An Interactive Node Link Visualization of Convolutional

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868 A W Harley, Fig 1 The proposed visualization an interactive node link diagram of a convolutional. neural network trained to recognize handwritten digits On the left is a drawing pad. where the user can draw numbers for the network to classify The activation level of. each node is encoded in hue and brightness Studying the architecture of the network. and experimenting with its input output process can enlighten students of machine. learning as to how the network performs its abstraction from images to digits. explore the layer by layer output of a network and build intuitions about how. neural networks perform hierarchical abstraction from input to output 5. This visualization is targeted towards students of machine learning who. are learning how to design code and train new neural networks To make the. visualization useful to that audience the visualization is based on the well. established node link diagram representation of fully connected neural networks. The visualization is supported by an actual neural network designed and trained. to recognize handwritten digits with high 99 accuracy In the neural network. literature handwritten digit recognition is a well known solved problem and. often serves as an example of an appropriate application of neural networks 6. Users are able to interact with this network through a drawing pad on which. they can write new numbers for the network to recognize A screenshot of the. visualization is shown in Fig 1, This paper begins by reviewing prior work on visualizing neural networks. with a special emphasis on identifying why the classic node link diagram repre. sentation has endured the test of time The paper then proceeds to describe the. approach to developing the current visualization considering the challenges of. revealing inner detail the use of color and the elements of interaction Finally. the e ectiveness of the visualization is discussed and future work is proposed. Contributions The proposed visualization is the rst to accurately and inter. actively illustrate the structure scale and low level inner workings of a CNN. applied to a practical computer vision problem Prior work on this topic was. limited to simpler architectures smaller problems or static visualizations The. new visualization can be explored at http scs ryerson ca aharley vis. Interactive Node Link Visualization of CNNs 869, Fig 2 Typical illustrations of fully connected left and convolutional right neural. networks adapted from 12,2 Background and Related Work. This section establishes the context of the current work by i de ning neural. networks and exploring why node link diagrams are typically used to represent. them ii examining the challenges of complexity and scale that arise when using. node link diagrams for large neural networks and iii considering the e ective. use of interaction,2 1 Neurons as Nodes in a Graph.
Neural networks compose many small functions in a network like architecture. creating a larger function capable of pattern recognition 7 In biological neural. networks the unitary function is a neuron and neurons are connected together. in extremely complex arrangements 8 Arti cial neural networks can be arbi. trarily simple One of the simplest arrangements is as a feed forward graph. with stacked layers of nodes where every pair of neighboring layers is fully. connected 9 10 see Fig 2 left This arrangement is called a fully connected. neural network A node link visualization of this type of network is a straight. forward outcome of i treating all neurons as identical processor units and ii. choosing an arrangement of neurons de ned by a simple graph architecture For. these reasons node link diagrams of fully connected networks are a mainstay in. the inventory of visualizations for machine learning educators and researchers. e g see 6 11, Modern implementations of neural networks often use more complex archi. tectures but the variations typically appear underneath a traditional fully. connected network That is these implementations process the raw input such. as an image with an alternative network and then use the output of that net. work as input to a fully connected network Convolutional networks interact with. fully connected networks in this way Figure 2 right shows a typical diagram. for illustrating a CNN The algorithm for CNNs relies heavily on the convolution. operation which is used to sequentially apply a series of learned lters to the. input A CNN can also be interpreted as a graph which although is di erent in. appearance from the fully connected network graph uses all the same mathe. matics for learning 12 Figure 3 illustrates how convolutions can be interpreted. as graph like connections For students learning about CNNs for the rst time. it can be di cult to mentally assimilate the relationship between node link dia. grams and convolutional nets One of the goals of the current visualization is to. make this relationship easier to understand,870 A W Harley. Fig 3 A 3 3 convolution lter is equivalent to a node with nine weighted connections. where the lter values correspond to the weights A convolution layer applies this lter. to every location in the input image producing a new ltered image. 2 2 Challenges of Complexity and Scale, The visualizations of neural networks in machine learning literature have changed. only slightly over the years The most signi cant trend is that the node link. diagrams have become smaller and less detailed over time This is consistent with. fully connected networks declining novelty and re ects an intent of emphasizing. things other than the structure of the networks The most common simpli ed. representation replaces each layer of nodes with a solid block and replaces the. dense connections between layers with either a single arrow pointing from one. layer to the next 1 or with edges connecting the outskirts of the layers 13. Simplifying the node link diagram into a block diagram also addresses a problem. of scale To solve problems of practical value the required network is often. enormously large A node link diagram of such a network would have enough. edges that the space in between layers would be opaque with lines A block. diagram is therefore an e ective way of overcoming this problem of scale The. fully connected portion of the CNN in Fig 2 shows a simpli cation along these. The main issue with grouping the nodes together by layer is that it eliminates. the possibility for interaction and detailed analysis In other domains where. analysis is often the primary focus other solutions have been introduced For. example it is sometimes possible to reveal a great deal of information about a set. of connected nodes by bundling related edges together 14 An alternative is to. display only a representative subset of the nodes or perhaps allow users to hover. over a node to see edges or stubs leading into it 15 16 A closely related strategy. to these is the use of multi scale navigation to search show context expand. on demand 17 In all visualization research indicates that focus plus context. techniques 18 could serve as reasonable alternatives to simply not showing the. edges The current work makes use of these ideas,2 3 Prior Interactive Visualizations. Many interactive neural network visualizations exist An early and popular visu. alization is the Stuttgart Neural Network Simulator SNNS 19 which shows. neural nets as 2D and 3D node link diagrams in which the nodes and edges. are colored in a scheme that maps negative and positive values to di erent ends. of a palette However SNNS is targeted toward researchers and accordingly. Interactive Node Link Visualization of CNNs 871, its interface and basic usage demand some expertise A similar tool is N2 VIS.
20 which additionally makes use of a compact matrix like visualization of. a neuron s weights in which each cell of the matrix represents a weight and. the cell is coloured according to the weight s magnitude This is very similar to. visualizing a CNN s parameters as lters although the networks and visualiza. tions in N2 VIS do not actually scale to convolutional networks and vision tasks. Interaction in these and similar research targeted applications e g 21 22 typ. ically centers around designing new networks and making minute adjustments. to trained networks to see how these changes a ect performance. Visualizations designed for a tutorial context are di erent For example. Neural Java 3 provides an extensive set of web based exercises and demos. allowing students to experiment with and learn about a variety of neural net. work designs In one application the user can make design choices on a network. tasked with solving a toy version of the handwritten digit recognition prob. lem Once the network is trained according to the user s settings the user can. use a cursor to draw new numbers for the network to classify and view the. network s classi cation output Despite there being no depiction of the actual. network being trained this type of application enables students to empirically. determine reasonable answers to a variety of challenging questions concerning. for example convergence the optimal number of nodes and layers translation. invariance and more These are the types of bene ts the current visualization. aims to deliver, Most interactive visualizations only depict fully connected networks and. furthermore only visualize networks that are too small to be e ective at com. puter vision problems A recent exception to this is ConvNetJS 23 which is a. JavaScript library for training neural networks The website for the project fea. tures a set of visualizations which have interactive examples of neural networks. As in Neural Java one example features a neural network solving a handwritten. digit recognition task although in this case using a standard dataset MNIST. 12 The visualization shows the network s layer by layer activation patterns in. response to example inputs which gives the user an in depth look at how the. network arrives at its nal classi cation A weakness of the visualization is that. the activation patterns are not organized in a way that shows the architecture. of the network e g in a node link diagram instead these are simply shown in. order from the zeroth layer to the nal layer Also unlike the example in Neural. Java this visualization does not allow users to interactively create new inputs. for the network to classify Nonetheless ConvNetJS sets a high benchmark for. scale and practical realism which the current visualization aims to match. 3 Technical Approach, This section describes the technical approach to creating the visualization framed. in the previous section The discussion begins with an analysis of the activities. that users of the visualization are expected to be interested in then proceeds to. describe the major visual elements employed to meet the requirements of those. 872 A W Harley, tasks The section concludes with a discussion of the various interactive elements. implemented,3 1 Task Analysis, The visualization should meet the following goals which summarize the unique. properties of convolutional networks in computer vision and re ect lessons. learned from prior work First the visualization should handle networks large. enough to solve practical vision tasks such as handwritten digit recognition Sec. ond the visualization should depict the entire network architecture with a node. link diagram Third the visualization should allow users to easily experiment. with the input output process of the network allowing them to judge the net. work s robustness to translational variance rotational variance and ambiguous. input Fourth the visualization should allow users to view details on individual. nodes such as the activation level the calculation being performed the learned. parameters i e the node s weights and the numerical inputs and outputs. 3 2 Visual Elements, This section describes the major visual elements of the visualization emphasizing.
their justi cation through the points established in the task analysis as well as. through theoretical principles of visualization Screenshots are shown in Fig 4. Node link Diagram The only issue with a straightforward implementation of. a node link diagram is that large networks yield a dense mass of edges between. layers This was addressed by only showing edges for one node at a time and only. on request This strategy is uniquely possible in domains with simple network. architectures unlike networks describing natural phenomena e g 15 24 the. edges of CNNs can be implied by their regular pattern This strategy achieves a. compromise between the block diagram s simplicity and the node link diagram s. potential for detail, Camera Users can zoom in and out by scrolling and translate the network by. dragging the right mouse button While exploring the visualization through these. controls the users can focus their attention on particular layers or features gain. familiarity with the architecture of the network and also build an appreciation. for the network s scale, Node Activations and Edge Strengths Displaying the activation levels. of individual nodes as well as the strength of edges between nodes is crucial. for creating an informative visualization of a neural network s behavior At the. zeroth layer of the network the individual nodes correspond to pixels in the input. image so the activation level of each node simply corresponds to the brightness. An Interactive Node Link Visualization of Convolutional Neural Networks Adam W Harley B Department of Computer Science Ryerson University Toronto ON M5B 2K3 Canada aharley scs ryerson ca Abstract Convolutional neural networks are at the core of state of the art approaches to a variety of computer vision tasks Visualizations of neural networks typically take the form of static diagrams

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