Furthermore, we prove a corresponding non-asymptotic result.

Regularization techniques play a crucial role in preventing overfitting and improving the generalization performance of neural networks. Dropout, a widely used regularization technique, randomly deactivates units during training to introduce redundancy and prevent co-adaptation among neurons. Despite its effectiveness, dropout has limitations, such as its static nature and lack of interpretability. In this paper, we propose a novel approach to regularization by substituting dropout with Conway's Game of Life (GoL), a cellular automata with simple rules that govern the evolution of a grid of cells. We introduce dynamic unit deactivation during training by representing neural network units as cells in a GoL grid and applying the game's rules to deactivate units. This approach allows for the emergence of spatial patterns that adapt to the training data, potentially enhancing the network's ability to generalize. We demonstrate the effectiveness of our approach on the CIFAR-10 dataset, showing that dynamic unit deactivation using GoL achieves comparable performance to traditional dropout techniques while offering insights into the network's behavior through the visualization of evolving patterns. Furthermore, our discussion highlights the applicability of our proposal in deeper architectures, demonstrating how it enhances the performance of different dropout techniques.

Furthermore, we prove a corresponding non-asymptotic result.

Neural Information Processing Systems http://nips.cc/

Training deep feature hierarchies to solve supervised learning tasks has achieved state of the art performance on many problems in computer vision. However, a principled way in which to train such hierarchies in the unsupervised setting has remained elusive. In this work we suggest a new architecture and loss for training deep feature hierarchies that linearize the transformations observed in unlabeled natural video sequences. This is done by training a generative model to predict video frames. We also address the problem of inherent uncertainty in prediction by introducing latent variables that are non-deterministic functions of the input into the network architecture.

We study the node classification problem on feature-decorated graphs in the sparse setting, i.e., when the expected degree of a node is $O(1)$ in the number of nodes, in the fixed-dimensional asymptotic regime, i.e., the dimension of the feature data is fixed while the number of nodes is large. Such graphs are typically known to be locally tree-like. We introduce a notion of Bayes optimality for node classification tasks, called asymptotic local Bayes optimality, and compute the optimal classifier according to this criterion for a fairly general statistical data model with arbitrary distributions of the node features and edge connectivity. The optimal classifier is implementable using a message-passing graph neural network architecture. We then compute the generalization error of this classifier and compare its performance against existing learning methods theoretically on a well-studied statistical model with naturally identifiable signal-to-noise ratios (SNRs) in the data. We find that the optimal message-passing architecture interpolates between a standard MLP in the regime of low graph signal and a typical convolution in the regime of high graph signal. Furthermore, we prove a corresponding non-asymptotic result.

Note that most widely used benchmark datasets for point cloud classification only contain foreground objects. Therefore, we generate a new dataset, where each point cloud contains both the foreground object and the background. In this new dataset, the background is composed of points that carry no relevant information of the foreground. We will introduce details in Section 5. Metric 3, rotation robustness: The rotation robustness is proposed to measure whether a DNN uses similar subsets of two point clouds to compute the intermediate-layer feature, if the two point clouds have the same shape but different orientations. Let X θ 1 and X θ 2 denote the point clouds that have the same global shape but different orientations θ 1 and θ 2. To quantify the similarity of the attention on the two point clouds, we compute the Jensen-Shannon divergence between the distributions of the perturbed inputs ˆ X θ 1 X θ 1 δ 1 and ˆ X θ 2 X θ 2 δ 2. ˆ X θ 1 and ˆ X θ 2 denote the perturbed inputs, which are computed to measure information discarding in Equation (1).

Training deep feature hierarchies to solve supervised learning tasks has achieving state of the art performance on many problems in computer vision. However, a principled way in which to train such hierarchies in the unsupervised setting has remained elusive. In this work we suggest a new architecture and loss for training deep feature hierarchies that linearize the transformations observed in unlabelednatural video sequences. This is done by training a generative model to predict video frames. We also address the problem of inherent uncertainty in prediction by introducing a latent variables that are non-deterministic functions of the input into the network architecture.