M ULTILAYER D ENSE C ONNECTIONS FOR H IERARCHICAL C ONCEPT P REDICTION
Anonymous authors
Paper under double-blind review
A BSTRACT
Classiﬁcation is a pivotal function for many computer vision tasks such as image recognition, object detection, scene segmentation.
Multinomial logistic regression with a single ﬁnal layer of dense connections has become the ubiquitous technique for CNN-based classiﬁcation.
While these classiﬁers project a mapping between the input and a set of output category classes, they do not typically yield a comprehensive description of the category.
In particular, when a CNN based image classiﬁer correctly identiﬁes the image of a Chimpanzee, its output does not clarify that Chimpanzee is a member of Primate, Mammal, Chordate families and a living thing.
We propose a multilayer dense connectivity for a CNN to simultaneously predict the category and its conceptual superclasses in hierarchical order.
We experimentally demonstrate that our proposed dense connections, in conjunction with popular convolutional feature layers, can learn to predict the conceptual classes with minimal increase in network size while maintaining the categorical classiﬁcation accuracy.
I NTRODUCTION
Classiﬁcation is a core concept for numerous computer vision tasks.
Given the convolutional features, different architectures classify either the image itself (He et al., 2015; Szegedy et al., 2016), the region/bounding boxes for object detection (He et al., 2017; Liu et al., 2015), or, at the granular level, pixels for scene segmentation (Chen et al., 2018).
Although early image recognition works employed multilayer classiﬁcation layers (Krizhevsky et al., 2012; Simonyan & Zisserman, 2015), the more recent models have all been using single layer dense connection (
He et al., 2016; Szegedy et al., 2016) or convolutions (Lin et al., 2017).
The vision community has invented a multitude of techniques to enhance the capacity of feature computation layers (Xie et al., 2017; Huang et al., 2017;
Hu et al., 2018; Dai et al., 2017; Chollet, 2016; Tan & Le, 2019).
But, the classiﬁcation layer has mostly retained the form of a multinomial/softmax logistic regression performing a mapping from a set of inputs (images) to a set of categories/labels.
As such, the ﬁnal output of these networks do not furnish a comprehensive depiction about the input entity.
In particular, when an existing CNN correctly identiﬁes an image of an
English Setter, it is not laid out in the output that it is an instance of a dog, or more extensively, a hunting dog, a domestic animal and a living thing.
It rational to assume that convolutional layers construct some internal representation of the conceptual superclasses, e.g., dog, animal etc., during training.
We argue that, by appropriately harnessing such representation, one can retrieve a much broader description of the input image from a CNN than it is supplied by a single layer output.
Extensive information about most categories are freely available in repositories such as WordNet (Fellbaum, 1998).
WordNet provides the hierarchical organization of category classes (e.g., English Setter) and their conceptual superclasses (e.g., Hunting dog, Domestic animal, Living thing).
However, a surprisingly limited number of CNNs utilize the concept hierarchy.
The primary goal of almost all existing studies is to improve the category-wise classiﬁcation performance by exploiting the conceptual relations, often via a separate tool.
Deng et al.
(2014) and Ding et al.
(2015) apply graphical models to capture the interdependence among concept labels to improve category classiﬁcation accuracy.
Other works either do not clarify the semantic meaning of the ancestor concepts (Yan et al., 2015) or impose a level of complexity in the additional tool (RNN) that is perhaps unnecessary (Hu et al., 2016).
We have not found an existing (deep learning) model that attempts to predict both the ﬁner categories and the chain of ancestor concepts for an input image by a single network.
The classical hedging method (Deng et al., 2012) computes either the ﬁner labels or one of its superclasses exclusively , but not both simultaneously.
In this paper, we introduce a CNN to classify the category and the concept superclasses simultaneously.
As illustrated in Figure 1, in order to classify any category class (e.g., English Setter), our model is constrained to also predict the ancestor superclasses (e.g., Hunting dog, Domestic animal, Living thing) in the same order as deﬁned in a given ontology.
We propose a conﬁguration of multilayer dense connections to predict the category & concept superclasses as well as model their interrelations based on the ontology.
We also propose a simple method to prune and rearrange the label hierarchy for efﬁcient connectivity.
Capturing the hierarchical relationship within the CNN architecture itself enables us to train the model end-to-end (as opposed to attaching a separate tool) by applying existing optimization strategies for training deep networks 1 .
We experimentally demonstrate that one can train the proposed architecture using standard optimization protocols to predict the concept classes with two popular CNN backbones:
ResNet and InceptionV4, while maintaining their category-wise accuracy.
The proposed multilayer connection is shown to reﬁne the learned representations of these backbone CNNs further to yield better concept and category classiﬁcation than 1) multinomial logistic regression, and, 2) other existing works (that apply separate mechanisms) on standard datasets and challenging images.
Predicting coarser superclasses in addition to ﬁner level categories improves interpretability of the classiﬁer performance.
Even if an eagle is misclassiﬁed as a parrot, the capability of inferring that it is a bird, and not an artifact (e.g., drone), may be beneﬁcial in some applications (e.g., surveillance).
More importantly, an object detector can enhance its capability on unseen categories by adopting the proposed classiﬁcation scheme (as demonstrated in Section 4.4).
For example, a movie/TV violence recognition/detection tool can recognize an equipment as a ’weapon’ concept class even if that particular weapon category was not in the training set.
In visual question answering (VQA), encoding concept classes would expand the scope of query terms by allowing broader description (’how many vehicles are present’ in addition to ’how many buses’, ’how many trucks’ etc.; see
Cao et al.
; Wang et al.
In Appendix G, we point out how our architecture can be extended to object detectors to compute the concept classes.
In addition, we allude to the potential applications of our model to capture label structures different from concept graph, e.g., spatial or compositional dependence.
R ELEVANT WORKS
Use of hierarchical classiﬁers can be traced back to the early works of Torralba et al.
; Wu et al.
; Fergus et al.
(2010) that shared features for improved classiﬁcation.
Some studies claimed a hierarchical organization of categories resembles how human cognitive system stores knowledge (Zhao et al., 2011) while others experimentally showed a correspondence between structure of semantic hierarchy and visual confusion between categories (Deng et al., 2010).
Bengio et al.
; Deng et al.
(2011) learn a label tree for efﬁcient inference with low theoretical complexity and also suggest a label hierarchy is beneﬁcial for datasets with tens of thousands of categories.
Deng et al.
(2012) aim to predict either a coarse level concept or a ﬁne level category (but not both at the same time) given an initial classical classiﬁer.
Provided an initial classiﬁer output, this method determines category or the coarse concept node (exclusively) with max reward based on aggregated probabilities in a label hierarchy.
The reported results suggest the prediction of superclasses comes at the expense of the ﬁne level category classiﬁcation failure.
For CNN based classiﬁcation, Deng et al.
(2014) modeled the relationships such as subsumption, overlap and exclusion among the categories via a CRF.
Although the CRF parameter can be trained via gradient descent, the inference required a separate computation of message passing.
The work of Ding et al.
(2015) extended this model by utilizing probabilistic label relationships.
The HDCNN framework (Yan et al., 2015) groups the ﬁner classes into coarse concept using the category labels.
The framework comprises two modules for coarse and ﬁne categories where the coarse prediction modulates the layers for ﬁner classiﬁcation.
However, this work does not describe the coarser concept classes in order to analyze whether they, or their descendent categories, have any semantic meaning (see Appendix H).
Furthermore, the overlap among concept class descendants precludes a mechanism to predict the conceptual superclasses.
Hu et al.
(2016) present a structured inference model for hierarchical representation where the concepts representing scene attributes are predicted as indicator vectors of different length.
A bidirectional message passing, inspired by the bidirectional recurrent networks, establishes the relations among different levels of concepts.
The model leads to a large number of inter and intra-layer label interactions some which needed to be manually hard-coded to 0.
There are a few other studies that proposed to incorporate structural prediction techniques in their design (Guo et al., 2017; Liang, 2019); we provide their description in Appendix A due to space limitation.
Unlike us, the primary objective of almost all the aforementioned papers is to improve the category prediction performance by utilizing the superclass hierarchy as an auxiliary source of information or as intermediate result.
With the exception of Deng et al.
; Hu et al.
(2016), none of these studies were designed for, and demonstrate their effectiveness in, concept prediction.
The algorithms of Deng et al.
(2014); Guo et al.
(2017) require substantial modiﬁcations to be able to classify the concept classes.
Furthermore, in contrast to ours, most of these studies use a separate technique/tool for modeling the conceptual relations that need to be trained or applied separately with different mechanisms.
It is important to distinguish our work from the hyperbolic embedding studies (Nickel & Kiela, 2017;
Khrulkov et al., 2020).
Khrulkov et al.
(2020) present an algorithm to learn an embedding where images with same conceptual hierarchy are grouped together in the hyperbolic space.
However, the paper does not describe – and, it is neither obvious nor straightforward – how to determine the concept classes from these embedded points.
These studies, therefore, are not suitable for a comparison with our method for concurrent prediction of category and concept classes.
P ROPOSED M ETHOD
Given an input image, the goal of our proposed method is to determine its category (leaf node in the hierarchy) and a list of its concept superclasses (i.e., ancestors in the ontology).
As an example, for an image of a Chimpanzee, the proposed algorithm produces predictions for 1) the category
Chimpanzee, and 2) an ordered list of ancestor concepts: Living thing → Chordate → Mammal → Primate → Chimpanzee.
We illustrate (and experiment with) the proposed model for image classiﬁcation in this paper.
Our CNN architecture is designed to encompass the chain of relationships among the category and the predecessor concepts in the dense layers.
We utilize an existing label hierarchy/ontology to guide the design of the dense layers, but do not use the hierarchy in prediction.
In order to maximize the information within an ontology and to reduce the number of variables in the dense layers, we condense the original label hierarchy as explained in Section 3.1.
In our design of multilayer dense connections, each concept is associated with a set of hidden nodes.
These hidden nodes are in turn connected to those of its children (both category and concept) and the output prediction nodes.
Section 3.2 elaborates these connections and the loss functions to train the network.
3. C ONDENSED C ONCEPT H IERARCHY
In general, a concept class decomposes to multiple sub-concepts in an ontology, e.g., ImageNet12 (Deng et al., 2009) subset of WordNet (Fellbaum, 1998).
However, the lineage of a parent to a single child (e.g., Entity → Physical Entity → Abstraction ) is redundant and does not provide much information.
Similarly, parent concepts with highly imbalanced distribution of descendants are not informative as well.
Modeling the redundant and uninformative concepts will increase the network size with no information gain.
We reorganize the given ontology to reduce such redundancy.
We assume the hierarchy to be a directed acyclic graph (DAG) and perform a depth ﬁrst search (DFS) traversal on it.
During the traversal, we ﬁrst prune the label hierarchy based on the distribution of descendants of a concept node.
Let η γ denote the number of all descendants of a concept indexed by γ .
Any child node γ ch ∈ Children ( γ ) with η γ ch η γ ≥ τ , i e., the overlap between descendants γ and γ ch is more than τ , is absorbed by the parent γ .
This process is applied recursively to yield a balanced distribution of descendants of any concept in the resulting hierarchy.
In addition, we remove any concept γ in the structure with a descendant count η γ < δ and append the children set Children ( γ ) to those of its parent γ pa .
Conceptually, it is not worth modeling a concept node with only a few descendants.
We depict the differences between the original and modiﬁed ontologies in Figure 2.
The distributions of the descendants for children concepts are more balanced in the compressed version (right) than that in the original version (left).
Our strategy removes all the redundant single parent-child connections.
As the network connections are dependent on the concept hierarchy, this reduction of nodes and relationships in the ontologies are crucial for our method.
It is worth noting that the proposed modiﬁcation added direct concept-category relations in the middle layers of the hierarchy.
Executing a DFS on a DAG ontology may lead to a few ambiguous grouping of few concepts and categories as Deng et al.
(2014) pointed out.
We adopted DFS for simplicity to compute the compressed graph, which can be replaced by an unambiguous one whenever it is available; the methods of Deng et al.
(2011); Bengio et al.
(2010) can also be applied to generate the ontology.
3. N ETWORK A RCHITECTURE
Our proposed algorithm aims to model the abridged label hierarchy with dense connections.
As Figure 2 suggests, there are multiple kinds of dense connectivities in our proposed classiﬁcation layer.
Each concept in the hierarchy corresponds to one set of hidden nodes that essentially represent the concept. These hidden nodes are connected to those representing its children, if any.
For example, if Mammal, Bird and Reptile are the descendant concept of Chordate, there will be all to all connections from the hidden nodes representing Chordate to those accounting for Mammal, Bird and Reptile.
Consequently, the hidden representation for a child concept is computed from that of its parent. Given the representation in capture in the hidden nodes, two types of output prediction nodes detects the presence of the concept itself and any children category in the input.
An additional type of connectivity explicitly constrains the concept and category predictions to follow the hierarchical organization of the ontology.
We illustrate each of these connections below.
Modeling Concepts and Categories: Let us denote by z γ and h γ the output prediction variable and the set of hidden nodes associated with the concept γ .
The terms node and variables are used interchangeably in the description of our model.
Let concept γ ch and category j both be children of concept γ in the hierarchy and h γ ch and x j denote the hidden and the output prediction variables for them respectively.
The proposed model computes the output prediction z γ and initial values ˜h γ ch ,
[Equation]
In these equations, u, v, w and b are the weights/biases of the dense connectivity and h i corresponds to the i -th value of h .
The activation functions φ, ψ, ω utilized for these different quantities are φ =
Sigmoid , ψ = Identity , ω = ReLU.
In essence, h γ encodes an internal representation for concept γ and z γ predicts the presence of it in the input image.
The connections between h γ and h γ ch of its child concept enforces the representations for γ ch to be derived from, and therefore dependent on, that of its parent.
In our design, the number d γ = | h γ | of nodes representing a concept γ > 0 is directly proportional to the total number of descendants η γ of γ .
We have used d γ = µη γ for this study with µ = 2 .
The ﬂattened output of the ﬁnal feature layer of an existing network architecture (e.g., ResNetor InceptionV4 etc.) is utilized to populate h 0 and its size depends on the particular architecture used.
We do not predict the root concept z 0 of the hierarchy (e.g., Entity for ImageNet12) since all categories descend from it.
Concept Category Label Constraints: The values for category prediction x j and hidden nodes for child concept h γ ch are calculated by multiplying initial values of these quantities with the concept prediction z γ .
[Equation]
Note that, the Sigmoid activation constrains the value of z γ to be z γ ∈ [0 , 1] .
In effect, the node z γ plays an excitatory or inhibitory role based on the predicted value of the concept γ .
This constraint enforces that the nodes representing any child of concept γ , whether it is a category ( x j ) or another downstream sub-concept ( h γ ch ), be activated only if the concept itself is correctly predicted.
The category predictions for an input image are computed by applying Softmax activation over all category nodes { x 1 , x 2 , . . .
, x N } , where N is the total number of categories.
The predictions for M concepts are given by the collection of the variables { z 1 , z 2 , . . .
, z M } .
The hierarchical relationship among the variables { z 1 , z 2 , . .
, z M } are enforced by construction.
Observe that, while an image can be classiﬁed to only one (e.g., Chimpanzee) of the N categories, multiple concepts (e.g., Primate, Mammal, Chordate) at different levels of the hierarchy can be set to 1.
Figure 3 clariﬁes the proposed dense arrangement between the hidden nodes h γ and its children concept nodes as well as the prediction outputs.
The hidden nodes h γ (shown in empty circles) are connected to those of its Q children concepts and B category output variables (solid circles) to compute the initial quantities { ˜h γ ch 1 , . . .
, ˜h γ ch Q } and { ˜ x j 1 , . .
˜ x j B } respectively.
The concept prediction z γ (solid square) is computed by another dense connections which modulates the ﬁnal values of { h γ ch 1 , . . .
, h γ ch Q } and { x j 1 , . . .
, x j B } for the concept and category variables respectively via multiplication.
Number of Variables: The total number of weights in proposed multilayer dense connection with α -way decomposition is ≤ µd 0 (cid:0) N + ρ + 1 (1 − α ) (cid:1) where ρ is the height of the hierarchy and µ is the ﬁxed multiplier used to set the number of hidden nodes for concept γ (see Appendix B).
In comparison, conventional single layer CNN classiﬁers consist of d 0 N variables.
Loss Functions:
The proposed method minimizes two different losses for the two types of output nodes.
For the category predictions, we minimize a cross-entropy loss L CE ( x ) computed over the N category labels and the network outputs x j , j = 1 , . . .
, N .
We introduce a binary indicator quantity χ γ , γ = 1 , . . .
, M for an input image such that χ γ = 1 if γ is an ancestor concept for the category and χ γ = 0 otherwise.
With this indicator Although we use MSE for learning z in this work, any loss for multilabel classiﬁcation, e.g., binary cross-entropy for each z γ , may work as well.
The proposed method minimizes the combined loss L CE + λL CON with the balancing weight λ ﬁxed to λ
= 5 in all our experiments.
Note that, while the error for any category is backpropagated through its predecessor concepts due to the dependence imposed by construction, one needs to ensure that other concepts – that are not related to the category – to remain 0 in the z .
This is exactly the constraint enforced by L CON ( z ) .
E XPERIMENTS & R ESULTS 4. E XPERIEMNTAL S ETUP
We utilize the ontology provided by the ImageNet12 dataset Deng et al.
(2009) to design our dense layers.
All the labels of ImageNet12 between [1 , 1000] correspond to the N = 1000 category classes and labels > 1000 are assigned to the 860 concept superclasses.
In all our experiments, we ﬁxed the two quantities for compressing the concept hierarchy (Section 3.1) to be τ = 90% , δ = 20 .
After compressing the label hierarchy using the methods described in Section 3.1, there are 40 concept labels left in the hierarchy which has a height of ρ = 7 .
The proposed architecture has been trained on the ImageNet12 training dataset and tested on multiple datasets as described in next sections.
We used two popular CNN architectures for feature computation layers: ResNet-50 (He et al., 2015; 2016) and Inception V4 (Szegedy et al., 2015; 2016) 2 .
Adding the proposed multilayer dense connections increased the total number of variables of the ResNet-50 model by a factor of 1 . 182 ( 30 . 29 25 . 61 M).
For the InceptionV4 model, the increase is 1 .
24 M).
This suggests that the increase induced by our proposed model is far lower than the analytical estimate (Section 3.2) in practice and is tolerable with respect to overall network size.
Inference: During inference of the proposed network, we select the category with largest softmax probability for category classiﬁcation as usual.
The parent concepts are classiﬁed by thresholding z values.
We also set any z γ =
if the variable for its parent z γ pa =
(i.e., lower than a conﬁdence threshold).
If more than one child of any concept is detected, we select the one with the highest conﬁdence among them to compute the concept chain.
Evaluation measures: We report the single crop top-1 accuracy results Acc CAT for categories when they are available.
For concept inference, we report two measures based on hierarchical precision and recall (Costa et al., 2007), which computes the precision an recall between the predicted and true chain of concepts : 1) the mean hierarchical precision (mhP) and recall (mhR) over all images of test set, and, 2) percentage of images Acc CON that were predicted with 100% hP and hR. The combined accuracy, Acc COMB , denotes the percentage of images with both Acc CAT =
Acc CON = 1 .
Baselines: As the ﬁrst baseline, we build a CNN classiﬁer for N + M classes with a single ﬂat dense layer for each feature computation architecture.
These baselines are trained with the same loss functions of the their multilayer counterparts.
We utilize a modiﬁed version of the hedging method of Deng et al.
(2012) as the second baseline.
Our modiﬁed version uses ReasNet-50 and Inception V4 based classiﬁers instead of classical versions.
We observed the optimal strategy to compute category and concept chain from the output of the hedge model (which is either category or max reward concept) is to use the category prediction as is and use the concept with maximum reward, along with all its ancestors, as the predicted concept chain.
The hedge model utilizes the same underlying hierarchy as ours and we read off the prediction for concepts that overlap with our condensed hierarchy.
4. I MAGE N ET 12 D ATASET R ESULTS
We ﬁrst demonstrate the performance of two varaints of the proposed method that were trained on
ImageNet12 training set and tested on its validation set.
For one variant of our proposed CNN models, MD-RN with ResNet-50 and MD-IC with Inception V4 backbones, only the weights of [Table] the multilayer dense connections were trained; the weights of the feature layers were kept at their original pretrained values.
The other variant MD-RN-FT performs ﬁnetuning, i.e., it initiates the weights in the feature layer from the pretrained ResNet-50 and trains all variables in the network.
The corresponding ﬂat dense connection baselines are referred to as BL-RN, BL-IC, BL-RN-FT respectively.
The hedging model of Deng et al.
(2012) is dubbed HG-RN and HG-IC that utilizes a
ResNet-50 and Inception V4 initial classiﬁers respectively.
Training: We trained MD-RN, MD-RN-FT and MD-IC following standard training procedures of Szegedy et al.
; Chollet (2016).
The details of training parameters and techniques are described in Appendix C for space limitation.
The initial classiﬁers for HG-RN and HG-IC were trained from scratch on 93% of training examples for each class in ImageNet 2012 training set (achieving 74% and 76% category accuracy on validation set respectively).
The remaining 7% examples were used to estimate the dual variable maximizing the reward for multiple accuracy guarantees.
The results reported here correspond to the dual variable, accuracy guarantee with best overall Acc COMB .
Evaluation: Table 1 reports the accuracies for all the aforementioned models.
Table 1 demonstrates that the MD-RN, MD-RN-FT and MD-IC networks with proposed multilayer dense connections achieved a comparable category accuracy ACC CAT of the ﬂat baselines BL-RN, BL-RN-FT and
BL-IC (which are similar to the published results).
The category accuracy of HG-RN, HG-IC are signiﬁcantly lower than the aforementioned models – a phenomenon also observed by Deng et al.
This is due to the inherent design of the hedge model to only predict concept classes (and not the leaf categories) for some examples.
Table 1 also suggests that an unconstrained ﬂat dense connection is insufﬁcient for learning the superclass sequence.
The proposed models attains > 10% higher Acc CON and even larger combined
Acc COMB than the ﬂat baselines BL-RN, BL-RN-FT, BL-IC.
The baseline methods can either learn to classify the ﬁner categories or the concept chain correctly but the proposed CNN architecture can attain the ability to do both simultaneously with high accuracy.
The proposed models MD-RN,
MD-RN-FT and MD-IC achieves a signiﬁcantly higher overall accuracy Acc COMB than the hedging models HG-RN and HG-IC.
The inception based model MD-IC is also more accurate than HGIC for concept prediction – indeed, MD-IC leads to the best overall accuracy Acc COMB among all models.
The ﬂat baseline methods BL-RN, BL-RN-FT and BL-IC attempts to compute the concept classes independently using the same single layer dense connections that are utilized for category classiﬁcation.
Observe that the concept accuracies Acc CON of BL-RN, BL-RN-FT and BL-IC are approximately 7 ∼ 14% lower than category accuracies Acc CAT .
This suggests that the feature representations learned (in the last convolutional layer) by ResNet-50 and Inception V4 alone are not as informative for concept prediction as they are for category classiﬁcation.
The proposed multilayer design combines these representations to yield a reﬁned representation encoded in the hidden variables h γ to improve the concept prediction accuracy by > 13% .
The comparison implies that the proposed top-down hierarchical constraints on category classiﬁcation to preserve the ancestor concept chain is superior to the hedging technique of concept prediction distilled from the aggregated probabilities accumulated bottom-up from category conﬁdence.
As we will show in next section, a top-down constrained prediction is more robust to the challenging examples because it does not rely primarily on the category classiﬁcation probabilities.
Analysis: We provide an in-depth analysis of the failure cases of concept prediction, compared the distribution of category classiﬁcations and training times of different variants of the proposed models and baslines in Appendix D. Appendix E discusses the ablation studies with the network structure and λ values in loss function.
[Table]
4. P ERFORMANCE ON N ATURALLY A DVERSARIAL I MAGES
Our next experiment demonstrates the robustness of the proposed network on challenging images.
We use the images of naturally adversarial image dataset (Hendrycks et al., 2019) that the popular
CNN architectures (e.g. ResNet) trained on standard datasets classify to widely different semantic categories.
Results in this section examine whether or not algorithms (e
[Table]
g., Deng et al.
that compute marginal probabilities through bottom up aggregation are less effective for determining the ancestor concepts of challenging images.
There are 7500 images in this dataset that belong tocategories.
The ResNet-50 model we downloaded from the tensorﬂow website (pretrained on full
ImageNet 2012) could classify only 0.73% of the images.
Since these 200 categories are a subset of the N = 1000 categories of ImageNet 2012 dataset, one can use the same concept structure for hierarchical classiﬁcation.
In Table 2 the proposed MD-RN-FT and MD-IC model accuracies are compared with those of their ﬂat dense layer counterparts BL-RN-FT and BL-IC as well as those of the hedging model (Deng et al., 2012) with corresponding initial classiﬁers.
The proposed models MD-RN-FT and MD-IC were able to correctly classify the superclass sequences of more images than the baseline models.
With the exception of BL-IC, their categorical accuracies ACC CAT are also higher than the baselines.
We provide a qualitative comparison in Figure 4 between the proposed MD-RN-FT method and the pretrained ResNet-50 output.
One can observe that, without the constraints on predicting the concept chain correctly, the ResNet-50 can classify the images to semantically very different categories.
Aggregating these category-wise conﬁdences will consequently lower the ACC CON of the hedging model compared to those of the proposed model.
The proposed MD-RN-FT, on the other hand, determines the ancestor classes correctly even when the leaf level category is misclassiﬁed.
4. PASCAL VOC 12 C ONCEPT P REDICTION
In this section, we test the generalization of the knowledge learned by the proposed architecture.
Ideally, the proposed network should be able to extrapolate its understanding of the concept superclasses learned from one category set to previously unseen categories.
That is, after learning that a zebra is a mammal, it should be able to identify a horse (of any color) as a mammal too.
To test generalization capability, we test classiﬁers learned from the ImageNet12 dataset on the trainval split of
PASCAL VOC dataset (Everingham et al., 2010).
Note that, there is no one to one correspondence between the categories of ImageNet and VOC 3 .
Each of the VOC 12 categories were assigned to one of the concepts in the condensed label hierarchy of ImageNet dataset.
In Table 3, we show the average concept prediction accuracies of the different variants of the proposed model and the corresponding ﬂat dense layer baselines over 16 VOC categories.
Since there are no categories to predict, the second baseline predicts the concept classes by thresholding the aggregated probabilities as computed in Deng et al.
These are referred to as PrAggRN and
[Table] [Table]
PrAggIC when computed from the initial ResNet-50 and Inception V4 classiﬁers respectively.
As the table shows
[Table]
the proposed variants MD-RN-FT, MD-RN-SC and MD-IC achieved a higher average concept prediction accuracy over all classes than those of the baselines.
Appendix F details the performances for all classes and analyzes the results on this dataset.
4. A W A2 D ATASET R ESULTS
Our next experiment applies the proposed method on the Animals with Attributes (AwA
) dataset
(Lampert et al., 2014) utilized in multiple relevant studies (Deng et al., 2014; Hu et al., 2016).
AwA2 dataset provides the attribute as well as the category labels for 37322 images ofclasses.
For concept classes, we use the same 28 superclasses and follow the same hierarchical relations used in Hu et al.
Note that, this hierarchy is slightly modiﬁed from the ImageNet ontology (and therefore different from the compressed ontology we computed).
Following Hu et al.
(2016), we use a 60-40% split of the images for train/test and report the average ± std dev of the multiclass accuracy Acc CAT for category and the IoU acc for concept and attribute labels from 3 trials.
Table 4 compares the performances of the proposed MD-RN with that of (Hu et al., 2016) (values taken from the paper).
To determine the attributes, we extend our proposed architecture by adding a dense connection between concept and category prediction variables to the 85 attribute classes.
We also compare the performance of the ﬂat baseline BL-RN that predicts the attributes classes independently in addition to animal and concept labels.
Hu et al.
(2016) uses a weaker CNN base ((Krizhevsky et al., 2012)) than ours, which is perhaps a factor leading to its inferior performance.
The comparison implies that, given CNN backbone with enhanced capacity, one can attain highly correct category, concept and attribute classiﬁcation from our multilayer dense connection without relying on an additional complex tool, e.g., RNN.
However, the lower IoU concept, IoU attribute of the ﬂat baseline method attest that the improved performance of MD-RN does not arise solely from the ResNet-50 features and strengthen our claim that the proposed mulitlayer connectivity enhances the feature representation to improve accuracy.
It is interesting to observe a correlation between concept and attribute accuracies: determining the concepts correctly leads to a better prediction of attributes.
Appendix I examines the robustness of
MD-RN trained on AwA2 on ImageNet 12 images from categories overlapping with AwA2.
D ISCUSSION
In this paper, we have demonstrated the advantages of multilayer dense connections for classifying both the category and the ordered chain of ancestor concept classes with two popular architectures in different settings.
The experimental results show that the proposed dense layers can equip the existing CNN classiﬁers with additional capability of learning the coarse concepts without sacriﬁcing the category-wise accuracy.
Attaining this capability of determining the ancestor concept classes is relatively easy – one can only modify the ﬁnal classiﬁcation layers and train using the same optimization technique, for some cases without training the full network.
Our experiments demonstrate the advantage of the proposed architecture over a) multinomial regression that exploits the learned feature representation of pretrained CNNs; b) methods utilizing marginal probabilities accumulated in a bottom up fashion from CNN output given an ofﬂine hierarchy (Deng et al., 2012); and c) an algorithm that employs RNN for superclass prediction.
Our top-down constraints enforces the category classiﬁcation to conform to the semantically meaningful lineage of ancestor classes.
This property not only improves the superclass computation for challenging images but also allows zero-shot concept classiﬁcation for unseen categories.
We believe this study will encourage researchers in computer vision community to adopt and improve our multilayer dense connection to gather more descriptive output from CNNs.
A A PPENDIX : O THER R ELEVANT W ORKS
Guo et al.
(2017) attempted to classify the coarse labels or the conceptual superclasses of categories by augmenting an RNN to CNN output.
In addition to increased complexity imposed by the RNN, it is not clear how the hierarchy among labels was generated and how the hierarchy would scale up with increasing number of categories.
Liang (2019) employed graph based reinforcement learning to learn features of a set of modules each of which corresponds to a concept.
Once the network search is completed the activated module outputs are passed through prediction layers for generating ﬁnal output.
The algorithm demonstrated promising performance for classifying scene contexts for semantic segmentation.
Commercial vision solutions such as
Amazon
Rekognition (https://aws.amazon.com/blogs/aws/amazon-rekognition-image-detection-and-recognitionpowered-by-deep-learning/) or Google Vision (https://cloud.google.com/vision) seem to produce outputs that resemble concept classes.
Due to the proprietary nature of these solutions, it is not possible for us to conﬁrm whether or not they indeed predict concept classes and their relationships.
However, based on the description provided in (https://aws.amazon.com/blogs/aws/amazonrekognition-image-detection-and-recognition-powered-by-deep-learning/) and scrutiny of results, we speculate that Amazon rekognition does not use any hierarchy and probably uses a look-up from hard-coded ( undisclosed) relations strategy.
B A PPENDIX : N UMBER OF V ARIABLES IN M ULTILAYER D ENSE C ONNECTIONS
This section quantiﬁes the increase in the number of weights in the dense layers induced by our multilayer computations.
The CNN classiﬁers typically consists of d 0 N connections in dense layer, where d 0 and N are the size of the last feature layer and number of category classes respectively.
In proposed multilayer dense connections with a balanced α -way decomposition of the concepts, the total number of weights is ≤ µd 0 (cid:16) N + ρ +
[Equation]
(cid:17) where ρ is the height of the hierarchy and µ is the ﬁxed multiplier used to set the number of hidden nodes for concept γ (see Section 3.2).
In a balanced decomposition, the number of hidden nodes for concepts reduces by a constant factor α .
With the size of smallest set of hidden nodes as δ , the max layer of the dense connections is ρ = log α
( d 0 δ ) .
For any concept prediction z γ , we need d γ = µd 0 α l weights at layer l i.e., max number of weights for concept class prediction is µd 0 ρ = µd 0 log α ( d 0 δ ) .
The number of concept-concept connections can be calculated as d 0 ( µα + µα 2 + · · · + µα ρ ) = µd 0 (1 − α ρ ) (1 − α ) ≤ µd1 (1 − α ) .
In order to predict a category variable x j ∈ Children ( γ ) , d γ weights are necessary.
Since any µd 0 ≥ d γ = µ d 0 α l at any level l in a balanced decomposition, the total number of weights for category class prediction must be ≤ µd 0 N .
C A PPENDIX : T RAINING D ETAILS
For MD-RN, MD-RN-FT and MD-IC training, we used the RMSProp optimizer with momentum in our multi-GPU distributed training scheme similar to Szegedy et al.
; Chollet (2016).
The initial learning rate for this experiment was 0 . 1 and was multiplied by 0.94 every 2 epochs.
The epoch size is the same as the training set size with batch size 256 , momentum value 0 .
9 , and weight decay 0 . 0001 .
The training data were augmented by random crop and horizontal ﬂips.
For proposed network learning, the weights corresponding to the concept outputs and the concept interconnections were learned for ﬁrst 2 epochs before optimizing those for the category variables.
We did not use label smoothing for training the Inception v4 model.
The training was continued until the
CNN achieved the same or close accuracy for category classiﬁcation as reported in the original paper/repository.
We have also trained a ResNet-50 with proposed multilayer dense connections MD-RN-SC and baseline ﬂat dense connection BL-RN-SC from scatch on ImageNet 2012 training set.
In our training from scratch, we applied stochastic gradient descent (SGD) optimizer with momentum value 0.9 and initial learning rate 0.2.
The learning rate was decreased every 30 epochs by a factor of 10 (similar to Simonyan & Zisserman (2015);
He et al.
(2015) training).
All other values of the hyperparameters remain the same as those of MD-RN training.
Table 5 reports the accuracies of MD-RN-SC and BLRN-SC.
[Table]
D A PPENDIX : P ERFORMANCE A NALYSIS OF MD-RN AND MD-IC ON I MAGE N ET
Figure 5(a) shows some example categories where the proposed MD-IC model generated different concept orders than those in the condensed ontology.
Monitor and Space bar are children of
Equipment and Implement concepts respectively in the condensed ontology.
But, they contain many images of Desktop computer and Computer keyboards – both of which are children of the Device concept.
As a result, 68% and 88% of Monitor and Space bar images respectively were classiﬁed as Artifact → Instrumentality → Device.
Similarly, although it is grouped to Matter → Solid concepts, 75% of the Mushroom images were predicted as Living thing which consists of Earthstar,
Stinkhorn categories that are visually very similar to Mushroom images.
Motor scooter was placed in Wheeled vehicle in our compressed hierarchy; but at test time, 94% of the time its images was predicted as Self propelled vehicle.
In general, predictions from our proposed model concur more
[Figure]
thing it does
Since different category classes are predicted at different layers of the proposed dense structure, it is rational to verify whether or not the category classiﬁcation capability is impaired by the depth of layer.
To test this, we have plotted in Figure 5(b) the category prediction accuracies for each of the
N = 1000 classes of the baseline against those of the proposed CNN with ResNet50 backbone.
The plot implies no clear effect of the prediction depths on the classiﬁcation performances on different categories as they remain same or very close to those of the original architecture.
Due to the increased number of dense layers and additional sigmoid activations, it is perhaps natural to expect the proposed architecture to require more iteration to converge.
As Figure 5(c) demonstrates, our model indeed takes more epochs(x-axis) to attain a category classiﬁcation performance (y axis) similar to that of baseline built upon ResNet50.
E A PPENDIX : A BLATION STUDIES
We have conducted ablation studies with model MD-RN.
In our ﬁrst ablation study, we model the dense layers based on the original uncompressed hierarchy instead of the condensed hierarchy.
Adopting the original ontology in ResNet-50 increased the number of z variables to 806, depth of dense layers to 17 and model size to 43M (compare with 40, 7, 30M resp.
of compressed).
Our attempts with different hyperparameters ( λ , lr etc) achieved at most { Acc CAT , Acc CON , Acc COMB , mhP, mhR } = { 44.02,1.12, 1.03, 60.05, 47.6 } at 30 epoch (compare Acc CAT with ours Fig 5(c).
The training is perhaps smothered by 1) increased depth with many redundant single parent-child connections, and 2) imbalance in descendent distribution where smaller concept classes are underrepresented.
The second analysis is performed with varying the values of the balancing term λ in the combined loss function (Section 3.2).
As can be inferred from the network architecture for multiple dense connections and the loss functions, with λ =
the category-wise loss drive concept z variables of only the ancestor concepts to 1.
However, with λ = 0 , the optimization will not force z variables of the other non-ancestor concepts to 0 .
Consequently, concept and combined accuracy of a model trained with λ = 0 will be very low.
As Table 6 shows, we observe a very low Acc CON , Acc COMB for MD-RN- λ 0 while achieving close
Acc CAT to the published results.
It is also apparent that a small λ (= 2) favors improving Acc CAT while a relatively large λ (=8) favors improving Acc CON compared to those of the MD-RN model reported on Table 1.
This is expected behavior with the loss function we are optimizing.
[Table]
F A PPENDIX : P ERFORMANCE A NALYSIS ON PASCAL VOC D ATASET
We have excluded the classes { Person, Pottedplant } since these categories were underrepresented in the ImageNet12 dataset.
For example, Person is represented by three rare subclasses Scuba diver,
Ballplayer, Groom.
On the other hand, the { Dog, Bird } categories were over represented in ImageNet12 and their subcategories were assigned to multiple concepts in our hierarchy.
These classes could lead to inconsistency and therefore also excluded in evaluation.
After removing the images that overlaps with multiple categories, we are left with 6941 images from 16 categories.
For these images, we report the Acc CON in Table 7 ( Acc CAT and Acc COMB cannot be computed as there is no one to one correspondence between categories of the two datasets).
The accuracy values for concept classiﬁcation on VOC 2012 clearly indicate the superiority of the proposed architecture to generalize the knowledge it learned from ImageNet12 hierarchy of ancestor superclasses.
All the CNN models resulted in weak performances of categories { Train, Car,
[Table]
Diningtable } .
Such a performance can be attributed to equivocal ancestry within the condensed ontology.
For the category Train, the proposed model with InceptionV4 architecture predicted
Entity → Artifact → Instrumentality → Container → Wheeled vehicle → Self propelled vehicle for 56% of images whereas the compressed ontology assigns it the concept order : Entity → Artifact →
Instrumentality → Conveyance.
It is important to note though that for the ambiguous categories, both the baseline and the proposed models performed poorly – i.e., the proposed method is not drawing any inequitable advantage due to the label ambiguity.
G A PPENDIX : P OSSIBLE A PPLICATIONS AND E XTENSIONS
Our dense connectivity can also be extended to two-stage object detection algorithms (He et al., 2017; Lin et al., 2017) by replacing the ﬁnal detection head with proposed mulitlayer connections.
For SSD-type architectures (Liu et al., 2015; Lin et al., 2017), the dense computations can be carried out by 1 × 1 convolutions (or extended to 3 × 3 ) and added to the classiﬁcation branches at each scale.
The convolutional form should conceptually enable the semantic segmentation techniques
(Chen et al., 2017; 2018; Zhao et al., 2016) to adopt our model as well.
Furthermore, rather than capturing the conceptual class lineage, the dense layers can be modeled after a different contextual relationship such as spatial or compositional consistency (via can-coexistwith
(Hu et al., 2015) or is-part-of (Brust & Denzler, 2018; Wang et al., 2016) relations.
These relationship graph, e.g., parsing graph (Tu et al., 2005), can be either precomputed or learned for the particular task at hand.
H A PPENDIX : G ROUPING C ATEGORIES USING HDCNN T ECHNIQUE
We also attempted to group the ImageNet 2012 categories following the strategy suggested by the
HDCNN paper, Section 4 of (Yan et al., 2015).
For this purpose we exploited the ResNet-50 classiﬁer trained on 93% training examples of ImageNet 2012 (i.e., the initial classiﬁer for HG-RN).
The remaining 7% of the training set was used to compute 100 disjoint clusters of categories.
While some of the animal and vegetable/fruit categories were correctly grouped into the same clusters, many of the clusters comprises semantically very different classes.
We are listing a few of these clusters below.
Yan et al.
(2015) further created some overlapping groups for their algorithm.
It is not clear how to assign concept class labels to these undersegmented clusters of categories and how they can be predicted using a classiﬁer.
That is why we cannot compare our method with HDCNN.
Cluster 1 : { n02509815 lesser-panda, n02346627 porcupine, n01872401 echidna, n02172182 dung-beetle, n02319095 sea-urchin, n03717622 manhole-cover, n04033901 quill, n03733281 maze } .
Cluster 2 : { n04086273 revolver, n02804414 bassinet, n plane, n03995372 power-drill, n03483316 hand-blower, n oxygen-mask, n03759954 microphone, n02841315 binoculars, n assault-rifle, n04090263 rifle, n03602883 joystick, n tripod, n04517823 vacuum, n04554684 washer, n03724870 mask, n04069434 reflex-camera, n03424325 gasmask } .
Cluster 3: { n02389026 sorrel, n02403003 ox, n
Arabian-camel, n03538406 horse-cart, n03868242 oxcart, n thatch } .
Cluster 4: { n03447447 gondola, n02951358 canoe, n shopping-cart, n03933933 pier, n04311004 steel-arch-bridge, n04366367 suspension-bridge, n04532670 viaduct, n03160309 dam, n03873416 paddle } .
I A PPENDIX : R OBUSTNESS OF MD-RN TRAINED ON A W A
In order to test the robustness of the proposed MD-RN network trained on AwA2 dataset, we evaluate its performance on ImageNet 12 images with overlapping categories.
There are
AwA2 categories that are also present in ImageNet 12 dataset.
We applied our MD-RN trained on AwA2 on 800 ImageNet 12 validation images and achieved category, concept and combined accuracies { Acc CAT , Acc CON , Acc COMB } = { 89 . 87 , 89 . 37 , 85 . 75 } .
For comparison, we also applied the ﬂat baseline BL-RN on these images and achieved { Acc CAT , Acc CON , Acc COMB } = { 88 . 87 , 78 .
This experiment shows that the proposed dense layers in MD-RN learned on AwA2 can generalize better than the single layer in BL-RN.
Note that, the convolutional feature layer of both MD-RN and BL-RN have not changed because only dense layers of these two networks were trained (see Section 4.2).
Figure 6 shows a few examples of output from the proposed network on ImageNet 12 validation images.