We propose associative domain adaptation, a novel technique for end-to-end domain adaptation with neural networks, the task of inferring class labels for an unlabeled target domain based on the statistical properties of a labeled source domain. Our training scheme follows the paradigm that in order to effectively derive class labels for the target domain, a network should produce statistically domain invariant embeddings, while minimizing the classification error on the labeled source domain. We accomplish this by reinforcing associations between source and target data directly in embedding space. Our method can easily be added to any existing classification network with no structural and almost no computational overhead. We demonstrate the effectiveness of our approach on various benchmarks and achieve state-of-the-art results across the board with a generic convolutional neural network architecture not specifically tuned to the respective tasks. Finally, we show that the proposed association loss produces embeddings that are more effective for domain adaptation compared to methods employing maximum mean discrepancy as a similarity measure in embedding space.
We propose proximal backpropagation (ProxProp) as a novel algorithm that takes implicit instead of explicit gradient steps to update the network parameters during neural network training. Our algorithm is motivated by the step size limitation of explicit gradient descent, which poses an impediment for optimization. Prox-Prop is developed from a general point of view on the backpropagation algorithm, currently the most common technique to train neural networks via stochastic gradient descent and variants thereof. Specifically, we show that backpropagation of a prediction error is equivalent to sequential gradient descent steps on a quadratic penalty energy, which comprises the network activations as variables of the optimization. We further analyze theoretical properties of ProxProp and in particular prove that the algorithm yields a descent direction in parameter space and can therefore be combined with a wide variety of convergent algorithms. Finally, we devise an efficient numerical implementation that integrates well with popular deep learning frameworks. We conclude by demonstrating promising numerical results and show that ProxProp can be effectively combined with common first order optimizers such as Adam.
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We propose a method to impose homogeneous linear inequality constraints of the form Ax ≤ 0 on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the task. One way to achieve this task is by means of a projection step at test time after unconstrained training. However, this is an expensive operation. By directly incorporating the constraints into the architecture, we can significantly speed-up inference at test time; for instance, our experiments show a speed-up of up to two orders of magnitude over a projection method. Our algorithm computes a suitable parameterization of the feasible set at initialization and uses standard variants of stochastic gradient descent to find solutions to the constrained network. Thus, the modeling constraints are always satisfied during training. Crucially, our approach avoids to solve an optimization problem at each training step or to manually trade-off data and constraint fidelity with additional hyperparameters. We consider constrained generative modeling as an important application domain and experimentally demonstrate the proposed method by constraining a variational autoencoder.
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