Modern neural networks demonstrate state-of-the-art performance on numerous existing benchmarks; however, their high computational requirements and energy consumption prompt researchers to seek more efficient solutions for real-world deployment. Logic gate networks (LGNs) learns a large network of logic gates for efficient image classification. However, learning a network that can solve a simple problem like CIFAR-10 can take days to weeks to train. Even then, almost half of the network remains unused, causing a discretization gap. This discretization gap hinders real-world deployment of LGNs, as the performance drop between training and inference negatively impacts accuracy. We inject Gumbel noise with a straight-through estimator during training to significantly speed up training, improve neuron utilization, and decrease the discretization gap. We theoretically show that this results from implicit Hessian regularization, which improves the convergence properties of LGNs. We train networks $4.5 \times$ faster in wall-clock time, reduce the discretization gap by $98\%$, and reduce the number of unused gates by $100\%$.

Habibian et al., 2019, Y ang et al., 2020a], which can reduce a sizable amount of global internet traffic. State-of-the-art neural methods for lossy image compression [Ballé et al., 2018, Minnen et al., 2018, Lee et al., 2019] learn a mapping between images and latent variables with a variational

We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation of each data point. Drawing on the variational inference perspective on compression, we identify three approximation gaps which limit performance in the conventional approach: (i) an amortization gap, (ii) a discretization gap, and (iii) a marginalization gap. We propose improvements to each of these three shortcomings based on ideas related to iterative inference, stochastic annealing for discrete optimization, and bits-back coding, resulting in the first application of bits-back coding to lossy compression. In our experiments, which include extensive baseline comparisons and ablation studies, we achieve new state-of-the-art performance on lossy image compression using an established VAE architecture, by changing only the inference method.

Conservation efforts in green security domains to protect wildlife and forests are constrained by the limited availability of defenders (i.e., patrollers), who must patrol vast areas to protect from attackers (e.g., poachers or illegal loggers). Defenders must choose how much time to spend in each region of the protected area, balancing exploration of infrequently visited regions and exploitation of known hotspots. We formulate the problem as a stochastic multi-armed bandit, where each action represents a patrol strategy, enabling us to guarantee the rate of convergence of the patrolling policy. However, a naive bandit approach would compromise short-term performance for long-term optimality, resulting in animals poached and forests destroyed. To speed up performance, we leverage smoothness in the reward function and decomposability of actions. We show a synergy between Lipschitz-continuity and decomposition as each aids the convergence of the other. In doing so, we bridge the gap between combinatorial and Lipschitz bandits, presenting a no-regret approach that tightens existing guarantees while optimizing for short-term performance. We demonstrate that our algorithm, LIZARD, improves performance on real-world poaching data from Cambodia.