BS06jhkim/slides/iclr2017_slides.pdfMultimodal Learning ... taking advantage of residual learning. ... question-answering annotations of Visual Genome (Krishna et al., 2016) are used

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Hadamard Product for Low-rank Bilinear Pooling

Jin-Hwa Kim, Kyoung-Woon On, Woosang Lim, Min-Oh Heo, Jeonghee Kim, Jung-Woo Ha,

Byoung-Tak Zhang

ICLR 2017

Low-rank Bilinear Model

■ Bilinear Model

■ Low-rank Restriction

fi = wijkk=1

M

∑j=1

N

∑ x jyk + bi = xTWiy + bi

fi = xTWiy + bi = x

TUiViTy + bi = 1

T (UiTx !Vi

Ty)+ bif = PT (UTx !VTy)+ b

N x D D x M

rank(Wi) <= min(N,M)

Linear

x

Linear

y

Linear

f


x1 x2 … xN

WT

∑wixi ∑wjxj … ∑wkxk


x1 x2 … xN

WxT

∑wixi ∑wjxj … ∑wkxk

y1 y2 … yN

WyT

∑wlyl ∑wmym

… ∑wnyn

∑∑wiwlxiyl

∑∑wjwmxjym

… ∑∑wkwnxkyn

Hadamard�Product�(element-wise�multiplication)

Multimodal Learning

■ Importance of Embeddings • Appropriate embeddings for each modality is important in multimodal

learning (Ngiam et al., 2011; Srivastava & Salakhutdinov, 2012)

■ Element-wise Multiplication • A simple method of element-wise multiplication (Hadamard product)

after linear-tanh embeddings (Lu et al., Github 2015) • Outperform other sophisticated models, DPPnet (Noh et al., 2015) and D-NMN (Andreas, et al., 2016).

Linear

Q

Tanh

Linear

V

Tanh

Softmax

Low-rank Bilinear Pooling in Attention Mechanism

A

TanhConv

TanhLinear

Replicate

Q V

SoftmaxConv

TanhLinear

TanhLinearLinear

Softmax

■ Low-rank Bilinear Pooling (LBP) • Generalize a low-rank bilinear model as a pooling in neural networks

■ Attention Mechanism in Multimodal LBP (MLB)

Under review as a conference paper at ICLR 2017

4.1 LOW-RANK BILINEAR POOLING IN ATTENTION MECHANISM

Attention mechanism uses an attention probability distribution ↵ over S ⇥ S lattice space. Here,using the low-rank bilinear pooling, the attention probability distribution ↵ for the soft attention isdefined as

↵ = softmax⇣P

T

↵

��(UT

q

q · 1T ) � �(VT

F

F

T

)

�⌘(8)

where ↵ 2 RG⇥S

2

, P↵

2 Rd⇥G, � is a hyperbolic tangent function, Uq

2 RN⇥d, q 2 RN ,1 2 RS

2

, VF

2 RM⇥d, and F 2 RS

2⇥M . If G > 1, multiple glimpses are explicitly expressedas in Fukui et al. (2016), conceptually similar to Jaderberg et al. (2015). And, the softmax functionapplies to each row vector of ↵. The bias terms are omitted for simplicity.

4.2 MULTIMODAL LOW-RANK BILINEAR ATTENTION NETWORKS

Attended visual feature ˆ

v is a linear combination of visual feature vectors Fi

with coefficients ↵g,i

.Each attention probability distribution ↵

g

is for a glimpse g. For G > 1, ˆv is the concatenation ofresulting vectors ˆ

v

g

.

ˆ

v =

Gn

g=1

S

2X

s=1

↵g,s

F

s

(9)

wheref

denotes concatenation of vectors.

The posterior probability distribution of answers is an output of a softmax function, whose input isthe result of another low-rank bilinear pooling of q and ˆ

v as

p(a|q,F;⇥) = softmax⇣P

T

o

��(WT

q

q) � �(VT

v

ˆ

v)

�⌘(10)

and the predicted answer a is

a = argmax

a2⌦p(a|q,F;⇥) (11)

where ⌦ is a set of candidate answers and ⇥ is an aggregation of entire model parameters.

5 EXPERIMENTS

In this section, we conduct six experiments to select the proposed model, Multimodal Low-rankBilinear Attention Networks (MLB). Each experiment controls other factors except one factor to as-sess the effect on accuracies. Based on MRN (Kim et al., 2016b), we start our assessments with aninitial option of G = 1 and shortcut connections of MRN, called as Multimodal Attention ResidualNetworks (MARN). Notice that we use one embeddings for each visual feature for better perfor-mance, based on our preliminary experiment (not shown). We attribute this choice to the attentionmechanism for visual features, which provides more capacity to learn visual features. We use thesame hyper-parameters of MRN (Kim et al., 2016b), without any explicit mention of this.

The VQA dataset (Antol et al., 2015) is used as a primary dataset, and, for data augmentation,question-answering annotations of Visual Genome (Krishna et al., 2016) are used. Validation isperformed on the VQA test-dev split, and model comparison is based on the results of the VQAtest-standard split. For the comprehensive reviews of VQA tasks, please refer to Wu et al. (2016a)and Kafle & Kanan (2016a).

Number of Learning Blocks Kim et al. (2016b) argue that three-block layered MRN shows thebest performance among one to four-block layered models, taking advantage of residual learning.However, we speculate that an introduction of attention mechanism makes deep networks hard tooptimize. Therefore, we explore the number of learning blocks of MARN, which have an attentionmechanism using low-rank bilinear pooling.

Number of Glimpses Fukui et al. (2016) show that the attention mechanism of two glimpses wasan optimal choice. In a similar way, we assess one, two, and four-glimpse models.

4




↵ = softmax⇣P

T

↵

��(UT

q

q · 1T ) � �(VT

F

F

T

)

�⌘(8)

where ↵ 2 RG⇥S

2

, P↵


2 RN⇥d, q 2 RN ,1 2 RS

2

, VF








g


v

g

.

ˆ

v =

Gn

g=1

S

2X

s=1

↵g,s

F

s

(9)

wheref



v as


T

o

��(WT

q

q) � �(VT

v

ˆ

v)

�⌘(10)


a = argmax

a2⌦p(a|q,F;⇥) (11)


5 EXPERIMENTS





4




↵ = softmax⇣P

T

↵

��(UT

q

q · 1T ) � �(VT

F

F

T

)

�⌘(8)

where ↵ 2 RG⇥S

2

, P↵


2 RN⇥d, q 2 RN ,1 2 RS

2

, VF








g


v

g

.

ˆ

v =

Gn

g=1

S

2X

s=1

↵g,s

F

s

(9)

wheref



v as


T

o

��(WT

q

q) � �(VT

v

ˆ

v)

�⌘(10)


a = argmax

a2⌦p(a|q,F;⇥) (11)


5 EXPERIMENTS





4

Exploring Alternatives

■ Baseline • Three-block layered MRN (Kim et al., 2016b) • with Attention Mechanism

■ Exploring Options

1. Number of Layers

2. Number of Glimpse

3. Position of Tanh

4. Answer Sampling

5. Shortcut Connection

6. Augmentation

Number of Glimpse



1. Number of Layers


3. Position of Tanh

4. Answer Sampling


6. Augmentation

ModelCimpoi ’15 [5] 66.7Zhang ’14 [39] 74.9Branson ’14 [3] 75.7Lin ’15 [23] 80.9Simon ’15 [29] 81.0CNN (ours) 224px 82.32⇥ST-CNN 224px 83.12⇥ST-CNN 448px 83.94⇥ST-CNN 448px 84.1

Table 3: Left: The accuracy on CUB-200-2011 bird classification dataset. Spatial transformer networks withtwo spatial transformers (2⇥ST-CNN) and four spatial transformers (4⇥ST-CNN) in parallel achieve higheraccuracy. 448px resolution images can be used with the ST-CNN without an increase in computational costdue to downsampling to 224px after the transformers. Right: The transformation predicted by the spatialtransformers of 2⇥ST-CNN (top row) and 4⇥ST-CNN (bottom row) on the input image. Notably for the2⇥ST-CNN, one of the transformers (shown in red) learns to detect heads, while the other (shown in green)detects the body, and similarly for the 4⇥ST-CNN.

The results of this experiment are shown in Table 2 (left) – the spatial transformer models obtainstate-of-the-art results, reaching 3.6% error on 64⇥64 images compared to previous state-of-the-artof 3.9% error. Interestingly on 128 ⇥ 128 images, while other methods degrade in performance,an ST-CNN achieves 3.9% error while the previous state of the art at 4.5% error is with a recurrentattention model that uses an ensemble of models with Monte Carlo averaging – in contrast the ST-CNN models require only a single forward pass of a single model. This accuracy is achieved due tothe fact that the spatial transformers crop and rescale the parts of the feature maps that correspondto the digit, focussing resolution and network capacity only on these areas (see Table 2 (right) (b)for some examples). In terms of computation speed, the ST-CNN Multi model is only 6% slower(forward and backward pass) than the CNN.

4.3 Fine-Grained Classification

In this section, we use a spatial transformer network with multiple transformers in parallel to performfine-grained bird classification. We evaluate our models on the CUB-200-2011 birds dataset [37],containing 6k training images and 5.8k test images, covering 200 species of birds. The birds appearat a range of scales and orientations, are not tightly cropped, and require detailed texture and shapeanalysis to distinguish. In our experiments, we only use image class labels for training.

We consider a strong baseline CNN model – an Inception architecture with batch normalisation [18]pre-trained on ImageNet [26] and fine-tuned on CUB – which by itself achieves the state-of-the-art accuracy of 82.3% (previous best result is 81.0% [29]). We then train a spatial transformernetwork, ST-CNN, which contains 2 or 4 parallel spatial transformers, parameterised for attentionand acting on the input image. Discriminative image parts, captured by the transformers, are passedto the part description sub-nets (each of which is also initialised by Inception). The resulting partrepresentations are concatenated and classified with a single softmax layer. The whole architectureis trained on image class labels end-to-end with backpropagation (full details in Appendix A).

The results are shown in Table 3 (left). The ST-CNN achieves an accuracy of 84.1%, outperformingthe baseline by 1.8%. In the visualisations of the transforms predicted by 2⇥ST-CNN (Table 3(right)) one can see interesting behaviour has been learnt: one spatial transformer (red) has learntto become a head detector, while the other (green) fixates on the central part of the body of a bird.The resulting output from the spatial transformers for the classification network is a somewhat pose-normalised representation of a bird. While previous work such as [3] explicitly define parts of thebird, training separate detectors for these parts with supplied keypoint training data, the ST-CNN isable to discover and learn part detectors in a data-driven manner without any additional supervision.In addition, the use of spatial transformers allows us to use 448px resolution input images withoutany impact in performance, as the output of the transformed 448px images are downsampled to224px before being processed.

5 ConclusionIn this paper we introduced a new self-contained module for neural networks – the spatial trans-former. This module can be dropped into a network and perform explicit spatial transformations

8

Jaderberg et al., 2015

Position of Tanh



1. Number of Layers


3. Position of Tanh

4. Answer Sampling


6. Augmentation

Linear Linear

Linear

Linear LinearTanhTanh

Linear

Linear Linear

Tanh

Linear

Position of Tanh



1. Number of Layers


3. Position of Tanh

4. Answer Sampling


6. Augmentation

Linear Linear

Linear

Linear LinearTanhTanh

Linear

Linear Linear

Tanh

Linear

with the same # of parameters

Results for Exploring Alternatives


Table 1: The accuracies of our experimental model, Multimodal Attention Residual Networks(MARN), with respect to the number of learning blocks (L#), the number of glimpse (G#), the po-sition of activation functions (tanh), answer sampling, shortcut connections, and data augmentationusing Visual Genome dataset, for VQA test-dev split and Open-Ended task. Note that our proposedmodel, Multimodal Low-rank Bilinear Attention Networks (MLB) have not shortcut connections,compared with MARN. MODEL: model name, SIZE: number of parameters, ALL: overall accu-racy in percentage, Y/N: accuracy of yes-or-no binary answers, NUM: accuracy of number answers,and ETC: accuracy of other answers. Since Fukui et al. (2016) only report the accuracy of the en-semble model on the test-standard, the test-dev results of their single models are included in the lastsector. Some figures have different precisions which are rounded. ⇤ indicates the selected model foreach experiment.

MODEL SIZE ALL Y/N NUM ETC

MRN-L3 65.0M 61.68 82.28 38.82 49.25MARN-L3 65.5M 62.37 82.31 38.06 50.83MARN-L2 56.3M 63.92 82.88 37.98 53.59

* MARN-L1 47.0M 63.79 82.73 37.92 53.46

MARN-L1-G1 47.0M 63.79 82.73 37.92 53.46* MARN-L1-G2 57.7M 64.53 83.41 37.82 54.43

MARN-L1-G4 78.9M 64.61 83.72 37.86 54.33

No Tanh 57.7M 63.58 83.18 37.23 52.79* Before-Product 57.7M 64.53 83.41 37.82 54.43

After-Product 57.7M 64.53 83.53 37.06 54.50

Mode Answer 57.7M 64.53 83.41 37.82 54.43* Sampled Answer 57.7M 64.80 83.59 38.38 54.73

Shortcut 57.7M 64.80 83.59 38.38 54.73* No Shortcut 51.9M 65.08 84.14 38.21 54.87

MLB 51.9M 65.08 84.14 38.21 54.87MLB+VG 51.9M 65.84 83.87 37.87 56.76

MCB+Att (Fukui et al., 2016) 69.2M 64.2 82.2 37.7 54.8MCB+Att+GloVe (Fukui et al., 2016) 70.5M 64.7 82.5 37.6 55.6

MCB+Att+Glove+VG (Fukui et al., 2016) 70.5M 65.4 82.3 37.2 57.4

Non-Linearity We assess three options applying non-linearity on low-rank bilinear pooling,vanilla, before Hadamard product as in Equation 5, and after Hadamard product as in Equation 6.

Answer Sampling VQA (Antol et al., 2015) dataset has ten answers from unique persons for eachquestion, while Visual Genome (Krishna et al., 2016) dataset has a single answer for each question.Since difficult or ambiguous questions may have divided answers, the probabilistic sampling fromthe distribution of answers can be utilized to optimize for the multiple answers. An instance 1 canbe found in Fukui et al. (2016). We simplify the procedure as follows:

p(a1) =

⇢|a1|/⌃i

|ai

|, if |a1| � 3

0, otherwise(12)

p(a0) = 1� p(a1) (13)

where |ai

| denotes the number of unique answer ai

in a set of multiple answers, a0 denotes a mode,which is the most frequent answer, and a1 denotes the secondly most frequent answer. We definethe divided answers as having at least three answers which are the secondly frequent one, for theevaluation metric of VQA (Antol et al., 2015),

accuracy(ak

) = min (|ak

|/3, 1) . (14)1https://github.com/akirafukui/vqa-mcb/blob/5fea8/train/multi_att_2_

glove/vqa_data_provider_layer.py#L130

5

■ Single Models

■ Ensemble

VQA test-standard Results


Non-Linearity The results confirm that activation functions are useful to improve performances.Surprisingly, there is no empirical difference between two options, before-Hadamard product andafter-Hadamard product. This result may build a bridge to relate with studies on multiplicativeintegration with recurrent neural networks (Wu et al., 2016c).

Answer Sampling Sampled answers (64.80%) result better performance than mode answers(64.53%). It confirms that the distribution of answers from annotators can be used to improve theperformance. However, the number of multiple answers is usually limited due to the cost of datacollection.

Shortcut Connection Though, MRN (Kim et al., 2016b) effectively uses shortcut connectionsto improve model performance, one-block layered MARN shows better performance without theshortcut connection. In other words, the residual learning is not used in our proposed model, MLB.It seems that there is a trade-off between introducing attention mechanism and residual learning. Weleave a careful study on this trade-off for future work.

Data Augmentation Data augmentation using Visual Genome (Krishna et al., 2016) question an-swer annotations significantly improves the performance by 0.76% in accuracy for VQA test-devsplit. Especially, the accuracy of others (ETC)-type answers is notably improved from the dataaugmentation.

6.2 COMPARISON WITH STATE-OF-THE-ART

The comparison with other single models on VQA test-standard is shown in Table 2. The overallaccuracy of our model is approximately 1.9% above the next best model (Noh & Han, 2016) on theOpen-Ended task of VQA. The major improvements are from yes-or-no (Y/N) and others (ETC)-type answers. In Table 3, we also report the accuracy of our ensemble model to compare with otherensemble models on VQA test-standard, which won 1st to 5th places in VQA Challenge 20162. Webeat the previous state-of-the-art with a margin of 0.42%.

Table 3: The VQA test-standard results for ensemble models to compare with state-of-the-art. Forunpublished entries, their team names are used instead of their model names. Some of their figuresare updated after the challenge.

Open-Ended MCMODEL ALL Y/N NUM ETC ALL

RAU (Noh & Han, 2016) 64.12 83.33 38.02 53.37 67.34MRN (Kim et al., 2016b) 63.18 83.16 39.14 51.33 67.54DLAIT (not published) 64.83 83.23 40.80 54.32 68.30Naver Labs (not published) 64.79 83.31 38.70 54.79 69.26MCB (Fukui et al., 2016) 66.47 83.24 39.47 58.00 70.10

MLB (ours) 66.89 84.61 39.07 57.79 70.29Human (Antol et al., 2015) 83.30 95.77 83.39 72.67 91.54

7 RELATED WORKS

7.1 COMPACT BILINEAR POOLING

Compact bilinear pooling (Gao et al., 2015) approximates full bilinear pooling using a sampling-based computation, Tensor Sketch Projection (Charikar et al., 2002; Pham & Pagh, 2013):

(x⌦ y, h, s) = (x, h, s) ⇤ (y, h, s) (15)

= FFT�1(FFT( (x, h, s) � FFT( (y, h, s)) (16)

2http://visualqa.org/challenge.html

7


Table 2: The VQA test-standard results to compare with state-of-the-art. Notice that these resultsare trained by provided VQA train and validation splits, without any data augmentation.

Open-Ended MCMODEL ALL Y/N NUM ETC ALL

iBOWIMG (Zhou et al., 2015) 55.89 76.76 34.98 42.62 61.97DPPnet (Noh et al., 2016) 57.36 80.28 36.92 42.24 62.69Deeper LSTM+Normalized CNN (Lu et al., 2015) 58.16 80.56 36.53 43.73 63.09SMem (Xu & Saenko, 2016) 58.24 80.80 37.53 43.48 -Ask Your Neuron (Malinowski et al., 2016) 58.43 78.24 36.27 46.32 -SAN (Yang et al., 2016) 58.85 79.11 36.41 46.42 -D-NMN (Andreas et al., 2016) 59.44 80.98 37.48 45.81 -ACK (Wu et al., 2016b) 59.44 81.07 37.12 45.83 -FDA (Ilievski et al., 2016) 59.54 81.34 35.67 46.10 64.18HYBRID (Kafle & Kanan, 2016b) 60.06 80.34 37.82 47.56 -DMN+ (Xiong et al., 2016) 60.36 80.43 36.82 48.33 -MRN (Kim et al., 2016b) 61.84 82.39 38.23 49.41 66.33HieCoAtt (Lu et al., 2016) 62.06 79.95 38.22 51.95 66.07RAU (Noh & Han, 2016) 63.2 81.7 38.2 52.8 67.3

MLB (ours) 65.07 84.02 37.90 54.77 68.89

The rate of the divided answers is approximately 16.40%, and only 0.23% of questions have morethan two divided answers in VQA dataset. We assume that it eases the difficulty of convergencewithout severe degradation of performance.

Shortcut Connection The performance contribution of shortcut connections for residual learningis explored. This experiment is conducted based on the observation of the competitive performanceof single-block layered model. Since the usefulness of shortcut connections is linked to the networkdepth (He et al., 2016).

Data Augmentation The data augmentation with Visual Genome (Krishna et al., 2016) questionanswer annotations is explored. Visual Genome (Krishna et al., 2016) originally provides 1.7 Millionvisual question answer annotations. After aligning to VQA, the valid number of question-answeringpairs for training is 837,298, which is for distinct 99,280 images.

6 RESULTS

The six experiments are conducted sequentially to narrow down architectural choices. Each experi-ment determines experimental variables one by one. Refer to Table 1, which has six sectors dividedby mid-rules.

6.1 SIX EXPERIMENT RESULTS

Number of Learning Blocks Though, MRN (Kim et al., 2016b) has the three-block layered ar-chitecture, MARN shows the best performance with two-block layered models (63.92%). For themultiple glimpse models in the next experiment, we choose one-block layered model for its simplic-ity to extend, and competitive performance (63.79%).

Number of Glimpses Compared with the results of Fukui et al. (2016), four-glimpse MARN(64.61%) is better than other comparative models. However, for a parsimonious choice, two-glimpseMARN (64.53%) is chosen for later experiments. We speculate that multiple glimpses are one ofkey factors for the competitive performance of MCB (Fukui et al., 2016), based on a large margin inaccuracy, compared with one-glimpse MARN (63.79%).

6

Q&A

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BS06jhkim/slides/iclr2017_slides.pdfMultimodal Learning ... taking advantage of residual learning. ... question-answering annotations of Visual Genome (Krishna et al., 2016) are used