Understanding why and how certain neural networks outperform others is key to guiding future development of network architectures and optimization methods. To this end, we introduce a novel visualization algorithm that reveals the internal geometry of such networks: Multislice PHATE (M-PHATE), the first method designed explicitly to visualize how a neural network's hidden representations of data evolve throughout the course of training. We demonstrate that our visualization provides intuitive, detailed summaries of the learning dynamics beyond simple global measures (i.e., validation loss and accuracy), without the need to access validation data. Furthermore, M-PHATE better captures both the dynamics and community structure of the hidden units as compared to visualization based on standard dimensionality reduction methods (e.g., ISOMAP, t-SNE). We demonstrate M-PHATE with two vignettes: continual learning and generalization. In the former, the M-PHATE visualizations display the mechanism of catastrophic forgetting which is a major challenge for learning in task-switching contexts. In the latter, our visualizations reveal how increased heterogeneity among hidden units correlates with improved generalization performance.

This paper proposes a method to visualize the discrimination power of intermediate-layer visual patterns encoded by a DNN. Specifically, we visualize (1) how the DNN gradually learns regional visual patterns in each intermediate layer during the training process, and (2) the effects of the DNN using non-discriminative patterns in low layers to construct disciminative patterns in middle/high layers through the forward propagation. Based on our visualization method, we can quantify knowledge points (i.e. the number of discriminative visual patterns) learned by the DNN to evaluate the representation capacity of the DNN. Furthermore, this method also provides new insights into signal-processing behaviors of existing deep-learning techniques, such as adversarial attacks and knowledge distillation.

Neural network training relies on our ability to find good minimizers of highly non-convex loss functions. It is well known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce minimizers that generalize better. However, the reasons for these differences, and their effect on the underlying loss landscape, is not well understood. In this paper, we explore the structure of neural loss functions, and the effect of loss landscapes on generalization, using a range of visualization methods. First, we introduce a simple filter normalization method that helps us visualize loss function curvature, and make meaningful side-by-side comparisons between loss functions. Then, using a variety of visualizations, we explore how network architecture affects the loss landscape, and how training parameters affect the shape of minimizers.

Understanding why and how certain neural networks outperform others is key to guiding future development of network architectures and optimization methods. To this end, we introduce a novel visualization algorithm that reveals the internal geometry of such networks: Multislice PHATE (M-PHATE), the first method designed explicitly to visualize how a neural network's hidden representations of data evolve throughout the course of training. We demonstrate that our visualization provides intuitive, detailed summaries of the learning dynamics beyond simple global measures (i.e., validation loss and accuracy), without the need to access validation data. Furthermore, M-PHATE better captures both the dynamics and community structure of the hidden units as compared to visualization based on standard dimensionality reduction methods (e.g., ISOMAP, t-SNE). We demonstrate M-PHATE with two vignettes: continual learning and generalization.

Update after author response: Taking on faith the results the authors report in their author response (namely ability to identify generalization performance using only the training set, results on CIFAR10 and white noise datasets, and the quantitative evaluation of the task-switching), I would raise my score to a 6 (actually if they did achieve everything they claimed in the author response, I would be inclined to give it a 7, but I'd need to see all the results for that). Originality: I think the originality is fairly high. Although the PHATE algorithm exists in the literature, the Multislice kernel is novel, and the idea of visualizing the learning dynamics of the hidden neurons to ascertain things like catastrophic forgetting or poor generalization is (to my knowledge) novel. Quality: I think the Experiments sections could be substantially improved: (1) For the experiments on continual learning, from looking at Figure 3 it is not obvious to me that Adagrad does better than Rehearsal for the "Domain" learning setting, or that Adagrad outperforms Adam at class learning. Adam apparently does the best at task learning, but again, I wouldn't have guessed from the trajectories.

The reviewers are all positive if not wildly so, and as the response suggests I would like to not put too much weight on the specific scores. This is a good submission that has a small number of clearly defined improvements outlined in the extensive and helpful reviews.

Information can be expressed in multiple formats including natural language, images, and motions. Human intelligence usually faces little difficulty to convert from one format to another format, which often shows a true understanding of encoded information. Moreover, such conversions have broad application in many real-world applications. In this paper, we present a text visualization system that can visualize free text with animations. Our system is illustrated by visualizing example sentences of elementary Physics laws.

Understanding why and how certain neural networks outperform others is key to guiding future development of network architectures and optimization methods. To this end, we introduce a novel visualization algorithm that reveals the internal geometry of such networks: Multislice PHATE (M-PHATE), the first method designed explicitly to visualize how a neural network's hidden representations of data evolve throughout the course of training. We demonstrate that our visualization provides intuitive, detailed summaries of the learning dynamics beyond simple global measures (i.e., validation loss and accuracy), without the need to access validation data. Furthermore, M-PHATE better captures both the dynamics and community structure of the hidden units as compared to visualization based on standard dimensionality reduction methods (e.g., ISOMAP, t-SNE). We demonstrate M-PHATE with two vignettes: continual learning and generalization.

This paper proposes a method to visualize the discrimination power of intermediate-layer visual patterns encoded by a DNN. Specifically, we visualize (1) how the DNN gradually learns regional visual patterns in each intermediate layer during the training process, and (2) the effects of the DNN using non-discriminative patterns in low layers to construct disciminative patterns in middle/high layers through the forward propagation. Based on our visualization method, we can quantify knowledge points (i.e. the number of discriminative visual patterns) learned by the DNN to evaluate the representation capacity of the DNN. Furthermore, this method also provides new insights into signal-processing behaviors of existing deep-learning techniques, such as adversarial attacks and knowledge distillation.

Overview: Visualizing the loss landscape of the parameters in neural nets is hard, as the dimension of parameters in neural network is huge. Being able to visualize the loss landscape in neural net could help us understand how different techniques are helping to shape the loss surface, and how the loss surface "sharpness" vs "flatness" are related to generalization error. Previous works include interpolating a 1D loss path between the parameters of two models to reveal the loss surface along the paths. However, 1D visualization sometimes can be misleading and losing critical information about the surrounding loss surface and local minimums. For 2D visualizations, usually 2 directions are selected for interpolating the loss surface along the 2 directions from an origin. However, as the neural net has a "scale-invariant" problem, which means the weights in different layers can appear in different orders but remain the same effect.