We explore whether useful temporal neural generative models can be learned from sequential data without back-propagation through time. We investigate the viability of a more neurocognitively-grounded approach in the context of unsupervised generative modeling of sequences. Specifically, we build on the concept of predictive coding, which has gained influence in cognitive science, in a neural framework. To do so we develop a novel architecture, the Temporal Neural Coding Network, and its learning algorithm, Discrepancy Reduction. The underlying directed generative model is fully recurrent, meaning that it employs structural feedback connections and temporal feedback connections, yielding information propagation cycles that create local learning signals. This facilitates a unified bottom-up and top-down approach for information transfer inside the architecture. Our proposed algorithm shows promise on the bouncing balls generative modeling problem. Further experiments could be conducted to explore the strengths and weaknesses of our approach.
@cite_0: The recurrent temporal restricted Boltzmann machine (RTRBM) is a probabilistic time-series model. The topology of the RTRBM graphical model, however, assumes full connectivity between all the pairs of visible units and hidden units, thereby ignoring the dependency structure within the observations. Learning this structure has the potential for not only improving the prediction performance, but also revealing important dependency patterns in the data. For example, given a meteorological dataset, we could identify regional weather patterns. In this work, we propose a new class of RTRBM, which we refer to as the structured RTRBM (SRTRBM), which explicitly uses a graph to model the dependency structure. Our technique is related to methods such as graphical lasso, which are used to learn the topology of Gaussian graphical models. We also develop a spike-and-slab version of the RTRBM, and combine it with the SRTRBM to learn dependency structures in datasets with real-valued observations. Our experimental results using synthetic and real datasets demonstrate that the SRTRBM can significantly improve the prediction performance of the RTRBM, particularly when the number of visible units is large and the size of the training set is small. It also reveals the dependency structures underlying our benchmark datasets.
@cite_10: We propose a non-linear generative model for human motion data that uses an undirected model with binary latent variables and real-valued "visible" variables that represent joint angles. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. Such an architecture makes on-line inference efficient and allows us to use a simple approximate learning procedure. After training, the model finds a single set of parameters that simultaneously capture several different kinds of motion. We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line filling in of data lost during motion capture.
@cite_3: Everyone knows what bottom-up is, and how it is different from top-down. At least one is tempted to think so, given that both terms are ubiquitously used, but only rarely defined in the psychology and neuroscience literature. In this review, we highlight the problems and limitations of our current understanding of bottom-up and top-down processes, and we propose a reformulation of this distinction in terms of predictive coding.
@cite_2: We investigate the problem of modeling symbolic sequences of polyphonic music in a completely general piano-roll representation. We introduce a probabilistic model based on distribution estimators conditioned on a recurrent neural network that is able to discover temporal dependencies in high-dimensional sequences. Our approach outperforms many traditional models of polyphonic music on a variety of realistic datasets. We show how our musical language model can serve as a symbolic prior to improve the accuracy of polyphonic transcription.
The contrastive divergence recipe , well-known for being the primary learning algorithm of restricted Boltzmann machines, and the Wake-Sleep algorithm for training deeper Boltzmann-based architectures, were largely inspired by the role of sleep in human learning. However, these approaches to learning, which rely on Markov Chain Monte Carlo methods, suffer from a variety of problems including slow convergence to steady-state distributions due to poor mixing of modes and the constraint that the weights of the model must be symmetric. With some success, Boltzmann-based architectures have been applied to stateful problems @cite_10 @cite_3 @cite_2 @cite_0 , but require hybridizing the Contrastive Divergence approach with back-propagation through time, incurring the limitations and criticisms of both algorithms. Other approaches inspired by Boltzmann-based learning (and energy-based learning in general) include the algorithm and . However, these algorithms have only been investigated on static modeling problems and it is not clear how one might extend them to stateful problems.