Equilibrium propagation (EP) is presented as a biologically motivated alternative to backpropagation for training neural networks. EP operates with two dynamical phases: a free phase, during which the network relaxes toward an equilibrium given input, and a nudged phase, during which the output is perturbed toward a target using a teaching signal. While EP provides a local learning rule compatible with continuous-time network dynamics, a key open question is whether biological systems have access to explicit, full vector-valued target signals required for conventional nudging.
The work motivating the new approach recognizes that biological learning may instead rely on sparse, action-specific feedback such as reward or correctness signals. Prior related frameworks, such as Attention-Gated Brain Propagation (BrainProp), served as inspiration for developing a reward-driven variant of EP that reduces reliance on explicit target vectors.
The central contribution is a reward-based equilibrium propagation method that replaces full target-based nudging with a selected-output binary reward signal. Under this scheme, when the network produces a class choice, learning updates use information limited to which class was selected and whether that selected choice was correct. The full supervised target vector is not revealed to the network during the nudged phase.
This modification aims to increase biological plausibility by aligning the learning signal with sparse, action-contingent reward information, which more closely resembles reinforcement-style feedback available to nervous systems. The update rule and overall EP framework remain in spirit aligned with equilibrium dynamics, but the target information is compressed to a binary success/failure indicator tied to the chosen output.
The method is evaluated on standard image-classification benchmarks to test its effectiveness relative to conventional EP. Datasets used are MNIST, Fashion-MNIST, and CIFAR-10. Architectures include both multilayer perceptrons and convolutional neural networks to assess the approach across feedforward and convolutional model families.
Comparisons focus on final performance (accuracy), convergence behavior during training, and the training–test generalization gap. The implementation details, hyperparameter settings, and exact network topologies are reported in the source preprint and were used to ensure direct comparison between reward-based EP and conventional EP.
Across MNIST, Fashion-MNIST, and CIFAR-10, reward-based EP achieves performance close to conventional EP. A consistent observation is that reward-based EP tends to converge more slowly during the early stages of training compared with conventional EP that has full target nudging.
This early-stage slow convergence likely reflects the sparser and less informative nature of selected-output reward signals relative to full target vectors. Despite slower early learning, the reward-based method reduces the information needed to drive weight changes and still reaches near-parity in eventual performance on the tested benchmarks.
The study reports analyses of the difference between training and test accuracy (the generalization gap) for both methods. On MNIST and Fashion-MNIST, reward-based EP and conventional EP show similar generalization-gap behavior. On CIFAR-10, an interesting divergence appears: reward-based EP exhibits a smaller training–test accuracy gap during later phases of training relative to conventional EP.
This pattern suggests that, at least for a more challenging dataset like CIFAR-10, the sparser reward-based supervision can yield comparable or even somewhat improved generalization properties during later training, although performance and dynamics remain dataset-dependent.
The reward-based method incorporates stochastic class selection controlled by an exploration probability. The author investigates how this exploration parameter influences learning. Results indicate that moderate exploration can offer small performance benefits, but the magnitude and direction of the effect depend on the dataset.
Thus, exploration introduces a trade-off: it may help discover better actions and thereby improve learning signals, yet its utility is not uniform across tasks and requires tuning according to dataset characteristics.
The study demonstrates that equilibrium propagation can be adapted to learn from sparse, action-specific reward feedback rather than requiring full supervised targets. Reward-based EP attains performance close to conventional EP on MNIST, Fashion-MNIST, and CIFAR-10, with slower early convergence but comparable final accuracy and potentially improved later-stage generalization on CIFAR-10.
These findings support the plausibility of EP-like mechanisms in biological learning systems that primarily receive sparse reward signals. The source is a preprint and has not undergone peer review; the author notes the preprint status and provides full methodological detail in the original manuscript. Any further technical specifics, quantitative metrics, or architectural hyperparameters should be consulted directly in the preprint document.