Equilibrium Propagation
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Related Articles from SNS
Training a Predictive Coding Network on ImageNet using Equilibrium Propagation
Announce Type: new Abstract: Equilibrium Propagation (EP) is a physics-based training framework that has primarily been employed in energy-based models, including continuous Hopfield networks, nonlinear resistive networks and coupled phase oscillators. However, EP's practical applications have so far remained limited to relatively small-scale problems. Predictive coding networks (PCNs), another class of energy-based models rooted in computational neuroscience, are typically trained with a...
Equilibrium Propagation for Non-Conservative Systems
arXiv:2602.03670v2 Announce Type: replace Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to dynamics which derive from an energy function. Given their applications, it is important to extend EP to non-conservative systems, $\textit{i.e.}$ systems with non-reciprocal interactions.
Equilibrium Propagation for Non-Conservative Systems
arXiv:2602.03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to dynamics which derive from an energy function. Given their applications, it is important to extend EP to non-conservative systems, $\textit{i.e.}$ systems with non-reciprocal interactions.
Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning
arXiv:2606.09112v1 Announce Type: new Abstract: The rapid evolution of artificial intelligence has led to substantial advances in deep neural networks. Nonetheless, conventional GPU-based training remains highly energy-demanding, motivating the exploration of physical dynamics and compatible energy-based learning schemes, such as equilibrium propagation (EP). EP-based training, however, frequently suffers from convergence to local minima due to phase-space contraction.
Optimizing Energy-based Neural Network Training with Coherent Ising Machine
Announce Type: new Abstract: While Ising machines serve as advanced physical solvers for the Ising model,enabling applications in combinatorial optimization and neural network training,their scalability for large-scale neural networks remains constrained by hardware connectivity limitations and suboptimal training methodologies. In this work,we leverage a Coherent Ising Machine (CIM) to train an energy-based neural network using Equilibrium Propagation, achieving performance comparable to...
Perturbative Contrastive Physical Learning
arXiv:2606.09756v1 Announce Type: new Abstract: Responses to perturbations are key to understanding physical systems. The ability to contrast such responses by comparing how a system reacts under slightly different conditions provides a mechanism for learning. Here, we introduce Perturbative Contrastive Physical Learning (PCPL), a general framework in which learning emerges from measurable contrasts between physical states produced by controlled changes to inputs, boundary conditions,...
N-Player Binary Games with Unidirectional Dependencies: Cycle Robustness and Induced Indifference
new Abstract: The present study provides a closed-form characterisation of Nash equilibria in N-player binary games with unidirectional dependencies. While general network games are PPAD-complete, prior work has established that trees or paths admit polynomial-time solutions via dynamic programming. We provide a deterministic characterisation for the subclass of directed cycle graphical games, demonstrating that non-zero boundary incentives linearize the topology into a feed-forward propagation.
Bubbles vs. Baselines: Token Valuation and Institutional Capital in PoS Networks under EIP-1559
arXiv:2606.07445v1 Announce Type: cross Abstract: This paper presents an open-economy macroeconomic equilibrium model for Proof-of-Stake (PoS) networks with fee-burn mechanics (EIP-1559) that formalizes the strategic interplay between a Kelly-optimizing rational institutional investor and a utility-driven retail consumer. We analyze network dynamics across two behavioral regimes. In The Unbounded Accumulation Model, the consumer purely accumulates tokens, creating an exclusive buy-side...
Linear causality and stability constraints on relativistic second-order magnetohydrodynamics
Announce Type: new Abstract: In this work, we construct a theoretical framework for relativistic second-order magnetohydrodynamics based on entropy current analysis. The formalism consistently incorporates the relaxation dynamics of dissipative fluxes, ensuring the hyperbolic nature of the evolution equations. Utilizing linear mode analysis, we investigate the constraints imposed by causality and stability on this anisotropic system.
Augmented Lagrangian Predictive Coding
arXiv:2605.31022v1 Announce Type: new Abstract: Predictive coding (PC) is a local-learning alternative to backpropagation (BP), training deep networks via local energy-minimization dynamics rather than a global backward pass. We introduce Augmented Lagrangian Predictive Coding (PC-ALM), which maintains PC's inference budget but aligns each weight update toward BP by accumulating per-layer constraint errors into a layer-local Lagrange multiplier. In linear PC networks, PC-ALM converges to an...