We revisit the importance of the individual units in Convolutional Neural Networks (CNNs) for visual recognition. By conducting unit ablation experiments on CNNs trained on large scale image datasets, we demonstrate that, though ablating any individual unit does not hurt overall classification accuracy, it does lead to significant damage on the accuracy of specific classes. This result shows that an individual unit is specialized to encode information relevant to a subset of classes. We compute the correlation between the accuracy drop under unit ablation and various attributes of an individual unit such as class selectivity and weight L1 norm. We confirm that unit attributes such as class selectivity are a poor predictor for impact on overall accuracy as found previously in recent work morcos2018importance . However, our results show that class selectivity along with other attributes are good predictors of the importance of one unit to individual classes. We evaluate the impact of random rotation, batch normalization, and dropout to the importance of units to specific classes. Our results show that units with high selectivity play an important role in network classification power at the individual class level. Understanding and interpreting the behavior of these units is necessary and meaningful.
Finally, the role of individual network units has been studied. It has been found that individual units are sensitive to specific concepts that can be visualized by generating or sampling inputs that maximize unit activations @cite_1 @cite_14 , and that unit directions match meaningful concepts more closely than other random directions in representation space @cite_2 . However, whether meaningful units are helpful or harmful to a network's ability to generalize has been questioned: @cite_18 found that units that are selective to one class do not appear to damage overall classification performance more than other units when removed from a network. Our current work is a further examination of the impact of individual units on generalization accuracy: we ask, what is the role of a single unit in contributing to classification performance, and what characteristics of units are predictive of their contribution?
@cite_18 @cite_14 @cite_1 @cite_2
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Despite their ability to memorize large datasets, deep neural networks often achieve good generalization performance. However, the differences between the learned solutions of networks which generalize and those which do not remain unclear. Additionally, the tuning properties of single directions (defined as the activation of a single unit or some linear combination of units in response to some input) have been highlighted, but their importance has not been evaluated. Here, we connect these lines of inquiry to demonstrate that a network’s reliance on single directions is a good predictor of its generalization performance, across networks trained on datasets with different fractions of corrupted labels, across ensembles of networks trained on datasets with unmodified labels, across different hyper- parameters, and over the course of training. While dropout only regularizes this quantity up to a point, batch normalization implicitly discourages single direction reliance, in part by decreasing the class selectivity of individual units. Finally, we find that class selectivity is a poor predictor of task importance, suggesting not only that networks which generalize well minimize their dependence on individual units by reducing their selectivity, but also that individually selective units may not be necessary for strong network performance. Despite their ability to memorize large datasets, deep neural networks often achieve good generalization performance. However, the differences between the learned solutions of networks which generalize and those which do not remain unclear. Additionally, the tuning properties of single directions (defined as the activation of a single unit or some linear combination of units in response to some input) have been highlighted, but their importance has not been evaluated. Here, we connect these lines of inquiry to demonstrate that a network's reliance on single directions is a good predictor of its generalization performance, across networks trained on datasets with different fractions of corrupted labels, across ensembles of networks trained on datasets with unmodified labels, across different hyperparameters, and over the course of training. While dropout only regularizes this quantity up to a point, batch normalization implicitly discourages single direction reliance, in part by decreasing the class selectivity of individual units. Finally, we find that class selectivity is a poor predictor of task importance, suggesting not only that networks which generalize well minimize their dependence on individual units by reducing their selectivity, but also that individually selective units may not be necessary for strong network performance. Abstract We develop a technique to test the hypothesis that multilayered, feed-forward networks with few units on the first hidden layer generalize better than networks with many units in the first layer. Large networks are trained to perform a classification task and the redundant units are removed (“pruning”) to produce the smallest network capable of performing the task. A technique for inserting layers where pruning has introduced linear inseparability is also described. Two tests of ability to generalize are used—the ability to classify training inputs corrupted by noise and the ability to classify new patterns from each class. The hypothesis is found to be false for networks trained with noisy inputs. Pruning to the minimum number of units in the first layer produces networks which correctly classify the training set but generalize poorly compared with larger networks. The success of recent deep convolutional neural networks (CNNs) depends on learning hidden representations that can summarize the important factors of variation behind the data. In this work, we describe Network Dissection, a method that interprets networks by providing meaningful labels to their individual units. The proposed method quantifies the interpretability of CNN representations by evaluating the alignment between individual hidden units and visual semantic concepts. By identifying the best alignments, units are given interpretable labels ranging from colors, materials, textures, parts, objects and scenes. The method reveals that deep representations are more transparent and interpretable than they would be under a random equivalently powerful basis. We apply our approach to interpret and compare the latent representations of several network architectures trained to solve a wide range of supervised and self-supervised tasks. We then examine factors affecting the network interpretability such as the number of the training iterations, regularizations, different initialization parameters, as well as networks depth and width. Finally we show that the interpreted units can be used to provide explicit explanations of a given CNN prediction for an image. Our results highlight that interpretability is an important property of deep neural networks that provides new insights into what hierarchical structures can learn. Deep convolutional networks have achieved successful performance in data mining field. However, training large networks still remains a challenge, as the training data may be insufficient and the model can easily get overfitted. Hence the training process is usually combined with a model regularization. Typical regularizers include weight decay, Dropout, etc. In this paper, we propose a novel regularizer, named Structured Decorrelation Constraint (SDC), which is applied to the activations of the hidden layers to prevent overfitting and achieve better generalization. SDC impels the network to learn structured representations by grouping the hidden units and encouraging the units within the same group to have strong connections during the training procedure. Meanwhile, it forces the units in different groups to learn non-redundant representations by minimizing the cross-covariance between them. Compared with Dropout, SDC reduces the co-adaptions between the hidden units in an explicit way. Besides, we propose a novel approach called Reg-Conv that can help SDC to regularize the complex convolutional layers. Experiments on extensive datasets show that SDC significantly reduces overfitting and yields very meaningful improvements on classification performance (on CIFAR-10 6.22 accuracy promotion and on CIFAR-100 9.63 promotion). The success of recent deep convolutional neural networks (CNNs) depends on learning hidden representations that can summarize the important factors of variation behind the data. However, CNNs often criticized as being black boxes that lack interpretability, since they have millions of unexplained model parameters. In this work, we describe Network Dissection, a method that interprets networks by providing labels for the units of their deep visual representations. The proposed method quantifies the interpretability of CNN representations by evaluating the alignment between individual hidden units and a set of visual semantic concepts. By identifying the best alignments, units are given human interpretable labels across a range of objects, parts, scenes, textures, materials, and colors. The method reveals that deep representations are more transparent and interpretable than expected: we find that representations are significantly more interpretable than they would be under a random equivalently powerful basis. We apply the method to interpret and compare the latent representations of various network architectures trained to solve different supervised and self-supervised training tasks. We then examine factors affecting the network interpretability such as the number of the training iterations, regularizations, different initializations, and the network depth and width. Finally we show that the interpreted units can be used to provide explicit explanations of a prediction given by a CNN for an image. Our results highlight that interpretability is an important property of deep neural networks that provides new insights into their hierarchical structure. Estimating the effects of interventions in networks is complicated when the units are interacting, such that the outcomes for one unit may depend on the treatment assignment and behavior of many or all other units (i.e., there is interference). When most or all units are in a single connected component, it is impossible to directly experimentally compare outcomes under two or more global treatment assignments since the network can only be observed under a single assignment. Familiar formalism, experimental designs, and analysis methods assume the absence of these interactions, and result in biased estimators of causal effects of interest. While some assumptions can lead to unbiased estimators, these assumptions are generally unrealistic, and we focus this work on realistic assumptions. Thus, in this work, we evaluate methods for designing and analyzing randomized experiments that aim to reduce this bias and thereby reduce overall error. In design, we consider the ability to perform random assignment to treatments that is correlated in the network, such as through graph cluster randomization. In analysis, we consider incorporating information about the treatment assignment of network neighbors. We prove sufficient conditions for bias reduction through both design and analysis in the presence of potentially global interference. Through simulations of the entire process of experimentation in networks, we measure the performance of these methods under varied network structure and varied social behaviors, finding substantial bias and error reductions. These improvements are largest for networks with more clustering and data generating processes with both stronger direct effects of the treatment and stronger interactions between units. Recently, neuron activations extracted from a pre-trained convolutional neural network (CNN) show promising performance in various visual tasks. However, due to the domain and task bias, using the features generated from the model pre-trained for image classification as image representations for instance retrieval is problematic. In this paper, we propose quartet-net learning to improve the discriminative power of CNN features for instance retrieval. The general idea is to map the features into a space where the image similarity can be better evaluated. Our network differs from the traditional Siamese-net in two ways. First, we adopt a double-margin contrastive loss with a dynamic margin tuning strategy to train the network which leads to more robust performance. Second, we introduce in the mimic learning regularization to improve the generalization ability of the network by preventing it from overfitting to the training data. Catering for the network learning, we collect a large-scale dataset, namely GeoPair, which consists of 68k matching image pairs and 63k non-matching pairs. Experiments on several standard instance retrieval datasets demonstrate the effectiveness of our method. We propose a general framework called Network Dissection for quantifying the interpretability of latent representations of CNNs by evaluating the alignment between individual hidden units and a set of semantic concepts. Given any CNN model, the proposed method draws on a broad data set of visual concepts to score the semantics of hidden units at each intermediate convolutional layer. The units with semantics are given labels across a range of objects, parts, scenes, textures, materials, and colors. We use the proposed method to test the hypothesis that interpretability of units is equivalent to random linear combinations of units, then we apply our method to compare the latent representations of various networks when trained to solve different supervised and self-supervised training tasks. We further analyze the effect of training iterations, compare networks trained with different initializations, examine the impact of network depth and width, and measure the effect of dropout and batch normalization on the interpretability of deep visual representations. We demonstrate that the proposed method can shed light on characteristics of CNN models and training methods that go beyond measurements of their discriminative power. We propose a general framework called Network Dissection for quantifying the interpretability of latent representations of CNNs by evaluating the alignment between individual hidden units and a set of semantic concepts. Given any CNN model, the proposed method draws on a data set of concepts to score the semantics of hidden units at each intermediate convolutional layer. The units with semantics are labeled across a broad range of visual concepts including objects, parts, scenes, textures, materials, and colors. We use the proposed method to test the hypothesis that interpretability is an axis-independent property of the representation space, then we apply the method to compare the latent representations of various networks when trained to solve different classification problems. We further analyze the effect of training iterations, compare networks trained with different initializations, and measure the effect of dropout and batch normalization on the interpretability of deep visual representations. We demonstrate that the proposed method can shed light on characteristics of CNN models and training methods that go beyond measurements of their discriminative power. Publisher Summary Connectionist networks in which information is stored in weights on connections among simple processing units have attracted considerable interest in cognitive science. Much of the interest centers around two characteristics of these networks. First, the weights on connections between units need not be prewired by the model builder but rather may be established through training in which items to be learned are presented repeatedly to the network and the connection weights are adjusted in small increments according to a learning algorithm. Second, the networks may represent information in a distributed fashion. This chapter discusses the catastrophic interference in connectionist networks. Distributed representations established through the application of learning algorithms have several properties that are claimed to be desirable from the standpoint of modeling human cognition. These properties include content-addressable memory and so-called automatic generalization in which a network trained on a set of items responds correctly to other untrained items within the same domain. New learning may interfere catastrophically with old learning when networks are trained sequentially. The analysis of the causes of interference implies that at least some interference will occur whenever new learning may alter weights involved in representing old learning, and the simulation results demonstrate only that interference is catastrophic in some specific networks. We introduce the "exponential linear unit" (ELU) which speeds up learning in deep neural networks and leads to higher classification accuracies. Like rectified linear units (ReLUs), leaky ReLUs (LReLUs) and parametrized ReLUs (PReLUs), ELUs alleviate the vanishing gradient problem via the identity for positive values. However, ELUs have improved learning characteristics compared to the units with other activation functions. In contrast to ReLUs, ELUs have negative values which allows them to push mean unit activations closer to zero like batch normalization but with lower computational complexity. Mean shifts toward zero speed up learning by bringing the normal gradient closer to the unit natural gradient because of a reduced bias shift effect. While LReLUs and PReLUs have negative values, too, they do not ensure a noise-robust deactivation state. ELUs saturate to a negative value with smaller inputs and thereby decrease the forward propagated variation and information. Therefore, ELUs code the degree of presence of particular phenomena in the input, while they do not quantitatively model the degree of their absence. In experiments, ELUs lead not only to faster learning, but also to significantly better generalization performance than ReLUs and LReLUs on networks with more than 5 layers. On CIFAR-100 ELUs networks significantly outperform ReLU networks with batch normalization while batch normalization does not improve ELU networks. ELU networks are among the top 10 reported CIFAR-10 results and yield the best published result on CIFAR-100, without resorting to multi-view evaluation or model averaging. On ImageNet, ELU networks considerably speed up learning compared to a ReLU network with the same architecture, obtaining less than 10 classification error for a single crop, single model network. Generalization continues to be one of the most important topic in neural networks and other classifiers. In the last number of years, number of different methods have been developed to improve generalization accuracy. Any classifier that uses induction to find the class concept from the training patterns will have a hard time to achieve an acceptable level of generalization accuracy when the problem to be learned is a statistically neutral problem. A problem is statistically neutral if the probability of mapping an input onto an output is always the chance value of 0.5. We examine the generalization behaviour of multilayer neural networks on learning statistically neutral problems using single level learning models (e.g., conventional cross-validation scheme) as well as multiple level learning models (e.g., stacked generalization method). We show that for statistically neutral problems such as parity and majority function, the stacked generalization scheme improves classification performance and generalization accuracy over the single level cross-validation model. Our goal is to combine the rich multistep inference of symbolic logical reasoning with the generalization capabilities of neural networks. We are particularly interested in complex reasoning about entities and relations in text and large-scale knowledge bases (KBs). (2015) use RNNs to compose the distributed semantics of multi-hop paths in KBs; however for multiple reasons, the approach lacks accuracy and practicality. This paper proposes three significant modeling advances: (1) we learn to jointly reason about relations, entities, and entity-types; (2) we use neural attention modeling to incorporate multiple paths; (3) we learn to share strength in a single RNN that represents logical composition across all relations. On a largescale Freebase+ClueWeb prediction task, we achieve 25 error reduction, and a 53 error reduction on sparse relations due to shared strength. On chains of reasoning in WordNet we reduce error in mean quantile by 84 versus previous state-of-the-art. The code and data are available at this https URL I propose a novel general principle for unsupervised learning of distributed nonredundant internal representations of input patterns. The principle is based on two opposing forces. For each representational unit there is an adaptive predictor, which tries to predict the unit from the remaining units. In turn, each unit tries to react to the environment such that it minimizes its predictability. This encourages each unit to filter "abstract concepts" out of the environmental input such that these concepts are statistically independent of those on which the other units focus. I discuss various simple yet potentially powerful implementations of the principle that aim at finding binary factorial codes ( 1989), i.e., codes where the probability of the occurrence of a particular input is simply the product of the probabilities of the corresponding code symbols. Such codes are potentially relevant for (1) segmentation tasks, (2) speeding up supervised learning, and (3) novelty detection. Methods for... Deep convolutional neural networks (DCNNs) have shown remarkable performance in image classification tasks in recent years. Generally, deep neural network architectures are stacks consisting of a large number of convolutional layers, and they perform downsampling along the spatial dimension via pooling to reduce memory usage. Concurrently, the feature map dimension (i.e., the number of channels) is sharply increased at downsampling locations, which is essential to ensure effective performance because it increases the diversity of high-level attributes. This also applies to residual networks and is very closely related to their performance. In this research, instead of sharply increasing the feature map dimension at units that perform downsampling, we gradually increase the feature map dimension at all units to involve as many locations as possible. This design, which is discussed in depth together with our new insights, has proven to be an effective means of improving generalization ability. Furthermore, we propose a novel residual unit capable of further improving the classification accuracy with our new network architecture. Experiments on benchmark CIFAR-10, CIFAR-100, and ImageNet datasets have shown that our network architecture has superior generalization ability compared to the original residual networks. Code is available at this https URL There has been a quickly growing interest in networks, since they can represent the structure of a wide class of complex systems occurring from the level of cells to society. Data obtained on real networks show that the corresponding graphs exhibit unexpected nontrivial properties, e.g., anomalous degree distributions, diameter, spreading phenomena, clustering coefficient, and correlations [1]. Very recently great attention has been paid to the local structural units of networks. Small and well defined subgraphs have been introduced as ‘‘motifs’’ [2]. Their distribution and clustering properties [2,3] can be used to interpret global features as well. Somewhat larger units, made up of vertices that are more densely connected to each other than to the rest of the network, are often referred to as communities [4], and have been considered to be the essential structural units of real networks. They have no obvious definition, and most of the recent methods for their identification rely on dividing the network into smaller pieces. The biggest drawback of these methods is that they do not allow for overlapping communities, although overlaps are generally assumed to be crucial features of communities. In this Letter we lay down the fundamentals of a kind of percolation phenomenon on graphs, which can also be used as an effective and deterministic method for uniquely identifying overlapping communities in large real networks [5]. Meanwhile, the various aspects of the classical Erdo ýs The optimal selection of neural network architecture is a problem of significant theoretical and practical importance. The functional capacity of the network architecture determines the generalization properties and the computational complexity of the algorithm. For supervised training of feed-forward networks, current generalization theories tell us to minimize the functional capacity, i.e., the number of weights subject to the constraints imposed by the rule implicit in the training examples see e.g., (, 91). Several schemes have been proposed for pruning of the network architecture. The optimal brain damage method for network pruning proposed in (, 90) has been successful for pruning of classifiers as well as for pruning of regression networks for time series processing (, 93). The optimal brain surgeon (OBS) advanced in (Hassihi and Stork, 92) provides a refined estimate of the weight saliency, by incorporating the effects of quadratic retraining; however, at the expense of Irignificant additional computation. Likewise, growth algorithms are legio. Among these, Fahlman’s cascade correlation stands out for solving hard classification problems (Fahlman and Lebiere, 89). In the standard implementation cascade correlation adds hidden units that are fully connected to all input units and to all previously added hidden units, thereby rapidly increasing the number of weights in the network with the obvious danger of overfitting. This paper proposes a means of using the knowledge in a network to determine the functionality or relevance of individual units, both for the purpose of understanding the network's behavior and improving its performance. The basic idea is to iteratively train the network to a certain performance criterion, compute a measure of relevance that identifies which input or hidden units are most critical to performance, and automatically trim the least relevant units. This skeletonization technique can be used to simplify networks by eliminating units that convey redundant information; to improve learning performance by first learning with spare hidden units and then trimming the unnecessary ones away, thereby constraining generalization; and to understand the behavior of networks in terms of minimal "rules." Convolutional neural nets (CNNs) have demonstrated remarkable performance in recent history. Such approaches tend to work in a "unidirectional" bottom-up feed-forward fashion. However, practical experience and biological evidence tells us that feedback plays a crucial role, particularly for detailed spatial understanding tasks. This work explores "bidirectional" architectures that also reason with top-down feedback: neural units are influenced by both lower and higher-level units. We do so by treating units as rectified latent variables in a quadratic energy function, which can be seen as a hierarchical Rectified Gaussian model (RGs) [39]. We show that RGs can be optimized with a quadratic program (QP), that can in turn be optimized with a recurrent neural network (with rectified linear units). This allows RGs to be trained with GPU-optimized gradient descent. From a theoretical perspective, RGs help establish a connection between CNNs and hierarchical probabilistic models. From a practical perspective, RGs are well suited for detailed spatial tasks that can benefit from top-down reasoning. We illustrate them on the challenging task of keypoint localization under occlusions, where local bottom-up evidence may be misleading. We demonstrate state-of-the-art results on challenging benchmarks.