Linear Memory Networks

Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled. We introduce a novel recurrent architecture based on the conceptual separation between the functional input-output transformation and the memory mechanism, showing how they can be implemented through different neural components. By building on such conceptualization, we introduce the Linear Memory Network, a recurrent model comprising a feedforward neural network, realizing the non-linear functional transformation, and a linear autoencoder for sequences, implementing the memory component. The resulting architecture can be efficiently trained by building on closed-form solutions to linear optimization problems. Further, by exploiting equivalence results between feedforward and recurrent neural networks we devise a pretraining schema for the proposed architecture. Experiments on polyphonic music datasets show competitive results against gated recurrent networks and other state of the art models

Bridging the Gaps Between Residual Learning, Recurrent Neural Networks and Visual Cortex

We discuss relations between Residual Networks (ResNet), Recurrent Neural Networks (RNNs) and the primate visual cortex. We begin with the observation that a shallow RNN is exactly equivalent to a very deep ResNet with weight sharing among the layers. A direct implementation of such a RNN, although having orders of magnitude fewer parameters, leads to a performance similar to the corresponding ResNet. We propose 1) a generalization of both RNN and ResNet architectures and 2) the conjecture that a class of moderately deep RNNs is a biologically-plausible model of the ventral stream in visual cortex. We demonstrate the effectiveness of the architectures by testing them on the CIFAR-10 dataset.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF – 1231216

Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation

We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made) and the second phase of training (after the target or prediction error is revealed). Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point, or stationary distribution) towards a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged towards their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal 'back-propagated' during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not