Research map / Probabilistic and scientific modeling / Molecules and proteins
Nature-Inspired Local Propagation
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Derives spatiotemporally local learning laws from a Hamiltonian/optimal-control view of recurrent networks, showing backpropagation emerges as the infinite-propagation-speed limit, and proposes a Hamiltonian Sign Flip policy to solve the boundary-value problem with Cauchy conditions.
Problem
Backpropagation is non-local in time and space and biologically implausible; learning in online settings needs local propagation, but Hamilton's equations for learning come with boundary conditions that prevent forward causal computation.
Approach
Formulates learning as an optimal control variational problem yielding Hamilton equations with finite propagation speed; shows backprop is the c→∞ limit; and replaces boundary conditions with Cauchy initial conditions via time-reversal sign flips (Hamiltonian Sign Flip) guided by a Hamiltonian track.
Key results
- Shows that as propagation speed c goes to infinity, the costate equations reduce to the Backprop delta-error recursion, and the weight dynamics become gradient descent with momentum.
- Proves BIBO stability of the continuous-time RNN model used in the framework.
- On linear quadratic tracking with a 5-neuron recurrent net, the Hamiltonian Sign Flip policy yields approximation of sinusoidal and hard-to-predict signals, with experiments reported only qualitatively.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| apply Hamiltonian Sign Flip (HSF) | recurrent neural network for Linear Quadratic Tracking · LQT tracking | tracking quality | Helped |
Limitations
- Locality relies on boundary-value solutions; the Cauchy-condition approximation is heuristic and only the conjecture for fixed c is unproven.
- Experiments are small (5-neuron networks, synthetic tracking signals) and purely theoretical in scope.
- Real-world applicability is not demonstrated.
Experimental setup
Metrics: tracking error Lagrangian Hamiltonian
Baselines: BPTT RTRL
Builds on: Cognitive Action Principle Backpropagation Hamilton-Jacobi-Bellman theory
Closest papers by meaning
- Identifying Physical Law of Hamiltonian Systems via Meta-Learning (ICLR 2021 · similarity 0.84)
- From Kepler to Newton: Inductive Biases Guide Learned World Models in Transformers (ICML 2026 · similarity 0.83)
- Discovering Physics Laws of Dynamical Systems via Invariant Function Learning (ICML 2025 · similarity 0.83)
- Nonlinear dynamics of localization in neural receptive fields (NeurIPS 2024 · similarity 0.83)
- Two Tales of Single-Phase Contrastive Hebbian Learning (ICML 2024 · similarity 0.83)
- Learning Physics Informed Neural ODEs with Partial Measurements (AAAI 2025 · similarity 0.82)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.