Scalable and Sustainable Deep Learning via Randomized Hashing

Current deep learning architectures are growing larger in order to learn from complex datasets. These architectures require giant matrix multiplication operations to train millions of parameters. Conversely, there is another growing trend to bring deep learning to low-power, embedded devices. The matrix operations, associated with both training and testing of deep networks, are very expensive from a computational and energy standpoint. We present a novel hashing based technique to drastically reduce the amount of computation needed to train and test deep networks. Our approach combines recent ideas from adaptive dropouts and randomized hashing for maximum inner product search to select the nodes with the highest activation efficiently. Our new algorithm for deep learning reduces the overall computational cost of forward and back-propagation by operating on significantly fewer (sparse) nodes. As a consequence, our algorithm uses only 5% of the total multiplications, while keeping on average within 1% of the accuracy of the original model. A unique property of the proposed hashing based back-propagation is that the updates are always sparse. Due to the sparse gradient updates, our algorithm is ideally suited for asynchronous and parallel training leading to near linear speedup with increasing number of cores. We demonstrate the scalability and sustainability (energy efficiency) of our proposed algorithm via rigorous experimental evaluations on several real datasets

End-to-end Sampling Patterns

Sample patterns have many uses in Computer Graphics, ranging from procedural object placement over Monte Carlo image synthesis to non-photorealistic depiction. Their properties such as discrepancy, spectra, anisotropy, or progressiveness have been analyzed extensively. However, designing methods to produce sampling patterns with certain properties can require substantial hand-crafting effort, both in coding, mathematical derivation and compute time. In particular, there is no systematic way to derive the best sampling algorithm for a specific end-task. Tackling this issue, we suggest another level of abstraction: a toolkit to end-to-end optimize over all sampling methods to find the one producing user-prescribed properties such as discrepancy or a spectrum that best fit the end-task. A user simply implements the forward losses and the sampling method is found automatically -- without coding or mathematical derivation -- by making use of back-propagation abilities of modern deep learning frameworks. While this optimization takes long, at deployment time the sampling method is quick to execute as iterated unstructured non-linear filtering using radial basis functions (RBFs) to represent high-dimensional kernels. Several important previous methods are special cases of this approach, which we compare to previous work and demonstrate its usefulness in several typical Computer Graphics applications. Finally, we propose sampling patterns with properties not shown before, such as high-dimensional blue noise with projective properties

Connectionist-Symbolic Machine Intelligence using Cellular Automata based Reservoir-Hyperdimensional Computing

We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is capable of long short-term memory and it requires orders of magnitude less computation compared to Echo State Networks. We prove that cellular automaton reservoir holds a distributed representation of attribute statistics, which provides a more effective computation than local representation. It is possible to estimate the kernel for linear cellular automata via metric learning, that enables a much more efficient distance computation in support vector machine framework. Also, binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing.Comment: Corrected Typos. Responded some comments on section 8. Added appendix for details. Recurrent architecture emphasize

Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders

Multivariate time series (MTS) imputation is a widely studied problem in recent years. Existing methods can be divided into two main groups, including (1) deep recurrent or generative models that primarily focus on time series features, and (2) graph neural networks (GNNs) based models that utilize the topological information from the inherent graph structure of MTS as relational inductive bias for imputation. Nevertheless, these methods either neglect topological information or assume the graph structure is fixed and accurately known. Thus, they fail to fully utilize the graph dynamics for precise imputation in more challenging MTS data such as networked time series (NTS), where the underlying graph is constantly changing and might have missing edges. In this paper, we propose a novel approach to overcome these limitations. First, we define the problem of imputation over NTS which contains missing values in both node time series features and graph structures. Then, we design a new model named PoGeVon which leverages variational autoencoder (VAE) to predict missing values over both node time series features and graph structures. In particular, we propose a new node position embedding based on random walk with restart (RWR) in the encoder with provable higher expressive power compared with message-passing based graph neural networks (GNNs). We further design a decoder with 3-stage predictions from the perspective of multi-task learning to impute missing values in both time series and graph structures reciprocally. Experiment results demonstrate the effectiveness of our model over baselines.Comment: KDD 202

Graph Interpolation via Fast Fused-Gromovization

Graph data augmentation has proven to be effective in enhancing the generalizability and robustness of graph neural networks (GNNs) for graph-level classifications. However, existing methods mainly focus on augmenting the graph signal space and the graph structure space independently, overlooking their joint interaction. This paper addresses this limitation by formulating the problem as an optimal transport problem that aims to find an optimal strategy for matching nodes between graphs considering the interactions between graph structures and signals. To tackle this problem, we propose a novel graph mixup algorithm dubbed FGWMixup, which leverages the Fused Gromov-Wasserstein (FGW) metric space to identify a "midpoint" of the source graphs. To improve the scalability of our approach, we introduce a relaxed FGW solver that accelerates FGWMixup by enhancing the convergence rate from $\mathcal{O}(t^{-1})$ to $\mathcal{O}(t^{-2})$. Extensive experiments conducted on five datasets, utilizing both classic (MPNNs) and advanced (Graphormers) GNN backbones, demonstrate the effectiveness of FGWMixup in improving the generalizability and robustness of GNNs