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

By Benjamin Scellier, Yoshua Bengio. 2016

662 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Cognitive Neuroscience, Electrical and Electronic Engineering

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Citations in the corpus

Deep Equilibrium Models (2019, background): “[41] proposes a biologically inspired equilibrium propagation framework for an energy-based model whose prediction is the ﬁxed-point of the energy dynamics at its local minimum.”
Theories of Error Back-Propagation in the Brain (2019, background): “It has been shown that network error can be minimised if the synaptic weights are modi ﬁ ed in two steps (schematically illustrated by the two displays in the top box; [22]).”
Advancing Neuromorphic Computing With Loihi: A Survey of Results and Outlook (2021, background): “Longer term, more general algorithms, such as eligibility propagation [47] and equilibrium propagation [131] that approximate BPTT without the anticausal requirement of propagating information back in time, may succeed in scaling up online learning.”
Neuroscience-Inspired Artificial Intelligence. (2017, background): “Indeed, concrete connections have been drawn between learning in such networks and spike-timing dependent plasticity (Scellier and Bengio, 2016), a Hebbian mechanism instantiated widely across the brain (Bi and Poo, 1998).”
Improved Contrastive Divergence Training of Energy Based Models (2020, background): “…generation (Deng et al., 2020), video generation (Xie et al., 2017), reinforcement learning (Haarnoja et al., 2017; Du et al., 2019), continual learning (Li et al., 2020), protein design and folding (Ingraham et al.; Du et al., 2020b) and biologically-plausible training (Scellier & Bengio, 2017).”
Dendritic cortical microcircuits approximate the backpropagation algorithm (2018, methodology): “This link between the two algorithms was first established for an unsupervised learning task (Hinton and McClelland, 1988) and later analyzed (Xie and Seung, 2003) and generalized to broader classes of models (O’Reilly, 1996; Scellier and Bengio, 2017).”
Reviving and Improving Recurrent Back-Propagation (2018, background): “A recent investigation (Scellier & Bengio, 2017a) shows that RBP is related to equilibrium propagation (Scellier & Bengio, 2017b) which is motivated from the perspective of biological plausibility.”
Training Neural Networks with Local Error Signals (2019, background): “…for error-driven learning have so far focused on how to transport the error back to hidden layers (Lillicrap et al., 2014; Nøkland, 2016), or how to transport a target back to hidden layers (Xie & Seung, 2003; Bengio, 2014; Lee et al., 2015b; Scellier & Bengio, 2017; Whittington & Bogacz, 2017).”
Unsupervised learning by competing hidden units (2018, methodology): “This is significantly better than the previously published benchmarks on other biologically inspired algorithms, for example 2−3% in [7], 1.”
Switching between internal and external modes: A multiscale learning principle (2017, background): “Contrastive Hebbian learning is a supervised learning approach that Supervised learning: A learning process in which input data are paired with explicit labels or feedback. can approximate backpropagation in multilayer settings (O’Reilly, 1996; Xie & Seung, 2003; see also Scellier & Bengio, 2017).”
Energy-Based Models for Continual Learning (2020, background): “…(Haarnoja et al., 2017; Du et al., 2019), image generation (Salakhutdinov & Hinton, 2009; Xie et al., 2016; 2018; Grathwohl et al., 2019), memory modeling (Bartunov et al., 2019), biologicallyplausible training (Scellier & Bengio, 2017), and protein design and folding (Ingraham et al., 2019).”
Greedy InfoMax for Biologically Plausible Self-Supervised Representation Learning (2019, background): “There are a number of optimization algorithms that eliminate the need for backpropagation altogether [Balduzzi et al., 2015, Kohan et al., 2018, Lee et al., 2015, Lillicrap et al., 2016, Scellier and Bengio, 2017].”
The Forward-Forward Algorithm: Some Preliminary Investigations (2022, background): “As a model of how cortex learns, backpropagation remains implausible despite considerable effort to invent ways in which it could be implemented by real neurons (Lillicrap et al., 2020; Richards and Lillicrap, 2019; Guerguiev et al., 2017; Scellier and Bengio, 2017).”