Exponential Consensus and Flocking in Multi-Agent Systems with Infinite Fading Memory
arXiv:2609.02454
2026
Dynamics
2 ideas extracted · analyzed Sep 3, 2026
What the math gives to ML
The paper's transferable mechanism is that infinite fading-memory interactions can be rewritten as a Markovian dynamical system on an augmented history space, where the memory itself supplies a dissipative Lyapunov term. Under a nonnegative decreasing kernel with exponential decay, disagreement decays exponentially; for flocking, a divergent-tail influence function yields unconditional alignment. A useful neural-network transfer is a history-augmented optimizer or recurrent state update in which parameters or hidden states are attracted to a fading average of their own past. The key falsifiable prediction is an exponential decay rate and stability boundary governed by the memory decay and local curvature or recurrent gain.
Ideas from this paper
✗ Failed on benchmark
2026
Add a fading-memory consensus force to parameter dynamics, pulling the current parameter toward a distributed average of its past while preserving the ordinary gradient step. Implement the infinite memory through one or several recursive exponential states, and tune the memory decay so that quadratic-mode dynamics remain exponentially stable. This should suppress oscillations and catastrophic steps without relying on conventional momentum alone.
Useful7/10
Difficulty4/10
Novelty6/10
Unverified
2026
Replace an unrestricted recurrent state with a current input-driven state coupled to a fading average of its own history. The memory coupling provides a distributed dissipative channel, while the recurrent Jacobian is constrained below a measurable contraction boundary. This creates a recurrent or state-space block whose long-horizon sensitivity can be tested against explicit characteristic roots.
Useful6/10
Difficulty5/10
Novelty7/10