Globally Gated Deep Linear Networks

Recently proposed Gated Linear Networks present a tractable nonlinear network architecture, and exhibit interesting capabilities such as learning with local error signals and reduced forgetting in sequential learning. In this work, we introduce a novel gating architecture, named Globally Gated Deep Linear Networks (GGDLNs) where gating units are shared among all processing units in each layer, thereby decoupling the architectures of the nonlinear but unlearned gatings and the learned linear processing motifs. We derive exact equations for the generalization properties in these networks in the finite-width thermodynamic limit, defined by $P,N\rightarrow\infty, P/N\sim O(1)$, where P and N are the training sample size and the network width respectively. We find that the statistics of the network predictor can be expressed in terms of kernels that undergo shape renormalization through a data-dependent matrix compared to the GP kernels. Our theory accurately captures the behavior of finite width GGDLNs trained with gradient descent dynamics. We show that kernel shape renormalization gives rise to rich generalization properties w.r.t. network width, depth and L2 regularization amplitude. Interestingly, networks with sufficient gating units behave similarly to standard ReLU networks. Although gatings in the model do not participate in supervised learning, we show the utility of unsupervised learning of the gating parameters. Additionally, our theory allows the evaluation of the network's ability for learning multiple tasks by incorporating task-relevant information into the gating units. In summary, our work is the first exact theoretical solution of learning in a family of nonlinear networks with finite width. The rich and diverse behavior of the GGDLNs suggests that they are helpful analytically tractable models of learning single and multiple tasks, in finite-width nonlinear deep networks

Top-Down Processing: Top-Down Network Combines Back-Propagation with Attention

Early neural network models relied exclusively on bottom-up processing going from the input signals to higher-level representations. Many recent models also incorporate top-down networks going in the opposite direction. Top-down processing in deep learning models plays two primary roles: learning and directing attention. These two roles are accomplished in current models through distinct mechanisms. While top-down attention is often implemented by extending the model's architecture with additional units that propagate information from high to low levels of the network, learning is typically accomplished by an external learning algorithm such as back-propagation. In the current work, we present an integration of the two functions above, which appear unrelated, using a single unified mechanism. We propose a novel symmetric bottom-up top-down network structure that can integrate standard bottom-up networks with a symmetric top-down counterpart, allowing each network to guide and influence the other. The same top-down network is being used for both learning, via back-propagating feedback signals, and at the same time also for top-down attention, by guiding the bottom-up network to perform a selected task. We show that our method achieves competitive performance on a standard multi-task learning benchmark. Yet, we rely on standard single-task architectures and optimizers, without any task-specific parameters. Additionally, our learning algorithm addresses in a new way some neuroscience issues that arise in biological modeling of learning in the brain