In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low dimensional topological map for each of them. When it is trained as an autoencoder, the inherent topological structure of the data can be visualized, while when it is trained as a classifier, the topological structure is further constrained by the concept, for example the labels the data, hence the visualization is not only structural but also conceptual. The proposed neural network significantly differ from many dimensional reduction models, primarily in its ability to execute both supervised and unsupervised dimensional reduction. The neural network allows multi perspective visualization of the data, and thus giving more flexibility in data analysis. This paper is supported by preliminary but intuitive visualization experiments.

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t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions. However, it has a large computational cost, especially when the input data has many dimensions. Many use t-SNE to embed the output of a neural network, which is generally of much lower dimension than the original data. This limits the use of t-SNE in unsupervised scenarios. We propose using \textit{random} projections to embed high dimensional datasets into relatively few dimensions, and then using t-SNE to obtain a two dimensional embedding. We show that random projections preserve the desirable clustering achieved by t-SNE, while dramatically reducing the runtime of finding the embedding.

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In this short paper, a neural network that is able to form a low dimensional topological hidden representation is explained. The neural network can be trained as an autoencoder, a classifier or mix of both, and produces different low dimensional topological map for each of them. When it is trained as an autoencoder, the inherent topological structure of the data can be visualized, while when it is trained as a classifier, the topological structure is further constrained by the concept, for example the labels the data, hence the visualization is not only structural but also conceptual. The proposed neural network significantly differ from many dimensional reduction models, primarily in its ability to execute both supervised and unsupervised dimensional reduction. The neural network allows multi perspective visualization of the data, and thus giving more flexibility in data analysis. This paper is supported by preliminary but intuitive visualization experiments.

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Despite the success of deep neural networks (DNNs), state-of-the-art models are too large to deploy on low-resource devices or common server configurations in which multiple models are held in memory. Model compression methods address this limitation by reducing the memory footprint, latency, or energy consumption of a model with minimal impact on accuracy. We focus on the task of reducing the number of learnable variables in the model. In this work we combine ideas from weight hashing and dimensionality reductions resulting in a simple and powerful structured multi-hashing method based on matrix products that allows direct control of model size of any deep network and is trained end-to-end. We demonstrate the strength of our approach by compressing models from the ResNet, EfficientNet, and MobileNet architecture families. Our method allows us to drastically decrease the number of variables while maintaining high accuracy. For instance, by applying our approach to EfficentNet-B4 (16M parameters) we reduce it to to the size of B0 (5M parameters), while gaining over 3% in accuracy over B0 baseline. On the commonly used benchmark CIFAR10 we reduce the ResNet32 model by 75% with no loss in quality, and are able to do a 10x compression while still achieving above 90% accuracy.

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The unification of low-level perception and high-level reasoning is a long-standing problem in artificial intelligence, which has the potential to not only bring the areas of logic and learning closer together but also demonstrate how abstract concepts might emerge from sensory data. Precisely because deep learning methods dominate perception-based learning, including vision, speech, and linguistic grammar, there is fast-growing literature on how to integrate symbolic reasoning and deep learning. Broadly, efforts seem to fall into three camps: those focused on defining a logic whose formulas capture deep learning, ones that integrate symbolic constraints in deep learning, and others that allow neural computations and symbolic reasoning to co-exist separately, to enjoy the strengths of both worlds. In this paper, we identify another dimension to this inquiry: what do the hidden layers really capture, and how can we reason about that logically? In particular, we consider autoencoders that are widely used for dimensionality reduction and inject a symbolic generative framework onto the feature layer. This allows us, among other things, to generate example images for a class to get a sense of what was learned. Moreover, the modular structure of the proposed model makes it possible to learn relations over multiple images at a time, as well as handle noisy labels. Our empirical evaluations show the promise of this inquiry.

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