these for validation (i.e. model selection and early stopping) and another 20k random fraction depending on the experiment. The code to generate our toy dataset and replicate the experiments will be made available once anonymization issues cleared.
test set. The remaining serves the training data, of which we use
C IMPLEMENTATION OF THE BASELINE MODEL FOR VQA
The VQA model within our method follows the description of Teney et al. (011)). We started with publicly available implementation of the model. Importantly, all hyperparameters of the BUTD model were first selected for the best baseline performance on the GQA dataset, and were not specifically re-tuned for the contributions of this paper. They were selected by grid search and follow closely Teney et al. (2018).
More specifically, the non-linear operations in the network use gated hyperbolic tangent units. We use the "bottom-up attention" features from Anderson et al. (2018) of size 2642088, pre-extracted and provided by Anderson et al The word embeddings are initialized as random vectors (rather than pretrained GloVe vectors) and normalized to unit L2 norm before being passed to a GRU. We found this to help with the stability of the training and final accuracy, independently from the contributions of our paper. The word embeddings are of dimension 300, and all other layers use embeddings of size 512. The output of the network passed through a logistic function to produce scores in [0, 1]. The final classifier is trained from random initialization, rather than the visual and text embeddings of Teney al. 2018). We use Adadelta as the optimization algorithm.
C.1 TIME COMPLEXITY
The time complexity as a function of dataset size is the same with our method as with standard training. There is a fixed overhead, for each mini batch, to retrieve the data needed to compute the regularizer (e.g. equivalent questions), which is stored alongside the training examples. There is also an additional cost in running the second training phase (distillation). This only involves retraining few layers for a handful of epochs.
D IMPLEMENTATION OF THE PROPOSED APPROACH
Every experiment was repeated four times with different random seeds. We report the mean and standard deviation of answer accuracy of each of the four runs, as well as the result of ensembling the four models by simple averaging of their outputs (predicted scores). Other metrics proposed Hudson Manning (2019) are also reported. During training, mini-batches are sampled nor- mally. At most one equivalent and one entailed question (depending on the experiment) are then selected at random, for each question in the mini-batch. Note that many training question do not
13

---

Under review as a conference paper at ICLR 2020
have any equivalent/entailed one, while some have several. In the projection by gradient descent in Section 3.2, the number of steps T=10 and the step size a=0.01. To train networks with distillation, the switch from the first to the second phrase of training occurs when the accuracy the validation set (test-dev) stops increasing for three epochs.
During the first phase of training, we need backpropagate the gradient of the loss through the projection function. When using equivalent and entailed questions, the gradient of the projection trivial. When using functional programs, the projection is fixed number of steps of gradient descent (see details in the main paper). For the ease of implementation, we approximate its gradient with the identity function.
E VQA DATASET
We used the GQA dataset for all our experiments (Hudson & Manning 2019). It contains all three types of annotations discussed in this paper. More precisely, for each training question, the dataset provides a set of variable size (possibly empty) of equivalent and entailed questions. It also provides a list of reasoning operations involved in the question. This list uniquely defines the question and vice versa. We use all relations of equivalence. For the relations of entailment, we only keep those involving questions with the same answer. This constitutes most of them, and exceptions are of form such as What is the color of the car? ? Blue. + Is the car blue ? Yes. or Is the kid to the left of the tree ? Yes. Is the tree to the left of the kid ? Yes.. To use the annotations of functional programs, we pre-build a vocabulary of possible operations. We select operations (unique function/argument combinations) that appear least 1,000 times in the training set. This corresponds 354 operations that cover 78% of all annotated operations. All other operations are not used. We use the official balanced training set for training, and the official validation set for hyperparameter tuning and model selection. We used the test-dev and test set for evaluation in tables and respectively.
Equivalent and entailed questions In the annotations provided with the GQA dataset (Hudson & Manning, 2019), number of pairs of entailed questions are also equivalent questions. We specif- ically removed those from the entailed questions, such that they form two disjoint sets. Since we propose two techniques for these two types of annotations, it allows evaluating them in isolation. is also worth mentioning that entailment relations are occasionally dependent on the answer to the premise. For example, the question Is there a couch or a table that is not brown entails the ques- tion Do you see white table in picture only if its answer is negative. In our method, constraints are enforced on the embedding of the question alone. However, this does not prevent the whole network to encode answer-dependent relations, since the (constrained) question embeddings further interact with the image and answer representations in the latter layers of the network.
Vocabulary of operations We use annotations of questions as functional programs only with a limited set of operations. The set of all possible operations (combinations of functions and argu- ments, see (Hudson & Manning 2019) very large, follows a long-tail distribution, and the rare operations will not provide our method with useful information (since it relies the re-occurrence of operations across multiple questions). To define the vocabulary of operations O used in our exper- iments, we selected operations (unique function/argument combinations) that appear at least 1 1,000 times in the training set. This corresponds to 354 operations that cover 78% of all annotated opera- tions. Annotations of other operations are discarded and not used in our experiments. The threshold of 1,000 was chosen among the values {100, 200, 500, 1000, 2000, 4000) for best performance. A larger vocabulary (smaller threshold) did not, but much smaller vocabularly (higher threshold) clearly decreased the benefit of our method.
14

---

Under review as a conference paper at ICLR 2020
Table 3: Additional results: extended metrics the GQA test (Hudson & Manning 2019
Our method consistently improves the consistency metric, which measures agreement across related questions about a same image.
Method
Accuracy
Open
Binary
Validity
Plausibility
Consistency
Humans
89.30
87.40
91.20
98.90
97.20
98.40
CNN+LSTM
46.55
31.80
63.26
96,02
84.25
74.57
MAC (Hudson & Manning 2019
54.06
38.91
71.23
96.16
84.48
81.59
Our BUTD baseline
53.53
38.54
70.57
96.29
84.20
83.30
W. equivalent questions (6)
54.86
40.27
71.45
96.72
85.02
84.92
W. entailed questions (11)
54.33
39.63
71.04
96.71
84.98
85.48
W. functional programs (15)
54.66
40.86
70.36
96.63
84.63
85.11
Combination (19)
55.35
40.68
72.05
96.72
84.92
87.83
15


Reviews:
[{"review_id": "rkgQW97pKS", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 3, "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 proposes the incorporation of “prior knowledge” which enters in the form of the relations between training instances in neural network training. The proposed method is tested on VQA problem, bringing improvements upon the popular soft regularizer. \nThe authors claim that their method is a general technique but in fact, the constraints are drawn from specific tasks (VQA for example). So, I believe the contribution is rather domain-dependent and not general. Can you explain more how this method can be applied to general problems?\n\nOther than that, I have some concerns:\n1. Although the authors claim that they are the first to bring these annotations to VQA, I see their training procedure is closely related to cycle-consistent learning. Recent work in VQA also applied cycle consistency as an online data-augmentation technique (See Shah et al. 2019).\n“Shah, M., Chen, X., Rohrbach, M., & Parikh, D. (2019). Cycle-consistency for robust visual question answering.”\n2. In Section 2, the authors say “constraints on the parameter space of a model are often non-intuitive”. How are they \"non-intuitive\" and why the proposed method is more intuitive in terms of theory? Please clarify this.\n3. Each question in Hud et al. is associated with a functional program, therefore, questions are compositional. However, arbitrary questions don’t need to strictly follow this constraint. Natural language is not exactly suited to functional programming I think. I have doubts about the claim in Section 4 “Our method can use partial annotations and should more easily extend to other datasets and human-produced annotations”. Also, the definition “A question is defined as a set of operations” does not seem correct. A question can be translated into a program that is composed of a set of operations.\n4. Experimental results are not strong enough for such strong claims I believe. Regarding GQA dataset, the authors should compare the proposed method with more works, for example, Hu et al. 2019 and Hudson et al. 2019 achieve much favorable performance upon MAC.\n\"Hu, R., Rohrbach, A., Darrell, T., & Saenko, K. (2019). Language-Conditioned Graph Networks for Relational Reasoning.\" \n\"Hudson, D. A., & Manning, C. D. (2019). Learning by abstraction: The neural state machine.\"\n\nMinor comments: The paper is not really well written. I even found a wrong reference (Section 3).\n", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "SyxXGwWjKB", "reviewer": "AnonReviewer2", "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": "The paper argues for encoding external knowledge in the (linguistic) embedding layer of a multimodal neural network, as a set of hard constraints. The domain that the method is applied to is VQA, with various relations on the questions translated into hard constraints on the embedding space. A technique which involves distillation is used to satisfy those constraints during learning.\n\nThe question of how to encode external knowledge in neural networks is a crucial one, and the limitations of end-to-end learning with supervised data is well-made. Overall I feel that this is a potentially interesting paper, addressing an important question in a novel way, but I found the current version a highly-frustrating read (and I read the paper carefully a number of times); in fact, so frustrating that it is hard for me to recommend acceptance in its current form. More detailed comments below.\n\nMajor comments\n--\nThe main problem I have with the paper lies with the first part of section 3, which is a key section describing the main method by which the constraints are satisfied during learning. This is very confusing. The need for the two-step procedure, in particular, and the importance of distillation needs much more explanation, and not relegated to the Appendix (which reviewers are not required to read - see call for papers). I'm not suggesting that the whole of the appendix needs moving to the body of the paper, but I would suggest perhaps 1/2 a page.\n\nA related comment is the use of the distillation technique. This looks crucial, but I don't believe distillation is mentioned at all until the end of the related work section, and even there it comes as a bit of a surprise since there's no mention anywhere of this technique in the introduction.\n\nI would say a little more about the distinction between the embedding space and parameter space, since you say that the external knowledge is encoded in the former and not the latter, and this is important to the overall method. Since embeddings are typically learned (or at least fine-tuned) it's not clear where the boundary is here. Another comment is that embedding space in this paper means the linguistic embedding space. Since this is ICLR and not, eg, ACL, I would make clear what you mean by embedding space.\n\nI don't understand the diagram in Fig. 3 of the architecture, nor the explanation. What's an operation here? Is it *, or *6? I don't get why 3 is embedded by itself in the diagram, and then combined with the remainder using the MLP. Why not just run the RNN over the sequence?\n\nWhy are the training instances {3,+1...} and {4,*2,...} equivalent. I stared at this a while, and still have no idea. Also, how are these \"known to be equivalent\" - what's the procedure?\n\nMinor comments including typos etc.\n--\nThe paper has the potential to be really nicely written and well-presented. Currently it reads like it was thrown together just before the deadline (which only adds to the overall frustration as a reader).\n\nIn fig. 1 the second equivalent question example is interesting, since strictly speaking \"box\" and \"rectangular container\" are not synonyms (e.g. boxes can be round). Since strict synonymy is hard to find, does that matter? (I realise the dataset already exists and was presented elsewhere, but this might be worth a footnote).\n\nmissing (additional) right bracket after Herbert (2016)\n\nNot sure footnote 1 needs to be a footnote. It's already been said, I think, but if it does need repeating it probably deserves to be in the body of the text.\n\nbetween pairs questions\n\nsee Fig.3 -> figure 2?\n\nsee Fig.1 -> Tab. 1? (on p.5)\n\nfootnote 1 missing a right bracket\n\nusually involve -> involves\n\n+9]) - extraneous bracket\n\nFig. 4.1 -> Fig. 3? (p.6)\n\np.7 wastes a lot of space. In order to bring some of the appendix into the main body, I would do away with the very large bulleted list. (I don't mean lose the content - just present it more efficiently)\n\nRemember than\n\nFinally in Fig. 4.2 - some other figure\n\ndue of the long chains", "extra_scores": {"experience_assessment": "I have published in this field for several years.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I assessed the sensibility of the derivations and theory."}, "extra_text": {}}, {"review_id": "B1l7jf5rFS", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "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": "The authors propose a framework to incorporate additional semantic prior knowledge into the traditional training of deep learning models such that the additional knowledge acts as both soft and hard constraints to regularize the embedding space instead of the parameter space. To illustrate the idea, the authors use 3 different annotated knowledge that are already available in a public dataset that contains equivalent statements, entailed statements as well as functional programs and show that the final performance indeed increases. \n\nIn general, the paper is well-written and easy to follow. The motivation is clear, i.e., to boost the performance of supervised learning tasks with additional knowledge constraints in a hard way. Compared with the existing models that treat the constraints as soft regularizers, the authors propose to additionally distill the knowledge using teacher-student framework. And this paper contributes in a novel way to incorporate the constraints with both soft and hard training strategies. However, there are several considerations which limits the contribution of this paper:\n\n1. As a teach-student distillation framework, there are several papers using a posterior regularizer with hard constraints, e.g., \"Harnessing deep neural networks with logic rules\", \"Constrained Convolutional Neural Networks for Weakly Supervised Segmentation\". More discussions and comparisons with these models should be addressed, and even experimental comparisons if possible, since they also use knowledge distillation to convey the knowledge expressed in the constraints.\n\n2. The proposed model differs with other soft-regularization-based methods in terms of an additional distillation process. The authors state that the combination of task loss with soft regularization lead to over-fitting. To my point of view, the distillation step actually makes similar effect with the case when only optimize the regularizer without the task loss. Hence, I am wondering what's the performance of first using the combined loss and then fix the subsequent layers to only optimize the embedding layers using only the regularization loss. This could demonstrate the difference between the distillation process and the regularization process.\n\n3. Many recent models for VQA have been proposed, e.g, \"The Neuro-Symbolic Concept Learner: Interpreting Scenes, Words, and Sentences from Natural Supervision\" which also combines extra knowledge as symbolic reasoning. The authors should also compare with such models.\n\n4. It seems the model need to sample a pair of data each time at training to compute the regularizer and also conducting the distillation process. In this case, the time cost should be non-trivial because the distillation process requires optimizing the distance between the current embedding with the hard constraint. Then the question comes as how's the time complexity of the model? What's the convergence speed?", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper thoroughly."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper proposes a technique for incorporating prior knowledge as relations between training instances.

The reviewers had a mixed set of concerns, with one common one being an insufficient comparison with / discussion of related work. Some reviewers also found the clarity lacking, but were satisfied with the revision. One reviewer found the claim of the approach being general but only tested and valid for the VQA dataset problematic.

Following the discussion, I recommend rejection at this time, but encourage the authors to take the feedback into account and resubmit to another venue.
Decision: Reject