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Register a new userDifferentiable Programs with Neural Libraries
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Added by
Marc Brockschmidt
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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We develop a framework for combining differentiable programming languages with neural networks. Using this framework we create end-to-end trainable systems that learn to write interpretable algorithms with perceptual components. We explore the benefits of inductive biases for strong generalization and modularity that come from the program-like structure of our models. In particular, modularity allows us to learn a library of (neural) functions which grows and improves as more tasks are solved. Empirically, we show that this leads to lifelong learning systems that transfer knowledge to new tasks more effectively than baselines.
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We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program architectures. We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.
Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance of GNNs as the number of layers increases. It is because the stacked aggregators would make node representations converge to indistinguishable vectors. Several attempts have been made to tackle the issue by bringing linked node pairs close and unlinked pairs distinct. However, they often ignore the intrinsic community structures and would result in sub-optimal performance. The representations of nodes within the same community/class need be similar to facilitate the classification, while different classes are expected to be separated in embedding space. To bridge the gap, we introduce two over-smoothing metrics and a novel technique, i.e., differentiable group normalization (DGN). It normalizes nodes within the same group independently to increase their smoothness, and separates node distributions among different groups to significantly alleviate the over-smoothing issue. Experiments on real-world datasets demonstrate that DGN makes GNN models more robust to over-smoothing and achieves better performance with deeper GNNs.
We make three related contributions motivated by the challenge of training stochastic neural networks, particularly in a PAC-Bayesian setting: (1) we show how averaging over an ensemble of stochastic neural networks enables a new class of emph{partially-aggregated} estimators; (2) we show that these lead to provably lower-variance gradient estimates for non-differentiable signed-output networks; (3) we reformulate a PAC-Bayesian bound for these networks to derive a directly optimisable, differentiable objective and a generalisation guarantee, without using a surrogate loss or loosening the bound. This bound is twice as tight as that of Letarte et al. (2019) on a similar network type. We show empirically that these innovations make training easier and lead to competitive guarantees.
Automated neural network design has received ever-increasing attention with the evolution of deep convolutional neural networks (CNNs), especially involving their deployment on embedded and mobile platforms. One of the biggest problems that neural architecture search (NAS) confronts is that a large number of candidate neural architectures are required to train, using, for instance, reinforcement learning and evolutionary optimisation algorithms, at a vast computation cost. Even recent differentiable neural architecture search (DNAS) samples a small number of candidate neural architectures based on the probability distribution of learned architecture parameters to select the final neural architecture. To address this computational complexity issue, we introduce a novel emph{architecture parameterisation} based on scaled sigmoid function, and propose a general emph{Differentiable Neural Architecture Learning} (DNAL) method to optimize the neural architecture without the need to evaluate candidate neural networks. Specifically, for stochastic supernets as well as conventional CNNs, we build a new channel-wise module layer with the architecture components controlled by a scaled sigmoid function. We train these neural network models from scratch. The network optimization is decoupled into the weight optimization and the architecture optimization. We address the non-convex optimization problem of neural architecture by the continuous scaled sigmoid method with convergence guarantees. Extensive experiments demonstrate our DNAL method delivers superior performance in terms of neural architecture search cost. The optimal networks learned by DNAL surpass those produced by the state-of-the-art methods on the benchmark CIFAR-10 and ImageNet-1K dataset in accuracy, model size and computational complexity.
In seeking for sparse and efficient neural network models, many previous works investigated on enforcing L1 or L0 regularizers to encourage weight sparsity during training. The L0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values, but it cannot provide useful gradients, and therefore requires complex optimization techniques. The L1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent. Yet it is not scale-invariant, causing the same shrinking rate to all parameters, which is inefficient in increasing sparsity. Inspired by the Hoyer measure (the ratio between L1 and L2 norms) used in traditional compressed sensing problems, we present DeepHoyer, a set of sparsity-inducing regularizers that are both differentiable almost everywhere and scale-invariant. Our experiments show that enforcing DeepHoyer regularizers can produce even sparser neural network models than previous works, under the same accuracy level. We also show that DeepHoyer can be applied to both element-wise and structural pruning.
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