Dataset Information

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

ABSTRACT: 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) toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward 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. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST task.

SUBMITTER: Scellier B

PROVIDER: S-EPMC5415673 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

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

Scellier Benjamin B Bengio Yoshua Y

Frontiers in computational neuroscience 20170504

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. Equilibr ...[more]

PMID: 28522969

Similar Datasets

Project description:BackgroundDespite the close association between gene expression and metabolism, experimental evidence shows that gene expression levels alone cannot predict metabolic phenotypes, indicating a knowledge gap in our understanding of how these processes are connected. Here, we present a method that integrates transcriptome, fluxome, and metabolome data using kinetic models to create a mechanistic link between gene expression and metabolism.ResultsWe developed a modeling framework to construct kinetic models that connect the transcriptional and metabolic responses of a cell to exogenous perturbations. The framework allowed us to avoid extensive experimental characterization, literature mining, and optimization problems by estimating most model parameters directly from fluxome and transcriptome data. We applied the framework to investigate how gene expression changes led to observed phenotypic alterations of Saccharomyces cerevisiae treated with weak organic acids (i.e., acetate, benzoate, propionate, or sorbate) and the histidine synthesis inhibitor 3-aminotriazole under steady-state conditions. We found that the transcriptional response led to alterations in yeast metabolism that mimicked measured metabolic fluxes and concentration changes. Further analyses generated mechanistic insights of how S. cerevisiae responds to these stresses. In particular, these results suggest that S. cerevisiae uses different regulation strategies for responding to these insults: regulation of two reactions accounted for most of the tolerance to the four weak organic acids, whereas the response to 3-aminotriazole was distributed among multiple reactions. Moreover, we observed that the magnitude of the gene expression changes was not directly correlated with their effect on the ability of S. cerevisiae to grow under these treatments. In addition, we identified another potential mechanism of action of 3-aminotriazole associated with the depletion of tetrahydrofolate.ConclusionsOur simulation results show that the modeling framework provided an accurate mechanistic link between gene expression and cellular metabolism. The proposed method allowed us to integrate transcriptome, fluxome, and metabolome data to determine and interpret important features of the physiological response of yeast to stresses. Importantly, given its flexibility and robustness, our approach can be applied to investigate the transcriptional-metabolic response in other cellular systems of medical and industrial relevance.

Project description:The condensational growth of submicrometer aerosol particles to climate relevant sizes is sensitive to their ability to accommodate vapor molecules, which is described by the mass accommodation coefficient. However, the underlying processes are not yet fully understood. We have simulated the mass accommodation and evaporation processes of water using molecular dynamics, and the results are compared to the condensation equations derived from the kinetic gas theory to shed light on the compatibility of the two. Molecular dynamics simulations were performed for a planar TIP4P-Ew water surface at four temperatures in the range 268-300 K as well as two droplets, with radii of 1.92 and 4.14 nm at T = 273.15 K. The evaporation flux from molecular dynamics was found to be in good qualitative agreement with that predicted by the simple kinetic condensation equations. Water droplet growth was also modeled with the kinetic multilayer model KM-GAP of Shiraiwa et al. [Atmos. Chem. Phys. 2012, 12, 2777]. It was found that, due to the fast transport across the interface, the growth of a pure water droplet is controlled by gas phase diffusion. These facts indicate that the simple kinetic treatment is sufficient in describing pure water condensation and evaporation. The droplet size was found to have minimal effect on the value of the mass accommodation coefficient. The mass accommodation coefficient was found to be unity (within 0.004) for all studied surfaces, which is in agreement with previous simulation work. Additionally, the simulated evaporation fluxes imply that the evaporation coefficient is also unity. Comparing the evaporation rates of the mass accommodation and evaporation simulations indicated that the high collision flux, corresponding to high supersaturation, present in typical molecular dynamics mass accommodation simulations can under certain conditions lead to an increase in the evaporation rate. Consequently, in such situations the mass accommodation coefficient can be overestimated, but in the present cases the corrected values were still close to unity with the lowest value at ≈0.99.

Dataset Information

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

Publications

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

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets