Gated Linear Networks

This paper presents a new family of backpropagation-free neural architectures, Gated Linear Networks (GLNs). What distinguishes GLNs from contemporary neural networks is the distributed and local nature of their credit assignment mechanism; each neuron directly predicts the target, forgoing the ability to learn feature representations in favor of rapid online learning. Individual neurons can model nonlinear functions via the use of data-dependent gating in conjunction with online convex optimization. We show that this architecture gives rise to universal learning capabilities in the limit, with effective model capacity increasing as a function of network size in a manner comparable with deep ReLU networks. Furthermore, we demonstrate that the GLN learning mechanism possesses extraordinary resilience to catastrophic forgetting, performing comparably to a MLP with dropout and Elastic Weight Consolidation on standard benchmarks. These desirable theoretical and empirical properties position GLNs as a complementary technique to contemporary offline deep learning methods.Comment: arXiv admin note: substantial text overlap with arXiv:1712.0189

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

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

Extending Gated Linear Networks for Continual Learning

To incrementally learn multiple tasks from an indefinitely long stream of data is a real challenge for traditional machine learning models. If not carefully controlled, the learning of new knowledge strongly impacts on a model’s learned abilities, making it to forget how to solve past tasks. Continual learning faces this problem, called catastrophic forgetting, developing models able to continually learn new tasks and adapt to changes in the data distribution. In this dissertation, we consider the recently proposed family of continual learning models, called Gated Linear Networks (GLNs), and study two crucial aspects impacting on the amount of catastrophic forgetting affecting gated linear networks, namely, data standardization and gating mechanism. Data standardization is particularly challenging in the online/continual learning setting because data from future tasks is not available beforehand. The results obtained using an online standardization method show a considerably higher amount of forgetting compared to an offline –static– standardization. Interestingly, with the latter standardization, we observe that GLNs show almost no forgetting on the considered benchmark datasets. Secondly, for an effective GLNs, it is essential to tailor the hyperparameters of the gating mechanism to the data distribution. In this dissertation, we propose a gating strategy based on a set of prototypes and the resulting Voronoi tessellation. The experimental assessment shows that, in an ideal setting where the data distribution is known, the proposed approach is more robust to different data standardizations compared to the original one, based on a halfspace gating mechanism, and shows improved predictive performance. Finally, we propose an adaptive mechanism for the choice of prototypes, which expands and shrinks the set of prototypes in an online fashion, making the model suitable for practical continual learning applications. The experimental results show that the adaptive model performances are close to the ideal scenario where prototypes are directly sampled from the data distribution.To incrementally learn multiple tasks from an indefinitely long stream of data is a real challenge for traditional machine learning models. If not carefully controlled, the learning of new knowledge strongly impacts on a model’s learned abilities, making it to forget how to solve past tasks. Continual learning faces this problem, called catastrophic forgetting, developing models able to continually learn new tasks and adapt to changes in the data distribution. In this dissertation, we consider the recently proposed family of continual learning models, called Gated Linear Networks (GLNs), and study two crucial aspects impacting on the amount of catastrophic forgetting affecting gated linear networks, namely, data standardization and gating mechanism. Data standardization is particularly challenging in the online/continual learning setting because data from future tasks is not available beforehand. The results obtained using an online standardization method show a considerably higher amount of forgetting compared to an offline –static– standardization. Interestingly, with the latter standardization, we observe that GLNs show almost no forgetting on the considered benchmark datasets. Secondly, for an effective GLNs, it is essential to tailor the hyperparameters of the gating mechanism to the data distribution. In this dissertation, we propose a gating strategy based on a set of prototypes and the resulting Voronoi tessellation. The experimental assessment shows that, in an ideal setting where the data distribution is known, the proposed approach is more robust to different data standardizations compared to the original one, based on a halfspace gating mechanism, and shows improved predictive performance. Finally, we propose an adaptive mechanism for the choice of prototypes, which expands and shrinks the set of prototypes in an online fashion, making the model suitable for practical continual learning applications. The experimental results show that the adaptive model performances are close to the ideal scenario where prototypes are directly sampled from the data distribution

Toward Abstraction from Multi-modal Data: Empirical Studies on Multiple Time-scale Recurrent Models

The abstraction tasks are challenging for multi- modal sequences as they require a deeper semantic understanding and a novel text generation for the data. Although the recurrent neural networks (RNN) can be used to model the context of the time-sequences, in most cases the long-term dependencies of multi-modal data make the back-propagation through time training of RNN tend to vanish in the time domain. Recently, inspired from Multiple Time-scale Recurrent Neural Network (MTRNN), an extension of Gated Recurrent Unit (GRU), called Multiple Time-scale Gated Recurrent Unit (MTGRU), has been proposed to learn the long-term dependencies in natural language processing. Particularly it is also able to accomplish the abstraction task for paragraphs given that the time constants are well defined. In this paper, we compare the MTRNN and MTGRU in terms of its learning performances as well as their abstraction representation on higher level (with a slower neural activation). This was done by conducting two studies based on a smaller data- set (two-dimension time sequences from non-linear functions) and a relatively large data-set (43-dimension time sequences from iCub manipulation tasks with multi-modal data). We conclude that gated recurrent mechanisms may be necessary for learning long-term dependencies in large dimension multi-modal data-sets (e.g. learning of robot manipulation), even when natural language commands was not involved. But for smaller learning tasks with simple time-sequences, generic version of recurrent models, such as MTRNN, were sufficient to accomplish the abstraction task.Comment: Accepted by IJCNN 201